1,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3*(d*sin(f*x + e))^n, x)","F",0
2,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*(d*sin(f*x + e))^n, x)","F",0
3,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
4,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a*sin(f*x + e) + a), x)","F",0
5,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a*sin(f*x + e) + a)^2, x)","F",0
6,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a*sin(f*x + e) + a)^3, x)","F",0
7,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e))^n, x)","F",0
8,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e))^n, x)","F",0
9,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
10,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/sqrt(a*sin(f*x + e) + a), x)","F",0
11,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
13,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^n*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","-\int {\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}\,{d x}"," ",0,"-integrate((a*sin(f*x + e) - a)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
14,0,0,0,0.000000," ","integrate(sin(d*x+c)^n*(a+a*sin(d*x+c))^(-2-n)*(-1-n-(-2-n)*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left({\left(n + 2\right)} \sin\left(d x + c\right) - n - 1\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{-n - 2} \sin\left(d x + c\right)^{n}\,{d x}"," ",0,"integrate(((n + 2)*sin(d*x + c) - n - 1)*(a*sin(d*x + c) + a)^(-n - 2)*sin(d*x + c)^n, x)","F",0
15,0,0,0,0.000000," ","integrate(sin(d*x+c)^(-2-m)*(a+a*sin(d*x+c))^m*(1+m-m*sin(d*x+c)),x, algorithm=""maxima"")","-\int {\left(m \sin\left(d x + c\right) - m - 1\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{-m - 2}\,{d x}"," ",0,"-integrate((m*sin(d*x + c) - m - 1)*(a*sin(d*x + c) + a)^m*sin(d*x + c)^(-m - 2), x)","F",0
16,-2,0,0,0.000000," ","integrate(sin(f*x+e)^2*(A+B*sin(f*x+e))/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
17,1,336,0,0.601709," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a c^{4} - 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a c^{4} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a c^{4} - 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c^{4} - 960 \, {\left(f x + e\right)} A a c^{4} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a c^{4} - 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c^{4} - 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{4} - 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{4} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{4} - 2880 \, A a c^{4} \cos\left(f x + e\right) + 960 \, B a c^{4} \cos\left(f x + e\right)}{960 \, f}"," ",0,"-1/960*(64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a*c^4 - 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*c^4 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a*c^4 - 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c^4 - 960*(f*x + e)*A*a*c^4 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a*c^4 - 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c^4 - 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a*c^4 - 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*c^4 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^4 - 2880*A*a*c^4*cos(f*x + e) + 960*B*a*c^4*cos(f*x + e))/f","A",0
18,1,200,0,0.328186," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a c^{3} - 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a c^{3} + 480 \, {\left(f x + e\right)} A a c^{3} + 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a c^{3} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{3} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{3} + 960 \, A a c^{3} \cos\left(f x + e\right) - 480 \, B a c^{3} \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*c^3 - 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a*c^3 + 480*(f*x + e)*A*a*c^3 + 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a*c^3 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*c^3 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^3 + 960*A*a*c^3*cos(f*x + e) - 480*B*a*c^3*cos(f*x + e))/f","A",0
19,1,179,0,0.334399," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a c^{2} - 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c^{2} + 96 \, {\left(f x + e\right)} A a c^{2} - 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c^{2} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{2} - 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{2} + 96 \, A a c^{2} \cos\left(f x + e\right) - 96 \, B a c^{2} \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*c^2 - 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c^2 + 96*(f*x + e)*A*a*c^2 - 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c^2 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*c^2 - 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^2 + 96*A*a*c^2*cos(f*x + e) - 96*B*a*c^2*cos(f*x + e))/f","B",0
20,1,73,0,0.383481," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c - 12 \, {\left(f x + e\right)} A a c + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c + 12 \, B a c \cos\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c - 12*(f*x + e)*A*a*c + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c + 12*B*a*c*cos(f*x + e))/f","A",0
21,1,265,0,0.588377," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(B a {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + A a {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + B a {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{A a}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(B*a*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + A*a*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) + B*a*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - A*a/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
22,1,456,0,0.435046," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(B a {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} - \frac{A a {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{A a {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B a {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(B*a*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) - A*a*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + A*a*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*a*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
23,1,737,0,0.532703," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A a {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, A a {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B a {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, B a {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(A*a*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*A*a*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*a*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*B*a*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
24,1,1080,0,0.386484," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A a {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{B a {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{3 \, A a {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{4 \, B a {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{105 \, f}"," ",0,"2/105*(A*a*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + B*a*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 3*A*a*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 4*B*a*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
25,1,1425,0,0.398103," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A a {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{5 \, A a {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{5 \, B a {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{14 \, B a {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(A*a*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 5*A*a*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 5*B*a*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 14*B*a*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
26,1,571,0,0.543357," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{3072 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} A a^{2} c^{5} - 7168 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{2} c^{5} - 179200 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c^{5} - 1680 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{5} + 16800 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{5} - 26880 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{5} - 107520 \, {\left(f x + e\right)} A a^{2} c^{5} - 9216 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{2} c^{5} - 35840 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} c^{5} - 35840 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{5} + 35 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{5} + 560 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{5} - 16800 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{5} + 80640 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{5} - 322560 \, A a^{2} c^{5} \cos\left(f x + e\right) + 107520 \, B a^{2} c^{5} \cos\left(f x + e\right)}{107520 \, f}"," ",0,"-1/107520*(3072*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*A*a^2*c^5 - 7168*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^2*c^5 - 179200*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c^5 - 1680*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^2*c^5 + 16800*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*c^5 - 26880*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^5 - 107520*(f*x + e)*A*a^2*c^5 - 9216*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^2*c^5 - 35840*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*c^5 - 35840*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^5 + 35*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*B*a^2*c^5 + 560*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^2*c^5 - 16800*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c^5 + 80640*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^5 - 322560*A*a^2*c^5*cos(f*x + e) + 107520*B*a^2*c^5*cos(f*x + e))/f","B",0
27,1,460,0,0.340530," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{896 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{2} c^{4} + 8960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c^{4} + 35 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{4} - 210 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{4} - 1680 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{4} + 6720 \, {\left(f x + e\right)} A a^{2} c^{4} + 192 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{2} c^{4} + 448 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} c^{4} - 2240 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{4} - 70 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{4} + 840 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{4} - 3360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{4} + 13440 \, A a^{2} c^{4} \cos\left(f x + e\right) - 6720 \, B a^{2} c^{4} \cos\left(f x + e\right)}{6720 \, f}"," ",0,"1/6720*(896*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^2*c^4 + 8960*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c^4 + 35*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^2*c^4 - 210*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*c^4 - 1680*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^4 + 6720*(f*x + e)*A*a^2*c^4 + 192*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^2*c^4 + 448*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*c^4 - 2240*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^4 - 70*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^2*c^4 + 840*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c^4 - 3360*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^4 + 13440*A*a^2*c^4*cos(f*x + e) - 6720*B*a^2*c^4*cos(f*x + e))/f","B",0
28,1,360,0,0.468243," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{2} c^{3} + 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c^{3} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{3} - 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{3} + 960 \, {\left(f x + e\right)} A a^{2} c^{3} - 64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} c^{3} - 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{3} - 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{3} + 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{3} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{3} + 960 \, A a^{2} c^{3} \cos\left(f x + e\right) - 960 \, B a^{2} c^{3} \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^2*c^3 + 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c^3 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*c^3 - 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^3 + 960*(f*x + e)*A*a^2*c^3 - 64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*c^3 - 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^3 - 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^2*c^3 + 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c^3 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^3 + 960*A*a^2*c^3*cos(f*x + e) - 960*B*a^2*c^3*cos(f*x + e))/f","B",0
29,1,164,0,0.490051," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{2} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{2} + 480 \, {\left(f x + e\right)} A a^{2} c^{2} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} c^{2} - 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{2} - 480 \, B a^{2} c^{2} \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*c^2 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^2 + 480*(f*x + e)*A*a^2*c^2 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*c^2 - 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^2 - 480*B*a^2*c^2*cos(f*x + e))/f","B",0
30,1,179,0,0.365016," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c - 96 \, {\left(f x + e\right)} A a^{2} c + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c - 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c + 96 \, A a^{2} c \cos\left(f x + e\right) + 96 \, B a^{2} c \cos\left(f x + e\right)}{96 \, f}"," ",0,"-1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c - 96*(f*x + e)*A*a^2*c + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c - 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c + 96*A*a^2*c*cos(f*x + e) + 96*B*a^2*c*cos(f*x + e))/f","A",0
31,1,624,0,0.484021," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, A a^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 4 \, B a^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + B a^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 4}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 4 \, A a^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 2 \, B a^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{2 \, A a^{2}}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"-(2*A*a^2*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 4*B*a^2*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + B*a^2*((sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 4*A*a^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) + 2*B*a^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - 2*A*a^2/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
32,1,839,0,0.441128," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, B a^{2} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 5}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + A a^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 2 \, B a^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} - \frac{A a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, A a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B a^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(2*B*a^2*((12*sin(f*x + e)/(cos(f*x + e) + 1) - 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + A*a^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 2*B*a^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) - A*a^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*A*a^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*a^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
33,1,1139,0,0.627996," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(B a^{2} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 22}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{3}}\right)} + \frac{A a^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, A a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, A a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{4 \, B a^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(B*a^2*((95*sin(f*x + e)/(cos(f*x + e) + 1) - 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 22)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^3) + A*a^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*A*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*A*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 4*B*a^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
34,1,1571,0,0.612391," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, A a^{2} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{B a^{2} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{3 \, A a^{2} {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{4 \, A a^{2} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{8 \, B a^{2} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{6 \, B a^{2} {\left(\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{105 \, f}"," ",0,"2/105*(2*A*a^2*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + B*a^2*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 3*A*a^2*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 4*A*a^2*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 8*B*a^2*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 6*B*a^2*(7*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
35,1,2087,0,0.422395," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A a^{2} {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{10 \, A a^{2} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{5 \, B a^{2} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{10 \, B a^{2} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{14 \, A a^{2} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{28 \, B a^{2} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(A*a^2*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 10*A*a^2*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 5*B*a^2*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 10*B*a^2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 63*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 14*A*a^2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 28*B*a^2*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
36,1,2604,0,0.454962," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, A a^{2} {\left(\frac{913 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4565 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12540 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25080 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33726 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{33726 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{23100 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{11550 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 146\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{6 \, A a^{2} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{3 \, B a^{2} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{2 \, B a^{2} {\left(\frac{341 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1705 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5115 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9471 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4851 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3465 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 31\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{4 \, A a^{2} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{8 \, B a^{2} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}}\right)}}{3465 \, f}"," ",0,"-2/3465*(5*A*a^2*(913*sin(f*x + e)/(cos(f*x + e) + 1) - 4565*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12540*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25080*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33726*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 33726*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 23100*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 11550*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 146)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 6*A*a^2*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 3*B*a^2*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 2*B*a^2*(341*sin(f*x + e)/(cos(f*x + e) + 1) - 1705*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5115*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9471*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4851*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3465*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 31)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 4*A*a^2*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 8*B*a^2*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11))/f","B",0
37,1,3120,0,0.688750," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, A a^{2} {\left(\frac{4771 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{28626 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{74932 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{187330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{265122 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{353496 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{276276 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{207207 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75075 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 367\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{4 \, B a^{2} {\left(\frac{4771 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{28626 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{74932 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{187330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{265122 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{353496 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{276276 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{207207 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75075 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 367\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{15 \, A a^{2} {\left(\frac{3796 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{22776 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{77506 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{193765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{339768 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{453024 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{444444 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{333333 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{180180 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{72072 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{18018 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{3003 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 523\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{70 \, A a^{2} {\left(\frac{611 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2379 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8723 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{18590 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33462 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{40326 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40326 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{27027 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{4719 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 47\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{35 \, B a^{2} {\left(\frac{611 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2379 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8723 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{18590 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33462 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{40326 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40326 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{27027 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{4719 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 47\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{462 \, B a^{2} {\left(\frac{13 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{286 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{520 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{936 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{858 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{858 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{351 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{195 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 1\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}}\right)}}{45045 \, f}"," ",0,"-2/45045*(2*A*a^2*(4771*sin(f*x + e)/(cos(f*x + e) + 1) - 28626*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 74932*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 187330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 265122*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 353496*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 276276*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 207207*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75075*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 367)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 4*B*a^2*(4771*sin(f*x + e)/(cos(f*x + e) + 1) - 28626*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 74932*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 187330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 265122*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 353496*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 276276*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 207207*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75075*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 367)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 15*A*a^2*(3796*sin(f*x + e)/(cos(f*x + e) + 1) - 22776*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 77506*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 193765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 339768*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 453024*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 444444*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 333333*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 180180*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 72072*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 18018*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 3003*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 523)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 70*A*a^2*(611*sin(f*x + e)/(cos(f*x + e) + 1) - 2379*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8723*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 18590*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33462*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 40326*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40326*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 27027*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15015*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 4719*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 47)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 35*B*a^2*(611*sin(f*x + e)/(cos(f*x + e) + 1) - 2379*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8723*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 18590*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33462*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 40326*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40326*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 27027*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15015*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 4719*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 47)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 462*B*a^2*(13*sin(f*x + e)/(cos(f*x + e) + 1) - 78*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 286*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 520*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 936*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 858*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 858*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 351*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 195*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13))/f","B",0
38,1,661,0,0.358580," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2048 \, {\left(35 \, \cos\left(f x + e\right)^{9} - 180 \, \cos\left(f x + e\right)^{7} + 378 \, \cos\left(f x + e\right)^{5} - 420 \, \cos\left(f x + e\right)^{3} + 315 \, \cos\left(f x + e\right)\right)} A a^{3} c^{6} - 258048 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} c^{6} - 1720320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{6} + 630 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{6} - 26880 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{6} + 120960 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{6} - 645120 \, {\left(f x + e\right)} A a^{3} c^{6} - 6144 \, {\left(35 \, \cos\left(f x + e\right)^{9} - 180 \, \cos\left(f x + e\right)^{7} + 378 \, \cos\left(f x + e\right)^{5} - 420 \, \cos\left(f x + e\right)^{3} + 315 \, \cos\left(f x + e\right)\right)} B a^{3} c^{6} - 147456 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{3} c^{6} - 258048 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c^{6} + 63 \, {\left(32 \, \sin\left(2 \, f x + 2 \, e\right)^{5} - 640 \, \sin\left(2 \, f x + 2 \, e\right)^{3} - 2520 \, f x - 2520 \, e - 25 \, \sin\left(8 \, f x + 8 \, e\right) - 600 \, \sin\left(4 \, f x + 4 \, e\right) + 2560 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{6} + 20160 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{6} - 161280 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{6} + 483840 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{6} - 1935360 \, A a^{3} c^{6} \cos\left(f x + e\right) + 645120 \, B a^{3} c^{6} \cos\left(f x + e\right)}{645120 \, f}"," ",0,"-1/645120*(2048*(35*cos(f*x + e)^9 - 180*cos(f*x + e)^7 + 378*cos(f*x + e)^5 - 420*cos(f*x + e)^3 + 315*cos(f*x + e))*A*a^3*c^6 - 258048*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*c^6 - 1720320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^6 + 630*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*A*a^3*c^6 - 26880*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^3*c^6 + 120960*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c^6 - 645120*(f*x + e)*A*a^3*c^6 - 6144*(35*cos(f*x + e)^9 - 180*cos(f*x + e)^7 + 378*cos(f*x + e)^5 - 420*cos(f*x + e)^3 + 315*cos(f*x + e))*B*a^3*c^6 - 147456*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^3*c^6 - 258048*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c^6 + 63*(32*sin(2*f*x + 2*e)^5 - 640*sin(2*f*x + 2*e)^3 - 2520*f*x - 2520*e - 25*sin(8*f*x + 8*e) - 600*sin(4*f*x + 4*e) + 2560*sin(2*f*x + 2*e))*B*a^3*c^6 + 20160*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*c^6 - 161280*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^6 + 483840*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^6 - 1935360*A*a^3*c^6*cos(f*x + e) + 645120*B*a^3*c^6*cos(f*x + e))/f","B",0
39,1,617,0,0.347027," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","\frac{18432 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} A a^{3} c^{5} + 129024 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} c^{5} + 645120 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{5} - 105 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{5} + 3360 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{5} - 161280 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{5} + 322560 \, {\left(f x + e\right)} A a^{3} c^{5} + 1024 \, {\left(35 \, \cos\left(f x + e\right)^{9} - 180 \, \cos\left(f x + e\right)^{7} + 378 \, \cos\left(f x + e\right)^{5} - 420 \, \cos\left(f x + e\right)^{3} + 315 \, \cos\left(f x + e\right)\right)} B a^{3} c^{5} + 18432 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{3} c^{5} - 215040 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{5} + 210 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{5} - 10080 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{5} + 60480 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{5} - 161280 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{5} + 645120 \, A a^{3} c^{5} \cos\left(f x + e\right) - 322560 \, B a^{3} c^{5} \cos\left(f x + e\right)}{322560 \, f}"," ",0,"1/322560*(18432*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*A*a^3*c^5 + 129024*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*c^5 + 645120*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^5 - 105*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*A*a^3*c^5 + 3360*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^3*c^5 - 161280*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^5 + 322560*(f*x + e)*A*a^3*c^5 + 1024*(35*cos(f*x + e)^9 - 180*cos(f*x + e)^7 + 378*cos(f*x + e)^5 - 420*cos(f*x + e)^3 + 315*cos(f*x + e))*B*a^3*c^5 + 18432*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^3*c^5 - 215040*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^5 + 210*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*B*a^3*c^5 - 10080*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*c^5 + 60480*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^5 - 161280*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^5 + 645120*A*a^3*c^5*cos(f*x + e) - 322560*B*a^3*c^5*cos(f*x + e))/f","B",0
40,1,571,0,0.355891," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{3072 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} A a^{3} c^{4} + 21504 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} c^{4} + 107520 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{4} - 560 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{4} + 10080 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{4} - 80640 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{4} + 107520 \, {\left(f x + e\right)} A a^{3} c^{4} - 3072 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{3} c^{4} - 21504 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c^{4} - 107520 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{4} + 35 \, {\left(128 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 840 \, f x + 840 \, e + 3 \, \sin\left(8 \, f x + 8 \, e\right) + 168 \, \sin\left(4 \, f x + 4 \, e\right) - 768 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{4} - 1680 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{4} + 10080 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{4} - 26880 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{4} + 107520 \, A a^{3} c^{4} \cos\left(f x + e\right) - 107520 \, B a^{3} c^{4} \cos\left(f x + e\right)}{107520 \, f}"," ",0,"1/107520*(3072*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*A*a^3*c^4 + 21504*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*c^4 + 107520*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^4 - 560*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^3*c^4 + 10080*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c^4 - 80640*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^4 + 107520*(f*x + e)*A*a^3*c^4 - 3072*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^3*c^4 - 21504*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c^4 - 107520*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^4 + 35*(128*sin(2*f*x + 2*e)^3 + 840*f*x + 840*e + 3*sin(8*f*x + 8*e) + 168*sin(4*f*x + 4*e) - 768*sin(2*f*x + 2*e))*B*a^3*c^4 - 1680*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*c^4 + 10080*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^4 - 26880*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^4 + 107520*A*a^3*c^4*cos(f*x + e) - 107520*B*a^3*c^4*cos(f*x + e))/f","B",0
41,1,264,0,0.382513," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{35 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{3} - 630 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{3} + 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{3} - 6720 \, {\left(f x + e\right)} A a^{3} c^{3} + 192 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{3} c^{3} + 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c^{3} + 6720 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{3} + 6720 \, B a^{3} c^{3} \cos\left(f x + e\right)}{6720 \, f}"," ",0,"-1/6720*(35*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^3*c^3 - 630*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c^3 + 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^3 - 6720*(f*x + e)*A*a^3*c^3 + 192*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^3*c^3 + 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c^3 + 6720*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^3 + 6720*B*a^3*c^3*cos(f*x + e))/f","B",0
42,1,360,0,0.343764," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} c^{2} + 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{2} - 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{2} + 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{2} - 960 \, {\left(f x + e\right)} A a^{3} c^{2} + 64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c^{2} + 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{2} - 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} + 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} + 960 \, A a^{3} c^{2} \cos\left(f x + e\right) + 960 \, B a^{3} c^{2} \cos\left(f x + e\right)}{960 \, f}"," ",0,"-1/960*(64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*c^2 + 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^2 - 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c^2 + 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^2 - 960*(f*x + e)*A*a^3*c^2 + 64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c^2 + 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^2 - 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*c^2 + 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^2 - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^2 + 960*A*a^3*c^2*cos(f*x + e) + 960*B*a^3*c^2*cos(f*x + e))/f","B",0
43,1,200,0,0.524039," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c - 480 \, {\left(f x + e\right)} A a^{3} c - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c - 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c + 960 \, A a^{3} c \cos\left(f x + e\right) + 480 \, B a^{3} c \cos\left(f x + e\right)}{480 \, f}"," ",0,"-1/480*(320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c - 480*(f*x + e)*A*a^3*c - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c - 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c + 960*A*a^3*c*cos(f*x + e) + 480*B*a^3*c*cos(f*x + e))/f","A",0
44,1,1139,0,0.468849," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{B a^{3} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 16}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3 \, c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 18 \, A a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 18 \, B a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 3 \, A a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 4}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 9 \, B a^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 4}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c}\right)} + 18 \, A a^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 6 \, B a^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c} - \frac{1}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{6 \, A a^{3}}{c - \frac{c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{3 \, f}"," ",0,"-1/3*(B*a^3*((7*sin(f*x + e)/(cos(f*x + e) + 1) - 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 16)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3*c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 18*A*a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 18*B*a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 3*A*a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 9*B*a^3*((sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4)/(c - c*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c) + 18*A*a^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) + 6*B*a^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c - 1/(c - c*sin(f*x + e)/(cos(f*x + e) + 1))) - 6*A*a^3/(c - c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
45,1,1386,0,0.608098," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{B a^{3} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 32}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{7 \, c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 4 \, A a^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 5}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 12 \, B a^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 5}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 6 \, A a^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} + 6 \, B a^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 4}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{2}}\right)} - \frac{2 \, A a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 2\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{6 \, A a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, B a^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}}{c^{2} - \frac{3 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(B*a^3*((75*sin(f*x + e)/(cos(f*x + e) + 1) - 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 32)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 7*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*c^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 4*A*a^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) - 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 12*B*a^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) - 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 6*A*a^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) + 6*B*a^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^2) - 2*A*a^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 6*A*a^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*B*a^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 1)/(c^2 - 3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
46,1,1685,0,0.702065," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, B a^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 24}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{15 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{11 \, c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{3}}\right)} + A a^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 22}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{3}}\right)} + 3 \, B a^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 22}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{3}}\right)} + \frac{A a^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 7\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{9 \, A a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, A a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, B a^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{c^{3} - \frac{5 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(3*B*a^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) - 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 24)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 15*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 11*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^3) + A*a^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) - 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 22)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^3) + 3*B*a^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) - 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 22)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^3) + A*a^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) - 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 9*A*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*A*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*B*a^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(c^3 - 5*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
47,1,2118,0,0.581071," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{2 \, {\left(5 \, B a^{3} {\left(\frac{\frac{203 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{525 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{686 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{434 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{147 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 32}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{c^{4}}\right)} + \frac{3 \, A a^{3} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{B a^{3} {\left(\frac{91 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{168 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{175 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 13\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{3 \, A a^{3} {\left(\frac{49 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{147 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{210 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{105 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 12\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{12 \, A a^{3} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} - \frac{12 \, B a^{3} {\left(\frac{14 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{42 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 2\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{6 \, A a^{3} {\left(\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{18 \, B a^{3} {\left(\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{c^{4} - \frac{7 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{35 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{21 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}\right)}}{105 \, f}"," ",0,"2/105*(5*B*a^3*((203*sin(f*x + e)/(cos(f*x + e) + 1) - 525*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 686*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 434*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 147*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 32)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/c^4) + 3*A*a^3*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + B*a^3*(91*sin(f*x + e)/(cos(f*x + e) + 1) - 168*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 175*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 13)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 3*A*a^3*(49*sin(f*x + e)/(cos(f*x + e) + 1) - 147*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 210*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 210*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 12)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 12*A*a^3*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) - 12*B*a^3*(14*sin(f*x + e)/(cos(f*x + e) + 1) - 42*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 6*A*a^3*(7*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 18*B*a^3*(7*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(c^4 - 7*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 35*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 21*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7))/f","B",0
48,1,2701,0,0.537274," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A a^{3} {\left(\frac{432 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1728 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3612 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5418 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5040 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3360 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1260 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 83\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{15 \, A a^{3} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{5 \, B a^{3} {\left(\frac{45 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{117 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{273 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{315 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{147 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 5\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{10 \, A a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} - \frac{30 \, B a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{8 \, B a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{126 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{42 \, A a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{42 \, B a^{3} {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{54 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{81 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{45 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{5} - \frac{9 \, c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{84 \, c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{126 \, c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{36 \, c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}\right)}}{315 \, f}"," ",0,"-2/315*(A*a^3*(432*sin(f*x + e)/(cos(f*x + e) + 1) - 1728*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3612*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5418*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5040*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3360*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1260*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 315*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 83)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 15*A*a^3*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 5*B*a^3*(45*sin(f*x + e)/(cos(f*x + e) + 1) - 117*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 273*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 315*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 147*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 10*A*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 63*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) - 30*B*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 63*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 8*B*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 126*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 42*A*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 42*B*a^3*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 54*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 81*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 45*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 30*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^5 - 9*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 36*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 84*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 126*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 36*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9))/f","B",0
49,1,3390,0,0.529469," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, A a^{3} {\left(\frac{913 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4565 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12540 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25080 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33726 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{33726 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{23100 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{11550 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{3465 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{693 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 146\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{9 \, A a^{3} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{3 \, B a^{3} {\left(\frac{671 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2200 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6600 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10890 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15246 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{12936 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{9240 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1155 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 61\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{2 \, A a^{3} {\left(\frac{341 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1705 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5115 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9471 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4851 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3465 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 31\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} - \frac{6 \, B a^{3} {\left(\frac{341 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1705 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5115 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9471 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{4851 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3465 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 31\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{12 \, A a^{3} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{12 \, B a^{3} {\left(\frac{253 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{1265 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2640 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5280 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5313 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{5313 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1155 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 23\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{48 \, B a^{3} {\left(\frac{11 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{55 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{165 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{231 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{231 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{c^{6} - \frac{11 \, c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{165 \, c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{462 \, c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{330 \, c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, c^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{55 \, c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}}\right)}}{3465 \, f}"," ",0,"-2/3465*(5*A*a^3*(913*sin(f*x + e)/(cos(f*x + e) + 1) - 4565*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12540*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25080*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33726*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 33726*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 23100*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 11550*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 3465*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 693*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 146)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 9*A*a^3*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 3*B*a^3*(671*sin(f*x + e)/(cos(f*x + e) + 1) - 2200*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6600*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10890*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15246*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 12936*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 9240*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3465*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1155*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 61)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 2*A*a^3*(341*sin(f*x + e)/(cos(f*x + e) + 1) - 1705*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5115*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9471*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4851*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3465*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 31)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) - 6*B*a^3*(341*sin(f*x + e)/(cos(f*x + e) + 1) - 1705*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5115*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9471*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 4851*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3465*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 31)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 12*A*a^3*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 12*B*a^3*(253*sin(f*x + e)/(cos(f*x + e) + 1) - 1265*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2640*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5280*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5313*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 5313*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1155*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 23)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 48*B*a^3*(11*sin(f*x + e)/(cos(f*x + e) + 1) - 55*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 165*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 231*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 231*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(c^6 - 11*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 55*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 165*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 462*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 330*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*c^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 55*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11))/f","B",0
50,1,4078,0,0.571961," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{6 \, A a^{3} {\left(\frac{4771 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{28626 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{74932 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{187330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{265122 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{353496 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{276276 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{207207 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75075 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 367\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{6 \, B a^{3} {\left(\frac{4771 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{28626 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{74932 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{187330 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{265122 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{353496 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{276276 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{207207 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75075 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{30030 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 367\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{15 \, A a^{3} {\left(\frac{3796 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{22776 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{77506 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{193765 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{339768 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{453024 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{444444 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{333333 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{180180 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{72072 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{18018 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{3003 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 523\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{105 \, A a^{3} {\left(\frac{611 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2379 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8723 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{18590 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33462 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{40326 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40326 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{27027 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{4719 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 47\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{35 \, B a^{3} {\left(\frac{611 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2379 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8723 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{18590 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{33462 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{40326 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40326 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{27027 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15015 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{4719 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{1287 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 47\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} + \frac{8 \, B a^{3} {\left(\frac{559 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3354 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12298 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{30745 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{37323 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{49764 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{24024 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{18018 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 43\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{462 \, A a^{3} {\left(\frac{13 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{286 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{520 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{936 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{858 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{858 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{351 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{195 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 1\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}} - \frac{1386 \, B a^{3} {\left(\frac{13 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{286 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{520 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{936 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{858 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{858 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{351 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{195 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 1\right)}}{c^{7} - \frac{13 \, c^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{78 \, c^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{286 \, c^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{715 \, c^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{1287 \, c^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1716 \, c^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{1716 \, c^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1287 \, c^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{715 \, c^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{286 \, c^{7} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{78 \, c^{7} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{13 \, c^{7} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{c^{7} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}}}\right)}}{45045 \, f}"," ",0,"-2/45045*(6*A*a^3*(4771*sin(f*x + e)/(cos(f*x + e) + 1) - 28626*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 74932*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 187330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 265122*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 353496*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 276276*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 207207*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75075*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 367)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 6*B*a^3*(4771*sin(f*x + e)/(cos(f*x + e) + 1) - 28626*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 74932*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 187330*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 265122*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 353496*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 276276*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 207207*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75075*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 30030*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 367)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 15*A*a^3*(3796*sin(f*x + e)/(cos(f*x + e) + 1) - 22776*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 77506*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 193765*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 339768*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 453024*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 444444*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 333333*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 180180*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 72072*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 18018*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 3003*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 523)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 105*A*a^3*(611*sin(f*x + e)/(cos(f*x + e) + 1) - 2379*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8723*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 18590*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33462*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 40326*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40326*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 27027*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15015*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 4719*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 47)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 35*B*a^3*(611*sin(f*x + e)/(cos(f*x + e) + 1) - 2379*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8723*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 18590*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 33462*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 40326*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40326*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 27027*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15015*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 4719*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 1287*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 47)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) + 8*B*a^3*(559*sin(f*x + e)/(cos(f*x + e) + 1) - 3354*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12298*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 30745*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 37323*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 49764*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24024*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 18018*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 43)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 462*A*a^3*(13*sin(f*x + e)/(cos(f*x + e) + 1) - 78*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 286*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 520*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 936*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 858*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 858*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 351*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 195*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13) - 1386*B*a^3*(13*sin(f*x + e)/(cos(f*x + e) + 1) - 78*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 286*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 520*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 936*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 858*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 858*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 351*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 195*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1)/(c^7 - 13*c^7*sin(f*x + e)/(cos(f*x + e) + 1) + 78*c^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 286*c^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 715*c^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1287*c^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1716*c^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1716*c^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1287*c^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 715*c^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 286*c^7*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 78*c^7*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 13*c^7*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - c^7*sin(f*x + e)^13/(cos(f*x + e) + 1)^13))/f","B",0
51,1,4765,0,0.683108," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^8,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, A a^{3} {\left(\frac{17715 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78960 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{342160 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{891345 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1960959 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3043040 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3912480 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3687255 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2867865 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{1585584 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{720720 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{195195 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45045 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - 1181\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} + \frac{B a^{3} {\left(\frac{17715 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{78960 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{342160 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{891345 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1960959 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{3043040 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3912480 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3687255 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2867865 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{1585584 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{720720 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{195195 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45045 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - 1181\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{7 \, A a^{3} {\left(\frac{7845 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{54915 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{222950 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{668850 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1444443 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{2407405 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{3063060 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3063060 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2357355 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{1414413 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{630630 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{210210 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45045 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{6435 \, \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - 952\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{12 \, A a^{3} {\left(\frac{1740 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{12180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{37765 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{113295 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{204204 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{340340 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{373230 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{373230 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{240240 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{144144 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{45045 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{15015 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 116\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{12 \, B a^{3} {\left(\frac{1740 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{12180 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{37765 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{113295 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{204204 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{340340 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{373230 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{373230 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{240240 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{144144 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{45045 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{15015 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 116\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} + \frac{6 \, A a^{3} {\left(\frac{675 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4725 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20475 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{46410 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{102102 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{130130 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{167310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{122265 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{95095 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{33033 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{15015 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 45\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} + \frac{18 \, B a^{3} {\left(\frac{675 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4725 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20475 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{46410 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{102102 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{130130 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{167310 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{122265 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{95095 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{33033 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{15015 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 45\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}} - \frac{48 \, B a^{3} {\left(\frac{60 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{420 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{1820 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5460 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9009 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{15015 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12870 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{12870 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{5005 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{3003 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 4\right)}}{c^{8} - \frac{15 \, c^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{105 \, c^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{455 \, c^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1365 \, c^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{3003 \, c^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5005 \, c^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6435 \, c^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6435 \, c^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{5005 \, c^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3003 \, c^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{1365 \, c^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{455 \, c^{8} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{105 \, c^{8} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{15 \, c^{8} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{c^{8} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}}}\right)}}{45045 \, f}"," ",0,"2/45045*(3*A*a^3*(17715*sin(f*x + e)/(cos(f*x + e) + 1) - 78960*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 342160*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 891345*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1960959*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3043040*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3912480*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3687255*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2867865*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1585584*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 720720*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 195195*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45045*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 1181)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) + B*a^3*(17715*sin(f*x + e)/(cos(f*x + e) + 1) - 78960*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 342160*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 891345*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1960959*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 3043040*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3912480*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3687255*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2867865*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1585584*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 720720*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 195195*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45045*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 1181)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 7*A*a^3*(7845*sin(f*x + e)/(cos(f*x + e) + 1) - 54915*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 222950*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 668850*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1444443*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2407405*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3063060*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3063060*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2357355*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 1414413*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 630630*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 210210*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45045*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 6435*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - 952)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 12*A*a^3*(1740*sin(f*x + e)/(cos(f*x + e) + 1) - 12180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 37765*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 113295*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 204204*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 340340*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 373230*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 373230*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 240240*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 144144*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 45045*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 15015*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 116)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 12*B*a^3*(1740*sin(f*x + e)/(cos(f*x + e) + 1) - 12180*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 37765*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 113295*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 204204*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 340340*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 373230*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 373230*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 240240*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 144144*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 45045*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 15015*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 116)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) + 6*A*a^3*(675*sin(f*x + e)/(cos(f*x + e) + 1) - 4725*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20475*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 46410*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 102102*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 130130*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 167310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 122265*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 95095*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 33033*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 15015*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 45)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) + 18*B*a^3*(675*sin(f*x + e)/(cos(f*x + e) + 1) - 4725*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20475*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 46410*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 102102*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 130130*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 167310*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 122265*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 95095*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 33033*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 15015*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 45)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15) - 48*B*a^3*(60*sin(f*x + e)/(cos(f*x + e) + 1) - 420*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1820*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5460*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9009*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 15015*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12870*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 12870*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 5005*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 3003*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 4)/(c^8 - 15*c^8*sin(f*x + e)/(cos(f*x + e) + 1) + 105*c^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 455*c^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1365*c^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 3003*c^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5005*c^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6435*c^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6435*c^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 5005*c^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3003*c^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1365*c^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 455*c^8*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 105*c^8*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 15*c^8*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - c^8*sin(f*x + e)^15/(cos(f*x + e) + 1)^15))/f","B",0
52,1,1796,0,0.644246," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{B c^{4} {\left(\frac{\frac{19 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{211 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{91 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{219 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{165 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{165 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{45 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 64}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{6 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{4 \, a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{4 \, a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{a \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{45 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 4 \, A c^{4} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 16 \, B c^{4} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 48 \, A c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 72 \, B c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 144 \, A c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 96 \, B c^{4} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 96 \, A c^{4} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 24 \, B c^{4} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{24 \, A c^{4}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{12 \, f}"," ",0,"1/12*(B*c^4*((19*sin(f*x + e)/(cos(f*x + e) + 1) + 211*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 91*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 219*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 165*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 165*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 45*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 64)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 6*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 4*a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 4*a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + a*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 45*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 4*A*c^4*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 16*B*c^4*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 48*A*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 72*B*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 144*A*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 96*B*c^4*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 96*A*c^4*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 24*B*c^4*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 24*A*c^4/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
53,1,1120,0,0.455927," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{B c^{3} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 3 \, A c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 9 \, B c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 18 \, A c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 18 \, B c^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 18 \, A c^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 6 \, B c^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{6 \, A c^{3}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{3 \, f}"," ",0,"1/3*(B*c^3*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 3*A*c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 9*B*c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 18*A*c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 18*B*c^3*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 18*A*c^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 6*B*c^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 6*A*c^3/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
54,1,608,0,0.427968," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{B c^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 2 \, A c^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 4 \, B c^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 4 \, A c^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 2 \, B c^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{2 \, A c^{2}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"(B*c^2*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 2*A*c^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 4*B*c^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 4*A*c^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 2*B*c^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 2*A*c^2/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
55,1,256,0,0.548959," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(B c {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - A c {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + B c {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{A c}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"2*(B*c*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - A*c*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + B*c*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - A*c/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
56,1,35,0,0.321369," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{A \tan\left(f x + e\right)}{a c} + \frac{B}{a c \cos\left(f x + e\right)}}{f}"," ",0,"(A*tan(f*x + e)/(a*c) + B/(a*c*cos(f*x + e)))/f","A",0
57,1,266,0,0.627190," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{B {\left(\frac{2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - 1\right)}}{a c^{2} - \frac{2 \, a c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{A {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a c^{2} - \frac{2 \, a c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a c^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}\right)}}{3 \, f}"," ",0,"-2/3*(B*(2*sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 1)/(a*c^2 - 2*a*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - A*(sin(f*x + e)/(cos(f*x + e) + 1) - 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a*c^2 - 2*a*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a*c^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4))/f","B",0
58,1,423,0,0.637953," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{B {\left(\frac{4 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{20 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - 1\right)}}{a c^{3} - \frac{4 \, a c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, a c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{3 \, A {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{10 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - 2\right)}}{a c^{3} - \frac{4 \, a c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, a c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}\right)}}{15 \, f}"," ",0,"-2/15*(B*(4*sin(f*x + e)/(cos(f*x + e) + 1) - 20*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 1)/(a*c^3 - 4*a*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*a*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + 3*A*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 10*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2)/(a*c^3 - 4*a*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a*c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*a*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6))/f","B",0
59,1,619,0,0.350026," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{43 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{77 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{105 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{175 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{105 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{35 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 13\right)}}{a c^{4} - \frac{6 \, a c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} - \frac{B {\left(\frac{6 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{56 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{105 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{70 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{35 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 1\right)}}{a c^{4} - \frac{6 \, a c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{14 \, a c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}\right)}}{35 \, f}"," ",0,"-2/35*(A*(43*sin(f*x + e)/(cos(f*x + e) + 1) - 77*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 105*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 175*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 105*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 35*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 13)/(a*c^4 - 6*a*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 14*a*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 14*a*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 14*a*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) - B*(6*sin(f*x + e)/(cos(f*x + e) + 1) + 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 56*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 105*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 70*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 35*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 1)/(a*c^4 - 6*a*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 14*a*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 14*a*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 14*a*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8))/f","B",0
60,1,2982,0,0.758137," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{B c^{5} {\left(\frac{\frac{603 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{1297 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2228 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{2628 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3014 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2618 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1980 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1100 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{495 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{165 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + 256}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{13 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{18 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{22 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{22 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{18 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{13 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{165 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 20 \, A c^{5} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 40 \, B c^{5} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 8 \, A c^{5} {\left(\frac{\frac{57 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{99 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{155 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{153 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{135 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{85 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 24}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 40 \, B c^{5} {\left(\frac{\frac{57 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{99 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{155 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{153 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{135 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{85 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 24}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 160 \, A c^{5} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 160 \, B c^{5} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 80 \, A c^{5} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 40 \, B c^{5} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{8 \, A c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{40 \, A c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{8 \, B c^{5} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{12 \, f}"," ",0,"-1/12*(B*c^5*((603*sin(f*x + e)/(cos(f*x + e) + 1) + 1297*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2228*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 2628*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3014*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2618*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1980*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1100*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 495*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 165*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 256)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 7*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 13*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 18*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 22*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 18*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 13*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 7*a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 3*a^2*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + a^2*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 165*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 20*A*c^5*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 40*B*c^5*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 8*A*c^5*((57*sin(f*x + e)/(cos(f*x + e) + 1) + 99*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 155*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 153*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 135*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 85*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 24)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 10*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 40*B*c^5*((57*sin(f*x + e)/(cos(f*x + e) + 1) + 99*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 155*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 153*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 135*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 85*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 24)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 10*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 160*A*c^5*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 160*B*c^5*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 80*A*c^5*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 40*B*c^5*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 8*A*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 40*A*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 8*B*c^5*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
61,1,2094,0,0.521995," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{A c^{4} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 4 \, B c^{4} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 2 \, B c^{4} {\left(\frac{\frac{57 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{99 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{155 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{153 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{135 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{85 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 24}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{10 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{6 \, a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 16 \, A c^{4} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 24 \, B c^{4} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 12 \, A c^{4} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 8 \, B c^{4} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, A c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{8 \, A c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{2 \, B c^{4} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(A*c^4*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 4*B*c^4*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*B*c^4*((57*sin(f*x + e)/(cos(f*x + e) + 1) + 99*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 155*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 153*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 135*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 85*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 45*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 24)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 10*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 6*a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3*a^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^2*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 16*A*c^4*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 24*B*c^4*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 12*A*c^4*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 8*B*c^4*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*A*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 8*A*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 2*B*c^4*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
62,1,1378,0,0.482430," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{B c^{3} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 4 \, A c^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 12 \, B c^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 6 \, A c^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 6 \, B c^{3} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{2 \, A c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{6 \, A c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, B c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"-1/3*(B*c^3*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 4*A*c^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 12*B*c^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 6*A*c^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 6*B*c^3*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 2*A*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 6*A*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*B*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
63,1,833,0,0.461291," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, B c^{2} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - A c^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 2 \, B c^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{A c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{2 \, A c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(2*B*c^2*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - A*c^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 2*B*c^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + A*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 2*A*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
64,1,452,0,0.456742," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(B c {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{A c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{A c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(B*c*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + A*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - A*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
65,1,265,0,0.348923," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{B {\left(\frac{2 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{2} c + \frac{2 \, a^{2} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a^{2} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{A {\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - 1\right)}}{a^{2} c + \frac{2 \, a^{2} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a^{2} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}\right)}}{3 \, f}"," ",0,"2/3*(B*(2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^2*c + 2*a^2*c*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a^2*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + A*(sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1)/(a^2*c + 2*a^2*c*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a^2*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4))/f","B",0
66,1,47,0,0.385925," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(\tan\left(f x + e\right)^{3} + 3 \, \tan\left(f x + e\right)\right)} A}{a^{2} c^{2}} + \frac{B}{a^{2} c^{2} \cos\left(f x + e\right)^{3}}}{3 \, f}"," ",0,"1/3*((tan(f*x + e)^3 + 3*tan(f*x + e))*A/(a^2*c^2) + B/(a^2*c^2*cos(f*x + e)^3))/f","A",0
67,1,651,0,0.472228," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{13 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{25 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + 3\right)}}{a^{2} c^{3} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{2} c^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} - \frac{B {\left(\frac{6 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{9 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - 3\right)}}{a^{2} c^{3} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, a^{2} c^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2 \, a^{2} c^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{2} c^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}\right)}}{15 \, f}"," ",0,"2/15*(A*(9*sin(f*x + e)/(cos(f*x + e) + 1) - 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 13*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 25*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 3)/(a^2*c^3 - 2*a^2*c^3*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6*a^2*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*a^2*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^2*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2*a^2*c^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^2*c^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) - B*(6*sin(f*x + e)/(cos(f*x + e) + 1) - 9*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 10*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 3)/(a^2*c^3 - 2*a^2*c^3*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^2*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 6*a^2*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*a^2*c^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^2*c^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2*a^2*c^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^2*c^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8))/f","B",0
68,1,835,0,0.367800," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{B {\left(\frac{36 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{132 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{68 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{14 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{84 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{140 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{140 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{105 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - 9\right)}}{a^{2} c^{4} - \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{a^{2} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}} + \frac{5 \, A {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{24 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{76 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{28 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{42 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{56 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{28 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{42 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{21 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - 6\right)}}{a^{2} c^{4} - \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{14 \, a^{2} c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{8 \, a^{2} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3 \, a^{2} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{4 \, a^{2} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{a^{2} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}}\right)}}{105 \, f}"," ",0,"-2/105*(B*(36*sin(f*x + e)/(cos(f*x + e) + 1) - 132*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 68*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 14*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 84*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 140*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 140*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 105*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 9)/(a^2*c^4 - 4*a^2*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*a^2*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 14*a^2*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 14*a^2*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 8*a^2*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3*a^2*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 4*a^2*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - a^2*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10) + 5*A*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 24*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 76*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 28*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 42*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 56*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 28*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 42*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 21*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 6)/(a^2*c^4 - 4*a^2*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*a^2*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 14*a^2*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 14*a^2*c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 8*a^2*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3*a^2*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 4*a^2*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - a^2*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10))/f","B",0
69,1,998,0,0.570763," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{51 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{235 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{450 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{306 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{294 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{378 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{63 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{273 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{189 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{63 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - 19\right)}}{a^{2} c^{5} - \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{2} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}} + \frac{B {\left(\frac{6 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{75 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{128 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{162 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{36 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{42 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{189 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{126 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{63 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 1\right)}}{a^{2} c^{5} - \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{36 \, a^{2} c^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{27 \, a^{2} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{2 \, a^{2} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{12 \, a^{2} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{6 \, a^{2} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{2} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}}\right)}}{63 \, f}"," ",0,"-2/63*(A*(51*sin(f*x + e)/(cos(f*x + e) + 1) - 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 235*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 450*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 306*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 294*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 378*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 63*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 273*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 189*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 63*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 19)/(a^2*c^5 - 6*a^2*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^2*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*a^2*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 27*a^2*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 36*a^2*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 36*a^2*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 27*a^2*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2*a^2*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 12*a^2*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 6*a^2*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^2*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12) + B*(6*sin(f*x + e)/(cos(f*x + e) + 1) - 75*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 128*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 162*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 36*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 42*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 189*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 126*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 63*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 1)/(a^2*c^5 - 6*a^2*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^2*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*a^2*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 27*a^2*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 36*a^2*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 36*a^2*c^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 27*a^2*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 2*a^2*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 12*a^2*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 6*a^2*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^2*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12))/f","B",0
70,1,3282,0,0.566029," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{B c^{5} {\left(\frac{\frac{2375 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5347 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9230 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{12622 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{13340 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{11684 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{8050 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{4370 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{1725 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{345 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + 544}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{13 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{25 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{38 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{46 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{46 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{38 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{25 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{13 \, a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}} + \frac{345 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - A c^{5} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 5 \, B c^{5} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 30 \, A c^{5} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 60 \, B c^{5} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 20 \, A c^{5} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 20 \, B c^{5} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{2 \, A c^{5} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{40 \, A c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{20 \, B c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{30 \, A c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, B c^{5} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}}{15 \, f}"," ",0,"1/15*(B*c^5*((2375*sin(f*x + e)/(cos(f*x + e) + 1) + 5347*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9230*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 12622*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 13340*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 11684*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 8050*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 4370*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 1725*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 345*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 544)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 13*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 25*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 38*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 46*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 46*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 38*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 25*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 13*a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 5*a^3*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + a^3*sin(f*x + e)^11/(cos(f*x + e) + 1)^11) + 345*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*c^5*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 5*B*c^5*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 30*A*c^5*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 60*B*c^5*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 20*A*c^5*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 20*B*c^5*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 2*A*c^5*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 40*A*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 20*B*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 30*A*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*B*c^5*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
71,1,2394,0,0.519958," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{B c^{4} {\left(\frac{\frac{1325 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2673 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 6 \, A c^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 24 \, B c^{4} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 8 \, A c^{4} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 12 \, B c^{4} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{2 \, A c^{4} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{24 \, A c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{16 \, B c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{24 \, A c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, B c^{4} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}}{15 \, f}"," ",0,"1/15*(B*c^4*((1325*sin(f*x + e)/(cos(f*x + e) + 1) + 2673*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3805*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 4329*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3575*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2275*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 975*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 195*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 304)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 12*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 12*a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 5*a^3*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^3*sin(f*x + e)^9/(cos(f*x + e) + 1)^9) + 195*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 6*A*c^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 24*B*c^4*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 8*A*c^4*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 12*B*c^4*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 2*A*c^4*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 24*A*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 16*B*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 24*A*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*B*c^4*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
72,1,1679,0,0.521625," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, B c^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - A c^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + 3 \, B c^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{A c^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, A c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, B c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{9 \, A c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"2/15*(3*B*c^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*c^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + 3*B*c^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*c^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*A*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*B*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 9*A*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
73,1,1134,0,0.468101," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(B c^{2} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{A c^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{2 \, A c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{4 \, B c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, A c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"2/15*(B*c^2*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*c^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 2*A*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 4*B*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*A*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
74,1,733,0,0.354029," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A c {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{2 \, B c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, A c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, B c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(A*c*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 2*B*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*A*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*B*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
75,1,423,0,0.419573," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{B {\left(\frac{4 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{20 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 1\right)}}{a^{3} c + \frac{4 \, a^{3} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{3} c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a^{3} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{4 \, a^{3} c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a^{3} c \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} - \frac{3 \, A {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{10 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{10 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + 2\right)}}{a^{3} c + \frac{4 \, a^{3} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{3} c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{5 \, a^{3} c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{4 \, a^{3} c \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{a^{3} c \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}\right)}}{15 \, f}"," ",0,"2/15*(B*(4*sin(f*x + e)/(cos(f*x + e) + 1) + 20*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1)/(a^3*c + 4*a^3*c*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^3*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a^3*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4*a^3*c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a^3*c*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) - 3*A*(3*sin(f*x + e)/(cos(f*x + e) + 1) - 10*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 10*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2)/(a^3*c + 4*a^3*c*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^3*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 5*a^3*c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4*a^3*c*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - a^3*c*sin(f*x + e)^6/(cos(f*x + e) + 1)^6))/f","B",0
76,1,650,0,0.373772," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{A {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{13 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{25 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{5 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - 3\right)}}{a^{3} c^{2} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{3} c^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} + \frac{B {\left(\frac{6 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{9 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 3\right)}}{a^{3} c^{2} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, a^{3} c^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{2 \, a^{3} c^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{a^{3} c^{2} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}\right)}}{15 \, f}"," ",0,"2/15*(A*(9*sin(f*x + e)/(cos(f*x + e) + 1) + 21*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 13*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 25*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3)/(a^3*c^2 + 2*a^3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 6*a^3*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*a^3*c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^3*c^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 2*a^3*c^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^3*c^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) + B*(6*sin(f*x + e)/(cos(f*x + e) + 1) + 9*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 10*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 3)/(a^3*c^2 + 2*a^3*c^2*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^3*c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 6*a^3*c^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*a^3*c^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*a^3*c^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 2*a^3*c^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - a^3*c^2*sin(f*x + e)^8/(cos(f*x + e) + 1)^8))/f","B",0
77,1,60,0,0.363056," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, \tan\left(f x + e\right)^{5} + 10 \, \tan\left(f x + e\right)^{3} + 15 \, \tan\left(f x + e\right)\right)} A}{a^{3} c^{3}} + \frac{3 \, B}{a^{3} c^{3} \cos\left(f x + e\right)^{5}}}{15 \, f}"," ",0,"1/15*((3*tan(f*x + e)^5 + 10*tan(f*x + e)^3 + 15*tan(f*x + e))*A/(a^3*c^3) + 3*B/(a^3*c^3*cos(f*x + e)^5))/f","A",0
78,1,1019,0,0.407597," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{B {\left(\frac{30 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{45 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{80 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{110 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{188 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{266 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{112 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{35 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{70 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{105 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - 15\right)}}{a^{3} c^{4} - \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{4} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}} - \frac{3 \, A {\left(\frac{25 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{55 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{130 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{26 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{182 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{126 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{105 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{35 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{35 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{35 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + 5\right)}}{a^{3} c^{4} - \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20 \, a^{3} c^{4} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{5 \, a^{3} c^{4} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{10 \, a^{3} c^{4} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{4 \, a^{3} c^{4} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{2 \, a^{3} c^{4} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{4} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}}\right)}}{105 \, f}"," ",0,"-2/105*(B*(30*sin(f*x + e)/(cos(f*x + e) + 1) - 45*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 80*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 110*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 188*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 266*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 112*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 35*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 70*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 105*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 15)/(a^3*c^4 - 2*a^3*c^4*sin(f*x + e)/(cos(f*x + e) + 1) - 4*a^3*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5*a^3*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 10*a^3*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 4*a^3*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 2*a^3*c^4*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^4*sin(f*x + e)^12/(cos(f*x + e) + 1)^12) - 3*A*(25*sin(f*x + e)/(cos(f*x + e) + 1) - 55*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 130*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 26*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 182*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 126*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 105*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 35*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 35*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 35*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 5)/(a^3*c^4 - 2*a^3*c^4*sin(f*x + e)/(cos(f*x + e) + 1) - 4*a^3*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20*a^3*c^4*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 5*a^3*c^4*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 10*a^3*c^4*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 4*a^3*c^4*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 2*a^3*c^4*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^4*sin(f*x + e)^12/(cos(f*x + e) + 1)^12))/f","B",0
79,1,1201,0,0.565878," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{B {\left(\frac{100 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{340 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{55 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{88 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{1608 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1032 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{483 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{588 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{420 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{420 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{315 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - 25\right)}}{a^{3} c^{5} - \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{3} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}} - \frac{7 \, A {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{80 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{190 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{50 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{269 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{96 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{516 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{354 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{69 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{240 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{30 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{90 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{45 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + 10\right)}}{a^{3} c^{5} - \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{3} c^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{45 \, a^{3} c^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{20 \, a^{3} c^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{19 \, a^{3} c^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{16 \, a^{3} c^{5} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{4 \, a^{3} c^{5} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{a^{3} c^{5} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}}\right)}}{315 \, f}"," ",0,"-2/315*(B*(100*sin(f*x + e)/(cos(f*x + e) + 1) - 340*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 55*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 88*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1608*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1032*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 483*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 588*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 420*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 420*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 315*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 25)/(a^3*c^5 - 4*a^3*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + a^3*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 16*a^3*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 19*a^3*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 45*a^3*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 45*a^3*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 20*a^3*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 19*a^3*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 16*a^3*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 4*a^3*c^5*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - a^3*c^5*sin(f*x + e)^14/(cos(f*x + e) + 1)^14) - 7*A*(5*sin(f*x + e)/(cos(f*x + e) + 1) - 80*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 190*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 50*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 269*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 96*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 516*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 354*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 69*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 240*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 30*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 90*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 45*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 10)/(a^3*c^5 - 4*a^3*c^5*sin(f*x + e)/(cos(f*x + e) + 1) + a^3*c^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 16*a^3*c^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 19*a^3*c^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 20*a^3*c^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 45*a^3*c^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 45*a^3*c^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 20*a^3*c^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 19*a^3*c^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 16*a^3*c^5*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - a^3*c^5*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 4*a^3*c^5*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - a^3*c^5*sin(f*x + e)^14/(cos(f*x + e) + 1)^14))/f","B",0
80,1,1387,0,0.576677," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{255 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{235 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3065 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3775 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{667 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{8217 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2035 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{8745 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{11715 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{33 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{4917 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{2475 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{1815 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{1485 \, \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - \frac{495 \, \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}} - 125\right)}}{a^{3} c^{6} - \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} + \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}} - \frac{a^{3} c^{6} \sin\left(f x + e\right)^{16}}{{\left(\cos\left(f x + e\right) + 1\right)}^{16}}} + \frac{3 \, B {\left(\frac{30 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{215 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{280 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{245 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{434 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{231 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{880 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{1815 \, \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{330 \, \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{99 \, \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{264 \, \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} - \frac{495 \, \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{330 \, \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{165 \, \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} - 5\right)}}{a^{3} c^{6} - \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{110 \, a^{3} c^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} - \frac{66 \, a^{3} c^{6} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} - \frac{34 \, a^{3} c^{6} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{50 \, a^{3} c^{6} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} - \frac{10 \, a^{3} c^{6} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}} + \frac{6 \, a^{3} c^{6} \sin\left(f x + e\right)^{15}}{{\left(\cos\left(f x + e\right) + 1\right)}^{15}} - \frac{a^{3} c^{6} \sin\left(f x + e\right)^{16}}{{\left(\cos\left(f x + e\right) + 1\right)}^{16}}}\right)}}{495 \, f}"," ",0,"-2/495*(A*(255*sin(f*x + e)/(cos(f*x + e) + 1) + 235*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3065*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3775*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 667*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 8217*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2035*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 8745*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 11715*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 33*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 4917*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 2475*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 1815*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 1485*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - 495*sin(f*x + e)^15/(cos(f*x + e) + 1)^15 - 125)/(a^3*c^6 - 6*a^3*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 50*a^3*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 34*a^3*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 66*a^3*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 110*a^3*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 110*a^3*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 66*a^3*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 34*a^3*c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 50*a^3*c^6*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 10*a^3*c^6*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 10*a^3*c^6*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 + 6*a^3*c^6*sin(f*x + e)^15/(cos(f*x + e) + 1)^15 - a^3*c^6*sin(f*x + e)^16/(cos(f*x + e) + 1)^16) + 3*B*(30*sin(f*x + e)/(cos(f*x + e) + 1) - 215*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 280*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 245*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 434*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 231*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 880*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 1815*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 330*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 99*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 264*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 - 495*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 330*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 165*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 - 5)/(a^3*c^6 - 6*a^3*c^6*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*c^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*c^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 50*a^3*c^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 34*a^3*c^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 66*a^3*c^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 110*a^3*c^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 110*a^3*c^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 - 66*a^3*c^6*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 - 34*a^3*c^6*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 50*a^3*c^6*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 - 10*a^3*c^6*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 - 10*a^3*c^6*sin(f*x + e)^14/(cos(f*x + e) + 1)^14 + 6*a^3*c^6*sin(f*x + e)^15/(cos(f*x + e) + 1)^15 - a^3*c^6*sin(f*x + e)^16/(cos(f*x + e) + 1)^16))/f","B",0
81,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
82,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
83,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
84,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
85,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)/sqrt(-c*sin(f*x + e) + c), x)","F",0
86,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
88,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
89,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
90,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
91,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
92,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*sqrt(-c*sin(f*x + e) + c), x)","F",0
93,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
94,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
95,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
96,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
97,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
98,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
99,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
100,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
101,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3*sqrt(-c*sin(f*x + e) + c), x)","F",0
102,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/sqrt(-c*sin(f*x + e) + c), x)","F",0
103,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
104,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
105,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
106,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
107,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^3/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
108,1,478,0,0.496680," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{7 \, {\left(91 \, c^{\frac{7}{2}} + \frac{86 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{336 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{266 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{490 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{266 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{336 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{86 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{91 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} A}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}} - \frac{2 \, {\left(407 \, c^{\frac{7}{2}} + \frac{407 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{1442 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{1337 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{2030 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1337 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1442 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{407 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{407 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} B}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}\right)}}{35 \, f}"," ",0,"2/35*(7*(91*c^(7/2) + 86*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 336*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 266*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 490*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 266*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 336*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 86*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 91*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*A/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)) - 2*(407*c^(7/2) + 407*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 1442*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1337*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 2030*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1337*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1442*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 407*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 407*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*B/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)))/f","B",0
109,1,386,0,0.462691," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{5 \, {\left(23 \, c^{\frac{5}{2}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{65 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{40 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{65 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{23 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} A}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} - \frac{2 \, {\left(79 \, c^{\frac{5}{2}} + \frac{79 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{205 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{170 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{205 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{79 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{79 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} B}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{15 \, f}"," ",0,"2/15*(5*(23*c^(5/2) + 20*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 65*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 40*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 65*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 20*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 23*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*A/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) - 2*(79*c^(5/2) + 79*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 205*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 170*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 205*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 79*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 79*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*B/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
110,1,294,0,0.463172," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, {\left(3 \, c^{\frac{3}{2}} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} A}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(7 \, c^{\frac{3}{2}} + \frac{7 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{12 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} B}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{3 \, f}"," ",0,"2/3*(3*(3*c^(3/2) + 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 6*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*A/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) - 2*(7*c^(3/2) + 7*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 12*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*B/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
111,1,174,0,0.452044," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, B {\left(\sqrt{c} + \frac{\sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} - \frac{A {\left(\sqrt{c} + \frac{\sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}}{{\left(a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{f}"," ",0,"-2*(2*B*(sqrt(c) + sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) - A*(sqrt(c) + sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/((a + a*sin(f*x + e)/(cos(f*x + e) + 1))*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
112,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
113,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
114,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
115,1,762,0,0.462445," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{7 \, {\left(723 \, c^{\frac{9}{2}} + \frac{2184 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5370 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10696 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15021 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{21168 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{20748 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{21168 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{15021 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{10696 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{5370 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{2184 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{723 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} A}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}} - \frac{2 \, {\left(4707 \, c^{\frac{9}{2}} + \frac{14121 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{35250 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{68549 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{99549 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{134802 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{138012 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{134802 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{99549 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{68549 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{35250 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{14121 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{4707 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} B}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}}\right)}}{105 \, f}"," ",0,"-2/105*(7*(723*c^(9/2) + 2184*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 5370*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10696*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15021*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 21168*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 20748*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 21168*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 15021*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 10696*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 5370*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 2184*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 723*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*A/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2)) - 2*(4707*c^(9/2) + 14121*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 35250*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 68549*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 99549*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 134802*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 138012*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 134802*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 99549*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 68549*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 35250*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 14121*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 4707*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*B/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2)))/f","B",0
116,1,670,0,0.529157," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, {\left(45 \, c^{\frac{7}{2}} + \frac{138 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{285 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{544 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{630 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{812 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{630 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{544 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{285 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{138 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{45 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} A}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}} - \frac{2 \, {\left(249 \, c^{\frac{7}{2}} + \frac{747 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{1611 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2896 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3612 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4298 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3612 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{2896 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1611 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{747 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{249 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} B}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}\right)}}{15 \, f}"," ",0,"-2/15*(5*(45*c^(7/2) + 138*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 285*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 544*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 630*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 812*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 630*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 544*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 285*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 138*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 45*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*A/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)) - 2*(249*c^(7/2) + 747*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 1611*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2896*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3612*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4298*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3612*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 2896*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1611*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 747*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 249*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*B/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)))/f","B",0
117,1,577,0,0.460752," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(11 \, c^{\frac{5}{2}} + \frac{36 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{56 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{108 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{90 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{108 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{56 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{36 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{11 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} A}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} - \frac{2 \, {\left(17 \, c^{\frac{5}{2}} + \frac{51 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{92 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{149 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{150 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{149 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{92 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{51 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{17 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} B}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{3 \, f}"," ",0,"-2/3*((11*c^(5/2) + 36*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 56*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 108*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 90*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 108*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 56*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 36*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 11*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*A/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) - 2*(17*c^(5/2) + 51*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 92*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 149*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 150*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 149*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 92*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 51*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 17*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*B/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
118,1,482,0,0.581196," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(c^{\frac{3}{2}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} A}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(5 \, c^{\frac{3}{2}} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{21 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} B}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{3 \, f}"," ",0,"-2/3*((c^(3/2) + 6*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 6*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*A/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) - 2*(5*c^(3/2) + 15*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 21*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 21*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*B/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
119,1,343,0,0.456742," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, B {\left(\sqrt{c} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} + \frac{A {\left(\sqrt{c} + \frac{2 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)}}{{\left(a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{3 \, f}"," ",0,"2/3*(2*B*(sqrt(c) + 3*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) + A*(sqrt(c) + 2*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)/((a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
120,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{2} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^2*sqrt(-c*sin(f*x + e) + c)), x)","F",0
121,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,1,945,0,0.493319," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{{\left(363 \, c^{\frac{9}{2}} + \frac{1800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5301 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{11600 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{21343 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{30200 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{40065 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{40800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{40065 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{30200 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{21343 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{11600 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{5301 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{1800 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{363 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}\right)} A}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}} - \frac{6 \, {\left(181 \, c^{\frac{9}{2}} + \frac{905 \, c^{\frac{9}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2627 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5870 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{10521 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15351 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{19695 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{20772 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{19695 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{15351 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{10521 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{5870 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{2627 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}} + \frac{905 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{13}}{{\left(\cos\left(f x + e\right) + 1\right)}^{13}} + \frac{181 \, c^{\frac{9}{2}} \sin\left(f x + e\right)^{14}}{{\left(\cos\left(f x + e\right) + 1\right)}^{14}}\right)} B}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{9}{2}}}\right)}}{15 \, f}"," ",0,"2/15*((363*c^(9/2) + 1800*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 5301*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 11600*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 21343*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 30200*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 40065*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 40800*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 40065*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 30200*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 21343*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 11600*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 5301*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 1800*c^(9/2)*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 363*c^(9/2)*sin(f*x + e)^14/(cos(f*x + e) + 1)^14)*A/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2)) - 6*(181*c^(9/2) + 905*c^(9/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2627*c^(9/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5870*c^(9/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 10521*c^(9/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15351*c^(9/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 19695*c^(9/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 20772*c^(9/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 19695*c^(9/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 15351*c^(9/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 10521*c^(9/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 5870*c^(9/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 2627*c^(9/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12 + 905*c^(9/2)*sin(f*x + e)^13/(cos(f*x + e) + 1)^13 + 181*c^(9/2)*sin(f*x + e)^14/(cos(f*x + e) + 1)^14)*B/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(9/2)))/f","B",0
124,1,854,0,1.254542," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{3 \, {\left(23 \, c^{\frac{7}{2}} + \frac{110 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{318 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{590 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1065 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1220 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1540 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1220 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{1065 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{590 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{318 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{110 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{23 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} A}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}} - \frac{2 \, {\left(147 \, c^{\frac{7}{2}} + \frac{735 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{1992 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4015 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6605 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{8370 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9520 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{8370 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{6605 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{4015 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{1992 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{735 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}} + \frac{147 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{12}}{{\left(\cos\left(f x + e\right) + 1\right)}^{12}}\right)} B}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{7}{2}}}\right)}}{15 \, f}"," ",0,"2/15*(3*(23*c^(7/2) + 110*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 318*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 590*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1065*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1220*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1540*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1220*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1065*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 590*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 318*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 110*c^(7/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 23*c^(7/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*A/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)) - 2*(147*c^(7/2) + 735*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 1992*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4015*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6605*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 8370*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9520*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 8370*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 6605*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 4015*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 1992*c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + 735*c^(7/2)*sin(f*x + e)^11/(cos(f*x + e) + 1)^11 + 147*c^(7/2)*sin(f*x + e)^12/(cos(f*x + e) + 1)^12)*B/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(7/2)))/f","B",0
125,1,761,0,0.482819," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{{\left(7 \, c^{\frac{5}{2}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{95 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{80 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{250 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{120 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{250 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{80 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{95 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{20 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{7 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} A}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} - \frac{2 \, {\left(31 \, c^{\frac{5}{2}} + \frac{155 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{395 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{680 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{1030 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1050 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{1030 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{680 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{395 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{155 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{31 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} B}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{15 \, f}"," ",0,"2/15*((7*c^(5/2) + 20*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 95*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 80*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 250*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 120*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 250*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 80*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 95*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 20*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 7*c^(5/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*A/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) - 2*(31*c^(5/2) + 155*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 395*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 680*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1030*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1050*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1030*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 680*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 395*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 155*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 31*c^(5/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*B/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
126,1,663,0,0.475850," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{{\left(c^{\frac{3}{2}} - \frac{10 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{30 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{6 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{30 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{10 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} A}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} - \frac{6 \, {\left(c^{\frac{3}{2}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{14 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{26 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{14 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}\right)} B}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{15 \, f}"," ",0,"2/15*((c^(3/2) - 10*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 4*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 30*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 6*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 30*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 4*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 10*c^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(3/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*A/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) - 6*(c^(3/2) + 5*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 14*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 26*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 14*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5*c^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(3/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)*B/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
127,1,505,0,0.508443," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, B {\left(\sqrt{c} + \frac{5 \, \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, \sqrt{c} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} + \frac{3 \, A {\left(\sqrt{c} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{\sqrt{c} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)}}{{\left(a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{15 \, f}"," ",0,"2/15*(2*B*(sqrt(c) + 5*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*sqrt(c)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + sqrt(c)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) + 3*A*(sqrt(c) + 3*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + sqrt(c)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)/((a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
128,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,0,0,0,0.000000," ","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=""maxima"")","\int {\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)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
132,0,0,0,0.000000," ","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=""maxima"")","\int {\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)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
133,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
134,0,0,0,0.000000," ","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=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
135,1,175,0,0.550509," ","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=""maxima"")","\frac{B {\left(\frac{2 \, \sqrt{a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{c}} - \frac{\sqrt{a} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{c}} + \frac{2 \, \sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{{\left(c + \frac{c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} + A {\left(\frac{2 \, \sqrt{a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{c}} - \frac{\sqrt{a} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{c}}\right)}}{f}"," ",0,"(B*(2*sqrt(a)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(c) - sqrt(a)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(c) + 2*sqrt(a)*sqrt(c)*sin(f*x + e)/((c + c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) + A*(2*sqrt(a)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(c) - sqrt(a)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(c)))/f","A",0
136,0,0,0,0.000000," ","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=""maxima"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
137,0,0,0,0.000000," ","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=""maxima"")","\int \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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
138,0,0,0,0.000000," ","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=""maxima"")","\int \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)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
139,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
140,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
141,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
142,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
143,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
144,1,366,0,0.570628," ","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=""maxima"")","-\frac{B {\left(\frac{6 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{3}{2}}} - \frac{3 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{3}{2}}} + \frac{2 \, {\left(\frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{c^{\frac{3}{2}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}\right)} + A {\left(\frac{2 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{3}{2}}} - \frac{a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{3}{2}}} + \frac{4 \, a^{\frac{3}{2}} \sqrt{c} \sin\left(f x + e\right)}{{\left(c^{2} - \frac{2 \, c^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{c^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)}}{f}"," ",0,"-(B*(6*a^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(3/2) - 3*a^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(3/2) + 2*(3*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(c^(3/2) - 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)) + A*(2*a^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(3/2) - a^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(3/2) + 4*a^(3/2)*sqrt(c)*sin(f*x + e)/((c^2 - 2*c^2*sin(f*x + e)/(cos(f*x + e) + 1) + c^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))))/f","B",0
145,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
146,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
147,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
148,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
149,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
150,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
151,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
152,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
153,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
154,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
155,1,506,0,0.480368," ","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=""maxima"")","-\frac{{\left(\frac{8 \, a^{\frac{5}{2}} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(c^{3} - \frac{4 \, c^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, c^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{c^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{5}{2}}} + \frac{a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{5}{2}}}\right)} A - B {\left(\frac{10 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{5}{2}}} - \frac{5 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{5}{2}}} + \frac{2 \, {\left(\frac{5 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{16 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{14 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{16 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{c^{\frac{5}{2}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{7 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}\right)}}{f}"," ",0,"-((8*a^(5/2)*sqrt(c)*sin(f*x + e)^2/((c^3 - 4*c^3*sin(f*x + e)/(cos(f*x + e) + 1) + 6*c^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + c^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(cos(f*x + e) + 1)^2) - 2*a^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(5/2) + a^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(5/2))*A - B*(10*a^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(5/2) - 5*a^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(5/2) + 2*(5*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 16*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 14*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 16*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^(5/2) - 4*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 7*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 8*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)))/f","B",0
156,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
157,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
158,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
159,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(9/2), x)","F",0
161,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
162,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
163,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
164,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
165,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
166,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
167,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
168,1,749,0,1.185382," ","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=""maxima"")","-\frac{B {\left(\frac{42 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{7}{2}}} - \frac{21 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{7}{2}}} + \frac{2 \, {\left(\frac{21 \, a^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{102 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{227 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{228 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{227 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{102 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{21 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)}}{c^{\frac{7}{2}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{16 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{26 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{30 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{26 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{16 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}\right)} + A {\left(\frac{6 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{7}{2}}} - \frac{3 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{7}{2}}} + \frac{4 \, {\left(\frac{3 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{6 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{22 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a^{\frac{7}{2}} \sqrt{c} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{c^{4} - \frac{6 \, c^{4} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{15 \, c^{4} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{20 \, c^{4} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, c^{4} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{6 \, c^{4} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{4} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}\right)}}{3 \, f}"," ",0,"-1/3*(B*(42*a^(7/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(7/2) - 21*a^(7/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(7/2) + 2*(21*a^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 102*a^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 227*a^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 228*a^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 227*a^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 102*a^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 21*a^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(c^(7/2) - 6*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 16*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 26*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 30*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 26*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 16*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 6*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8)) + A*(6*a^(7/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(7/2) - 3*a^(7/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(7/2) + 4*(3*a^(7/2)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) - 6*a^(7/2)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 22*a^(7/2)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*a^(7/2)*sqrt(c)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a^(7/2)*sqrt(c)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^4 - 6*c^4*sin(f*x + e)/(cos(f*x + e) + 1) + 15*c^4*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 20*c^4*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*c^4*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 6*c^4*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^4*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)))/f","B",0
169,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
170,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
171,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(5/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
175,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(3/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
176,1,176,0,0.794734," ","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=""maxima"")","\frac{B {\left(\frac{2 \, \sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{a}} - \frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{a}} - \frac{2 \, \sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{{\left(a + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)} - A {\left(\frac{2 \, \sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{a}} - \frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{\sqrt{a}}\right)}}{f}"," ",0,"(B*(2*sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(a) - sqrt(c)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(a) - 2*sqrt(a)*sqrt(c)*sin(f*x + e)/((a + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))) - A*(2*sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(a) - sqrt(c)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/sqrt(a)))/f","A",0
177,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
178,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
179,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
180,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
181,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
182,1,367,0,0.548500," ","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=""maxima"")","-\frac{B {\left(\frac{6 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{3}{2}}} - \frac{3 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{3}{2}}} - \frac{2 \, {\left(\frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}\right)} - A {\left(\frac{2 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{3}{2}}} - \frac{c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{3}{2}}} - \frac{4 \, \sqrt{a} c^{\frac{3}{2}} \sin\left(f x + e\right)}{{\left(a^{2} + \frac{2 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}}\right)}}{f}"," ",0,"-(B*(6*c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(3/2) - 3*c^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(3/2) - 2*(3*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^(3/2) + 2*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)) - A*(2*c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(3/2) - c^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(3/2) - 4*sqrt(a)*c^(3/2)*sin(f*x + e)/((a^2 + 2*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*(cos(f*x + e) + 1))))/f","B",0
183,0,0,0,0.000000," ","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=""maxima"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
184,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
185,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
186,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
187,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(9/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
188,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
189,1,504,0,0.493452," ","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=""maxima"")","\frac{{\left(\frac{8 \, \sqrt{a} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(a^{3} + \frac{4 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}\right)} {\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{5}{2}}} + \frac{c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{5}{2}}}\right)} A + B {\left(\frac{10 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{5}{2}}} - \frac{5 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{5}{2}}} - \frac{2 \, {\left(\frac{5 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{16 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{14 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{16 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{\frac{5}{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{7 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}\right)}}{f}"," ",0,"((8*sqrt(a)*c^(5/2)*sin(f*x + e)^2/((a^3 + 4*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 6*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4)*(cos(f*x + e) + 1)^2) - 2*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(5/2) + c^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(5/2))*A + B*(10*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(5/2) - 5*c^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(5/2) - 2*(5*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 16*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 14*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 16*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^(5/2) + 4*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 7*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)))/f","B",0
190,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(-c*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
191,0,0,0,0.000000," ","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=""maxima"")","\int \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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
192,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
193,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
194,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
195,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
196,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"-integrate((B*sin(f*x + e) + A)*(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
197,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
198,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"-integrate((B*sin(f*x + e) + A)*(c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m, x)","F",0
199,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m, x)","F",0
200,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \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}\,{d x}"," ",0,"-integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
201,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \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)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^2, x)","F",0
202,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int \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)}^{3}}\,{d x}"," ",0,"-integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^3, x)","F",0
203,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
204,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(c \sin\left(f x + e\right) + c\right)}^{m}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(c*sin(f*x + e) + c)^m/sqrt(-a*sin(f*x + e) + a), x)","F",0
205,1,725,0,0.545646," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left({\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, {\left(4 \, m^{2} + 8 \, m + 35\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(12 \, m^{2} + 40 \, m - 15\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(4 \, m^{2} + 24 \, m + 43\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}} - \frac{2 \, {\left({\left(4 \, m^{2} + 40 \, m + 115\right)} a^{m} c^{\frac{5}{2}} - \frac{2 \, {\left(4 \, m^{3} + 40 \, m^{2} + 115 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, {\left(12 \, m^{3} + 76 \, m^{2} + 97 \, m + 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{{\left(16 \, m^{3} + 76 \, m^{2} + 260 \, m - 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{{\left(16 \, m^{3} + 76 \, m^{2} + 260 \, m - 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2 \, {\left(12 \, m^{3} + 76 \, m^{2} + 97 \, m + 175\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{2 \, {\left(4 \, m^{3} + 40 \, m^{2} + 115 \, m\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{{\left(4 \, m^{2} + 40 \, m + 115\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + \frac{{\left(16 \, m^{4} + 128 \, m^{3} + 344 \, m^{2} + 352 \, m + 105\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 105\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}\right)}}{f}"," ",0,"-2*(((4*m^2 + 24*m + 43)*a^m*c^(5/2) - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*(4*m^2 + 8*m + 35)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (12*m^2 + 40*m - 15)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (4*m^2 + 24*m + 43)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + 15)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)) - 2*((4*m^2 + 40*m + 115)*a^m*c^(5/2) - 2*(4*m^3 + 40*m^2 + 115*m)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2*(12*m^3 + 76*m^2 + 97*m + 175)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - (16*m^3 + 76*m^2 + 260*m - 175)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - (16*m^3 + 76*m^2 + 260*m - 175)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2*(12*m^3 + 76*m^2 + 97*m + 175)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2*(4*m^3 + 40*m^2 + 115*m)*a^m*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + (4*m^2 + 40*m + 115)*a^m*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((16*m^4 + 128*m^3 + 344*m^2 + 352*m + (16*m^4 + 128*m^3 + 344*m^2 + 352*m + 105)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 105)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2)))/f","B",0
206,1,498,0,0.533354," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m - 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 5\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + 3\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a^{m} c^{\frac{3}{2}} {\left(2 \, m + 9\right)} - \frac{2 \, {\left(2 \, m^{2} + 9 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{{\left(4 \, m^{2} + 15\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(4 \, m^{2} + 15\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{2 \, {\left(2 \, m^{2} + 9 \, m\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{m} c^{\frac{3}{2}} {\left(2 \, m + 9\right)} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + \frac{{\left(8 \, m^{3} + 36 \, m^{2} + 46 \, m + 15\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 15\right)} {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}\right)}}{f}"," ",0,"-2*((a^m*c^(3/2)*(2*m + 5) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)/(cos(f*x + e) + 1) - a^m*c^(3/2)*(2*m - 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^m*c^(3/2)*(2*m + 5)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + 3)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)) - 2*(a^m*c^(3/2)*(2*m + 9) - 2*(2*m^2 + 9*m)*a^m*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + (4*m^2 + 15)*a^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (4*m^2 + 15)*a^m*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 2*(2*m^2 + 9*m)*a^m*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^m*c^(3/2)*(2*m + 9)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 36*m^2 + 46*m + (8*m^3 + 36*m^2 + 46*m + 15)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15)*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2)))/f","B",0
207,1,323,0,0.536353," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{2 \, {\left(\frac{2 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a^{m} \sqrt{c} m \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - a^{m} \sqrt{c} - \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)} B e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 8 \, m + \frac{{\left(4 \, m^{2} + 8 \, m + 3\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 3\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}} + \frac{{\left(a^{m} \sqrt{c} + \frac{a^{m} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} A e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(2 \, m + 1\right)} \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}\right)}}{f}"," ",0,"-2*(2*(2*a^m*sqrt(c)*m*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a^m*sqrt(c)*m*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - a^m*sqrt(c) - a^m*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)*B*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 8*m + (4*m^2 + 8*m + 3)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)) + (a^m*sqrt(c) + a^m*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1))*A*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((2*m + 1)*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)))/f","B",0
208,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
209,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
211,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 4), x)","F",0
212,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3), x)","F",0
213,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
214,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
215,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^m),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
216,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
217,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
218,0,0,0,0.000000," ","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=""maxima"")","-\int {\left(B {\left(n + 4\right)} \sin\left(f x + e\right) + B {\left(n - 3\right)}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{3} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"-integrate((B*(n + 4)*sin(f*x + e) + B*(n - 3))*(a*sin(f*x + e) + a)^3*(-c*sin(f*x + e) + c)^n, x)","F",0
219,0,0,0,0.000000," ","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=""maxima"")","-\int {\left(B {\left(n + 4\right)} \sin\left(f x + e\right) - B {\left(n - 3\right)}\right)} {\left(a \sin\left(f x + e\right) - a\right)}^{3} {\left(c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"-integrate((B*(n + 4)*sin(f*x + e) - B*(n - 3))*(a*sin(f*x + e) - a)^3*(c*sin(f*x + e) + c)^n, x)","F",0
220,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B {\left(m + 4\right)} \sin\left(f x + e\right) - B {\left(m - 3\right)}\right)} {\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*(m + 4)*sin(f*x + e) - B*(m - 3))*(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
221,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B {\left(m + 4\right)} \sin\left(f x + e\right) + B {\left(m - 3\right)}\right)} {\left(c \sin\left(f x + e\right) + c\right)}^{3} {\left(-a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*(m + 4)*sin(f*x + e) + B*(m - 3))*(c*sin(f*x + e) + c)^3*(-a*sin(f*x + e) + a)^m, x)","F",0
222,0,0,0,0.000000," ","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=""maxima"")","-\int {\left(B {\left(m + n + 1\right)} \sin\left(f x + e\right) - B {\left(m - n\right)}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"-integrate((B*(m + n + 1)*sin(f*x + e) - B*(m - n))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
223,0,0,0,0.000000," ","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=""maxima"")","\int {\left(B {\left(m + n + 1\right)} \sin\left(f x + e\right) + B {\left(m - n\right)}\right)} {\left(-a \sin\left(f x + e\right) + a\right)}^{m} {\left(c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*(m + n + 1)*sin(f*x + e) + B*(m - n))*(-a*sin(f*x + e) + a)^m*(c*sin(f*x + e) + c)^n, x)","F",0
224,1,157,0,0.428730," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{96 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 21 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3} - 35 \, \cos\left(d x + c\right)\right)} A a^{3} - 1120 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} A a^{3} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3}}{3360 \, d}"," ",0,"-1/3360*(96*(5*cos(d*x + c)^7 - 21*cos(d*x + c)^5 + 35*cos(d*x + c)^3 - 35*cos(d*x + c))*A*a^3 - 1120*(cos(d*x + c)^3 - 3*cos(d*x + c))*A*a^3 + 35*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*A*a^3)/d","A",0
225,1,138,0,0.403948," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} A a^{3} + 640 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} A a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 60 \, d x + 60 \, c + 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 240 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3}}{960 \, d}"," ",0,"1/960*(128*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*A*a^3 + 640*(cos(d*x + c)^3 - 3*cos(d*x + c))*A*a^3 - 5*(4*sin(2*d*x + 2*c)^3 + 60*d*x + 60*c + 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 + 240*(2*d*x + 2*c - sin(2*d*x + 2*c))*A*a^3)/d","A",0
226,1,112,0,0.372354," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} A a^{3} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 120 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 240 \, A a^{3} \cos\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(16*(3*cos(d*x + c)^5 - 10*cos(d*x + c)^3 + 15*cos(d*x + c))*A*a^3 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*A*a^3 + 120*(2*d*x + 2*c - sin(2*d*x + 2*c))*A*a^3 - 240*A*a^3*cos(d*x + c))/d","A",0
227,1,86,0,0.389158," ","integrate((a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{64 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} A a^{3} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) - 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 96 \, {\left(d x + c\right)} A a^{3} + 192 \, A a^{3} \cos\left(d x + c\right)}{96 \, d}"," ",0,"-1/96*(64*(cos(d*x + c)^3 - 3*cos(d*x + c))*A*a^3 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) - 8*sin(2*d*x + 2*c))*A*a^3 - 96*(d*x + c)*A*a^3 + 192*A*a^3*cos(d*x + c))/d","A",0
228,1,85,0,0.390640," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} A a^{3} + 3 \, {\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 12 \, {\left(d x + c\right)} A a^{3} + 6 \, A a^{3} \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right)}{6 \, d}"," ",0,"-1/6*(2*(cos(d*x + c)^3 - 3*cos(d*x + c))*A*a^3 + 3*(2*d*x + 2*c - sin(2*d*x + 2*c))*A*a^3 - 12*(d*x + c)*A*a^3 + 6*A*a^3*log(cot(d*x + c) + csc(d*x + c)))/d","A",0
229,1,83,0,0.547905," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(2 \, d x + 2 \, c - \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} + 4 \, A a^{3} {\left(\log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 8 \, A a^{3} \cos\left(d x + c\right) + \frac{4 \, A a^{3}}{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*((2*d*x + 2*c - sin(2*d*x + 2*c))*A*a^3 + 4*A*a^3*(log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 8*A*a^3*cos(d*x + c) + 4*A*a^3/tan(d*x + c))/d","A",0
230,1,90,0,0.404985," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, {\left(d x + c\right)} A a^{3} - A a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, A a^{3} \cos\left(d x + c\right) + \frac{8 \, A a^{3}}{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(8*(d*x + c)*A*a^3 - A*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 4*A*a^3*cos(d*x + c) + 8*A*a^3/tan(d*x + c))/d","A",0
231,1,117,0,0.446728," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c\right)} A a^{3} - 3 \, A a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, A a^{3} {\left(\log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} A a^{3}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c)*A*a^3 - 3*A*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 6*A*a^3*(log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 2*(3*tan(d*x + c)^2 + 1)*A*a^3/tan(d*x + c)^3)/d","A",0
232,1,145,0,0.425797," ","integrate(csc(d*x+c)^5*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 24 \, A a^{3} {\left(\log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{96 \, A a^{3}}{\tan\left(d x + c\right)} - \frac{32 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} A a^{3}}{\tan\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*A*a^3*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 24*A*a^3*(log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 96*A*a^3/tan(d*x + c) - 32*(3*tan(d*x + c)^2 + 1)*A*a^3/tan(d*x + c)^3)/d","A",0
233,1,175,0,0.439801," ","integrate(csc(d*x+c)^6*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","\frac{15 \, A a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 60 \, A a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{120 \, A a^{3}}{\tan\left(d x + c\right)} - \frac{8 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} A a^{3}}{\tan\left(d x + c\right)^{5}}}{120 \, d}"," ",0,"1/120*(15*A*a^3*(2*(3*cos(d*x + c)^3 - 5*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 60*A*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 120*A*a^3/tan(d*x + c) - 8*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*A*a^3/tan(d*x + c)^5)/d","A",0
234,1,207,0,0.597779," ","integrate(csc(d*x+c)^7*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, A a^{3} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} + 33 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 120 \, A a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{320 \, {\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} A a^{3}}{\tan\left(d x + c\right)^{3}} - \frac{64 \, {\left(15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} + 3\right)} A a^{3}}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*A*a^3*(2*(15*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 33*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 120*A*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 320*(3*tan(d*x + c)^2 + 1)*A*a^3/tan(d*x + c)^3 - 64*(15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 + 3)*A*a^3/tan(d*x + c)^5)/d","A",0
235,1,715,0,0.588575," ","integrate(sin(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{1325 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2673 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4329 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3575 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2275 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{975 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{195 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 304}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{26 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{26 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{195 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + 6 \, A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{189 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{15 \, d}"," ",0,"-1/15*(A*((1325*sin(d*x + c)/(cos(d*x + c) + 1) + 2673*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4329*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3575*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2275*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 975*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 195*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 304)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 20*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 26*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 26*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 20*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 12*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 5*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 195*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 6*A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 189*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 200*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 160*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 75*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 24)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 11*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 11*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
236,1,543,0,0.560616," ","integrate(sin(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{189 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + A {\left(\frac{\frac{95 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{145 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}\right)}}{15 \, d}"," ",0,"2/15*(3*A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 189*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 200*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 160*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 75*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 24)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 11*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 11*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + A*((95*sin(d*x + c)/(cos(d*x + c) + 1) + 145*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 75*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 22)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
237,1,392,0,0.638590," ","integrate(sin(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(A {\left(\frac{\frac{95 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{145 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{2 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}\right)}}{15 \, d}"," ",0,"-2/15*(A*((95*sin(d*x + c)/(cos(d*x + c) + 1) + 145*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 75*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 22)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 2*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5))/d","B",0
238,1,348,0,0.623672," ","integrate(sin(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}\right)}}{15 \, d}"," ",0,"2/15*(2*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5))/d","B",0
239,1,387,0,0.531775," ","integrate((A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} - \frac{3 \, A {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}\right)}}{15 \, d}"," ",0,"-2/15*(A*(20*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 30*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 7)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) - 3*A*(5*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5))/d","B",0
240,1,433,0,0.586301," ","integrate(csc(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{A {\left(\frac{2 \, {\left(\frac{115 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{185 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{135 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 32\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} + \frac{2 \, A {\left(\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}}{15 \, d}"," ",0,"1/15*(A*(2*(115*sin(d*x + c)/(cos(d*x + c) + 1) + 185*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 135*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 32)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) + 2*A*(20*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 30*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 7)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5))/d","B",0
241,1,519,0,0.686206," ","integrate(csc(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, A {\left(\frac{\frac{121 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{410 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{610 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{425 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{125 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 5}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{5 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + 2 \, A {\left(\frac{2 \, {\left(\frac{115 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{185 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{135 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 32\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{30 \, d}"," ",0,"-1/30*(3*A*((121*sin(d*x + c)/(cos(d*x + c) + 1) + 410*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 610*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 425*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 125*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 5*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 30*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 5*sin(d*x + c)/(a^3*(cos(d*x + c) + 1))) + 2*A*(2*(115*sin(d*x + c)/(cos(d*x + c) + 1) + 185*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 135*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 32)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
242,1,622,0,0.409622," ","integrate(csc(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, A {\left(\frac{\frac{121 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{410 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{610 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{425 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{125 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 5}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{5 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2782 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9410 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{13645 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9285 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2580 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 15}{\frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} - \frac{15 \, {\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{3}} + \frac{780 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{120 \, d}"," ",0,"1/120*(12*A*((121*sin(d*x + c)/(cos(d*x + c) + 1) + 410*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 610*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 425*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 125*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 5*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 30*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 5*sin(d*x + c)/(a^3*(cos(d*x + c) + 1))) + A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 2782*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 9410*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 13645*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9285*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2580*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15)/(a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) - 15*(12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 780*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
243,1,706,0,0.458242," ","integrate(csc(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{A {\left(\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2782 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9410 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{13645 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9285 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2580 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 15}{\frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} - \frac{15 \, {\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{3}} + \frac{780 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)} - A {\left(\frac{\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{230 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4777 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15785 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{22390 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14940 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4005 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 5}{\frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{5 \, {\left(\frac{81 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}\right)}}{a^{3}} - \frac{1380 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{120 \, d}"," ",0,"-1/120*(A*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 2782*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 9410*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 13645*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9285*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2580*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15)/(a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) - 15*(12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 780*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3) - A*((20*sin(d*x + c)/(cos(d*x + c) + 1) - 230*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4777*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 15785*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 22390*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14940*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4005*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5)/(a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 10*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 5*(81*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 1380*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3))/d","B",0
244,1,406,0,0.363316," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{480 \, {\left(f x + e\right)} A a c^{3} + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{3} + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c^{2} d + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c^{2} d + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{2} d + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a c d^{2} + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c d^{2} + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c d^{2} + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a c d^{2} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a d^{3} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a d^{3} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a d^{3} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a d^{3} - 480 \, A a c^{3} \cos\left(f x + e\right) - 480 \, B a c^{3} \cos\left(f x + e\right) - 1440 \, A a c^{2} d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(480*(f*x + e)*A*a*c^3 + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^3 + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c^2*d + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c^2*d + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^2*d + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*c*d^2 + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c*d^2 + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c*d^2 + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*c*d^2 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*d^3 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a*d^3 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a*d^3 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*d^3 - 480*A*a*c^3*cos(f*x + e) - 480*B*a*c^3*cos(f*x + e) - 1440*A*a*c^2*d*cos(f*x + e))/f","A",0
245,1,264,0,0.371071," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{96 \, {\left(f x + e\right)} A a c^{2} + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c^{2} + 48 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a c d + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a c d + 48 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c d + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a d^{2} + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a d^{2} + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a d^{2} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a d^{2} - 96 \, A a c^{2} \cos\left(f x + e\right) - 96 \, B a c^{2} \cos\left(f x + e\right) - 192 \, A a c d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(96*(f*x + e)*A*a*c^2 + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c^2 + 48*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*c*d + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*c*d + 48*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c*d + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a*d^2 + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*d^2 + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*d^2 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a*d^2 - 96*A*a*c^2*cos(f*x + e) - 96*B*a*c^2*cos(f*x + e) - 192*A*a*c*d*cos(f*x + e))/f","A",0
246,1,143,0,0.374327," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{12 \, {\left(f x + e\right)} A a c + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a c + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a d + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a d + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a d - 12 \, A a c \cos\left(f x + e\right) - 12 \, B a c \cos\left(f x + e\right) - 12 \, A a d \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(12*(f*x + e)*A*a*c + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*c + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a*d + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a*d + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a*d - 12*A*a*c*cos(f*x + e) - 12*B*a*c*cos(f*x + e) - 12*A*a*d*cos(f*x + e))/f","A",0
247,1,57,0,0.445764," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} A a + {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a - 4 \, A a \cos\left(f x + e\right) - 4 \, B a \cos\left(f x + e\right)}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*A*a + (2*f*x + 2*e - sin(2*f*x + 2*e))*B*a - 4*A*a*cos(f*x + e) - 4*B*a*cos(f*x + e))/f","A",0
248,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
249,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
250,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
251,1,724,0,0.464607," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{3} + 960 \, {\left(f x + e\right)} A a^{2} c^{3} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{3} + 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{3} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c^{2} d + 1440 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{2} d + 1920 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{2} d + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{2} d + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{2} d + 1920 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c d^{2} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c d^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c d^{2} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} c d^{2} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c d^{2} + 180 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c d^{2} - 64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{2} d^{3} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} d^{3} + 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} d^{3} - 128 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} d^{3} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} d^{3} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} d^{3} - 1920 \, A a^{2} c^{3} \cos\left(f x + e\right) - 960 \, B a^{2} c^{3} \cos\left(f x + e\right) - 2880 \, A a^{2} c^{2} d \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(240*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^3 + 960*(f*x + e)*A*a^2*c^3 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^3 + 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^3 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c^2*d + 1440*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^2*d + 1920*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^2*d + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c^2*d + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^2*d + 1920*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c*d^2 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*c*d^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c*d^2 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*c*d^2 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c*d^2 + 180*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c*d^2 - 64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^2*d^3 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*d^3 + 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*d^3 - 128*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*d^3 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^2*d^3 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*d^3 - 1920*A*a^2*c^3*cos(f*x + e) - 960*B*a^2*c^3*cos(f*x + e) - 2880*A*a^2*c^2*d*cos(f*x + e))/f","A",0
252,1,478,0,0.440129," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c^{2} + 480 \, {\left(f x + e\right)} A a^{2} c^{2} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c^{2} + 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c^{2} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} c d + 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c d + 640 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c d + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c d + 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c d + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} d^{2} + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} d^{2} + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} d^{2} - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{2} d^{2} + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} d^{2} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} d^{2} - 960 \, A a^{2} c^{2} \cos\left(f x + e\right) - 480 \, B a^{2} c^{2} \cos\left(f x + e\right) - 960 \, A a^{2} c d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(120*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c^2 + 480*(f*x + e)*A*a^2*c^2 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c^2 + 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c^2 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*c*d + 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c*d + 640*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c*d + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*c*d + 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c*d + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*d^2 + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^2*d^2 + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*d^2 - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^2*d^2 + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*d^2 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*d^2 - 960*A*a^2*c^2*cos(f*x + e) - 480*B*a^2*c^2*cos(f*x + e) - 960*A*a^2*c*d*cos(f*x + e))/f","A",0
253,1,268,0,0.420316," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} c + 96 \, {\left(f x + e\right)} A a^{2} c + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} c + 48 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} c + 32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{2} d + 48 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} d + 64 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} d + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} d + 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} d - 192 \, A a^{2} c \cos\left(f x + e\right) - 96 \, B a^{2} c \cos\left(f x + e\right) - 96 \, A a^{2} d \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(24*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*c + 96*(f*x + e)*A*a^2*c + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*c + 48*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*c + 32*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^2*d + 48*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2*d + 64*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2*d + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^2*d + 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2*d - 192*A*a^2*c*cos(f*x + e) - 96*B*a^2*c*cos(f*x + e) - 96*A*a^2*d*cos(f*x + e))/f","A",0
254,1,114,0,0.438789," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{2} + 12 \, {\left(f x + e\right)} A a^{2} + 4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{2} + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{2} - 24 \, A a^{2} \cos\left(f x + e\right) - 12 \, B a^{2} \cos\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^2 + 12*(f*x + e)*A*a^2 + 4*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^2 - 24*A*a^2*cos(f*x + e) - 12*B*a^2*cos(f*x + e))/f","A",0
255,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
256,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
257,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
258,1,1056,0,0.627389," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2240 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{3} + 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{3} + 6720 \, {\left(f x + e\right)} A a^{3} c^{3} + 6720 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{3} + 210 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{3} + 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{3} + 20160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{2} d + 630 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{2} d + 15120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{2} d - 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c^{2} d + 20160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{2} d + 1890 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} d + 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} d - 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} c d^{2} + 20160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c d^{2} + 1890 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c d^{2} + 5040 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c d^{2} - 4032 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c d^{2} + 6720 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c d^{2} + 105 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c d^{2} + 1890 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c d^{2} - 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} d^{3} + 2240 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} d^{3} + 35 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d^{3} + 630 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d^{3} + 192 \, {\left(5 \, \cos\left(f x + e\right)^{7} - 21 \, \cos\left(f x + e\right)^{5} + 35 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)\right)} B a^{3} d^{3} - 1344 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} d^{3} + 105 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d^{3} + 210 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d^{3} - 20160 \, A a^{3} c^{3} \cos\left(f x + e\right) - 6720 \, B a^{3} c^{3} \cos\left(f x + e\right) - 20160 \, A a^{3} c^{2} d \cos\left(f x + e\right)}{6720 \, f}"," ",0,"1/6720*(2240*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^3 + 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^3 + 6720*(f*x + e)*A*a^3*c^3 + 6720*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^3 + 210*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^3 + 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^3 + 20160*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^2*d + 630*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c^2*d + 15120*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^2*d - 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c^2*d + 20160*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^2*d + 1890*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^2*d + 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^2*d - 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*c*d^2 + 20160*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c*d^2 + 1890*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c*d^2 + 5040*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c*d^2 - 4032*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c*d^2 + 6720*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c*d^2 + 105*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*c*d^2 + 1890*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c*d^2 - 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*d^3 + 2240*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*d^3 + 35*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*A*a^3*d^3 + 630*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*d^3 + 192*(5*cos(f*x + e)^7 - 21*cos(f*x + e)^5 + 35*cos(f*x + e)^3 - 35*cos(f*x + e))*B*a^3*d^3 - 1344*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*d^3 + 105*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*d^3 + 210*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*d^3 - 20160*A*a^3*c^3*cos(f*x + e) - 6720*B*a^3*c^3*cos(f*x + e) - 20160*A*a^3*c^2*d*cos(f*x + e))/f","A",0
259,1,704,0,0.461178," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c^{2} + 960 \, {\left(f x + e\right)} A a^{3} c^{2} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c^{2} + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} + 720 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c^{2} + 1920 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c d + 60 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c d + 1440 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c d - 128 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} c d + 1920 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c d + 180 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c d + 480 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c d - 64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} A a^{3} d^{2} + 960 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} d^{2} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d^{2} + 240 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d^{2} - 192 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} d^{2} + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} d^{2} + 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d^{2} + 90 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d^{2} - 2880 \, A a^{3} c^{2} \cos\left(f x + e\right) - 960 \, B a^{3} c^{2} \cos\left(f x + e\right) - 1920 \, A a^{3} c d \cos\left(f x + e\right)}{960 \, f}"," ",0,"1/960*(320*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c^2 + 960*(f*x + e)*A*a^3*c^2 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c^2 + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c^2 + 720*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c^2 + 1920*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c*d + 60*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*c*d + 1440*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c*d - 128*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*c*d + 1920*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c*d + 180*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c*d + 480*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c*d - 64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*A*a^3*d^2 + 960*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*d^2 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*d^2 + 240*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*d^2 - 192*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*d^2 + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*d^2 + 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*B*a^3*d^2 + 90*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*d^2 - 2880*A*a^3*c^2*cos(f*x + e) - 960*B*a^3*c^2*cos(f*x + e) - 1920*A*a^3*c*d*cos(f*x + e))/f","A",0
260,1,398,0,0.429691," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} c + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} c + 480 \, {\left(f x + e\right)} A a^{3} c + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} c + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} c + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} d + 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d + 360 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} d - 32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} B a^{3} d + 480 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} d + 45 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} d - 1440 \, A a^{3} c \cos\left(f x + e\right) - 480 \, B a^{3} c \cos\left(f x + e\right) - 480 \, A a^{3} d \cos\left(f x + e\right)}{480 \, f}"," ",0,"1/480*(160*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*c + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*c + 480*(f*x + e)*A*a^3*c + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*c + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*c + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*c + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3*d + 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*A*a^3*d + 360*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3*d - 32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*B*a^3*d + 480*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3*d + 45*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3*d + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3*d - 1440*A*a^3*c*cos(f*x + e) - 480*B*a^3*c*cos(f*x + e) - 480*A*a^3*d*cos(f*x + e))/f","B",0
261,1,171,0,0.380964," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} A a^{3} + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} A a^{3} + 96 \, {\left(f x + e\right)} A a^{3} + 96 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} B a^{3} + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} + 72 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} B a^{3} - 288 \, A a^{3} \cos\left(f x + e\right) - 96 \, B a^{3} \cos\left(f x + e\right)}{96 \, f}"," ",0,"1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*A*a^3 + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*A*a^3 + 96*(f*x + e)*A*a^3 + 96*(cos(f*x + e)^3 - 3*cos(f*x + e))*B*a^3 + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*B*a^3 + 72*(2*f*x + 2*e - sin(2*f*x + 2*e))*B*a^3 - 288*A*a^3*cos(f*x + e) - 96*B*a^3*cos(f*x + e))/f","A",0
262,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
263,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
264,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
265,1,1124,0,0.726711," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{B d^{3} {\left(\frac{\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 16}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 9 \, B c d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 3 \, A d^{3} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 18 \, B c^{2} d {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 18 \, A c d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 6 \, B c^{3} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - 18 \, A c^{2} d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{6 \, A c^{3}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{3 \, f}"," ",0,"-1/3*(B*d^3*((7*sin(f*x + e)/(cos(f*x + e) + 1) + 39*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 24*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 24*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 9*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 16)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 3*a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 9*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 9*B*c*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 3*A*d^3*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 18*B*c^2*d*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 18*A*c*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 6*B*c^3*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 18*A*c^2*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 6*A*c^3/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
266,1,606,0,0.725194," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{B d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 4 \, B c d {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - 2 \, A d^{2} {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} + 2 \, B c^{2} {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + 4 \, A c d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{2 \, A c^{2}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"(B*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 4)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2*a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 4*B*c*d*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - 2*A*d^2*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) + 2*B*c^2*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + 4*A*c*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - 2*A*c^2/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
267,1,256,0,0.491933," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(B d {\left(\frac{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a}\right)} - B c {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - A d {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} + \frac{A c}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"-2*(B*d*((sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a + a*sin(f*x + e)/(cos(f*x + e) + 1) + a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a) - B*c*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - A*d*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) + A*c/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
268,1,78,0,0.518120," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(B {\left(\frac{\arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)} - \frac{A}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}}{f}"," ",0,"2*(B*(arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a + 1/(a + a*sin(f*x + e)/(cos(f*x + e) + 1))) - A/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
269,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
270,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
271,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
272,1,1382,0,0.569837," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{B d^{3} {\left(\frac{\frac{75 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{97 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{98 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 32}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{7 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{21 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 12 \, B c d^{2} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 4 \, A d^{3} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 6 \, B c^{2} d {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + 6 \, A c d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{2 \, A c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{2 \, B c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{6 \, A c^{2} d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(B*d^3*((75*sin(f*x + e)/(cos(f*x + e) + 1) + 97*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 98*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 63*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 21*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 32)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 5*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 7*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 7*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 3*a^2*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^2*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 21*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 12*B*c*d^2*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 4*A*d^3*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 6*B*c^2*d*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + 6*A*c*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*A*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 2*B*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 6*A*c^2*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
273,1,831,0,0.575010," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(2 \, B d^{2} {\left(\frac{\frac{12 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{9 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 5}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - 2 \, B c d {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - A d^{2} {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} + \frac{A c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B c^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{2 \, A c d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(2*B*d^2*((12*sin(f*x + e)/(cos(f*x + e) + 1) + 11*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 9*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 4*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^2*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^2*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - 2*B*c*d*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - A*d^2*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) + A*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*c^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 2*A*c*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
274,1,454,0,0.502472," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(B d {\left(\frac{\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{2}}\right)} - \frac{A c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{B c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{A d {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"2/3*(B*d*((9*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 3*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^2) - A*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - B*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - A*d*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
275,1,214,0,0.350022," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{B {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}\right)}}{3 \, f}"," ",0,"-2/3*(A*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + B*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 1)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
276,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
277,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
278,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
279,1,1682,0,0.583665," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, B d^{3} {\left(\frac{\frac{105 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{189 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{160 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{75 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 24}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{11 \, a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - 3 \, B c d^{2} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - A d^{3} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} + \frac{A c^{3} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, B c^{2} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{6 \, A c d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, B c^{3} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{9 \, A c^{2} d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(3*B*d^3*((105*sin(f*x + e)/(cos(f*x + e) + 1) + 189*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 200*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 160*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 75*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 15*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 24)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 11*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 15*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 11*a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 5*a^3*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^3*sin(f*x + e)^7/(cos(f*x + e) + 1)^7) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - 3*B*c*d^2*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*d^3*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) + A*c^3*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*B*c^2*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 6*A*c*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*B*c^3*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 9*A*c^2*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
280,1,1132,0,0.548960," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(B d^{2} {\left(\frac{\frac{95 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{145 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a^{3}}\right)} - \frac{A c^{2} {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{4 \, B c d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{2 \, A d^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{3 \, B c^{2} {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} - \frac{6 \, A c d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"2/15*(B*d^2*((95*sin(f*x + e)/(cos(f*x + e) + 1) + 145*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 75*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 22)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 15*arctan(sin(f*x + e)/(cos(f*x + e) + 1))/a^3) - A*c^2*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 4*B*c*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 2*A*d^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 3*B*c^2*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) - 6*A*c*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
281,1,733,0,0.456077," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A c {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{2 \, B d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, B c {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, A d {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(A*c*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 2*B*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 10*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*B*c*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*A*d*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
282,1,387,0,0.393915," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{A {\left(\frac{20 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{40 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 7\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}} + \frac{3 \, B {\left(\frac{5 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + 1\right)}}{a^{3} + \frac{5 \, a^{3} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}\right)}}{15 \, f}"," ",0,"-2/15*(A*(20*sin(f*x + e)/(cos(f*x + e) + 1) + 40*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 30*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5) + 3*B*(5*sin(f*x + e)/(cos(f*x + e) + 1) + 5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 1)/(a^3 + 5*a^3*sin(f*x + e)/(cos(f*x + e) + 1) + 10*a^3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*a^3*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^3*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^3*sin(f*x + e)^5/(cos(f*x + e) + 1)^5))/f","B",0
283,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
284,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
285,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
286,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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)}^{3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^3, x)","F",0
287,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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)}^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^2, x)","F",0
288,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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)}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c), x)","F",0
289,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a), x)","F",0
290,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c), x)","F",0
291,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \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)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^2, x)","F",0
292,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \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)}^{3}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)/(d*sin(f*x + e) + c)^3, x)","F",0
293,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^3, x)","F",0
294,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^2, x)","F",0
295,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c), x)","F",0
296,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2), x)","F",0
297,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c), x)","F",0
298,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^2, x)","F",0
299,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)/(d*sin(f*x + e) + c)^3, x)","F",0
300,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^3, x)","F",0
301,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c)^2, x)","F",0
302,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \sin\left(f x + e\right) + c\right)}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)*(d*sin(f*x + e) + c), x)","F",0
303,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2), x)","F",0
304,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c), x)","F",0
305,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(5/2)/(d*sin(f*x + e) + c)^2, x)","F",0
306,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{3}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^3/sqrt(a*sin(f*x + e) + a), x)","F",0
308,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
309,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
310,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/sqrt(a*sin(f*x + e) + a), x)","F",0
311,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
312,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^2), x)","F",0
313,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{3}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^3/(a*sin(f*x + e) + a)^(3/2), x)","F",0
315,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
316,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
317,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
318,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)), x)","F",0
319,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{3}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^3/(a*sin(f*x + e) + a)^(5/2), x)","F",0
322,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
323,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
324,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
325,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
326,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n, x)","F",0
329,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
330,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
331,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
332,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^n, x)","F",0
333,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
334,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
335,0,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^(3/2), x)","F",0
336,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
337,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
338,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m, x)","F",0
339,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
340,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\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)}^{2}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^2, x)","F",0
341,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\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)}^{3}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^3, x)","F",0
342,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
343,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\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 x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
344,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
345,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c)^(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
347,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 1), x)","F",0
348,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","-\int {\left(a \sin\left(f x + e\right) - a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"-integrate((a*sin(f*x + e) - a)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
349,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","-\int {\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}\,{d x}"," ",0,"-integrate((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,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
353,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^(3/2)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
354,0,0,0,0.000000," ","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=""maxima"")","\int \frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*sqrt(d*sin(f*x + e) + c)/(b*sin(f*x + e) + a)^(3/2), x)","F",0
355,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((b*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
356,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(3/2)), x)","F",0
357,0,0,0,0.000000," ","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=""maxima"")","\int \frac{B \sin\left(f x + e\right) + A}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)/((b*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)^(5/2)), x)","F",0
358,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
