1,1,777,0,1.281843," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(16 \, C c^{2} m^{4} + 128 \, C c^{2} m^{3} + 344 \, C c^{2} m^{2} + 352 \, C c^{2} m + 105 \, C c^{2}\right)} \cos\left(f x + e\right)^{5} + 128 \, {\left(A + C\right)} c^{2} m^{2} - {\left(16 \, C c^{2} m^{4} + 224 \, C c^{2} m^{3} + 776 \, C c^{2} m^{2} + 904 \, C c^{2} m + 285 \, C c^{2}\right)} \cos\left(f x + e\right)^{4} + 512 \, {\left(2 \, A - C\right)} c^{2} m - {\left(16 \, {\left(A + 3 \, C\right)} c^{2} m^{4} + 32 \, {\left(5 \, A + 16 \, C\right)} c^{2} m^{3} + 8 \, {\left(65 \, A + 253 \, C\right)} c^{2} m^{2} + 8 \, {\left(75 \, A + 328 \, C\right)} c^{2} m + 3 \, {\left(63 \, A + 289 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{3} + 96 \, {\left(21 \, A + 13 \, C\right)} c^{2} + {\left(16 \, {\left(A + C\right)} c^{2} m^{4} + 224 \, {\left(A + C\right)} c^{2} m^{3} + 8 \, {\left(133 \, A + 85 \, C\right)} c^{2} m^{2} + 1864 \, {\left(A + C\right)} c^{2} m + 3 \, {\left(231 \, A + 263 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(16 \, {\left(A + C\right)} c^{2} m^{4} + 192 \, {\left(A + C\right)} c^{2} m^{3} + 856 \, {\left(A + C\right)} c^{2} m^{2} + 16 \, {\left(109 \, A + 85 \, C\right)} c^{2} m + 3 \, {\left(483 \, A + 419 \, C\right)} c^{2}\right)} \cos\left(f x + e\right) + {\left(128 \, {\left(A + C\right)} c^{2} m^{2} + {\left(16 \, C c^{2} m^{4} + 128 \, C c^{2} m^{3} + 344 \, C c^{2} m^{2} + 352 \, C c^{2} m + 105 \, C c^{2}\right)} \cos\left(f x + e\right)^{4} + 512 \, {\left(2 \, A - C\right)} c^{2} m + 2 \, {\left(16 \, C c^{2} m^{4} + 176 \, C c^{2} m^{3} + 560 \, C c^{2} m^{2} + 628 \, C c^{2} m + 195 \, C c^{2}\right)} \cos\left(f x + e\right)^{3} + 96 \, {\left(21 \, A + 13 \, C\right)} c^{2} - {\left(16 \, {\left(A + C\right)} c^{2} m^{4} + 160 \, {\left(A + C\right)} c^{2} m^{3} + 8 \, {\left(65 \, A + 113 \, C\right)} c^{2} m^{2} + 24 \, {\left(25 \, A + 57 \, C\right)} c^{2} m + 9 \, {\left(21 \, A + 53 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(16 \, {\left(A + C\right)} c^{2} m^{4} + 192 \, {\left(A + C\right)} c^{2} m^{3} + 792 \, {\left(A + C\right)} c^{2} m^{2} + 16 \, {\left(77 \, A + 101 \, C\right)} c^{2} m + 3 \, {\left(147 \, A + 211 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + {\left(32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + 945 \, f\right)} \cos\left(f x + e\right) - {\left(32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + 945 \, f\right)} \sin\left(f x + e\right) + 945 \, f}"," ",0,"2*((16*C*c^2*m^4 + 128*C*c^2*m^3 + 344*C*c^2*m^2 + 352*C*c^2*m + 105*C*c^2)*cos(f*x + e)^5 + 128*(A + C)*c^2*m^2 - (16*C*c^2*m^4 + 224*C*c^2*m^3 + 776*C*c^2*m^2 + 904*C*c^2*m + 285*C*c^2)*cos(f*x + e)^4 + 512*(2*A - C)*c^2*m - (16*(A + 3*C)*c^2*m^4 + 32*(5*A + 16*C)*c^2*m^3 + 8*(65*A + 253*C)*c^2*m^2 + 8*(75*A + 328*C)*c^2*m + 3*(63*A + 289*C)*c^2)*cos(f*x + e)^3 + 96*(21*A + 13*C)*c^2 + (16*(A + C)*c^2*m^4 + 224*(A + C)*c^2*m^3 + 8*(133*A + 85*C)*c^2*m^2 + 1864*(A + C)*c^2*m + 3*(231*A + 263*C)*c^2)*cos(f*x + e)^2 + 2*(16*(A + C)*c^2*m^4 + 192*(A + C)*c^2*m^3 + 856*(A + C)*c^2*m^2 + 16*(109*A + 85*C)*c^2*m + 3*(483*A + 419*C)*c^2)*cos(f*x + e) + (128*(A + C)*c^2*m^2 + (16*C*c^2*m^4 + 128*C*c^2*m^3 + 344*C*c^2*m^2 + 352*C*c^2*m + 105*C*c^2)*cos(f*x + e)^4 + 512*(2*A - C)*c^2*m + 2*(16*C*c^2*m^4 + 176*C*c^2*m^3 + 560*C*c^2*m^2 + 628*C*c^2*m + 195*C*c^2)*cos(f*x + e)^3 + 96*(21*A + 13*C)*c^2 - (16*(A + C)*c^2*m^4 + 160*(A + C)*c^2*m^3 + 8*(65*A + 113*C)*c^2*m^2 + 24*(25*A + 57*C)*c^2*m + 9*(21*A + 53*C)*c^2)*cos(f*x + e)^2 - 2*(16*(A + C)*c^2*m^4 + 192*(A + C)*c^2*m^3 + 792*(A + C)*c^2*m^2 + 16*(77*A + 101*C)*c^2*m + 3*(147*A + 211*C)*c^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + (32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + 945*f)*cos(f*x + e) - (32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + 945*f)*sin(f*x + e) + 945*f)","B",0
2,1,461,0,1.033574," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(8 \, C c m^{3} + 36 \, C c m^{2} + 46 \, C c m + 15 \, C c\right)} \cos\left(f x + e\right)^{4} - 16 \, {\left(A + C\right)} c m^{2} + {\left(8 \, C c m^{3} + 68 \, C c m^{2} + 110 \, C c m + 39 \, C c\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(3 \, A - C\right)} c m - {\left(8 \, {\left(A + C\right)} c m^{3} + 4 \, {\left(13 \, A + 5 \, C\right)} c m^{2} + 94 \, {\left(A + C\right)} c m + {\left(35 \, A + 43 \, C\right)} c\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(35 \, A + 19 \, C\right)} c - {\left(8 \, {\left(A + C\right)} c m^{3} + 68 \, {\left(A + C\right)} c m^{2} + 2 \, {\left(95 \, A + 63 \, C\right)} c m + {\left(175 \, A + 143 \, C\right)} c\right)} \cos\left(f x + e\right) - {\left(16 \, {\left(A + C\right)} c m^{2} + {\left(8 \, C c m^{3} + 36 \, C c m^{2} + 46 \, C c m + 15 \, C c\right)} \cos\left(f x + e\right)^{3} + 32 \, {\left(3 \, A - C\right)} c m - 8 \, {\left(4 \, C c m^{2} + 8 \, C c m + 3 \, C c\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(35 \, A + 19 \, C\right)} c - {\left(8 \, {\left(A + C\right)} c m^{3} + 52 \, {\left(A + C\right)} c m^{2} + 2 \, {\left(47 \, A + 79 \, C\right)} c m + {\left(35 \, A + 67 \, C\right)} c\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \cos\left(f x + e\right) - {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \sin\left(f x + e\right) + 105 \, f}"," ",0,"-2*((8*C*c*m^3 + 36*C*c*m^2 + 46*C*c*m + 15*C*c)*cos(f*x + e)^4 - 16*(A + C)*c*m^2 + (8*C*c*m^3 + 68*C*c*m^2 + 110*C*c*m + 39*C*c)*cos(f*x + e)^3 - 32*(3*A - C)*c*m - (8*(A + C)*c*m^3 + 4*(13*A + 5*C)*c*m^2 + 94*(A + C)*c*m + (35*A + 43*C)*c)*cos(f*x + e)^2 - 4*(35*A + 19*C)*c - (8*(A + C)*c*m^3 + 68*(A + C)*c*m^2 + 2*(95*A + 63*C)*c*m + (175*A + 143*C)*c)*cos(f*x + e) - (16*(A + C)*c*m^2 + (8*C*c*m^3 + 36*C*c*m^2 + 46*C*c*m + 15*C*c)*cos(f*x + e)^3 + 32*(3*A - C)*c*m - 8*(4*C*c*m^2 + 8*C*c*m + 3*C*c)*cos(f*x + e)^2 + 4*(35*A + 19*C)*c - (8*(A + C)*c*m^3 + 52*(A + C)*c*m^2 + 2*(47*A + 79*C)*c*m + (35*A + 67*C)*c)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*cos(f*x + e) - (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*sin(f*x + e) + 105*f)","A",0
3,1,261,0,0.948588," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(4 \, C m^{2} + 8 \, C m + 3 \, C\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(A + C\right)} m^{2} + {\left(4 \, C m^{2} - C\right)} \cos\left(f x + e\right)^{2} - 16 \, A m - {\left(4 \, {\left(A + C\right)} m^{2} + 8 \, {\left(2 \, A + C\right)} m + 15 \, A + 11 \, C\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A + C\right)} m^{2} - {\left(4 \, C m^{2} + 8 \, C m + 3 \, C\right)} \cos\left(f x + e\right)^{2} + 16 \, A m - 4 \, {\left(2 \, C m + C\right)} \cos\left(f x + e\right) + 15 \, A + 7 \, C\right)} \sin\left(f x + e\right) - 15 \, A - 7 \, C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \cos\left(f x + e\right) - {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \sin\left(f x + e\right) + 15 \, f}"," ",0,"-2*((4*C*m^2 + 8*C*m + 3*C)*cos(f*x + e)^3 - 4*(A + C)*m^2 + (4*C*m^2 - C)*cos(f*x + e)^2 - 16*A*m - (4*(A + C)*m^2 + 8*(2*A + C)*m + 15*A + 11*C)*cos(f*x + e) - (4*(A + C)*m^2 - (4*C*m^2 + 8*C*m + 3*C)*cos(f*x + e)^2 + 16*A*m - 4*(2*C*m + C)*cos(f*x + e) + 15*A + 7*C)*sin(f*x + e) - 15*A - 7*C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(8*f*m^3 + 36*f*m^2 + 46*f*m + (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*cos(f*x + e) - (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*sin(f*x + e) + 15*f)","A",0
4,0,0,0,1.192955," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
5,0,0,0,1.086526," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
6,0,0,0,0.922462," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
7,0,0,0,4.912790," ","integrate((A+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - a c^{2} \cos\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c^2*cos(f*x + e)^2*sin(f*x + e) - a*c^2*cos(f*x + e)^2), x)","F",0
8,0,0,0,1.192155," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - A - C)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
9,0,0,0,1.392264," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - A - C)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
10,0,0,0,1.276440," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - A - C)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2), x)","F",0
11,0,0,0,1.410580," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C c \cos\left(f x + e\right)^{2} - {\left(A + C\right)} c + {\left(C d \cos\left(f x + e\right)^{2} - {\left(A + C\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(C*c*cos(f*x + e)^2 - (A + C)*c + (C*d*cos(f*x + e)^2 - (A + C)*d)*sin(f*x + e))*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
12,0,0,0,1.050515," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2)*(A+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
13,0,0,0,1.309571," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - A - C)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
14,0,0,0,1.469805," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2), x)","F",0
15,0,0,0,1.246552," ","integrate((a+a*sin(f*x+e))^m*(A+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c d^{2} \cos\left(f x + e\right)^{2} - c^{3} - 3 \, c d^{2} + {\left(d^{3} \cos\left(f x + e\right)^{2} - 3 \, c^{2} d - d^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(3*c*d^2*cos(f*x + e)^2 - c^3 - 3*c*d^2 + (d^3*cos(f*x + e)^2 - 3*c^2*d - d^3)*sin(f*x + e)), x)","F",0
16,0,0,0,9.489906," ","integrate((A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - a c^{2} \cos\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c^2*cos(f*x + e)^2*sin(f*x + e) - a*c^2*cos(f*x + e)^2), x)","F",0
17,0,0,0,0.916180," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
18,1,937,0,1.245345," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(16 \, C c^{2} m^{4} + 128 \, C c^{2} m^{3} + 344 \, C c^{2} m^{2} + 352 \, C c^{2} m + 105 \, C c^{2}\right)} \cos\left(f x + e\right)^{5} + 128 \, {\left(A + B + C\right)} c^{2} m^{2} + {\left(16 \, {\left(B - C\right)} c^{2} m^{4} + 16 \, {\left(9 \, B - 14 \, C\right)} c^{2} m^{3} + 8 \, {\left(52 \, B - 97 \, C\right)} c^{2} m^{2} + 4 \, {\left(111 \, B - 226 \, C\right)} c^{2} m + 15 \, {\left(9 \, B - 19 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{4} + 256 \, {\left(4 \, A + B - 2 \, C\right)} c^{2} m - {\left(16 \, {\left(A - 2 \, B + 3 \, C\right)} c^{2} m^{4} + 16 \, {\left(10 \, A - 23 \, B + 32 \, C\right)} c^{2} m^{3} + 8 \, {\left(65 \, A - 169 \, B + 253 \, C\right)} c^{2} m^{2} + 4 \, {\left(150 \, A - 417 \, B + 656 \, C\right)} c^{2} m + 3 \, {\left(63 \, A - 180 \, B + 289 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{3} + 96 \, {\left(21 \, A - 15 \, B + 13 \, C\right)} c^{2} + {\left(16 \, {\left(A - B + C\right)} c^{2} m^{4} + 32 \, {\left(7 \, A - 5 \, B + 7 \, C\right)} c^{2} m^{3} + 8 \, {\left(133 \, A - 97 \, B + 85 \, C\right)} c^{2} m^{2} + 8 \, {\left(233 \, A - 235 \, B + 233 \, C\right)} c^{2} m + 3 \, {\left(231 \, A - 255 \, B + 263 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(16 \, {\left(A - B + C\right)} c^{2} m^{4} + 192 \, {\left(A - B + C\right)} c^{2} m^{3} + 8 \, {\left(107 \, A - 99 \, B + 107 \, C\right)} c^{2} m^{2} + 16 \, {\left(109 \, A - 89 \, B + 85 \, C\right)} c^{2} m + 3 \, {\left(483 \, A - 435 \, B + 419 \, C\right)} c^{2}\right)} \cos\left(f x + e\right) + {\left(128 \, {\left(A + B + C\right)} c^{2} m^{2} + {\left(16 \, C c^{2} m^{4} + 128 \, C c^{2} m^{3} + 344 \, C c^{2} m^{2} + 352 \, C c^{2} m + 105 \, C c^{2}\right)} \cos\left(f x + e\right)^{4} + 256 \, {\left(4 \, A + B - 2 \, C\right)} c^{2} m - {\left(16 \, {\left(B - 2 \, C\right)} c^{2} m^{4} + 16 \, {\left(9 \, B - 22 \, C\right)} c^{2} m^{3} + 32 \, {\left(13 \, B - 35 \, C\right)} c^{2} m^{2} + 4 \, {\left(111 \, B - 314 \, C\right)} c^{2} m + 15 \, {\left(9 \, B - 26 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{3} + 96 \, {\left(21 \, A - 15 \, B + 13 \, C\right)} c^{2} - {\left(16 \, {\left(A - B + C\right)} c^{2} m^{4} + 32 \, {\left(5 \, A - 7 \, B + 5 \, C\right)} c^{2} m^{3} + 8 \, {\left(65 \, A - 117 \, B + 113 \, C\right)} c^{2} m^{2} + 24 \, {\left(25 \, A - 51 \, B + 57 \, C\right)} c^{2} m + 9 \, {\left(21 \, A - 45 \, B + 53 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(16 \, {\left(A - B + C\right)} c^{2} m^{4} + 192 \, {\left(A - B + C\right)} c^{2} m^{3} + 8 \, {\left(99 \, A - 107 \, B + 99 \, C\right)} c^{2} m^{2} + 16 \, {\left(77 \, A - 97 \, B + 101 \, C\right)} c^{2} m + 3 \, {\left(147 \, A - 195 \, B + 211 \, C\right)} c^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + {\left(32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + 945 \, f\right)} \cos\left(f x + e\right) - {\left(32 \, f m^{5} + 400 \, f m^{4} + 1840 \, f m^{3} + 3800 \, f m^{2} + 3378 \, f m + 945 \, f\right)} \sin\left(f x + e\right) + 945 \, f}"," ",0,"2*((16*C*c^2*m^4 + 128*C*c^2*m^3 + 344*C*c^2*m^2 + 352*C*c^2*m + 105*C*c^2)*cos(f*x + e)^5 + 128*(A + B + C)*c^2*m^2 + (16*(B - C)*c^2*m^4 + 16*(9*B - 14*C)*c^2*m^3 + 8*(52*B - 97*C)*c^2*m^2 + 4*(111*B - 226*C)*c^2*m + 15*(9*B - 19*C)*c^2)*cos(f*x + e)^4 + 256*(4*A + B - 2*C)*c^2*m - (16*(A - 2*B + 3*C)*c^2*m^4 + 16*(10*A - 23*B + 32*C)*c^2*m^3 + 8*(65*A - 169*B + 253*C)*c^2*m^2 + 4*(150*A - 417*B + 656*C)*c^2*m + 3*(63*A - 180*B + 289*C)*c^2)*cos(f*x + e)^3 + 96*(21*A - 15*B + 13*C)*c^2 + (16*(A - B + C)*c^2*m^4 + 32*(7*A - 5*B + 7*C)*c^2*m^3 + 8*(133*A - 97*B + 85*C)*c^2*m^2 + 8*(233*A - 235*B + 233*C)*c^2*m + 3*(231*A - 255*B + 263*C)*c^2)*cos(f*x + e)^2 + 2*(16*(A - B + C)*c^2*m^4 + 192*(A - B + C)*c^2*m^3 + 8*(107*A - 99*B + 107*C)*c^2*m^2 + 16*(109*A - 89*B + 85*C)*c^2*m + 3*(483*A - 435*B + 419*C)*c^2)*cos(f*x + e) + (128*(A + B + C)*c^2*m^2 + (16*C*c^2*m^4 + 128*C*c^2*m^3 + 344*C*c^2*m^2 + 352*C*c^2*m + 105*C*c^2)*cos(f*x + e)^4 + 256*(4*A + B - 2*C)*c^2*m - (16*(B - 2*C)*c^2*m^4 + 16*(9*B - 22*C)*c^2*m^3 + 32*(13*B - 35*C)*c^2*m^2 + 4*(111*B - 314*C)*c^2*m + 15*(9*B - 26*C)*c^2)*cos(f*x + e)^3 + 96*(21*A - 15*B + 13*C)*c^2 - (16*(A - B + C)*c^2*m^4 + 32*(5*A - 7*B + 5*C)*c^2*m^3 + 8*(65*A - 117*B + 113*C)*c^2*m^2 + 24*(25*A - 51*B + 57*C)*c^2*m + 9*(21*A - 45*B + 53*C)*c^2)*cos(f*x + e)^2 - 2*(16*(A - B + C)*c^2*m^4 + 192*(A - B + C)*c^2*m^3 + 8*(99*A - 107*B + 99*C)*c^2*m^2 + 16*(77*A - 97*B + 101*C)*c^2*m + 3*(147*A - 195*B + 211*C)*c^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + (32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + 945*f)*cos(f*x + e) - (32*f*m^5 + 400*f*m^4 + 1840*f*m^3 + 3800*f*m^2 + 3378*f*m + 945*f)*sin(f*x + e) + 945*f)","B",0
19,1,563,0,1.012841," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(8 \, C c m^{3} + 36 \, C c m^{2} + 46 \, C c m + 15 \, C c\right)} \cos\left(f x + e\right)^{4} - 16 \, {\left(A + B + C\right)} c m^{2} - {\left(8 \, {\left(B - C\right)} c m^{3} + 4 \, {\left(11 \, B - 17 \, C\right)} c m^{2} + 2 \, {\left(31 \, B - 55 \, C\right)} c m + 3 \, {\left(7 \, B - 13 \, C\right)} c\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(3 \, A + B - C\right)} c m - {\left(8 \, {\left(A + C\right)} c m^{3} + 4 \, {\left(13 \, A - 6 \, B + 5 \, C\right)} c m^{2} + 2 \, {\left(47 \, A - 48 \, B + 47 \, C\right)} c m + {\left(35 \, A - 42 \, B + 43 \, C\right)} c\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(35 \, A - 21 \, B + 19 \, C\right)} c - {\left(8 \, {\left(A - B + C\right)} c m^{3} + 4 \, {\left(17 \, A - 13 \, B + 17 \, C\right)} c m^{2} + 2 \, {\left(95 \, A - 63 \, B + 63 \, C\right)} c m + {\left(175 \, A - 147 \, B + 143 \, C\right)} c\right)} \cos\left(f x + e\right) - {\left(16 \, {\left(A + B + C\right)} c m^{2} + {\left(8 \, C c m^{3} + 36 \, C c m^{2} + 46 \, C c m + 15 \, C c\right)} \cos\left(f x + e\right)^{3} + 32 \, {\left(3 \, A + B - C\right)} c m + {\left(8 \, B c m^{3} + 4 \, {\left(11 \, B - 8 \, C\right)} c m^{2} + 2 \, {\left(31 \, B - 32 \, C\right)} c m + 3 \, {\left(7 \, B - 8 \, C\right)} c\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(35 \, A - 21 \, B + 19 \, C\right)} c - {\left(8 \, {\left(A - B + C\right)} c m^{3} + 4 \, {\left(13 \, A - 17 \, B + 13 \, C\right)} c m^{2} + 2 \, {\left(47 \, A - 79 \, B + 79 \, C\right)} c m + {\left(35 \, A - 63 \, B + 67 \, C\right)} c\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \cos\left(f x + e\right) - {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \sin\left(f x + e\right) + 105 \, f}"," ",0,"-2*((8*C*c*m^3 + 36*C*c*m^2 + 46*C*c*m + 15*C*c)*cos(f*x + e)^4 - 16*(A + B + C)*c*m^2 - (8*(B - C)*c*m^3 + 4*(11*B - 17*C)*c*m^2 + 2*(31*B - 55*C)*c*m + 3*(7*B - 13*C)*c)*cos(f*x + e)^3 - 32*(3*A + B - C)*c*m - (8*(A + C)*c*m^3 + 4*(13*A - 6*B + 5*C)*c*m^2 + 2*(47*A - 48*B + 47*C)*c*m + (35*A - 42*B + 43*C)*c)*cos(f*x + e)^2 - 4*(35*A - 21*B + 19*C)*c - (8*(A - B + C)*c*m^3 + 4*(17*A - 13*B + 17*C)*c*m^2 + 2*(95*A - 63*B + 63*C)*c*m + (175*A - 147*B + 143*C)*c)*cos(f*x + e) - (16*(A + B + C)*c*m^2 + (8*C*c*m^3 + 36*C*c*m^2 + 46*C*c*m + 15*C*c)*cos(f*x + e)^3 + 32*(3*A + B - C)*c*m + (8*B*c*m^3 + 4*(11*B - 8*C)*c*m^2 + 2*(31*B - 32*C)*c*m + 3*(7*B - 8*C)*c)*cos(f*x + e)^2 + 4*(35*A - 21*B + 19*C)*c - (8*(A - B + C)*c*m^3 + 4*(13*A - 17*B + 13*C)*c*m^2 + 2*(47*A - 79*B + 79*C)*c*m + (35*A - 63*B + 67*C)*c)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*cos(f*x + e) - (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*sin(f*x + e) + 105*f)","A",0
20,1,310,0,0.946191," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(4 \, C m^{2} + 8 \, C m + 3 \, C\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(A + B + C\right)} m^{2} + {\left(4 \, {\left(B + C\right)} m^{2} + 12 \, B m + 5 \, B - C\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(2 \, A + B\right)} m - {\left(4 \, {\left(A + C\right)} m^{2} + 4 \, {\left(4 \, A - B + 2 \, C\right)} m + 15 \, A - 10 \, B + 11 \, C\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A + B + C\right)} m^{2} - {\left(4 \, C m^{2} + 8 \, C m + 3 \, C\right)} \cos\left(f x + e\right)^{2} + 8 \, {\left(2 \, A + B\right)} m + {\left(4 \, B m^{2} + 4 \, {\left(3 \, B - 2 \, C\right)} m + 5 \, B - 4 \, C\right)} \cos\left(f x + e\right) + 15 \, A - 5 \, B + 7 \, C\right)} \sin\left(f x + e\right) - 15 \, A + 5 \, B - 7 \, C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \cos\left(f x + e\right) - {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \sin\left(f x + e\right) + 15 \, f}"," ",0,"-2*((4*C*m^2 + 8*C*m + 3*C)*cos(f*x + e)^3 - 4*(A + B + C)*m^2 + (4*(B + C)*m^2 + 12*B*m + 5*B - C)*cos(f*x + e)^2 - 8*(2*A + B)*m - (4*(A + C)*m^2 + 4*(4*A - B + 2*C)*m + 15*A - 10*B + 11*C)*cos(f*x + e) - (4*(A + B + C)*m^2 - (4*C*m^2 + 8*C*m + 3*C)*cos(f*x + e)^2 + 8*(2*A + B)*m + (4*B*m^2 + 4*(3*B - 2*C)*m + 5*B - 4*C)*cos(f*x + e) + 15*A - 5*B + 7*C)*sin(f*x + e) - 15*A + 5*B - 7*C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(8*f*m^3 + 36*f*m^2 + 46*f*m + (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*cos(f*x + e) - (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*sin(f*x + e) + 15*f)","A",0
21,0,0,0,0.765988," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
22,0,0,0,0.892503," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
23,0,0,0,0.986454," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
24,0,0,0,0.975476," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
25,0,0,0,1.344293," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
26,0,0,0,1.073233," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2), x)","F",0
27,0,0,0,1.138124," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(C c + B d\right)} \cos\left(f x + e\right)^{2} - {\left(A + C\right)} c - B d + {\left(C d \cos\left(f x + e\right)^{2} - B c - {\left(A + C\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-((C*c + B*d)*cos(f*x + e)^2 - (A + C)*c - B*d + (C*d*cos(f*x + e)^2 - B*c - (A + C)*d)*sin(f*x + e))*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
28,0,0,0,1.055923," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
29,0,0,0,0.901953," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
30,0,0,0,1.138912," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2), x)","F",0
31,0,0,0,1.106828," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c d^{2} \cos\left(f x + e\right)^{2} - c^{3} - 3 \, c d^{2} + {\left(d^{3} \cos\left(f x + e\right)^{2} - 3 \, c^{2} d - d^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(3*c*d^2*cos(f*x + e)^2 - c^3 - 3*c*d^2 + (d^3*cos(f*x + e)^2 - 3*c^2*d - d^3)*sin(f*x + e)), x)","F",0
32,1,71,0,0.847051," ","integrate((a+b*sin(d*x+c))*(A+B*sin(d*x+c)+C*sin(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, C b \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(2 \, A + C\right)} a + B b\right)} d x - 3 \, {\left(C a + B b\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, {\left(B a + {\left(A + C\right)} b\right)} \cos\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*C*b*cos(d*x + c)^3 + 3*((2*A + C)*a + B*b)*d*x - 3*(C*a + B*b)*cos(d*x + c)*sin(d*x + c) - 6*(B*a + (A + C)*b)*cos(d*x + c))/d","A",0
33,0,0,0,1.164671," ","integrate((a+b*sin(f*x+e))*(A+B*sin(f*x+e)+C*sin(f*x+e)^2)/sin(f*x+e)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(C a + B b\right)} \cos\left(f x + e\right)^{2} - {\left(A + C\right)} a - B b + {\left(C b \cos\left(f x + e\right)^{2} - B a - {\left(A + C\right)} b\right)} \sin\left(f x + e\right)\right)} \sqrt{\sin\left(f x + e\right)}}{\cos\left(f x + e\right)^{2} - 1}, x\right)"," ",0,"integral(((C*a + B*b)*cos(f*x + e)^2 - (A + C)*a - B*b + (C*b*cos(f*x + e)^2 - B*a - (A + C)*b)*sin(f*x + e))*sqrt(sin(f*x + e))/(cos(f*x + e)^2 - 1), x)","F",0
34,0,0,0,4.731476," ","integrate((a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n*(A+B*sin(f*x+e)+C*sin(f*x+e)^2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(C \cos\left(f x + e\right)^{2} - B \sin\left(f x + e\right) - A - C\right)} {\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(C*cos(f*x + e)^2 - B*sin(f*x + e) - A - C)*(b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
