1,1,373,0,0.8407834,"\int (d \sin (e+f x))^n (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]),x]","\frac{a^3 (A (4 n+11)+B (4 n+9)) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) (n+3) \sqrt{\cos ^2(e+f x)}}+\frac{a^3 \left(A \left(4 n^2+21 n+20\right)+B \left(4 n^2+19 n+15\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) (n+4) \sqrt{\cos ^2(e+f x)}}-\frac{a^3 \left(A \left(2 n^2+15 n+28\right)+B \left(2 n^2+14 n+27\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2) (n+3) (n+4)}-\frac{(A (n+4)+B (n+6)) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (d \sin (e+f x))^{n+1}}{d f (n+3) (n+4)}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (d \sin (e+f x))^{n+1}}{d f (n+4)}","\frac{a^3 (A (4 n+11)+B (4 n+9)) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) (n+3) \sqrt{\cos ^2(e+f x)}}+\frac{a^3 \left(A \left(4 n^2+21 n+20\right)+B \left(4 n^2+19 n+15\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) (n+4) \sqrt{\cos ^2(e+f x)}}-\frac{a^3 \left(A \left(2 n^2+15 n+28\right)+B \left(2 n^2+14 n+27\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2) (n+3) (n+4)}-\frac{(A (n+4)+B (n+6)) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (d \sin (e+f x))^{n+1}}{d f (n+3) (n+4)}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (d \sin (e+f x))^{n+1}}{d f (n+4)}",1,"-((a^3*(B*(27 + 14*n + 2*n^2) + A*(28 + 15*n + 2*n^2))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(2 + n)*(3 + n)*(4 + n))) + (a^3*(B*(15 + 19*n + 4*n^2) + A*(20 + 21*n + 4*n^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n)*(4 + n)*Sqrt[Cos[e + f*x]^2]) + (a^3*(B*(9 + 4*n) + A*(11 + 4*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(d^2*f*(2 + n)*(3 + n)*Sqrt[Cos[e + f*x]^2]) - (a*B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*(a + a*Sin[e + f*x])^2)/(d*f*(4 + n)) - ((A*(4 + n) + B*(6 + n))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*(a^3 + a^3*Sin[e + f*x]))/(d*f*(3 + n)*(4 + n))","A",7,5,33,0.1515,1,"{2976, 2968, 3023, 2748, 2643}"
2,1,277,0,0.49217,"\int (d \sin (e+f x))^n (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]),x]","\frac{a^2 (2 A (n+3)+B (2 n+5)) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) (n+3) \sqrt{\cos ^2(e+f x)}}+\frac{a^2 (A (2 n+3)+2 B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{a^2 (A (n+3)+B (n+4)) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2) (n+3)}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (d \sin (e+f x))^{n+1}}{d f (n+3)}","\frac{a^2 (2 A (n+3)+B (2 n+5)) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) (n+3) \sqrt{\cos ^2(e+f x)}}+\frac{a^2 (A (2 n+3)+2 B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{a^2 (A (n+3)+B (n+4)) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2) (n+3)}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (d \sin (e+f x))^{n+1}}{d f (n+3)}",1,"-((a^2*(A*(3 + n) + B*(4 + n))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(2 + n)*(3 + n))) + (a^2*(2*B*(1 + n) + A*(3 + 2*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n)*Sqrt[Cos[e + f*x]^2]) + (a^2*(2*A*(3 + n) + B*(5 + 2*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(d^2*f*(2 + n)*(3 + n)*Sqrt[Cos[e + f*x]^2]) - (B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*(a^2 + a^2*Sin[e + f*x]))/(d*f*(3 + n))","A",6,5,33,0.1515,1,"{2976, 2968, 3023, 2748, 2643}"
3,1,191,0,0.2173217,"\int (d \sin (e+f x))^n (a+a \sin (e+f x)) (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]),x]","\frac{a (A+B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}+\frac{a (A (n+2)+B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{a B \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2)}","\frac{a (A+B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}+\frac{a (A (n+2)+B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{d f (n+1) (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{a B \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (n+2)}",1,"-((a*B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(2 + n))) + (a*(B*(1 + n) + A*(2 + n))*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(d*f*(1 + n)*(2 + n)*Sqrt[Cos[e + f*x]^2]) + (a*(A + B)*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(d^2*f*(2 + n)*Sqrt[Cos[e + f*x]^2])","A",5,4,31,0.1290,1,"{2968, 3023, 2748, 2643}"
4,1,202,0,0.2238972,"\int \frac{(d \sin (e+f x))^n (A+B \sin (e+f x))}{a+a \sin (e+f x)} \, dx","Int[((d*Sin[e + f*x])^n*(A + B*Sin[e + f*x]))/(a + a*Sin[e + f*x]),x]","\frac{(n+1) (A-B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{a d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}+\frac{(-A n+B n+B) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{a d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (a \sin (e+f x)+a)}","\frac{(n+1) (A-B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{a d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}+\frac{(-A n+B n+B) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{a d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (a \sin (e+f x)+a)}",1,"((B - A*n + B*n)*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(a*d*f*(1 + n)*Sqrt[Cos[e + f*x]^2]) + ((A - B)*(1 + n)*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(a*d^2*f*(2 + n)*Sqrt[Cos[e + f*x]^2]) + ((A - B)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(a + a*Sin[e + f*x]))","A",4,3,33,0.09091,1,"{2978, 2748, 2643}"
5,1,279,0,0.4878999,"\int \frac{(d \sin (e+f x))^n (A+B \sin (e+f x))}{(a+a \sin (e+f x))^2} \, dx","Int[((d*Sin[e + f*x])^n*(A + B*Sin[e + f*x]))/(a + a*Sin[e + f*x])^2,x]","\frac{(n+1) (2 A (1-n)+2 B n+B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{3 a^2 d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{n (-2 A n+A+2 B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{3 a^2 d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(2 A (1-n)+2 B n+B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{3 a^2 d f (\sin (e+f x)+1)}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{3 d f (a \sin (e+f x)+a)^2}","\frac{(n+1) (2 A (1-n)+2 B n+B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{3 a^2 d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{n (-2 A n+A+2 B (n+1)) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{3 a^2 d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(2 A (1-n)+2 B n+B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{3 a^2 d f (\sin (e+f x)+1)}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{3 d f (a \sin (e+f x)+a)^2}",1,"-(n*(A - 2*A*n + 2*B*(1 + n))*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(3*a^2*d*f*(1 + n)*Sqrt[Cos[e + f*x]^2]) + ((1 + n)*(B + 2*A*(1 - n) + 2*B*n)*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(3*a^2*d^2*f*(2 + n)*Sqrt[Cos[e + f*x]^2]) + ((B + 2*A*(1 - n) + 2*B*n)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(3*a^2*d*f*(1 + Sin[e + f*x])) + ((A - B)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(3*d*f*(a + a*Sin[e + f*x])^2)","A",5,3,33,0.09091,1,"{2978, 2748, 2643}"
6,1,362,0,0.8461868,"\int \frac{(d \sin (e+f x))^n (A+B \sin (e+f x))}{(a+a \sin (e+f x))^3} \, dx","Int[((d*Sin[e + f*x])^n*(A + B*Sin[e + f*x]))/(a + a*Sin[e + f*x])^3,x]","\frac{(1-n) (n+1) (-4 A n+7 A+4 B n+3 B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{15 a^3 d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{n \left(A \left(4 n^2-9 n+2\right)+B \left(-4 n^2-n+3\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{15 a^3 d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(1-n) (-4 A n+7 A+4 B n+3 B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{15 d f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{(A (5-2 n)+2 B n) \cos (e+f x) (d \sin (e+f x))^{n+1}}{15 a d f (a \sin (e+f x)+a)^2}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{5 d f (a \sin (e+f x)+a)^3}","\frac{(1-n) (n+1) (-4 A n+7 A+4 B n+3 B) \cos (e+f x) (d \sin (e+f x))^{n+2} \, _2F_1\left(\frac{1}{2},\frac{n+2}{2};\frac{n+4}{2};\sin ^2(e+f x)\right)}{15 a^3 d^2 f (n+2) \sqrt{\cos ^2(e+f x)}}-\frac{n \left(A \left(4 n^2-9 n+2\right)+B \left(-4 n^2-n+3\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1} \, _2F_1\left(\frac{1}{2},\frac{n+1}{2};\frac{n+3}{2};\sin ^2(e+f x)\right)}{15 a^3 d f (n+1) \sqrt{\cos ^2(e+f x)}}+\frac{(1-n) (-4 A n+7 A+4 B n+3 B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{15 d f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{(A (5-2 n)+2 B n) \cos (e+f x) (d \sin (e+f x))^{n+1}}{15 a d f (a \sin (e+f x)+a)^2}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{5 d f (a \sin (e+f x)+a)^3}",1,"-(n*(B*(3 - n - 4*n^2) + A*(2 - 9*n + 4*n^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, (1 + n)/2, (3 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(1 + n))/(15*a^3*d*f*(1 + n)*Sqrt[Cos[e + f*x]^2]) + ((1 - n)*(1 + n)*(7*A + 3*B - 4*A*n + 4*B*n)*Cos[e + f*x]*Hypergeometric2F1[1/2, (2 + n)/2, (4 + n)/2, Sin[e + f*x]^2]*(d*Sin[e + f*x])^(2 + n))/(15*a^3*d^2*f*(2 + n)*Sqrt[Cos[e + f*x]^2]) + ((A - B)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(5*d*f*(a + a*Sin[e + f*x])^3) + ((A*(5 - 2*n) + 2*B*n)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(15*a*d*f*(a + a*Sin[e + f*x])^2) + ((1 - n)*(7*A + 3*B - 4*A*n + 4*B*n)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(15*d*f*(a^3 + a^3*Sin[e + f*x]))","A",6,3,33,0.09091,1,"{2978, 2748, 2643}"
7,1,336,0,0.8718633,"\int (d \sin (e+f x))^n (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]),x]","-\frac{2 a^3 \left(A \left(32 n^3+224 n^2+478 n+301\right)+2 B \left(16 n^3+104 n^2+203 n+115\right)\right) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) (2 n+5) (2 n+7) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(A \left(8 n^2+50 n+77\right)+2 B \left(4 n^2+23 n+35\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) (2 n+5) (2 n+7) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A (2 n+7)+2 B (n+5)) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (d \sin (e+f x))^{n+1}}{d f (2 n+5) (2 n+7)}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (d \sin (e+f x))^{n+1}}{d f (2 n+7)}","-\frac{2 a^3 \left(A \left(32 n^3+224 n^2+478 n+301\right)+2 B \left(16 n^3+104 n^2+203 n+115\right)\right) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) (2 n+5) (2 n+7) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(A \left(8 n^2+50 n+77\right)+2 B \left(4 n^2+23 n+35\right)\right) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) (2 n+5) (2 n+7) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A (2 n+7)+2 B (n+5)) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (d \sin (e+f x))^{n+1}}{d f (2 n+5) (2 n+7)}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (d \sin (e+f x))^{n+1}}{d f (2 n+7)}",1,"(-2*a^3*(2*B*(115 + 203*n + 104*n^2 + 16*n^3) + A*(301 + 478*n + 224*n^2 + 32*n^3))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - Sin[e + f*x]]*(d*Sin[e + f*x])^n)/(f*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]]) - (2*a^3*(2*B*(35 + 23*n + 4*n^2) + A*(77 + 50*n + 8*n^2))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*Sqrt[a + a*Sin[e + f*x]]) - (2*a^2*(2*B*(5 + n) + A*(7 + 2*n))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*Sqrt[a + a*Sin[e + f*x]])/(d*f*(5 + 2*n)*(7 + 2*n)) - (2*a*B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*(a + a*Sin[e + f*x])^(3/2))/(d*f*(7 + 2*n))","A",6,5,35,0.1429,1,"{2976, 2981, 2776, 67, 65}"
8,1,229,0,0.4935891,"\int (d \sin (e+f x))^n (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]),x]","-\frac{2 a^2 \left(A \left(8 n^2+30 n+25\right)+2 B \left(4 n^2+13 n+9\right)\right) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A (2 n+5)+2 B (n+3)) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (d \sin (e+f x))^{n+1}}{d f (2 n+5)}","-\frac{2 a^2 \left(A \left(8 n^2+30 n+25\right)+2 B \left(4 n^2+13 n+9\right)\right) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A (2 n+5)+2 B (n+3)) \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (d \sin (e+f x))^{n+1}}{d f (2 n+5)}",1,"(-2*a^2*(2*B*(9 + 13*n + 4*n^2) + A*(25 + 30*n + 8*n^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - Sin[e + f*x]]*(d*Sin[e + f*x])^n)/(f*(3 + 2*n)*(5 + 2*n)*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]]) - (2*a^2*(2*B*(3 + n) + A*(5 + 2*n))*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(3 + 2*n)*(5 + 2*n)*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n)*Sqrt[a + a*Sin[e + f*x]])/(d*f*(5 + 2*n))","A",5,5,35,0.1429,1,"{2976, 2981, 2776, 67, 65}"
9,1,137,0,0.2130689,"\int (d \sin (e+f x))^n \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]),x]","-\frac{2 a (A (2 n+3)+2 B (n+1)) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}","-\frac{2 a (A (2 n+3)+2 B (n+1)) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) (d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}",1,"(-2*a*(2*B*(1 + n) + A*(3 + 2*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - Sin[e + f*x]]*(d*Sin[e + f*x])^n)/(f*(3 + 2*n)*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(d*f*(3 + 2*n)*Sqrt[a + a*Sin[e + f*x]])","A",4,4,35,0.1143,1,"{2981, 2776, 67, 65}"
10,1,152,0,0.3961665,"\int \frac{(d \sin (e+f x))^n (A+B \sin (e+f x))}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((d*Sin[e + f*x])^n*(A + B*Sin[e + f*x]))/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{(A-B) \cos (e+f x) \sin ^{-n}(e+f x) F_1\left(\frac{1}{2};-n,1;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right) (d \sin (e+f x))^n}{f \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f \sqrt{a \sin (e+f x)+a}}","-\frac{(A-B) \cos (e+f x) \sin ^{-n}(e+f x) F_1\left(\frac{1}{2};-n,1;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right) (d \sin (e+f x))^n}{f \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{f \sqrt{a \sin (e+f x)+a}}",1,"-(((A - B)*AppellF1[1/2, -n, 1, 3/2, 1 - Sin[e + f*x], (1 - Sin[e + f*x])/2]*Cos[e + f*x]*(d*Sin[e + f*x])^n)/(f*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]])) - (2*B*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - Sin[e + f*x]]*(d*Sin[e + f*x])^n)/(f*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]])","A",9,9,35,0.2571,1,"{2987, 2787, 2786, 2785, 130, 429, 2776, 67, 65}"
11,1,226,0,0.6749208,"\int \frac{(d \sin (e+f x))^n (A+B \sin (e+f x))}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((d*Sin[e + f*x])^n*(A + B*Sin[e + f*x]))/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{(-4 A n+A+B (4 n+3)) \cos (e+f x) \sin ^{-n}(e+f x) F_1\left(\frac{1}{2};-n,1;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right) (d \sin (e+f x))^n}{4 a f \sqrt{a \sin (e+f x)+a}}-\frac{(2 n+1) (A-B) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{2 a f \sqrt{a \sin (e+f x)+a}}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{2 d f (a \sin (e+f x)+a)^{3/2}}","-\frac{(-4 A n+A+B (4 n+3)) \cos (e+f x) \sin ^{-n}(e+f x) F_1\left(\frac{1}{2};-n,1;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right) (d \sin (e+f x))^n}{4 a f \sqrt{a \sin (e+f x)+a}}-\frac{(2 n+1) (A-B) \cos (e+f x) \sin ^{-n}(e+f x) (d \sin (e+f x))^n \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};1-\sin (e+f x)\right)}{2 a f \sqrt{a \sin (e+f x)+a}}+\frac{(A-B) \cos (e+f x) (d \sin (e+f x))^{n+1}}{2 d f (a \sin (e+f x)+a)^{3/2}}",1,"((A - B)*Cos[e + f*x]*(d*Sin[e + f*x])^(1 + n))/(2*d*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - 4*A*n + B*(3 + 4*n))*AppellF1[1/2, -n, 1, 3/2, 1 - Sin[e + f*x], (1 - Sin[e + f*x])/2]*Cos[e + f*x]*(d*Sin[e + f*x])^n)/(4*a*f*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*(1 + 2*n)*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, 1 - Sin[e + f*x]]*(d*Sin[e + f*x])^n)/(2*a*f*Sin[e + f*x]^n*Sqrt[a + a*Sin[e + f*x]])","A",10,10,35,0.2857,1,"{2978, 2987, 2787, 2786, 2785, 130, 429, 2776, 67, 65}"
12,1,221,0,0.4533017,"\int (d \sin (e+f x))^n (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \, dx","Int[(d*Sin[e + f*x])^n*(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]),x]","-\frac{2^{m+\frac{1}{2}} (A-B) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} \sin ^{-n}(e+f x) (a \sin (e+f x)+a)^m (d \sin (e+f x))^n F_1\left(\frac{1}{2};-n,\frac{1}{2}-m;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right)}{f}-\frac{B 2^{m+\frac{3}{2}} \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} \sin ^{-n}(e+f x) (a \sin (e+f x)+a)^m (d \sin (e+f x))^n F_1\left(\frac{1}{2};-n,-m-\frac{1}{2};\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right)}{f}","-\frac{2^{m+\frac{1}{2}} (A-B) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} \sin ^{-n}(e+f x) (a \sin (e+f x)+a)^m (d \sin (e+f x))^n F_1\left(\frac{1}{2};-n,\frac{1}{2}-m;\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right)}{f}-\frac{B 2^{m+\frac{3}{2}} \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} \sin ^{-n}(e+f x) (a \sin (e+f x)+a)^m (d \sin (e+f x))^n F_1\left(\frac{1}{2};-n,-m-\frac{1}{2};\frac{3}{2};1-\sin (e+f x),\frac{1}{2} (1-\sin (e+f x))\right)}{f}",1,"-((2^(3/2 + m)*B*AppellF1[1/2, -n, -1/2 - m, 3/2, 1 - Sin[e + f*x], (1 - Sin[e + f*x])/2]*Cos[e + f*x]*(d*Sin[e + f*x])^n*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*Sin[e + f*x]^n)) - (2^(1/2 + m)*(A - B)*AppellF1[1/2, -n, 1/2 - m, 3/2, 1 - Sin[e + f*x], (1 - Sin[e + f*x])/2]*Cos[e + f*x]*(d*Sin[e + f*x])^n*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*Sin[e + f*x]^n)","A",9,5,33,0.1515,1,"{2987, 2787, 2786, 2785, 133}"
13,1,114,0,0.1559015,"\int (d \sin (e+f x))^n (a-a \sin (e+f x)) (a+a \sin (e+f x))^m \, dx","Int[(d*Sin[e + f*x])^n*(a - a*Sin[e + f*x])*(a + a*Sin[e + f*x])^m,x]","\frac{\sec (e+f x) (a-a \sin (e+f x)) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^m (d \sin (e+f x))^{n+1} F_1\left(n+1;-\frac{1}{2},\frac{1}{2}-m;n+2;\sin (e+f x),-\sin (e+f x)\right)}{d f (n+1) \sqrt{1-\sin (e+f x)}}","\frac{\sec (e+f x) (a-a \sin (e+f x)) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^m (d \sin (e+f x))^{n+1} F_1\left(n+1;-\frac{1}{2},\frac{1}{2}-m;n+2;\sin (e+f x),-\sin (e+f x)\right)}{d f (n+1) \sqrt{1-\sin (e+f x)}}",1,"(AppellF1[1 + n, -1/2, 1/2 - m, 2 + n, Sin[e + f*x], -Sin[e + f*x]]*Sec[e + f*x]*(d*Sin[e + f*x])^(1 + n)*(1 + Sin[e + f*x])^(1/2 - m)*(a - a*Sin[e + f*x])*(a + a*Sin[e + f*x])^m)/(d*f*(1 + n)*Sqrt[1 - Sin[e + f*x]])","A",4,3,34,0.08824,1,"{3008, 135, 133}"
14,1,37,0,0.1194673,"\int \sin ^n(c+d x) (a+a \sin (c+d x))^{-2-n} (-1-n-(-2-n) \sin (c+d x)) \, dx","Int[Sin[c + d*x]^n*(a + a*Sin[c + d*x])^(-2 - n)*(-1 - n - (-2 - n)*Sin[c + d*x]),x]","-\frac{\cos (c+d x) \sin ^{n+1}(c+d x) (a \sin (c+d x)+a)^{-n-2}}{d}","-\frac{\cos (c+d x) \sin ^{n+1}(c+d x) (a \sin (c+d x)+a)^{-n-2}}{d}",1,"-((Cos[c + d*x]*Sin[c + d*x]^(1 + n)*(a + a*Sin[c + d*x])^(-2 - n))/d)","A",1,1,43,0.02326,1,"{2974}"
15,1,35,0,0.0944697,"\int \sin ^{-2-m}(c+d x) (a+a \sin (c+d x))^m (1+m-m \sin (c+d x)) \, dx","Int[Sin[c + d*x]^(-2 - m)*(a + a*Sin[c + d*x])^m*(1 + m - m*Sin[c + d*x]),x]","-\frac{\cos (c+d x) \sin ^{-m-1}(c+d x) (a \sin (c+d x)+a)^m}{d}","-\frac{\cos (c+d x) \sin ^{-m-1}(c+d x) (a \sin (c+d x)+a)^m}{d}",1,"-((Cos[c + d*x]*Sin[c + d*x]^(-1 - m)*(a + a*Sin[c + d*x])^m)/d)","A",1,1,37,0.02703,1,"{2974}"
16,1,153,0,0.3934576,"\int \frac{\sin ^2(e+f x) (A+B \sin (e+f x))}{(a+b \sin (e+f x))^2} \, dx","Int[(Sin[e + f*x]^2*(A + B*Sin[e + f*x]))/(a + b*Sin[e + f*x])^2,x]","-\frac{2 a \left(a^2 A b-2 a^3 B+3 a b^2 B-2 A b^3\right) \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (e+f x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^3 f \left(a^2-b^2\right)^{3/2}}+\frac{a^2 (A b-a B) \cos (e+f x)}{b^2 f \left(a^2-b^2\right) (a+b \sin (e+f x))}+\frac{x (A b-2 a B)}{b^3}-\frac{B \cos (e+f x)}{b^2 f}","-\frac{2 a \left(a^2 A b-2 a^3 B+3 a b^2 B-2 A b^3\right) \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (e+f x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^3 f \left(a^2-b^2\right)^{3/2}}+\frac{a^2 (A b-a B) \cos (e+f x)}{b^2 f \left(a^2-b^2\right) (a+b \sin (e+f x))}+\frac{x (A b-2 a B)}{b^3}-\frac{B \cos (e+f x)}{b^2 f}",1,"((A*b - 2*a*B)*x)/b^3 - (2*a*(a^2*A*b - 2*A*b^3 - 2*a^3*B + 3*a*b^2*B)*ArcTan[(b + a*Tan[(e + f*x)/2])/Sqrt[a^2 - b^2]])/(b^3*(a^2 - b^2)^(3/2)*f) - (B*Cos[e + f*x])/(b^2*f) + (a^2*(A*b - a*B)*Cos[e + f*x])/(b^2*(a^2 - b^2)*f*(a + b*Sin[e + f*x]))","A",6,6,31,0.1935,1,"{2988, 3023, 2735, 2660, 618, 204}"
17,1,182,0,0.2950741,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^4 \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4,x]","\frac{7 a c^4 (2 A-B) \cos ^3(e+f x)}{24 f}+\frac{a (2 A-B) \cos ^3(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^2}{10 f}+\frac{7 a (2 A-B) \cos ^3(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{40 f}+\frac{7 a c^4 (2 A-B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{7}{16} a c^4 x (2 A-B)-\frac{a B c \cos ^3(e+f x) (c-c \sin (e+f x))^3}{6 f}","\frac{7 a c^4 (2 A-B) \cos ^3(e+f x)}{24 f}+\frac{a (2 A-B) \cos ^3(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^2}{10 f}+\frac{7 a (2 A-B) \cos ^3(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{40 f}+\frac{7 a c^4 (2 A-B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{7}{16} a c^4 x (2 A-B)-\frac{a B c \cos ^3(e+f x) (c-c \sin (e+f x))^3}{6 f}",1,"(7*a*(2*A - B)*c^4*x)/16 + (7*a*(2*A - B)*c^4*Cos[e + f*x]^3)/(24*f) + (7*a*(2*A - B)*c^4*Cos[e + f*x]*Sin[e + f*x])/(16*f) - (a*B*c*Cos[e + f*x]^3*(c - c*Sin[e + f*x])^3)/(6*f) + (a*(2*A - B)*Cos[e + f*x]^3*(c^2 - c^2*Sin[e + f*x])^2)/(10*f) + (7*a*(2*A - B)*Cos[e + f*x]^3*(c^4 - c^4*Sin[e + f*x]))/(40*f)","A",7,6,34,0.1765,1,"{2967, 2860, 2678, 2669, 2635, 8}"
18,1,142,0,0.2499617,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3,x]","\frac{a c^3 (5 A-2 B) \cos ^3(e+f x)}{12 f}+\frac{a (5 A-2 B) \cos ^3(e+f x) \left(c^3-c^3 \sin (e+f x)\right)}{20 f}+\frac{a c^3 (5 A-2 B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a c^3 x (5 A-2 B)-\frac{a B c \cos ^3(e+f x) (c-c \sin (e+f x))^2}{5 f}","\frac{a c^3 (5 A-2 B) \cos ^3(e+f x)}{12 f}+\frac{a (5 A-2 B) \cos ^3(e+f x) \left(c^3-c^3 \sin (e+f x)\right)}{20 f}+\frac{a c^3 (5 A-2 B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a c^3 x (5 A-2 B)-\frac{a B c \cos ^3(e+f x) (c-c \sin (e+f x))^2}{5 f}",1,"(a*(5*A - 2*B)*c^3*x)/8 + (a*(5*A - 2*B)*c^3*Cos[e + f*x]^3)/(12*f) + (a*(5*A - 2*B)*c^3*Cos[e + f*x]*Sin[e + f*x])/(8*f) - (a*B*c*Cos[e + f*x]^3*(c - c*Sin[e + f*x])^2)/(5*f) + (a*(5*A - 2*B)*Cos[e + f*x]^3*(c^3 - c^3*Sin[e + f*x]))/(20*f)","A",6,6,34,0.1765,1,"{2967, 2860, 2678, 2669, 2635, 8}"
19,1,105,0,0.1863523,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2,x]","\frac{a c^2 (4 A-B) \cos ^3(e+f x)}{12 f}+\frac{a c^2 (4 A-B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a c^2 x (4 A-B)-\frac{a B \cos ^3(e+f x) \left(c^2-c^2 \sin (e+f x)\right)}{4 f}","\frac{a c^2 (A-B) \cos ^3(e+f x)}{3 f}+\frac{a c^2 (4 A-B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a c^2 x (4 A-B)+\frac{a B c^2 \sin (e+f x) \cos ^3(e+f x)}{4 f}",1,"(a*(4*A - B)*c^2*x)/8 + (a*(4*A - B)*c^2*Cos[e + f*x]^3)/(12*f) + (a*(4*A - B)*c^2*Cos[e + f*x]*Sin[e + f*x])/(8*f) - (a*B*Cos[e + f*x]^3*(c^2 - c^2*Sin[e + f*x]))/(4*f)","A",5,5,34,0.1471,1,"{2967, 2860, 2669, 2635, 8}"
20,1,49,0,0.0826031,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]),x]","\frac{a A c \sin (e+f x) \cos (e+f x)}{2 f}+\frac{1}{2} a A c x-\frac{a B c \cos ^3(e+f x)}{3 f}","\frac{a A c \sin (e+f x) \cos (e+f x)}{2 f}+\frac{1}{2} a A c x-\frac{a B c \cos ^3(e+f x)}{3 f}",1,"(a*A*c*x)/2 - (a*B*c*Cos[e + f*x]^3)/(3*f) + (a*A*c*Cos[e + f*x]*Sin[e + f*x])/(2*f)","A",4,4,32,0.1250,1,"{2967, 2669, 2635, 8}"
21,1,56,0,0.1694624,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{c-c \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x]),x]","\frac{2 a (A+B) \cos (e+f x)}{f (c-c \sin (e+f x))}-\frac{a x (A+2 B)}{c}+\frac{a B \cos (e+f x)}{c f}","\frac{2 a (A+B) \cos (e+f x)}{f (c-c \sin (e+f x))}-\frac{a x (A+2 B)}{c}+\frac{a B \cos (e+f x)}{c f}",1,"-((a*(A + 2*B)*x)/c) + (a*B*Cos[e + f*x])/(c*f) + (2*a*(A + B)*Cos[e + f*x])/(f*(c - c*Sin[e + f*x]))","A",4,3,34,0.08824,1,"{2967, 2857, 2638}"
22,1,72,0,0.2245782,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^2,x]","-\frac{a (A+7 B) \cos (e+f x)}{3 c^2 f (1-\sin (e+f x))}+\frac{2 a (A+B) \cos (e+f x)}{3 f (c-c \sin (e+f x))^2}+\frac{a B x}{c^2}","-\frac{a (A+7 B) \cos (e+f x)}{3 c^2 f (1-\sin (e+f x))}+\frac{2 a (A+B) \cos (e+f x)}{3 f (c-c \sin (e+f x))^2}+\frac{a B x}{c^2}",1,"(a*B*x)/c^2 - (a*(A + 7*B)*Cos[e + f*x])/(3*c^2*f*(1 - Sin[e + f*x])) + (2*a*(A + B)*Cos[e + f*x])/(3*f*(c - c*Sin[e + f*x])^2)","A",4,4,34,0.1176,1,"{2967, 2857, 2735, 2648}"
23,1,104,0,0.2374881,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^3,x]","-\frac{a (A-4 B) \cos (e+f x)}{15 f \left(c^3-c^3 \sin (e+f x)\right)}-\frac{a c (A+11 B) \cos (e+f x)}{15 f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{2 a (A+B) \cos (e+f x)}{5 f (c-c \sin (e+f x))^3}","-\frac{a (A-4 B) \cos (e+f x)}{15 f \left(c^3-c^3 \sin (e+f x)\right)}-\frac{a c (A+11 B) \cos (e+f x)}{15 f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{2 a (A+B) \cos (e+f x)}{5 f (c-c \sin (e+f x))^3}",1,"(2*a*(A + B)*Cos[e + f*x])/(5*f*(c - c*Sin[e + f*x])^3) - (a*(A + 11*B)*c*Cos[e + f*x])/(15*f*(c^2 - c^2*Sin[e + f*x])^2) - (a*(A - 4*B)*Cos[e + f*x])/(15*f*(c^3 - c^3*Sin[e + f*x]))","A",4,4,34,0.1176,1,"{2967, 2857, 2750, 2648}"
24,1,142,0,0.2854451,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^4} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^4,x]","-\frac{a (2 A-5 B) \cos (e+f x)}{105 f \left(c^4-c^4 \sin (e+f x)\right)}-\frac{a (2 A-5 B) \cos (e+f x)}{105 f \left(c^2-c^2 \sin (e+f x)\right)^2}-\frac{a (A+15 B) \cos (e+f x)}{35 c f (c-c \sin (e+f x))^3}+\frac{2 a (A+B) \cos (e+f x)}{7 f (c-c \sin (e+f x))^4}","-\frac{a (2 A-5 B) \cos (e+f x)}{105 f \left(c^4-c^4 \sin (e+f x)\right)}-\frac{a (2 A-5 B) \cos (e+f x)}{105 f \left(c^2-c^2 \sin (e+f x)\right)^2}-\frac{a (A+15 B) \cos (e+f x)}{35 c f (c-c \sin (e+f x))^3}+\frac{2 a (A+B) \cos (e+f x)}{7 f (c-c \sin (e+f x))^4}",1,"(2*a*(A + B)*Cos[e + f*x])/(7*f*(c - c*Sin[e + f*x])^4) - (a*(A + 15*B)*Cos[e + f*x])/(35*c*f*(c - c*Sin[e + f*x])^3) - (a*(2*A - 5*B)*Cos[e + f*x])/(105*f*(c^2 - c^2*Sin[e + f*x])^2) - (a*(2*A - 5*B)*Cos[e + f*x])/(105*f*(c^4 - c^4*Sin[e + f*x]))","A",5,5,34,0.1471,1,"{2967, 2857, 2750, 2650, 2648}"
25,1,176,0,0.3070727,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^5} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^5,x]","-\frac{2 a (A-2 B) \cos (e+f x)}{315 f \left(c^5-c^5 \sin (e+f x)\right)}-\frac{2 a c (A-2 B) \cos (e+f x)}{315 f \left(c^3-c^3 \sin (e+f x)\right)^2}-\frac{a c (A-2 B) \cos (e+f x)}{105 f \left(c^2-c^2 \sin (e+f x)\right)^3}-\frac{a (A+19 B) \cos (e+f x)}{63 c f (c-c \sin (e+f x))^4}+\frac{2 a (A+B) \cos (e+f x)}{9 f (c-c \sin (e+f x))^5}","-\frac{2 a (A-2 B) \cos (e+f x)}{315 f \left(c^5-c^5 \sin (e+f x)\right)}-\frac{2 a c (A-2 B) \cos (e+f x)}{315 f \left(c^3-c^3 \sin (e+f x)\right)^2}-\frac{a c (A-2 B) \cos (e+f x)}{105 f \left(c^2-c^2 \sin (e+f x)\right)^3}-\frac{a (A+19 B) \cos (e+f x)}{63 c f (c-c \sin (e+f x))^4}+\frac{2 a (A+B) \cos (e+f x)}{9 f (c-c \sin (e+f x))^5}",1,"(2*a*(A + B)*Cos[e + f*x])/(9*f*(c - c*Sin[e + f*x])^5) - (a*(A + 19*B)*Cos[e + f*x])/(63*c*f*(c - c*Sin[e + f*x])^4) - (a*(A - 2*B)*c*Cos[e + f*x])/(105*f*(c^2 - c^2*Sin[e + f*x])^3) - (2*a*(A - 2*B)*c*Cos[e + f*x])/(315*f*(c^3 - c^3*Sin[e + f*x])^2) - (2*a*(A - 2*B)*Cos[e + f*x])/(315*f*(c^5 - c^5*Sin[e + f*x]))","A",6,5,34,0.1471,1,"{2967, 2857, 2750, 2650, 2648}"
26,1,229,0,0.3679152,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^5 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^5,x]","\frac{3 a^2 c^5 (8 A-3 B) \cos ^5(e+f x)}{80 f}+\frac{3 a^2 c^5 (8 A-3 B) \sin (e+f x) \cos ^3(e+f x)}{64 f}+\frac{a^2 c^3 (8 A-3 B) \cos ^5(e+f x) (c-c \sin (e+f x))^2}{56 f}+\frac{3 a^2 (8 A-3 B) \cos ^5(e+f x) \left(c^5-c^5 \sin (e+f x)\right)}{112 f}+\frac{9 a^2 c^5 (8 A-3 B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{9}{128} a^2 c^5 x (8 A-3 B)-\frac{a^2 B c^2 \cos ^5(e+f x) (c-c \sin (e+f x))^3}{8 f}","\frac{3 a^2 c^5 (8 A-3 B) \cos ^5(e+f x)}{80 f}+\frac{3 a^2 c^5 (8 A-3 B) \sin (e+f x) \cos ^3(e+f x)}{64 f}+\frac{a^2 c^3 (8 A-3 B) \cos ^5(e+f x) (c-c \sin (e+f x))^2}{56 f}+\frac{3 a^2 (8 A-3 B) \cos ^5(e+f x) \left(c^5-c^5 \sin (e+f x)\right)}{112 f}+\frac{9 a^2 c^5 (8 A-3 B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{9}{128} a^2 c^5 x (8 A-3 B)-\frac{a^2 B c^2 \cos ^5(e+f x) (c-c \sin (e+f x))^3}{8 f}",1,"(9*a^2*(8*A - 3*B)*c^5*x)/128 + (3*a^2*(8*A - 3*B)*c^5*Cos[e + f*x]^5)/(80*f) + (9*a^2*(8*A - 3*B)*c^5*Cos[e + f*x]*Sin[e + f*x])/(128*f) + (3*a^2*(8*A - 3*B)*c^5*Cos[e + f*x]^3*Sin[e + f*x])/(64*f) + (a^2*(8*A - 3*B)*c^3*Cos[e + f*x]^5*(c - c*Sin[e + f*x])^2)/(56*f) - (a^2*B*c^2*Cos[e + f*x]^5*(c - c*Sin[e + f*x])^3)/(8*f) + (3*a^2*(8*A - 3*B)*Cos[e + f*x]^5*(c^5 - c^5*Sin[e + f*x]))/(112*f)","A",8,6,36,0.1667,1,"{2967, 2860, 2678, 2669, 2635, 8}"
27,1,189,0,0.2960356,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^4 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4,x]","\frac{a^2 c^4 (7 A-2 B) \cos ^5(e+f x)}{30 f}+\frac{a^2 (7 A-2 B) \cos ^5(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{42 f}+\frac{a^2 c^4 (7 A-2 B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^2 c^4 (7 A-2 B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^2 c^4 x (7 A-2 B)-\frac{a^2 B \cos ^5(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^2}{7 f}","\frac{a^2 c^4 (7 A-2 B) \cos ^5(e+f x)}{30 f}+\frac{a^2 (7 A-2 B) \cos ^5(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{42 f}+\frac{a^2 c^4 (7 A-2 B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^2 c^4 (7 A-2 B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^2 c^4 x (7 A-2 B)-\frac{a^2 B \cos ^5(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^2}{7 f}",1,"(a^2*(7*A - 2*B)*c^4*x)/16 + (a^2*(7*A - 2*B)*c^4*Cos[e + f*x]^5)/(30*f) + (a^2*(7*A - 2*B)*c^4*Cos[e + f*x]*Sin[e + f*x])/(16*f) + (a^2*(7*A - 2*B)*c^4*Cos[e + f*x]^3*Sin[e + f*x])/(24*f) - (a^2*B*Cos[e + f*x]^5*(c^2 - c^2*Sin[e + f*x])^2)/(7*f) + (a^2*(7*A - 2*B)*Cos[e + f*x]^5*(c^4 - c^4*Sin[e + f*x]))/(42*f)","A",7,6,36,0.1667,1,"{2967, 2860, 2678, 2669, 2635, 8}"
28,1,147,0,0.2164626,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3,x]","\frac{a^2 c^3 (6 A-B) \cos ^5(e+f x)}{30 f}+\frac{a^2 c^3 (6 A-B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^2 c^3 (6 A-B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^2 c^3 x (6 A-B)-\frac{a^2 B \cos ^5(e+f x) \left(c^3-c^3 \sin (e+f x)\right)}{6 f}","\frac{a^2 c^3 (6 A-B) \cos ^5(e+f x)}{30 f}+\frac{a^2 c^3 (6 A-B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^2 c^3 (6 A-B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^2 c^3 x (6 A-B)-\frac{a^2 B \cos ^5(e+f x) \left(c^3-c^3 \sin (e+f x)\right)}{6 f}",1,"(a^2*(6*A - B)*c^3*x)/16 + (a^2*(6*A - B)*c^3*Cos[e + f*x]^5)/(30*f) + (a^2*(6*A - B)*c^3*Cos[e + f*x]*Sin[e + f*x])/(16*f) + (a^2*(6*A - B)*c^3*Cos[e + f*x]^3*Sin[e + f*x])/(24*f) - (a^2*B*Cos[e + f*x]^5*(c^3 - c^3*Sin[e + f*x]))/(6*f)","A",6,5,36,0.1389,1,"{2967, 2860, 2669, 2635, 8}"
29,1,89,0,0.1368761,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2,x]","\frac{a^2 A c^2 \sin (e+f x) \cos ^3(e+f x)}{4 f}+\frac{3 a^2 A c^2 \sin (e+f x) \cos (e+f x)}{8 f}+\frac{3}{8} a^2 A c^2 x-\frac{a^2 B c^2 \cos ^5(e+f x)}{5 f}","\frac{a^2 A c^2 \sin (e+f x) \cos ^3(e+f x)}{4 f}+\frac{3 a^2 A c^2 \sin (e+f x) \cos (e+f x)}{8 f}+\frac{3}{8} a^2 A c^2 x-\frac{a^2 B c^2 \cos ^5(e+f x)}{5 f}",1,"(3*a^2*A*c^2*x)/8 - (a^2*B*c^2*Cos[e + f*x]^5)/(5*f) + (3*a^2*A*c^2*Cos[e + f*x]*Sin[e + f*x])/(8*f) + (a^2*A*c^2*Cos[e + f*x]^3*Sin[e + f*x])/(4*f)","A",5,4,36,0.1111,1,"{2967, 2669, 2635, 8}"
30,1,98,0,0.1489191,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]),x]","-\frac{a^2 c (4 A+B) \cos ^3(e+f x)}{12 f}+\frac{a^2 c (4 A+B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a^2 c x (4 A+B)-\frac{B c \cos ^3(e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{4 f}","-\frac{a^2 c (4 A+B) \cos ^3(e+f x)}{12 f}+\frac{a^2 c (4 A+B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a^2 c x (4 A+B)-\frac{B c \cos ^3(e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{4 f}",1,"(a^2*(4*A + B)*c*x)/8 - (a^2*(4*A + B)*c*Cos[e + f*x]^3)/(12*f) + (a^2*(4*A + B)*c*Cos[e + f*x]*Sin[e + f*x])/(8*f) - (B*c*Cos[e + f*x]^3*(a^2 + a^2*Sin[e + f*x]))/(4*f)","A",5,5,34,0.1471,1,"{2967, 2860, 2669, 2635, 8}"
31,1,117,0,0.2885448,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{c-c \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x]),x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{f (c-c \sin (e+f x))^3}+\frac{3 a^2 (2 A+3 B) \cos (e+f x)}{2 c f}+\frac{a^2 (2 A+3 B) \cos ^3(e+f x)}{2 f (c-c \sin (e+f x))}-\frac{3 a^2 x (2 A+3 B)}{2 c}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{f (c-c \sin (e+f x))^3}+\frac{3 a^2 (2 A+3 B) \cos (e+f x)}{2 c f}+\frac{a^2 (2 A+3 B) \cos ^3(e+f x)}{2 f (c-c \sin (e+f x))}-\frac{3 a^2 x (2 A+3 B)}{2 c}",1,"(-3*a^2*(2*A + 3*B)*x)/(2*c) + (3*a^2*(2*A + 3*B)*Cos[e + f*x])/(2*c*f) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(f*(c - c*Sin[e + f*x])^3) + (a^2*(2*A + 3*B)*Cos[e + f*x]^3)/(2*f*(c - c*Sin[e + f*x]))","A",5,5,36,0.1389,1,"{2967, 2859, 2679, 2682, 8}"
32,1,109,0,0.283956,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^2,x]","-\frac{a^2 (A+4 B) \cos (e+f x)}{c^2 f}+\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{3 f (c-c \sin (e+f x))^4}+\frac{a^2 x (A+4 B)}{c^2}-\frac{2 a^2 (A+4 B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^2}","-\frac{a^2 (A+4 B) \cos (e+f x)}{c^2 f}+\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{3 f (c-c \sin (e+f x))^4}+\frac{a^2 x (A+4 B)}{c^2}-\frac{2 a^2 (A+4 B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^2}",1,"(a^2*(A + 4*B)*x)/c^2 - (a^2*(A + 4*B)*Cos[e + f*x])/(c^2*f) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(3*f*(c - c*Sin[e + f*x])^4) - (2*a^2*(A + 4*B)*Cos[e + f*x]^3)/(3*f*(c - c*Sin[e + f*x])^2)","A",5,5,36,0.1389,1,"{2967, 2859, 2680, 2682, 8}"
33,1,112,0,0.2770269,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^3,x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^5}+\frac{2 a^2 B \cos (e+f x)}{f \left(c^3-c^3 \sin (e+f x)\right)}-\frac{a^2 B x}{c^3}-\frac{2 a^2 B \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^3}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^5}+\frac{2 a^2 B \cos (e+f x)}{f \left(c^3-c^3 \sin (e+f x)\right)}-\frac{a^2 B x}{c^3}-\frac{2 a^2 B \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^3}",1,"-((a^2*B*x)/c^3) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(5*f*(c - c*Sin[e + f*x])^5) - (2*a^2*B*Cos[e + f*x]^3)/(3*f*(c - c*Sin[e + f*x])^3) + (2*a^2*B*Cos[e + f*x])/(f*(c^3 - c^3*Sin[e + f*x]))","A",5,4,36,0.1111,1,"{2967, 2859, 2680, 8}"
34,1,75,0,0.2288542,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^4} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^4,x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{7 f (c-c \sin (e+f x))^6}+\frac{a^2 c (A-6 B) \cos ^5(e+f x)}{35 f (c-c \sin (e+f x))^5}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{7 f (c-c \sin (e+f x))^6}+\frac{a^2 c (A-6 B) \cos ^5(e+f x)}{35 f (c-c \sin (e+f x))^5}",1,"(a^2*(A + B)*c^2*Cos[e + f*x]^5)/(7*f*(c - c*Sin[e + f*x])^6) + (a^2*(A - 6*B)*c*Cos[e + f*x]^5)/(35*f*(c - c*Sin[e + f*x])^5)","A",3,3,36,0.08333,1,"{2967, 2859, 2671}"
35,1,115,0,0.2856614,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^5} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^5,x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{9 f (c-c \sin (e+f x))^7}+\frac{a^2 (2 A-7 B) \cos ^5(e+f x)}{315 f (c-c \sin (e+f x))^5}+\frac{a^2 c (2 A-7 B) \cos ^5(e+f x)}{63 f (c-c \sin (e+f x))^6}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{9 f (c-c \sin (e+f x))^7}+\frac{a^2 (2 A-7 B) \cos ^5(e+f x)}{315 f (c-c \sin (e+f x))^5}+\frac{a^2 c (2 A-7 B) \cos ^5(e+f x)}{63 f (c-c \sin (e+f x))^6}",1,"(a^2*(A + B)*c^2*Cos[e + f*x]^5)/(9*f*(c - c*Sin[e + f*x])^7) + (a^2*(2*A - 7*B)*c*Cos[e + f*x]^5)/(63*f*(c - c*Sin[e + f*x])^6) + (a^2*(2*A - 7*B)*Cos[e + f*x]^5)/(315*f*(c - c*Sin[e + f*x])^5)","A",4,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
36,1,156,0,0.374481,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^6} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^6,x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{11 f (c-c \sin (e+f x))^8}+\frac{2 a^2 (3 A-8 B) \cos ^5(e+f x)}{3465 c f (c-c \sin (e+f x))^5}+\frac{2 a^2 (3 A-8 B) \cos ^5(e+f x)}{693 f (c-c \sin (e+f x))^6}+\frac{a^2 c (3 A-8 B) \cos ^5(e+f x)}{99 f (c-c \sin (e+f x))^7}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{11 f (c-c \sin (e+f x))^8}+\frac{2 a^2 (3 A-8 B) \cos ^5(e+f x)}{3465 c f (c-c \sin (e+f x))^5}+\frac{2 a^2 (3 A-8 B) \cos ^5(e+f x)}{693 f (c-c \sin (e+f x))^6}+\frac{a^2 c (3 A-8 B) \cos ^5(e+f x)}{99 f (c-c \sin (e+f x))^7}",1,"(a^2*(A + B)*c^2*Cos[e + f*x]^5)/(11*f*(c - c*Sin[e + f*x])^8) + (a^2*(3*A - 8*B)*c*Cos[e + f*x]^5)/(99*f*(c - c*Sin[e + f*x])^7) + (2*a^2*(3*A - 8*B)*Cos[e + f*x]^5)/(693*f*(c - c*Sin[e + f*x])^6) + (2*a^2*(3*A - 8*B)*Cos[e + f*x]^5)/(3465*c*f*(c - c*Sin[e + f*x])^5)","A",5,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
37,1,197,0,0.4645641,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^7} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^7,x]","\frac{2 a^2 (4 A-9 B) \cos ^5(e+f x)}{15015 c^2 f (c-c \sin (e+f x))^5}+\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{13 f (c-c \sin (e+f x))^9}+\frac{2 a^2 (4 A-9 B) \cos ^5(e+f x)}{3003 c f (c-c \sin (e+f x))^6}+\frac{a^2 (4 A-9 B) \cos ^5(e+f x)}{429 f (c-c \sin (e+f x))^7}+\frac{a^2 c (4 A-9 B) \cos ^5(e+f x)}{143 f (c-c \sin (e+f x))^8}","\frac{2 a^2 (4 A-9 B) \cos ^5(e+f x)}{15015 c^2 f (c-c \sin (e+f x))^5}+\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{13 f (c-c \sin (e+f x))^9}+\frac{2 a^2 (4 A-9 B) \cos ^5(e+f x)}{3003 c f (c-c \sin (e+f x))^6}+\frac{a^2 (4 A-9 B) \cos ^5(e+f x)}{429 f (c-c \sin (e+f x))^7}+\frac{a^2 c (4 A-9 B) \cos ^5(e+f x)}{143 f (c-c \sin (e+f x))^8}",1,"(a^2*(A + B)*c^2*Cos[e + f*x]^5)/(13*f*(c - c*Sin[e + f*x])^9) + (a^2*(4*A - 9*B)*c*Cos[e + f*x]^5)/(143*f*(c - c*Sin[e + f*x])^8) + (a^2*(4*A - 9*B)*Cos[e + f*x]^5)/(429*f*(c - c*Sin[e + f*x])^7) + (2*a^2*(4*A - 9*B)*Cos[e + f*x]^5)/(3003*c*f*(c - c*Sin[e + f*x])^6) + (2*a^2*(4*A - 9*B)*Cos[e + f*x]^5)/(15015*c^2*f*(c - c*Sin[e + f*x])^5)","A",6,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
38,1,265,0,0.3907838,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^6 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^6,x]","\frac{11 a^3 c^6 (10 A-3 B) \cos ^7(e+f x)}{560 f}+\frac{a^3 (10 A-3 B) \cos ^7(e+f x) \left(c^3-c^3 \sin (e+f x)\right)^2}{90 f}+\frac{11 a^3 (10 A-3 B) \cos ^7(e+f x) \left(c^6-c^6 \sin (e+f x)\right)}{720 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos ^5(e+f x)}{480 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos ^3(e+f x)}{384 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos (e+f x)}{256 f}+\frac{11}{256} a^3 c^6 x (10 A-3 B)-\frac{a^3 B \cos ^7(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^3}{10 f}","\frac{11 a^3 c^6 (10 A-3 B) \cos ^7(e+f x)}{560 f}+\frac{a^3 (10 A-3 B) \cos ^7(e+f x) \left(c^3-c^3 \sin (e+f x)\right)^2}{90 f}+\frac{11 a^3 (10 A-3 B) \cos ^7(e+f x) \left(c^6-c^6 \sin (e+f x)\right)}{720 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos ^5(e+f x)}{480 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos ^3(e+f x)}{384 f}+\frac{11 a^3 c^6 (10 A-3 B) \sin (e+f x) \cos (e+f x)}{256 f}+\frac{11}{256} a^3 c^6 x (10 A-3 B)-\frac{a^3 B \cos ^7(e+f x) \left(c^2-c^2 \sin (e+f x)\right)^3}{10 f}",1,"(11*a^3*(10*A - 3*B)*c^6*x)/256 + (11*a^3*(10*A - 3*B)*c^6*Cos[e + f*x]^7)/(560*f) + (11*a^3*(10*A - 3*B)*c^6*Cos[e + f*x]*Sin[e + f*x])/(256*f) + (11*a^3*(10*A - 3*B)*c^6*Cos[e + f*x]^3*Sin[e + f*x])/(384*f) + (11*a^3*(10*A - 3*B)*c^6*Cos[e + f*x]^5*Sin[e + f*x])/(480*f) - (a^3*B*Cos[e + f*x]^7*(c^2 - c^2*Sin[e + f*x])^3)/(10*f) + (a^3*(10*A - 3*B)*Cos[e + f*x]^7*(c^3 - c^3*Sin[e + f*x])^2)/(90*f) + (11*a^3*(10*A - 3*B)*Cos[e + f*x]^7*(c^6 - c^6*Sin[e + f*x]))/(720*f)","A",9,6,36,0.1667,1,"{2967, 2860, 2678, 2669, 2635, 8}"
39,1,222,0,0.3221087,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^5 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^5,x]","\frac{a^3 c^5 (9 A-2 B) \cos ^7(e+f x)}{56 f}+\frac{a^3 (9 A-2 B) \cos ^7(e+f x) \left(c^5-c^5 \sin (e+f x)\right)}{72 f}+\frac{a^3 c^5 (9 A-2 B) \sin (e+f x) \cos ^5(e+f x)}{48 f}+\frac{5 a^3 c^5 (9 A-2 B) \sin (e+f x) \cos ^3(e+f x)}{192 f}+\frac{5 a^3 c^5 (9 A-2 B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{5}{128} a^3 c^5 x (9 A-2 B)-\frac{a^3 B c^3 \cos ^7(e+f x) (c-c \sin (e+f x))^2}{9 f}","\frac{a^3 c^5 (9 A-2 B) \cos ^7(e+f x)}{56 f}+\frac{a^3 (9 A-2 B) \cos ^7(e+f x) \left(c^5-c^5 \sin (e+f x)\right)}{72 f}+\frac{a^3 c^5 (9 A-2 B) \sin (e+f x) \cos ^5(e+f x)}{48 f}+\frac{5 a^3 c^5 (9 A-2 B) \sin (e+f x) \cos ^3(e+f x)}{192 f}+\frac{5 a^3 c^5 (9 A-2 B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{5}{128} a^3 c^5 x (9 A-2 B)-\frac{a^3 B c^3 \cos ^7(e+f x) (c-c \sin (e+f x))^2}{9 f}",1,"(5*a^3*(9*A - 2*B)*c^5*x)/128 + (a^3*(9*A - 2*B)*c^5*Cos[e + f*x]^7)/(56*f) + (5*a^3*(9*A - 2*B)*c^5*Cos[e + f*x]*Sin[e + f*x])/(128*f) + (5*a^3*(9*A - 2*B)*c^5*Cos[e + f*x]^3*Sin[e + f*x])/(192*f) + (a^3*(9*A - 2*B)*c^5*Cos[e + f*x]^5*Sin[e + f*x])/(48*f) - (a^3*B*c^3*Cos[e + f*x]^7*(c - c*Sin[e + f*x])^2)/(9*f) + (a^3*(9*A - 2*B)*Cos[e + f*x]^7*(c^5 - c^5*Sin[e + f*x]))/(72*f)","A",8,6,36,0.1667,1,"{2967, 2860, 2678, 2669, 2635, 8}"
40,1,181,0,0.2336041,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^4 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4,x]","\frac{a^3 c^4 (8 A-B) \cos ^7(e+f x)}{56 f}+\frac{a^3 c^4 (8 A-B) \sin (e+f x) \cos ^5(e+f x)}{48 f}+\frac{5 a^3 c^4 (8 A-B) \sin (e+f x) \cos ^3(e+f x)}{192 f}+\frac{5 a^3 c^4 (8 A-B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{5}{128} a^3 c^4 x (8 A-B)-\frac{a^3 B \cos ^7(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{8 f}","\frac{a^3 c^4 (8 A-B) \cos ^7(e+f x)}{56 f}+\frac{a^3 c^4 (8 A-B) \sin (e+f x) \cos ^5(e+f x)}{48 f}+\frac{5 a^3 c^4 (8 A-B) \sin (e+f x) \cos ^3(e+f x)}{192 f}+\frac{5 a^3 c^4 (8 A-B) \sin (e+f x) \cos (e+f x)}{128 f}+\frac{5}{128} a^3 c^4 x (8 A-B)-\frac{a^3 B \cos ^7(e+f x) \left(c^4-c^4 \sin (e+f x)\right)}{8 f}",1,"(5*a^3*(8*A - B)*c^4*x)/128 + (a^3*(8*A - B)*c^4*Cos[e + f*x]^7)/(56*f) + (5*a^3*(8*A - B)*c^4*Cos[e + f*x]*Sin[e + f*x])/(128*f) + (5*a^3*(8*A - B)*c^4*Cos[e + f*x]^3*Sin[e + f*x])/(192*f) + (a^3*(8*A - B)*c^4*Cos[e + f*x]^5*Sin[e + f*x])/(48*f) - (a^3*B*Cos[e + f*x]^7*(c^4 - c^4*Sin[e + f*x]))/(8*f)","A",7,5,36,0.1389,1,"{2967, 2860, 2669, 2635, 8}"
41,1,117,0,0.1476861,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3,x]","\frac{a^3 A c^3 \sin (e+f x) \cos ^5(e+f x)}{6 f}+\frac{5 a^3 A c^3 \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{5 a^3 A c^3 \sin (e+f x) \cos (e+f x)}{16 f}+\frac{5}{16} a^3 A c^3 x-\frac{a^3 B c^3 \cos ^7(e+f x)}{7 f}","\frac{a^3 A c^3 \sin (e+f x) \cos ^5(e+f x)}{6 f}+\frac{5 a^3 A c^3 \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{5 a^3 A c^3 \sin (e+f x) \cos (e+f x)}{16 f}+\frac{5}{16} a^3 A c^3 x-\frac{a^3 B c^3 \cos ^7(e+f x)}{7 f}",1,"(5*a^3*A*c^3*x)/16 - (a^3*B*c^3*Cos[e + f*x]^7)/(7*f) + (5*a^3*A*c^3*Cos[e + f*x]*Sin[e + f*x])/(16*f) + (5*a^3*A*c^3*Cos[e + f*x]^3*Sin[e + f*x])/(24*f) + (a^3*A*c^3*Cos[e + f*x]^5*Sin[e + f*x])/(6*f)","A",6,4,36,0.1111,1,"{2967, 2669, 2635, 8}"
42,1,138,0,0.1998238,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2,x]","-\frac{a^3 c^2 (6 A+B) \cos ^5(e+f x)}{30 f}+\frac{a^3 c^2 (6 A+B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^3 c^2 (6 A+B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^3 c^2 x (6 A+B)-\frac{B c^2 \cos ^5(e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{6 f}","-\frac{a^3 c^2 (6 A+B) \cos ^5(e+f x)}{30 f}+\frac{a^3 c^2 (6 A+B) \sin (e+f x) \cos ^3(e+f x)}{24 f}+\frac{a^3 c^2 (6 A+B) \sin (e+f x) \cos (e+f x)}{16 f}+\frac{1}{16} a^3 c^2 x (6 A+B)-\frac{B c^2 \cos ^5(e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{6 f}",1,"(a^3*(6*A + B)*c^2*x)/16 - (a^3*(6*A + B)*c^2*Cos[e + f*x]^5)/(30*f) + (a^3*(6*A + B)*c^2*Cos[e + f*x]*Sin[e + f*x])/(16*f) + (a^3*(6*A + B)*c^2*Cos[e + f*x]^3*Sin[e + f*x])/(24*f) - (B*c^2*Cos[e + f*x]^5*(a^3 + a^3*Sin[e + f*x]))/(6*f)","A",6,5,36,0.1389,1,"{2967, 2860, 2669, 2635, 8}"
43,1,140,0,0.2221968,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]),x]","-\frac{a^3 c (5 A+2 B) \cos ^3(e+f x)}{12 f}-\frac{c (5 A+2 B) \cos ^3(e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{20 f}+\frac{a^3 c (5 A+2 B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a^3 c x (5 A+2 B)-\frac{a B c \cos ^3(e+f x) (a \sin (e+f x)+a)^2}{5 f}","-\frac{a^3 c (5 A+2 B) \cos ^3(e+f x)}{12 f}-\frac{c (5 A+2 B) \cos ^3(e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{20 f}+\frac{a^3 c (5 A+2 B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{1}{8} a^3 c x (5 A+2 B)-\frac{a B c \cos ^3(e+f x) (a \sin (e+f x)+a)^2}{5 f}",1,"(a^3*(5*A + 2*B)*c*x)/8 - (a^3*(5*A + 2*B)*c*Cos[e + f*x]^3)/(12*f) + (a^3*(5*A + 2*B)*c*Cos[e + f*x]*Sin[e + f*x])/(8*f) - (a*B*c*Cos[e + f*x]^3*(a + a*Sin[e + f*x])^2)/(5*f) - ((5*A + 2*B)*c*Cos[e + f*x]^3*(a^3 + a^3*Sin[e + f*x]))/(20*f)","A",6,6,34,0.1765,1,"{2967, 2860, 2678, 2669, 2635, 8}"
44,1,156,0,0.3103907,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{c-c \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x]),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{f (c-c \sin (e+f x))^4}+\frac{2 a^3 c^3 (3 A+4 B) \cos ^5(e+f x)}{f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{5 a^3 (3 A+4 B) \cos ^3(e+f x)}{3 c f}-\frac{5 a^3 (3 A+4 B) \sin (e+f x) \cos (e+f x)}{2 c f}-\frac{5 a^3 x (3 A+4 B)}{2 c}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{f (c-c \sin (e+f x))^4}+\frac{2 a^3 c^3 (3 A+4 B) \cos ^5(e+f x)}{f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{5 a^3 (3 A+4 B) \cos ^3(e+f x)}{3 c f}-\frac{5 a^3 (3 A+4 B) \sin (e+f x) \cos (e+f x)}{2 c f}-\frac{5 a^3 x (3 A+4 B)}{2 c}",1,"(-5*a^3*(3*A + 4*B)*x)/(2*c) + (5*a^3*(3*A + 4*B)*Cos[e + f*x]^3)/(3*c*f) - (5*a^3*(3*A + 4*B)*Cos[e + f*x]*Sin[e + f*x])/(2*c*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(f*(c - c*Sin[e + f*x])^4) + (2*a^3*(3*A + 4*B)*c^3*Cos[e + f*x]^5)/(f*(c^2 - c^2*Sin[e + f*x])^2)","A",6,6,36,0.1667,1,"{2967, 2859, 2680, 2682, 2635, 8}"
45,1,163,0,0.3477401,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^2,x]","-\frac{5 a^3 (2 A+5 B) \cos (e+f x)}{2 c^2 f}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{3 f (c-c \sin (e+f x))^5}-\frac{5 a^3 (2 A+5 B) \cos ^3(e+f x)}{6 f \left(c^2-c^2 \sin (e+f x)\right)}+\frac{5 a^3 x (2 A+5 B)}{2 c^2}-\frac{2 a^3 c (2 A+5 B) \cos ^5(e+f x)}{3 f (c-c \sin (e+f x))^3}","-\frac{5 a^3 (2 A+5 B) \cos (e+f x)}{2 c^2 f}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{3 f (c-c \sin (e+f x))^5}-\frac{5 a^3 (2 A+5 B) \cos ^3(e+f x)}{6 f \left(c^2-c^2 \sin (e+f x)\right)}+\frac{5 a^3 x (2 A+5 B)}{2 c^2}-\frac{2 a^3 c (2 A+5 B) \cos ^5(e+f x)}{3 f (c-c \sin (e+f x))^3}",1,"(5*a^3*(2*A + 5*B)*x)/(2*c^2) - (5*a^3*(2*A + 5*B)*Cos[e + f*x])/(2*c^2*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(3*f*(c - c*Sin[e + f*x])^5) - (2*a^3*(2*A + 5*B)*c*Cos[e + f*x]^5)/(3*f*(c - c*Sin[e + f*x])^3) - (5*a^3*(2*A + 5*B)*Cos[e + f*x]^3)/(6*f*(c^2 - c^2*Sin[e + f*x]))","A",6,6,36,0.1667,1,"{2967, 2859, 2680, 2679, 2682, 8}"
46,1,153,0,0.34216,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^3,x]","\frac{a^3 (A+6 B) \cos (e+f x)}{c^3 f}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{5 f (c-c \sin (e+f x))^6}+\frac{2 a^3 c^3 (A+6 B) \cos ^3(e+f x)}{3 f \left(c^3-c^3 \sin (e+f x)\right)^2}-\frac{a^3 x (A+6 B)}{c^3}-\frac{2 a^3 c (A+6 B) \cos ^5(e+f x)}{15 f (c-c \sin (e+f x))^4}","\frac{a^3 (A+6 B) \cos (e+f x)}{c^3 f}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{5 f (c-c \sin (e+f x))^6}+\frac{2 a^3 c^3 (A+6 B) \cos ^3(e+f x)}{3 f \left(c^3-c^3 \sin (e+f x)\right)^2}-\frac{a^3 x (A+6 B)}{c^3}-\frac{2 a^3 c (A+6 B) \cos ^5(e+f x)}{15 f (c-c \sin (e+f x))^4}",1,"-((a^3*(A + 6*B)*x)/c^3) + (a^3*(A + 6*B)*Cos[e + f*x])/(c^3*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(5*f*(c - c*Sin[e + f*x])^6) - (2*a^3*(A + 6*B)*c*Cos[e + f*x]^5)/(15*f*(c - c*Sin[e + f*x])^4) + (2*a^3*(A + 6*B)*c^3*Cos[e + f*x]^3)/(3*f*(c^3 - c^3*Sin[e + f*x])^2)","A",6,5,36,0.1389,1,"{2967, 2859, 2680, 2682, 8}"
47,1,151,0,0.3299748,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^4} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^4,x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{7 f (c-c \sin (e+f x))^7}+\frac{2 a^3 B c^2 \cos ^3(e+f x)}{3 f \left(c^2-c^2 \sin (e+f x)\right)^3}-\frac{2 a^3 B \cos (e+f x)}{f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{a^3 B x}{c^4}-\frac{2 a^3 B c \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^5}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{7 f (c-c \sin (e+f x))^7}+\frac{2 a^3 B c^2 \cos ^3(e+f x)}{3 f \left(c^2-c^2 \sin (e+f x)\right)^3}-\frac{2 a^3 B \cos (e+f x)}{f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{a^3 B x}{c^4}-\frac{2 a^3 B c \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^5}",1,"(a^3*B*x)/c^4 + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(7*f*(c - c*Sin[e + f*x])^7) - (2*a^3*B*c*Cos[e + f*x]^5)/(5*f*(c - c*Sin[e + f*x])^5) + (2*a^3*B*c^2*Cos[e + f*x]^3)/(3*f*(c^2 - c^2*Sin[e + f*x])^3) - (2*a^3*B*Cos[e + f*x])/(f*(c^4 - c^4*Sin[e + f*x]))","A",6,4,36,0.1111,1,"{2967, 2859, 2680, 8}"
48,1,77,0,0.2356345,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^5} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^5,x]","\frac{a^3 c^2 (A-8 B) \cos ^7(e+f x)}{63 f (c-c \sin (e+f x))^7}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{9 f (c-c \sin (e+f x))^8}","\frac{a^3 c^2 (A-8 B) \cos ^7(e+f x)}{63 f (c-c \sin (e+f x))^7}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{9 f (c-c \sin (e+f x))^8}",1,"(a^3*(A + B)*c^3*Cos[e + f*x]^7)/(9*f*(c - c*Sin[e + f*x])^8) + (a^3*(A - 8*B)*c^2*Cos[e + f*x]^7)/(63*f*(c - c*Sin[e + f*x])^7)","A",3,3,36,0.08333,1,"{2967, 2859, 2671}"
49,1,118,0,0.2892333,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^6} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^6,x]","\frac{a^3 c^2 (2 A-9 B) \cos ^7(e+f x)}{99 f (c-c \sin (e+f x))^8}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{11 f (c-c \sin (e+f x))^9}+\frac{a^3 c (2 A-9 B) \cos ^7(e+f x)}{693 f (c-c \sin (e+f x))^7}","\frac{a^3 c^2 (2 A-9 B) \cos ^7(e+f x)}{99 f (c-c \sin (e+f x))^8}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{11 f (c-c \sin (e+f x))^9}+\frac{a^3 c (2 A-9 B) \cos ^7(e+f x)}{693 f (c-c \sin (e+f x))^7}",1,"(a^3*(A + B)*c^3*Cos[e + f*x]^7)/(11*f*(c - c*Sin[e + f*x])^9) + (a^3*(2*A - 9*B)*c^2*Cos[e + f*x]^7)/(99*f*(c - c*Sin[e + f*x])^8) + (a^3*(2*A - 9*B)*c*Cos[e + f*x]^7)/(693*f*(c - c*Sin[e + f*x])^7)","A",4,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
50,1,156,0,0.3752099,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^7} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^7,x]","\frac{a^3 c^2 (3 A-10 B) \cos ^7(e+f x)}{143 f (c-c \sin (e+f x))^9}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{13 f (c-c \sin (e+f x))^{10}}+\frac{2 a^3 (3 A-10 B) \cos ^7(e+f x)}{9009 f (c-c \sin (e+f x))^7}+\frac{2 a^3 c (3 A-10 B) \cos ^7(e+f x)}{1287 f (c-c \sin (e+f x))^8}","\frac{a^3 c^2 (3 A-10 B) \cos ^7(e+f x)}{143 f (c-c \sin (e+f x))^9}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{13 f (c-c \sin (e+f x))^{10}}+\frac{2 a^3 (3 A-10 B) \cos ^7(e+f x)}{9009 f (c-c \sin (e+f x))^7}+\frac{2 a^3 c (3 A-10 B) \cos ^7(e+f x)}{1287 f (c-c \sin (e+f x))^8}",1,"(a^3*(A + B)*c^3*Cos[e + f*x]^7)/(13*f*(c - c*Sin[e + f*x])^10) + (a^3*(3*A - 10*B)*c^2*Cos[e + f*x]^7)/(143*f*(c - c*Sin[e + f*x])^9) + (2*a^3*(3*A - 10*B)*c*Cos[e + f*x]^7)/(1287*f*(c - c*Sin[e + f*x])^8) + (2*a^3*(3*A - 10*B)*Cos[e + f*x]^7)/(9009*f*(c - c*Sin[e + f*x])^7)","A",5,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
51,1,197,0,0.4440799,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^8} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^8,x]","\frac{a^3 c^2 (4 A-11 B) \cos ^7(e+f x)}{195 f (c-c \sin (e+f x))^{10}}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{15 f (c-c \sin (e+f x))^{11}}+\frac{2 a^3 (4 A-11 B) \cos ^7(e+f x)}{45045 c f (c-c \sin (e+f x))^7}+\frac{2 a^3 (4 A-11 B) \cos ^7(e+f x)}{6435 f (c-c \sin (e+f x))^8}+\frac{a^3 c (4 A-11 B) \cos ^7(e+f x)}{715 f (c-c \sin (e+f x))^9}","\frac{a^3 c^2 (4 A-11 B) \cos ^7(e+f x)}{195 f (c-c \sin (e+f x))^{10}}+\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{15 f (c-c \sin (e+f x))^{11}}+\frac{2 a^3 (4 A-11 B) \cos ^7(e+f x)}{45045 c f (c-c \sin (e+f x))^7}+\frac{2 a^3 (4 A-11 B) \cos ^7(e+f x)}{6435 f (c-c \sin (e+f x))^8}+\frac{a^3 c (4 A-11 B) \cos ^7(e+f x)}{715 f (c-c \sin (e+f x))^9}",1,"(a^3*(A + B)*c^3*Cos[e + f*x]^7)/(15*f*(c - c*Sin[e + f*x])^11) + (a^3*(4*A - 11*B)*c^2*Cos[e + f*x]^7)/(195*f*(c - c*Sin[e + f*x])^10) + (a^3*(4*A - 11*B)*c*Cos[e + f*x]^7)/(715*f*(c - c*Sin[e + f*x])^9) + (2*a^3*(4*A - 11*B)*Cos[e + f*x]^7)/(6435*f*(c - c*Sin[e + f*x])^8) + (2*a^3*(4*A - 11*B)*Cos[e + f*x]^7)/(45045*c*f*(c - c*Sin[e + f*x])^7)","A",6,4,36,0.1111,1,"{2967, 2859, 2672, 2671}"
52,1,190,0,0.3626382,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^4}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4)/(a + a*Sin[e + f*x]),x]","-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{f (a \sin (e+f x)+a)^5}-\frac{2 a^2 c^4 (4 A-5 B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^3}-\frac{35 c^4 (4 A-5 B) \cos ^3(e+f x)}{12 a f}-\frac{7 c^4 (4 A-5 B) \cos ^5(e+f x)}{4 f (a \sin (e+f x)+a)}-\frac{35 c^4 (4 A-5 B) \sin (e+f x) \cos (e+f x)}{8 a f}-\frac{35 c^4 x (4 A-5 B)}{8 a}","-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{f (a \sin (e+f x)+a)^5}-\frac{2 a^2 c^4 (4 A-5 B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^3}-\frac{35 c^4 (4 A-5 B) \cos ^3(e+f x)}{12 a f}-\frac{7 c^4 (4 A-5 B) \cos ^5(e+f x)}{4 f (a \sin (e+f x)+a)}-\frac{35 c^4 (4 A-5 B) \sin (e+f x) \cos (e+f x)}{8 a f}-\frac{35 c^4 x (4 A-5 B)}{8 a}",1,"(-35*(4*A - 5*B)*c^4*x)/(8*a) - (35*(4*A - 5*B)*c^4*Cos[e + f*x]^3)/(12*a*f) - (35*(4*A - 5*B)*c^4*Cos[e + f*x]*Sin[e + f*x])/(8*a*f) - (a^4*(A - B)*c^4*Cos[e + f*x]^9)/(f*(a + a*Sin[e + f*x])^5) - (2*a^2*(4*A - 5*B)*c^4*Cos[e + f*x]^7)/(f*(a + a*Sin[e + f*x])^3) - (7*(4*A - 5*B)*c^4*Cos[e + f*x]^5)/(4*f*(a + a*Sin[e + f*x]))","A",7,7,36,0.1944,1,"{2967, 2859, 2680, 2679, 2682, 2635, 8}"
53,1,157,0,0.3178914,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^3}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3)/(a + a*Sin[e + f*x]),x]","-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^4}-\frac{2 a^3 c^3 (3 A-4 B) \cos ^5(e+f x)}{f \left(a^2 \sin (e+f x)+a^2\right)^2}-\frac{5 c^3 (3 A-4 B) \cos ^3(e+f x)}{3 a f}-\frac{5 c^3 (3 A-4 B) \sin (e+f x) \cos (e+f x)}{2 a f}-\frac{5 c^3 x (3 A-4 B)}{2 a}","-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^4}-\frac{2 a^3 c^3 (3 A-4 B) \cos ^5(e+f x)}{f \left(a^2 \sin (e+f x)+a^2\right)^2}-\frac{5 c^3 (3 A-4 B) \cos ^3(e+f x)}{3 a f}-\frac{5 c^3 (3 A-4 B) \sin (e+f x) \cos (e+f x)}{2 a f}-\frac{5 c^3 x (3 A-4 B)}{2 a}",1,"(-5*(3*A - 4*B)*c^3*x)/(2*a) - (5*(3*A - 4*B)*c^3*Cos[e + f*x]^3)/(3*a*f) - (5*(3*A - 4*B)*c^3*Cos[e + f*x]*Sin[e + f*x])/(2*a*f) - (a^3*(A - B)*c^3*Cos[e + f*x]^7)/(f*(a + a*Sin[e + f*x])^4) - (2*a^3*(3*A - 4*B)*c^3*Cos[e + f*x]^5)/(f*(a^2 + a^2*Sin[e + f*x])^2)","A",6,6,36,0.1667,1,"{2967, 2859, 2680, 2682, 2635, 8}"
54,1,118,0,0.2784696,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^2}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2)/(a + a*Sin[e + f*x]),x]","-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{f (a \sin (e+f x)+a)^3}-\frac{3 c^2 (2 A-3 B) \cos (e+f x)}{2 a f}-\frac{c^2 (2 A-3 B) \cos ^3(e+f x)}{2 f (a \sin (e+f x)+a)}-\frac{3 c^2 x (2 A-3 B)}{2 a}","-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{f (a \sin (e+f x)+a)^3}-\frac{3 c^2 (2 A-3 B) \cos (e+f x)}{2 a f}-\frac{c^2 (2 A-3 B) \cos ^3(e+f x)}{2 f (a \sin (e+f x)+a)}-\frac{3 c^2 x (2 A-3 B)}{2 a}",1,"(-3*(2*A - 3*B)*c^2*x)/(2*a) - (3*(2*A - 3*B)*c^2*Cos[e + f*x])/(2*a*f) - (a^2*(A - B)*c^2*Cos[e + f*x]^5)/(f*(a + a*Sin[e + f*x])^3) - ((2*A - 3*B)*c^2*Cos[e + f*x]^3)/(2*f*(a + a*Sin[e + f*x]))","A",5,5,36,0.1389,1,"{2967, 2859, 2679, 2682, 8}"
55,1,57,0,0.1551838,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]))/(a + a*Sin[e + f*x]),x]","-\frac{2 c (A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)}-\frac{c x (A-2 B)}{a}+\frac{B c \cos (e+f x)}{a f}","-\frac{2 c (A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)}-\frac{c x (A-2 B)}{a}+\frac{B c \cos (e+f x)}{a f}",1,"-(((A - 2*B)*c*x)/a) + (B*c*Cos[e + f*x])/(a*f) - (2*(A - B)*c*Cos[e + f*x])/(f*(a + a*Sin[e + f*x]))","A",4,3,34,0.08824,1,"{2967, 2857, 2638}"
56,1,35,0,0.1355578,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])),x]","\frac{A \tan (e+f x)}{a c f}+\frac{B \sec (e+f x)}{a c f}","\frac{A \tan (e+f x)}{a c f}+\frac{B \sec (e+f x)}{a c f}",1,"(B*Sec[e + f*x])/(a*c*f) + (A*Tan[e + f*x])/(a*c*f)","A",4,4,36,0.1111,1,"{2967, 2669, 3767, 8}"
57,1,63,0,0.2021962,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])^2),x]","\frac{(2 A-B) \tan (e+f x)}{3 a c^2 f}+\frac{(A+B) \sec (e+f x)}{3 a f \left(c^2-c^2 \sin (e+f x)\right)}","\frac{(2 A-B) \tan (e+f x)}{3 a c^2 f}+\frac{(A+B) \sec (e+f x)}{3 a f \left(c^2-c^2 \sin (e+f x)\right)}",1,"((A + B)*Sec[e + f*x])/(3*a*f*(c^2 - c^2*Sin[e + f*x])) + ((2*A - B)*Tan[e + f*x])/(3*a*c^2*f)","A",4,4,36,0.1111,1,"{2967, 2859, 3767, 8}"
58,1,102,0,0.2570641,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])^3),x]","\frac{2 (3 A-2 B) \tan (e+f x)}{15 a c^3 f}+\frac{(3 A-2 B) \sec (e+f x)}{15 a f \left(c^3-c^3 \sin (e+f x)\right)}+\frac{(A+B) \sec (e+f x)}{5 a c f (c-c \sin (e+f x))^2}","\frac{2 (3 A-2 B) \tan (e+f x)}{15 a c^3 f}+\frac{(3 A-2 B) \sec (e+f x)}{15 a f \left(c^3-c^3 \sin (e+f x)\right)}+\frac{(A+B) \sec (e+f x)}{5 a c f (c-c \sin (e+f x))^2}",1,"((A + B)*Sec[e + f*x])/(5*a*c*f*(c - c*Sin[e + f*x])^2) + ((3*A - 2*B)*Sec[e + f*x])/(15*a*f*(c^3 - c^3*Sin[e + f*x])) + (2*(3*A - 2*B)*Tan[e + f*x])/(15*a*c^3*f)","A",5,5,36,0.1389,1,"{2967, 2859, 2672, 3767, 8}"
59,1,142,0,0.306909,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))^4} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])^4),x]","\frac{2 (4 A-3 B) \tan (e+f x)}{35 a c^4 f}+\frac{(4 A-3 B) \sec (e+f x)}{35 a f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{(4 A-3 B) \sec (e+f x)}{35 a f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{(A+B) \sec (e+f x)}{7 a c f (c-c \sin (e+f x))^3}","\frac{2 (4 A-3 B) \tan (e+f x)}{35 a c^4 f}+\frac{(4 A-3 B) \sec (e+f x)}{35 a f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{(4 A-3 B) \sec (e+f x)}{35 a f \left(c^2-c^2 \sin (e+f x)\right)^2}+\frac{(A+B) \sec (e+f x)}{7 a c f (c-c \sin (e+f x))^3}",1,"((A + B)*Sec[e + f*x])/(7*a*c*f*(c - c*Sin[e + f*x])^3) + ((4*A - 3*B)*Sec[e + f*x])/(35*a*f*(c^2 - c^2*Sin[e + f*x])^2) + ((4*A - 3*B)*Sec[e + f*x])/(35*a*f*(c^4 - c^4*Sin[e + f*x])) + (2*(4*A - 3*B)*Tan[e + f*x])/(35*a*c^4*f)","A",6,5,36,0.1389,1,"{2967, 2859, 2672, 3767, 8}"
60,1,240,0,0.4100406,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^5}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^5)/(a + a*Sin[e + f*x])^2,x]","\frac{35 c^5 (4 A-7 B) \cos ^3(e+f x)}{4 a^2 f}-\frac{a^5 c^5 (A-B) \cos ^{11}(e+f x)}{3 f (a \sin (e+f x)+a)^7}+\frac{2 a^3 c^5 (4 A-7 B) \cos ^9(e+f x)}{3 f (a \sin (e+f x)+a)^5}+\frac{6 a^4 c^5 (4 A-7 B) \cos ^7(e+f x)}{f \left(a^2 \sin (e+f x)+a^2\right)^3}+\frac{21 c^5 (4 A-7 B) \cos ^5(e+f x)}{4 f \left(a^2 \sin (e+f x)+a^2\right)}+\frac{105 c^5 (4 A-7 B) \sin (e+f x) \cos (e+f x)}{8 a^2 f}+\frac{105 c^5 x (4 A-7 B)}{8 a^2}","\frac{35 c^5 (4 A-7 B) \cos ^3(e+f x)}{4 a^2 f}-\frac{a^5 c^5 (A-B) \cos ^{11}(e+f x)}{3 f (a \sin (e+f x)+a)^7}+\frac{2 a^3 c^5 (4 A-7 B) \cos ^9(e+f x)}{3 f (a \sin (e+f x)+a)^5}+\frac{6 a^4 c^5 (4 A-7 B) \cos ^7(e+f x)}{f \left(a^2 \sin (e+f x)+a^2\right)^3}+\frac{21 c^5 (4 A-7 B) \cos ^5(e+f x)}{4 f \left(a^2 \sin (e+f x)+a^2\right)}+\frac{105 c^5 (4 A-7 B) \sin (e+f x) \cos (e+f x)}{8 a^2 f}+\frac{105 c^5 x (4 A-7 B)}{8 a^2}",1,"(105*(4*A - 7*B)*c^5*x)/(8*a^2) + (35*(4*A - 7*B)*c^5*Cos[e + f*x]^3)/(4*a^2*f) + (105*(4*A - 7*B)*c^5*Cos[e + f*x]*Sin[e + f*x])/(8*a^2*f) - (a^5*(A - B)*c^5*Cos[e + f*x]^11)/(3*f*(a + a*Sin[e + f*x])^7) + (2*a^3*(4*A - 7*B)*c^5*Cos[e + f*x]^9)/(3*f*(a + a*Sin[e + f*x])^5) + (6*a^4*(4*A - 7*B)*c^5*Cos[e + f*x]^7)/(f*(a^2 + a^2*Sin[e + f*x])^3) + (21*(4*A - 7*B)*c^5*Cos[e + f*x]^5)/(4*f*(a^2 + a^2*Sin[e + f*x]))","A",8,7,36,0.1944,1,"{2967, 2859, 2680, 2679, 2682, 2635, 8}"
61,1,180,0,0.3615704,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^4}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4)/(a + a*Sin[e + f*x])^2,x]","\frac{35 c^4 (A-2 B) \cos ^3(e+f x)}{3 a^2 f}-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{3 f (a \sin (e+f x)+a)^6}+\frac{2 a^2 c^4 (A-2 B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^4}+\frac{35 c^4 (A-2 B) \sin (e+f x) \cos (e+f x)}{2 a^2 f}+\frac{35 c^4 x (A-2 B)}{2 a^2}+\frac{14 c^4 (A-2 B) \cos ^5(e+f x)}{f (a \sin (e+f x)+a)^2}","\frac{35 c^4 (A-2 B) \cos ^3(e+f x)}{3 a^2 f}-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{3 f (a \sin (e+f x)+a)^6}+\frac{2 a^2 c^4 (A-2 B) \cos ^7(e+f x)}{f (a \sin (e+f x)+a)^4}+\frac{35 c^4 (A-2 B) \sin (e+f x) \cos (e+f x)}{2 a^2 f}+\frac{35 c^4 x (A-2 B)}{2 a^2}+\frac{14 c^4 (A-2 B) \cos ^5(e+f x)}{f (a \sin (e+f x)+a)^2}",1,"(35*(A - 2*B)*c^4*x)/(2*a^2) + (35*(A - 2*B)*c^4*Cos[e + f*x]^3)/(3*a^2*f) + (35*(A - 2*B)*c^4*Cos[e + f*x]*Sin[e + f*x])/(2*a^2*f) - (a^4*(A - B)*c^4*Cos[e + f*x]^9)/(3*f*(a + a*Sin[e + f*x])^6) + (2*a^2*(A - 2*B)*c^4*Cos[e + f*x]^7)/(f*(a + a*Sin[e + f*x])^4) + (14*(A - 2*B)*c^4*Cos[e + f*x]^5)/(f*(a + a*Sin[e + f*x])^2)","A",7,6,36,0.1667,1,"{2967, 2859, 2680, 2682, 2635, 8}"
62,1,162,0,0.3324058,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^3}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^2,x]","\frac{5 c^3 (2 A-5 B) \cos (e+f x)}{2 a^2 f}-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{3 f (a \sin (e+f x)+a)^5}+\frac{5 c^3 (2 A-5 B) \cos ^3(e+f x)}{6 f \left(a^2 \sin (e+f x)+a^2\right)}+\frac{5 c^3 x (2 A-5 B)}{2 a^2}+\frac{2 a c^3 (2 A-5 B) \cos ^5(e+f x)}{3 f (a \sin (e+f x)+a)^3}","\frac{5 c^3 (2 A-5 B) \cos (e+f x)}{2 a^2 f}-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{3 f (a \sin (e+f x)+a)^5}+\frac{5 c^3 (2 A-5 B) \cos ^3(e+f x)}{6 f \left(a^2 \sin (e+f x)+a^2\right)}+\frac{5 c^3 x (2 A-5 B)}{2 a^2}+\frac{2 a c^3 (2 A-5 B) \cos ^5(e+f x)}{3 f (a \sin (e+f x)+a)^3}",1,"(5*(2*A - 5*B)*c^3*x)/(2*a^2) + (5*(2*A - 5*B)*c^3*Cos[e + f*x])/(2*a^2*f) - (a^3*(A - B)*c^3*Cos[e + f*x]^7)/(3*f*(a + a*Sin[e + f*x])^5) + (2*a*(2*A - 5*B)*c^3*Cos[e + f*x]^5)/(3*f*(a + a*Sin[e + f*x])^3) + (5*(2*A - 5*B)*c^3*Cos[e + f*x]^3)/(6*f*(a^2 + a^2*Sin[e + f*x]))","A",6,6,36,0.1667,1,"{2967, 2859, 2680, 2679, 2682, 8}"
63,1,108,0,0.2768667,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^2}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^2,x]","\frac{c^2 (A-4 B) \cos (e+f x)}{a^2 f}-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{3 f (a \sin (e+f x)+a)^4}+\frac{c^2 x (A-4 B)}{a^2}+\frac{2 c^2 (A-4 B) \cos ^3(e+f x)}{3 f (a \sin (e+f x)+a)^2}","\frac{c^2 (A-4 B) \cos (e+f x)}{a^2 f}-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{3 f (a \sin (e+f x)+a)^4}+\frac{c^2 x (A-4 B)}{a^2}+\frac{2 c^2 (A-4 B) \cos ^3(e+f x)}{3 f (a \sin (e+f x)+a)^2}",1,"((A - 4*B)*c^2*x)/a^2 + ((A - 4*B)*c^2*Cos[e + f*x])/(a^2*f) - (a^2*(A - B)*c^2*Cos[e + f*x]^5)/(3*f*(a + a*Sin[e + f*x])^4) + (2*(A - 4*B)*c^2*Cos[e + f*x]^3)/(3*f*(a + a*Sin[e + f*x])^2)","A",5,5,36,0.1389,1,"{2967, 2859, 2680, 2682, 8}"
64,1,72,0,0.2072944,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]))/(a + a*Sin[e + f*x])^2,x]","\frac{c (A-7 B) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}-\frac{B c x}{a^2}-\frac{2 c (A-B) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}","\frac{c (A-7 B) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}-\frac{B c x}{a^2}-\frac{2 c (A-B) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}",1,"-((B*c*x)/a^2) + ((A - 7*B)*c*Cos[e + f*x])/(3*a^2*f*(1 + Sin[e + f*x])) - (2*(A - B)*c*Cos[e + f*x])/(3*f*(a + a*Sin[e + f*x])^2)","A",4,4,34,0.1176,1,"{2967, 2857, 2735, 2648}"
65,1,62,0,0.1965167,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])),x]","\frac{(2 A+B) \tan (e+f x)}{3 a^2 c f}-\frac{(A-B) \sec (e+f x)}{3 c f \left(a^2 \sin (e+f x)+a^2\right)}","\frac{(2 A+B) \tan (e+f x)}{3 a^2 c f}-\frac{(A-B) \sec (e+f x)}{3 c f \left(a^2 \sin (e+f x)+a^2\right)}",1,"-((A - B)*Sec[e + f*x])/(3*c*f*(a^2 + a^2*Sin[e + f*x])) + ((2*A + B)*Tan[e + f*x])/(3*a^2*c*f)","A",4,4,36,0.1111,1,"{2967, 2859, 3767, 8}"
66,1,62,0,0.1395377,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^2),x]","\frac{A \tan ^3(e+f x)}{3 a^2 c^2 f}+\frac{A \tan (e+f x)}{a^2 c^2 f}+\frac{B \sec ^3(e+f x)}{3 a^2 c^2 f}","\frac{A \tan ^3(e+f x)}{3 a^2 c^2 f}+\frac{A \tan (e+f x)}{a^2 c^2 f}+\frac{B \sec ^3(e+f x)}{3 a^2 c^2 f}",1,"(B*Sec[e + f*x]^3)/(3*a^2*c^2*f) + (A*Tan[e + f*x])/(a^2*c^2*f) + (A*Tan[e + f*x]^3)/(3*a^2*c^2*f)","A",4,3,36,0.08333,1,"{2967, 2669, 3767}"
67,1,93,0,0.2202918,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^3),x]","\frac{(4 A-B) \tan ^3(e+f x)}{15 a^2 c^3 f}+\frac{(4 A-B) \tan (e+f x)}{5 a^2 c^3 f}+\frac{(A+B) \sec ^3(e+f x)}{5 a^2 f \left(c^3-c^3 \sin (e+f x)\right)}","\frac{(4 A-B) \tan ^3(e+f x)}{15 a^2 c^3 f}+\frac{(4 A-B) \tan (e+f x)}{5 a^2 c^3 f}+\frac{(A+B) \sec ^3(e+f x)}{5 a^2 f \left(c^3-c^3 \sin (e+f x)\right)}",1,"((A + B)*Sec[e + f*x]^3)/(5*a^2*f*(c^3 - c^3*Sin[e + f*x])) + ((4*A - B)*Tan[e + f*x])/(5*a^2*c^3*f) + ((4*A - B)*Tan[e + f*x]^3)/(15*a^2*c^3*f)","A",4,3,36,0.08333,1,"{2967, 2859, 3767}"
68,1,135,0,0.2702653,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^4} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^4),x]","\frac{4 (5 A-2 B) \tan ^3(e+f x)}{105 a^2 c^4 f}+\frac{4 (5 A-2 B) \tan (e+f x)}{35 a^2 c^4 f}+\frac{(5 A-2 B) \sec ^3(e+f x)}{35 a^2 f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{(A+B) \sec ^3(e+f x)}{7 a^2 f \left(c^2-c^2 \sin (e+f x)\right)^2}","\frac{4 (5 A-2 B) \tan ^3(e+f x)}{105 a^2 c^4 f}+\frac{4 (5 A-2 B) \tan (e+f x)}{35 a^2 c^4 f}+\frac{(5 A-2 B) \sec ^3(e+f x)}{35 a^2 f \left(c^4-c^4 \sin (e+f x)\right)}+\frac{(A+B) \sec ^3(e+f x)}{7 a^2 f \left(c^2-c^2 \sin (e+f x)\right)^2}",1,"((A + B)*Sec[e + f*x]^3)/(7*a^2*f*(c^2 - c^2*Sin[e + f*x])^2) + ((5*A - 2*B)*Sec[e + f*x]^3)/(35*a^2*f*(c^4 - c^4*Sin[e + f*x])) + (4*(5*A - 2*B)*Tan[e + f*x])/(35*a^2*c^4*f) + (4*(5*A - 2*B)*Tan[e + f*x]^3)/(105*a^2*c^4*f)","A",5,4,36,0.1111,1,"{2967, 2859, 2672, 3767}"
69,1,175,0,0.3245756,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^5} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^5),x]","\frac{4 (2 A-B) \tan ^3(e+f x)}{63 a^2 c^5 f}+\frac{4 (2 A-B) \tan (e+f x)}{21 a^2 c^5 f}+\frac{(2 A-B) \sec ^3(e+f x)}{21 a^2 f \left(c^5-c^5 \sin (e+f x)\right)}+\frac{(2 A-B) \sec ^3(e+f x)}{21 a^2 c^3 f (c-c \sin (e+f x))^2}+\frac{(A+B) \sec ^3(e+f x)}{9 a^2 c^2 f (c-c \sin (e+f x))^3}","\frac{4 (2 A-B) \tan ^3(e+f x)}{63 a^2 c^5 f}+\frac{4 (2 A-B) \tan (e+f x)}{21 a^2 c^5 f}+\frac{(2 A-B) \sec ^3(e+f x)}{21 a^2 f \left(c^5-c^5 \sin (e+f x)\right)}+\frac{(2 A-B) \sec ^3(e+f x)}{21 a^2 c^3 f (c-c \sin (e+f x))^2}+\frac{(A+B) \sec ^3(e+f x)}{9 a^2 c^2 f (c-c \sin (e+f x))^3}",1,"((A + B)*Sec[e + f*x]^3)/(9*a^2*c^2*f*(c - c*Sin[e + f*x])^3) + ((2*A - B)*Sec[e + f*x]^3)/(21*a^2*c^3*f*(c - c*Sin[e + f*x])^2) + ((2*A - B)*Sec[e + f*x]^3)/(21*a^2*f*(c^5 - c^5*Sin[e + f*x])) + (4*(2*A - B)*Tan[e + f*x])/(21*a^2*c^5*f) + (4*(2*A - B)*Tan[e + f*x]^3)/(63*a^2*c^5*f)","A",6,4,36,0.1111,1,"{2967, 2859, 2672, 3767}"
70,1,243,0,0.4116676,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^5}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^5)/(a + a*Sin[e + f*x])^3,x]","-\frac{7 c^5 (3 A-8 B) \cos ^3(e+f x)}{a^3 f}-\frac{a^5 c^5 (A-B) \cos ^{11}(e+f x)}{5 f (a \sin (e+f x)+a)^8}+\frac{2 a^3 c^5 (3 A-8 B) \cos ^9(e+f x)}{15 f (a \sin (e+f x)+a)^6}-\frac{6 a^5 c^5 (3 A-8 B) \cos ^7(e+f x)}{5 f \left(a^2 \sin (e+f x)+a^2\right)^4}-\frac{42 a^5 c^5 (3 A-8 B) \cos ^5(e+f x)}{5 f \left(a^4 \sin (e+f x)+a^4\right)^2}-\frac{21 c^5 (3 A-8 B) \sin (e+f x) \cos (e+f x)}{2 a^3 f}-\frac{21 c^5 x (3 A-8 B)}{2 a^3}","-\frac{7 c^5 (3 A-8 B) \cos ^3(e+f x)}{a^3 f}-\frac{a^5 c^5 (A-B) \cos ^{11}(e+f x)}{5 f (a \sin (e+f x)+a)^8}+\frac{2 a^3 c^5 (3 A-8 B) \cos ^9(e+f x)}{15 f (a \sin (e+f x)+a)^6}-\frac{6 a^5 c^5 (3 A-8 B) \cos ^7(e+f x)}{5 f \left(a^2 \sin (e+f x)+a^2\right)^4}-\frac{42 a^5 c^5 (3 A-8 B) \cos ^5(e+f x)}{5 f \left(a^4 \sin (e+f x)+a^4\right)^2}-\frac{21 c^5 (3 A-8 B) \sin (e+f x) \cos (e+f x)}{2 a^3 f}-\frac{21 c^5 x (3 A-8 B)}{2 a^3}",1,"(-21*(3*A - 8*B)*c^5*x)/(2*a^3) - (7*(3*A - 8*B)*c^5*Cos[e + f*x]^3)/(a^3*f) - (21*(3*A - 8*B)*c^5*Cos[e + f*x]*Sin[e + f*x])/(2*a^3*f) - (a^5*(A - B)*c^5*Cos[e + f*x]^11)/(5*f*(a + a*Sin[e + f*x])^8) + (2*a^3*(3*A - 8*B)*c^5*Cos[e + f*x]^9)/(15*f*(a + a*Sin[e + f*x])^6) - (6*a^5*(3*A - 8*B)*c^5*Cos[e + f*x]^7)/(5*f*(a^2 + a^2*Sin[e + f*x])^4) - (42*a^5*(3*A - 8*B)*c^5*Cos[e + f*x]^5)/(5*f*(a^4 + a^4*Sin[e + f*x])^2)","A",8,6,36,0.1667,1,"{2967, 2859, 2680, 2682, 2635, 8}"
71,1,201,0,0.3916482,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^4}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^4)/(a + a*Sin[e + f*x])^3,x]","-\frac{7 c^4 (2 A-7 B) \cos (e+f x)}{2 a^3 f}-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{5 f (a \sin (e+f x)+a)^7}+\frac{2 a^2 c^4 (2 A-7 B) \cos ^7(e+f x)}{15 f (a \sin (e+f x)+a)^5}-\frac{7 c^4 (2 A-7 B) \cos ^3(e+f x)}{6 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{7 c^4 x (2 A-7 B)}{2 a^3}-\frac{14 c^4 (2 A-7 B) \cos ^5(e+f x)}{15 f (a \sin (e+f x)+a)^3}","-\frac{7 c^4 (2 A-7 B) \cos (e+f x)}{2 a^3 f}-\frac{a^4 c^4 (A-B) \cos ^9(e+f x)}{5 f (a \sin (e+f x)+a)^7}+\frac{2 a^2 c^4 (2 A-7 B) \cos ^7(e+f x)}{15 f (a \sin (e+f x)+a)^5}-\frac{7 c^4 (2 A-7 B) \cos ^3(e+f x)}{6 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{7 c^4 x (2 A-7 B)}{2 a^3}-\frac{14 c^4 (2 A-7 B) \cos ^5(e+f x)}{15 f (a \sin (e+f x)+a)^3}",1,"(-7*(2*A - 7*B)*c^4*x)/(2*a^3) - (7*(2*A - 7*B)*c^4*Cos[e + f*x])/(2*a^3*f) - (a^4*(A - B)*c^4*Cos[e + f*x]^9)/(5*f*(a + a*Sin[e + f*x])^7) + (2*a^2*(2*A - 7*B)*c^4*Cos[e + f*x]^7)/(15*f*(a + a*Sin[e + f*x])^5) - (14*(2*A - 7*B)*c^4*Cos[e + f*x]^5)/(15*f*(a + a*Sin[e + f*x])^3) - (7*(2*A - 7*B)*c^4*Cos[e + f*x]^3)/(6*f*(a^3 + a^3*Sin[e + f*x]))","A",7,6,36,0.1667,1,"{2967, 2859, 2680, 2679, 2682, 8}"
72,1,153,0,0.3310048,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^3}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^3,x]","-\frac{c^3 (A-6 B) \cos (e+f x)}{a^3 f}-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{5 f (a \sin (e+f x)+a)^6}-\frac{2 a^3 c^3 (A-6 B) \cos ^3(e+f x)}{3 f \left(a^3 \sin (e+f x)+a^3\right)^2}-\frac{c^3 x (A-6 B)}{a^3}+\frac{2 a c^3 (A-6 B) \cos ^5(e+f x)}{15 f (a \sin (e+f x)+a)^4}","-\frac{c^3 (A-6 B) \cos (e+f x)}{a^3 f}-\frac{a^3 c^3 (A-B) \cos ^7(e+f x)}{5 f (a \sin (e+f x)+a)^6}-\frac{2 a^3 c^3 (A-6 B) \cos ^3(e+f x)}{3 f \left(a^3 \sin (e+f x)+a^3\right)^2}-\frac{c^3 x (A-6 B)}{a^3}+\frac{2 a c^3 (A-6 B) \cos ^5(e+f x)}{15 f (a \sin (e+f x)+a)^4}",1,"-(((A - 6*B)*c^3*x)/a^3) - ((A - 6*B)*c^3*Cos[e + f*x])/(a^3*f) - (a^3*(A - B)*c^3*Cos[e + f*x]^7)/(5*f*(a + a*Sin[e + f*x])^6) + (2*a*(A - 6*B)*c^3*Cos[e + f*x]^5)/(15*f*(a + a*Sin[e + f*x])^4) - (2*a^3*(A - 6*B)*c^3*Cos[e + f*x]^3)/(3*f*(a^3 + a^3*Sin[e + f*x])^2)","A",6,5,36,0.1389,1,"{2967, 2859, 2680, 2682, 8}"
73,1,110,0,0.2648666,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^2}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^3,x]","-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{5 f (a \sin (e+f x)+a)^5}+\frac{2 B c^2 \cos (e+f x)}{f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{B c^2 x}{a^3}-\frac{2 B c^2 \cos ^3(e+f x)}{3 f (a \sin (e+f x)+a)^3}","-\frac{a^2 c^2 (A-B) \cos ^5(e+f x)}{5 f (a \sin (e+f x)+a)^5}+\frac{2 B c^2 \cos (e+f x)}{f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{B c^2 x}{a^3}-\frac{2 B c^2 \cos ^3(e+f x)}{3 f (a \sin (e+f x)+a)^3}",1,"(B*c^2*x)/a^3 - (a^2*(A - B)*c^2*Cos[e + f*x]^5)/(5*f*(a + a*Sin[e + f*x])^5) - (2*B*c^2*Cos[e + f*x]^3)/(3*f*(a + a*Sin[e + f*x])^3) + (2*B*c^2*Cos[e + f*x])/(f*(a^3 + a^3*Sin[e + f*x]))","A",5,4,36,0.1111,1,"{2967, 2859, 2680, 8}"
74,1,103,0,0.2250116,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]))/(a + a*Sin[e + f*x])^3,x]","\frac{c (A+4 B) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{a c (A-11 B) \cos (e+f x)}{15 f \left(a^2 \sin (e+f x)+a^2\right)^2}-\frac{2 c (A-B) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}","\frac{c (A+4 B) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{a c (A-11 B) \cos (e+f x)}{15 f \left(a^2 \sin (e+f x)+a^2\right)^2}-\frac{2 c (A-B) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}",1,"(-2*(A - B)*c*Cos[e + f*x])/(5*f*(a + a*Sin[e + f*x])^3) + (a*(A - 11*B)*c*Cos[e + f*x])/(15*f*(a^2 + a^2*Sin[e + f*x])^2) + ((A + 4*B)*c*Cos[e + f*x])/(15*f*(a^3 + a^3*Sin[e + f*x]))","A",4,4,34,0.1176,1,"{2967, 2857, 2750, 2648}"
75,1,102,0,0.2485332,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])),x]","\frac{2 (3 A+2 B) \tan (e+f x)}{15 a^3 c f}-\frac{(3 A+2 B) \sec (e+f x)}{15 c f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(A-B) \sec (e+f x)}{5 a c f (a \sin (e+f x)+a)^2}","\frac{2 (3 A+2 B) \tan (e+f x)}{15 a^3 c f}-\frac{(3 A+2 B) \sec (e+f x)}{15 c f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(A-B) \sec (e+f x)}{5 a c f (a \sin (e+f x)+a)^2}",1,"-((A - B)*Sec[e + f*x])/(5*a*c*f*(a + a*Sin[e + f*x])^2) - ((3*A + 2*B)*Sec[e + f*x])/(15*c*f*(a^3 + a^3*Sin[e + f*x])) + (2*(3*A + 2*B)*Tan[e + f*x])/(15*a^3*c*f)","A",5,5,36,0.1389,1,"{2967, 2859, 2672, 3767, 8}"
76,1,90,0,0.2044575,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^2),x]","\frac{(4 A+B) \tan ^3(e+f x)}{15 a^3 c^2 f}+\frac{(4 A+B) \tan (e+f x)}{5 a^3 c^2 f}-\frac{(A-B) \sec ^3(e+f x)}{5 c^2 f \left(a^3 \sin (e+f x)+a^3\right)}","\frac{(4 A+B) \tan ^3(e+f x)}{15 a^3 c^2 f}+\frac{(4 A+B) \tan (e+f x)}{5 a^3 c^2 f}-\frac{(A-B) \sec ^3(e+f x)}{5 c^2 f \left(a^3 \sin (e+f x)+a^3\right)}",1,"-((A - B)*Sec[e + f*x]^3)/(5*c^2*f*(a^3 + a^3*Sin[e + f*x])) + ((4*A + B)*Tan[e + f*x])/(5*a^3*c^2*f) + ((4*A + B)*Tan[e + f*x]^3)/(15*a^3*c^2*f)","A",4,3,36,0.08333,1,"{2967, 2859, 3767}"
77,1,84,0,0.1518529,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^3),x]","\frac{A \tan ^5(e+f x)}{5 a^3 c^3 f}+\frac{2 A \tan ^3(e+f x)}{3 a^3 c^3 f}+\frac{A \tan (e+f x)}{a^3 c^3 f}+\frac{B \sec ^5(e+f x)}{5 a^3 c^3 f}","\frac{A \tan ^5(e+f x)}{5 a^3 c^3 f}+\frac{2 A \tan ^3(e+f x)}{3 a^3 c^3 f}+\frac{A \tan (e+f x)}{a^3 c^3 f}+\frac{B \sec ^5(e+f x)}{5 a^3 c^3 f}",1,"(B*Sec[e + f*x]^5)/(5*a^3*c^3*f) + (A*Tan[e + f*x])/(a^3*c^3*f) + (2*A*Tan[e + f*x]^3)/(3*a^3*c^3*f) + (A*Tan[e + f*x]^5)/(5*a^3*c^3*f)","A",4,3,36,0.08333,1,"{2967, 2669, 3767}"
78,1,121,0,0.2232778,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^4} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^4),x]","\frac{(6 A-B) \tan ^5(e+f x)}{35 a^3 c^4 f}+\frac{2 (6 A-B) \tan ^3(e+f x)}{21 a^3 c^4 f}+\frac{(6 A-B) \tan (e+f x)}{7 a^3 c^4 f}+\frac{(A+B) \sec ^5(e+f x)}{7 a^3 f \left(c^4-c^4 \sin (e+f x)\right)}","\frac{(6 A-B) \tan ^5(e+f x)}{35 a^3 c^4 f}+\frac{2 (6 A-B) \tan ^3(e+f x)}{21 a^3 c^4 f}+\frac{(6 A-B) \tan (e+f x)}{7 a^3 c^4 f}+\frac{(A+B) \sec ^5(e+f x)}{7 a^3 f \left(c^4-c^4 \sin (e+f x)\right)}",1,"((A + B)*Sec[e + f*x]^5)/(7*a^3*f*(c^4 - c^4*Sin[e + f*x])) + ((6*A - B)*Tan[e + f*x])/(7*a^3*c^4*f) + (2*(6*A - B)*Tan[e + f*x]^3)/(21*a^3*c^4*f) + ((6*A - B)*Tan[e + f*x]^5)/(35*a^3*c^4*f)","A",4,3,36,0.08333,1,"{2967, 2859, 3767}"
79,1,162,0,0.2887913,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^5} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^5),x]","\frac{2 (7 A-2 B) \tan ^5(e+f x)}{105 a^3 c^5 f}+\frac{4 (7 A-2 B) \tan ^3(e+f x)}{63 a^3 c^5 f}+\frac{2 (7 A-2 B) \tan (e+f x)}{21 a^3 c^5 f}+\frac{(7 A-2 B) \sec ^5(e+f x)}{63 a^3 f \left(c^5-c^5 \sin (e+f x)\right)}+\frac{(A+B) \sec ^5(e+f x)}{9 a^3 c^3 f (c-c \sin (e+f x))^2}","\frac{2 (7 A-2 B) \tan ^5(e+f x)}{105 a^3 c^5 f}+\frac{4 (7 A-2 B) \tan ^3(e+f x)}{63 a^3 c^5 f}+\frac{2 (7 A-2 B) \tan (e+f x)}{21 a^3 c^5 f}+\frac{(7 A-2 B) \sec ^5(e+f x)}{63 a^3 f \left(c^5-c^5 \sin (e+f x)\right)}+\frac{(A+B) \sec ^5(e+f x)}{9 a^3 c^3 f (c-c \sin (e+f x))^2}",1,"((A + B)*Sec[e + f*x]^5)/(9*a^3*c^3*f*(c - c*Sin[e + f*x])^2) + ((7*A - 2*B)*Sec[e + f*x]^5)/(63*a^3*f*(c^5 - c^5*Sin[e + f*x])) + (2*(7*A - 2*B)*Tan[e + f*x])/(21*a^3*c^5*f) + (4*(7*A - 2*B)*Tan[e + f*x]^3)/(63*a^3*c^5*f) + (2*(7*A - 2*B)*Tan[e + f*x]^5)/(105*a^3*c^5*f)","A",5,4,36,0.1111,1,"{2967, 2859, 2672, 3767}"
80,1,205,0,0.3454203,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^6} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^6),x]","\frac{2 (8 A-3 B) \tan ^5(e+f x)}{165 a^3 c^6 f}+\frac{4 (8 A-3 B) \tan ^3(e+f x)}{99 a^3 c^6 f}+\frac{2 (8 A-3 B) \tan (e+f x)}{33 a^3 c^6 f}+\frac{(8 A-3 B) \sec ^5(e+f x)}{99 a^3 f \left(c^6-c^6 \sin (e+f x)\right)}+\frac{(8 A-3 B) \sec ^5(e+f x)}{99 a^3 f \left(c^3-c^3 \sin (e+f x)\right)^2}+\frac{(A+B) \sec ^5(e+f x)}{11 a^3 f \left(c^2-c^2 \sin (e+f x)\right)^3}","\frac{2 (8 A-3 B) \tan ^5(e+f x)}{165 a^3 c^6 f}+\frac{4 (8 A-3 B) \tan ^3(e+f x)}{99 a^3 c^6 f}+\frac{2 (8 A-3 B) \tan (e+f x)}{33 a^3 c^6 f}+\frac{(8 A-3 B) \sec ^5(e+f x)}{99 a^3 f \left(c^6-c^6 \sin (e+f x)\right)}+\frac{(8 A-3 B) \sec ^5(e+f x)}{99 a^3 f \left(c^3-c^3 \sin (e+f x)\right)^2}+\frac{(A+B) \sec ^5(e+f x)}{11 a^3 f \left(c^2-c^2 \sin (e+f x)\right)^3}",1,"((A + B)*Sec[e + f*x]^5)/(11*a^3*f*(c^2 - c^2*Sin[e + f*x])^3) + ((8*A - 3*B)*Sec[e + f*x]^5)/(99*a^3*f*(c^3 - c^3*Sin[e + f*x])^2) + ((8*A - 3*B)*Sec[e + f*x]^5)/(99*a^3*f*(c^6 - c^6*Sin[e + f*x])) + (2*(8*A - 3*B)*Tan[e + f*x])/(33*a^3*c^6*f) + (4*(8*A - 3*B)*Tan[e + f*x]^3)/(99*a^3*c^6*f) + (2*(8*A - 3*B)*Tan[e + f*x]^5)/(165*a^3*c^6*f)","A",6,4,36,0.1111,1,"{2967, 2859, 2672, 3767}"
81,1,198,0,0.4872023,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","\frac{256 a c^5 (11 A-5 B) \cos ^3(e+f x)}{3465 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a c^4 (11 A-5 B) \cos ^3(e+f x)}{1155 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a c^3 (11 A-5 B) \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{231 f}+\frac{2 a c^2 (11 A-5 B) \cos ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{99 f}-\frac{2 a B c \cos ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{11 f}","\frac{256 a c^5 (11 A-5 B) \cos ^3(e+f x)}{3465 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a c^4 (11 A-5 B) \cos ^3(e+f x)}{1155 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a c^3 (11 A-5 B) \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{231 f}+\frac{2 a c^2 (11 A-5 B) \cos ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{99 f}-\frac{2 a B c \cos ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{11 f}",1,"(256*a*(11*A - 5*B)*c^5*Cos[e + f*x]^3)/(3465*f*(c - c*Sin[e + f*x])^(3/2)) + (64*a*(11*A - 5*B)*c^4*Cos[e + f*x]^3)/(1155*f*Sqrt[c - c*Sin[e + f*x]]) + (8*a*(11*A - 5*B)*c^3*Cos[e + f*x]^3*Sqrt[c - c*Sin[e + f*x]])/(231*f) + (2*a*(11*A - 5*B)*c^2*Cos[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(99*f) - (2*a*B*c*Cos[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(11*f)","A",6,4,36,0.1111,1,"{2967, 2856, 2674, 2673}"
82,1,157,0,0.4123321,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","\frac{64 a c^4 (3 A-B) \cos ^3(e+f x)}{315 f (c-c \sin (e+f x))^{3/2}}+\frac{16 a c^3 (3 A-B) \cos ^3(e+f x)}{105 f \sqrt{c-c \sin (e+f x)}}+\frac{2 a c^2 (3 A-B) \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{21 f}-\frac{2 a B c \cos ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{9 f}","\frac{64 a c^4 (3 A-B) \cos ^3(e+f x)}{315 f (c-c \sin (e+f x))^{3/2}}+\frac{16 a c^3 (3 A-B) \cos ^3(e+f x)}{105 f \sqrt{c-c \sin (e+f x)}}+\frac{2 a c^2 (3 A-B) \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{21 f}-\frac{2 a B c \cos ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{9 f}",1,"(64*a*(3*A - B)*c^4*Cos[e + f*x]^3)/(315*f*(c - c*Sin[e + f*x])^(3/2)) + (16*a*(3*A - B)*c^3*Cos[e + f*x]^3)/(105*f*Sqrt[c - c*Sin[e + f*x]]) + (2*a*(3*A - B)*c^2*Cos[e + f*x]^3*Sqrt[c - c*Sin[e + f*x]])/(21*f) - (2*a*B*c*Cos[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(9*f)","A",5,4,36,0.1111,1,"{2967, 2856, 2674, 2673}"
83,1,116,0,0.3200174,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{2 a c^2 (7 A-B) \cos ^3(e+f x)}{35 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a c^3 (7 A-B) \cos ^3(e+f x)}{105 f (c-c \sin (e+f x))^{3/2}}-\frac{2 a B c \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{7 f}","\frac{2 a c^2 (7 A-B) \cos ^3(e+f x)}{35 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a c^3 (7 A-B) \cos ^3(e+f x)}{105 f (c-c \sin (e+f x))^{3/2}}-\frac{2 a B c \cos ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{7 f}",1,"(8*a*(7*A - B)*c^3*Cos[e + f*x]^3)/(105*f*(c - c*Sin[e + f*x])^(3/2)) + (2*a*(7*A - B)*c^2*Cos[e + f*x]^3)/(35*f*Sqrt[c - c*Sin[e + f*x]]) - (2*a*B*c*Cos[e + f*x]^3*Sqrt[c - c*Sin[e + f*x]])/(7*f)","A",4,4,36,0.1111,1,"{2967, 2856, 2674, 2673}"
84,1,73,0,0.2398249,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{2 a c^2 (5 A+B) \cos ^3(e+f x)}{15 f (c-c \sin (e+f x))^{3/2}}-\frac{2 a B c \cos ^3(e+f x)}{5 f \sqrt{c-c \sin (e+f x)}}","\frac{2 a c^2 (5 A+B) \cos ^3(e+f x)}{15 f (c-c \sin (e+f x))^{3/2}}-\frac{2 a B c \cos ^3(e+f x)}{5 f \sqrt{c-c \sin (e+f x)}}",1,"(2*a*(5*A + B)*c^2*Cos[e + f*x]^3)/(15*f*(c - c*Sin[e + f*x])^(3/2)) - (2*a*B*c*Cos[e + f*x]^3)/(5*f*Sqrt[c - c*Sin[e + f*x]])","A",3,3,36,0.08333,1,"{2967, 2856, 2673}"
85,1,122,0,0.3359192,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{2 a (3 A+5 B) \cos (e+f x)}{3 f \sqrt{c-c \sin (e+f x)}}+\frac{2 \sqrt{2} a (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}+\frac{2 a B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{3 c f}","-\frac{2 a (3 A+5 B) \cos (e+f x)}{3 f \sqrt{c-c \sin (e+f x)}}+\frac{2 \sqrt{2} a (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}+\frac{2 a B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{3 c f}",1,"(2*Sqrt[2]*a*(A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(Sqrt[c]*f) - (2*a*(3*A + 5*B)*Cos[e + f*x])/(3*f*Sqrt[c - c*Sin[e + f*x]]) + (2*a*B*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(3*c*f)","A",5,5,36,0.1389,1,"{2967, 2858, 2751, 2649, 206}"
86,1,115,0,0.3183425,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","-\frac{a (A+5 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{2} c^{3/2} f}+\frac{a (A+B) \cos (e+f x)}{f (c-c \sin (e+f x))^{3/2}}+\frac{2 a B \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}","-\frac{a (A+5 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{2} c^{3/2} f}+\frac{a (A+B) \cos (e+f x)}{f (c-c \sin (e+f x))^{3/2}}+\frac{2 a B \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}",1,"-((a*(A + 5*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(Sqrt[2]*c^(3/2)*f)) + (a*(A + B)*Cos[e + f*x])/(f*(c - c*Sin[e + f*x])^(3/2)) + (2*a*B*Cos[e + f*x])/(c*f*Sqrt[c - c*Sin[e + f*x]])","A",5,5,36,0.1389,1,"{2967, 2857, 2751, 2649, 206}"
87,1,126,0,0.3345081,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","-\frac{a (A-7 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} c^{5/2} f}-\frac{a (A+9 B) \cos (e+f x)}{8 c f (c-c \sin (e+f x))^{3/2}}+\frac{a (A+B) \cos (e+f x)}{2 f (c-c \sin (e+f x))^{5/2}}","-\frac{a (A-7 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} c^{5/2} f}-\frac{a (A+9 B) \cos (e+f x)}{8 c f (c-c \sin (e+f x))^{3/2}}+\frac{a (A+B) \cos (e+f x)}{2 f (c-c \sin (e+f x))^{5/2}}",1,"-(a*(A - 7*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(8*Sqrt[2]*c^(5/2)*f) + (a*(A + B)*Cos[e + f*x])/(2*f*(c - c*Sin[e + f*x])^(5/2)) - (a*(A + 9*B)*Cos[e + f*x])/(8*c*f*(c - c*Sin[e + f*x])^(3/2))","A",5,5,36,0.1389,1,"{2967, 2857, 2750, 2649, 206}"
88,1,163,0,0.3729459,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","-\frac{a (A-3 B) \cos (e+f x)}{32 c^2 f (c-c \sin (e+f x))^{3/2}}-\frac{a (A-3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{32 \sqrt{2} c^{7/2} f}-\frac{a (A+13 B) \cos (e+f x)}{24 c f (c-c \sin (e+f x))^{5/2}}+\frac{a (A+B) \cos (e+f x)}{3 f (c-c \sin (e+f x))^{7/2}}","-\frac{a (A-3 B) \cos (e+f x)}{32 c^2 f (c-c \sin (e+f x))^{3/2}}-\frac{a (A-3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{32 \sqrt{2} c^{7/2} f}-\frac{a (A+13 B) \cos (e+f x)}{24 c f (c-c \sin (e+f x))^{5/2}}+\frac{a (A+B) \cos (e+f x)}{3 f (c-c \sin (e+f x))^{7/2}}",1,"-(a*(A - 3*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(32*Sqrt[2]*c^(7/2)*f) + (a*(A + B)*Cos[e + f*x])/(3*f*(c - c*Sin[e + f*x])^(7/2)) - (a*(A + 13*B)*Cos[e + f*x])/(24*c*f*(c - c*Sin[e + f*x])^(5/2)) - (a*(A - 3*B)*Cos[e + f*x])/(32*c^2*f*(c - c*Sin[e + f*x])^(3/2))","A",6,6,36,0.1667,1,"{2967, 2857, 2750, 2650, 2649, 206}"
89,1,210,0,0.5543839,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","\frac{256 a^2 c^6 (13 A-3 B) \cos ^5(e+f x)}{15015 f (c-c \sin (e+f x))^{5/2}}+\frac{64 a^2 c^5 (13 A-3 B) \cos ^5(e+f x)}{3003 f (c-c \sin (e+f x))^{3/2}}+\frac{8 a^2 c^4 (13 A-3 B) \cos ^5(e+f x)}{429 f \sqrt{c-c \sin (e+f x)}}+\frac{2 a^2 c^3 (13 A-3 B) \cos ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{143 f}-\frac{2 a^2 B c^2 \cos ^5(e+f x) (c-c \sin (e+f x))^{3/2}}{13 f}","\frac{256 a^2 c^6 (13 A-3 B) \cos ^5(e+f x)}{15015 f (c-c \sin (e+f x))^{5/2}}+\frac{64 a^2 c^5 (13 A-3 B) \cos ^5(e+f x)}{3003 f (c-c \sin (e+f x))^{3/2}}+\frac{8 a^2 c^4 (13 A-3 B) \cos ^5(e+f x)}{429 f \sqrt{c-c \sin (e+f x)}}+\frac{2 a^2 c^3 (13 A-3 B) \cos ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{143 f}-\frac{2 a^2 B c^2 \cos ^5(e+f x) (c-c \sin (e+f x))^{3/2}}{13 f}",1,"(256*a^2*(13*A - 3*B)*c^6*Cos[e + f*x]^5)/(15015*f*(c - c*Sin[e + f*x])^(5/2)) + (64*a^2*(13*A - 3*B)*c^5*Cos[e + f*x]^5)/(3003*f*(c - c*Sin[e + f*x])^(3/2)) + (8*a^2*(13*A - 3*B)*c^4*Cos[e + f*x]^5)/(429*f*Sqrt[c - c*Sin[e + f*x]]) + (2*a^2*(13*A - 3*B)*c^3*Cos[e + f*x]^5*Sqrt[c - c*Sin[e + f*x]])/(143*f) - (2*a^2*B*c^2*Cos[e + f*x]^5*(c - c*Sin[e + f*x])^(3/2))/(13*f)","A",6,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
90,1,167,0,0.4528752,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","\frac{2 a^2 c^3 (11 A-B) \cos ^5(e+f x)}{99 f \sqrt{c-c \sin (e+f x)}}+\frac{16 a^2 c^4 (11 A-B) \cos ^5(e+f x)}{693 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a^2 c^5 (11 A-B) \cos ^5(e+f x)}{3465 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{11 f}","\frac{2 a^2 c^3 (11 A-B) \cos ^5(e+f x)}{99 f \sqrt{c-c \sin (e+f x)}}+\frac{16 a^2 c^4 (11 A-B) \cos ^5(e+f x)}{693 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a^2 c^5 (11 A-B) \cos ^5(e+f x)}{3465 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{11 f}",1,"(64*a^2*(11*A - B)*c^5*Cos[e + f*x]^5)/(3465*f*(c - c*Sin[e + f*x])^(5/2)) + (16*a^2*(11*A - B)*c^4*Cos[e + f*x]^5)/(693*f*(c - c*Sin[e + f*x])^(3/2)) + (2*a^2*(11*A - B)*c^3*Cos[e + f*x]^5)/(99*f*Sqrt[c - c*Sin[e + f*x]]) - (2*a^2*B*c^2*Cos[e + f*x]^5*Sqrt[c - c*Sin[e + f*x]])/(11*f)","A",5,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
91,1,120,0,0.3866644,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{2 a^2 c^3 (9 A+B) \cos ^5(e+f x)}{63 f (c-c \sin (e+f x))^{3/2}}+\frac{8 a^2 c^4 (9 A+B) \cos ^5(e+f x)}{315 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{9 f \sqrt{c-c \sin (e+f x)}}","\frac{2 a^2 c^3 (9 A+B) \cos ^5(e+f x)}{63 f (c-c \sin (e+f x))^{3/2}}+\frac{8 a^2 c^4 (9 A+B) \cos ^5(e+f x)}{315 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{9 f \sqrt{c-c \sin (e+f x)}}",1,"(8*a^2*(9*A + B)*c^4*Cos[e + f*x]^5)/(315*f*(c - c*Sin[e + f*x])^(5/2)) + (2*a^2*(9*A + B)*c^3*Cos[e + f*x]^5)/(63*f*(c - c*Sin[e + f*x])^(3/2)) - (2*a^2*B*c^2*Cos[e + f*x]^5)/(9*f*Sqrt[c - c*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
92,1,81,0,0.3303447,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{2 a^2 c^3 (7 A+3 B) \cos ^5(e+f x)}{35 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{7 f (c-c \sin (e+f x))^{3/2}}","\frac{2 a^2 c^3 (7 A+3 B) \cos ^5(e+f x)}{35 f (c-c \sin (e+f x))^{5/2}}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{7 f (c-c \sin (e+f x))^{3/2}}",1,"(2*a^2*(7*A + 3*B)*c^3*Cos[e + f*x]^5)/(35*f*(c - c*Sin[e + f*x])^(5/2)) - (2*a^2*B*c^2*Cos[e + f*x]^5)/(7*f*(c - c*Sin[e + f*x])^(3/2))","A",3,3,38,0.07895,1,"{2967, 2856, 2673}"
93,1,161,0,0.4421555,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{2 a^2 c (A+B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}-\frac{4 a^2 (A+B) \cos (e+f x)}{f \sqrt{c-c \sin (e+f x)}}+\frac{4 \sqrt{2} a^2 (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^{5/2}}","-\frac{2 a^2 c (A+B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}-\frac{4 a^2 (A+B) \cos (e+f x)}{f \sqrt{c-c \sin (e+f x)}}+\frac{4 \sqrt{2} a^2 (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}-\frac{2 a^2 B c^2 \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^{5/2}}",1,"(4*Sqrt[2]*a^2*(A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(Sqrt[c]*f) - (2*a^2*B*c^2*Cos[e + f*x]^5)/(5*f*(c - c*Sin[e + f*x])^(5/2)) - (2*a^2*(A + B)*c*Cos[e + f*x]^3)/(3*f*(c - c*Sin[e + f*x])^(3/2)) - (4*a^2*(A + B)*Cos[e + f*x])/(f*Sqrt[c - c*Sin[e + f*x]])","A",6,5,38,0.1316,1,"{2967, 2860, 2679, 2649, 206}"
94,1,176,0,0.4809169,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{2 f (c-c \sin (e+f x))^{7/2}}-\frac{\sqrt{2} a^2 (3 A+7 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{c^{3/2} f}+\frac{a^2 (3 A+7 B) \cos ^3(e+f x)}{6 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 (3 A+7 B) \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{2 f (c-c \sin (e+f x))^{7/2}}-\frac{\sqrt{2} a^2 (3 A+7 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{c^{3/2} f}+\frac{a^2 (3 A+7 B) \cos ^3(e+f x)}{6 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 (3 A+7 B) \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}",1,"-((Sqrt[2]*a^2*(3*A + 7*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(c^(3/2)*f)) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(2*f*(c - c*Sin[e + f*x])^(7/2)) + (a^2*(3*A + 7*B)*Cos[e + f*x]^3)/(6*f*(c - c*Sin[e + f*x])^(3/2)) + (a^2*(3*A + 7*B)*Cos[e + f*x])/(c*f*Sqrt[c - c*Sin[e + f*x]])","A",6,5,38,0.1316,1,"{2967, 2859, 2679, 2649, 206}"
95,1,175,0,0.4784184,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{4 f (c-c \sin (e+f x))^{9/2}}-\frac{3 a^2 (A+9 B) \cos (e+f x)}{8 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{3 a^2 (A+9 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} c^{5/2} f}-\frac{a^2 (A+9 B) \cos ^3(e+f x)}{8 f (c-c \sin (e+f x))^{5/2}}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{4 f (c-c \sin (e+f x))^{9/2}}-\frac{3 a^2 (A+9 B) \cos (e+f x)}{8 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{3 a^2 (A+9 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} c^{5/2} f}-\frac{a^2 (A+9 B) \cos ^3(e+f x)}{8 f (c-c \sin (e+f x))^{5/2}}",1,"(3*a^2*(A + 9*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(4*Sqrt[2]*c^(5/2)*f) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(4*f*(c - c*Sin[e + f*x])^(9/2)) - (a^2*(A + 9*B)*Cos[e + f*x]^3)/(8*f*(c - c*Sin[e + f*x])^(5/2)) - (3*a^2*(A + 9*B)*Cos[e + f*x])/(8*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",6,6,38,0.1579,1,"{2967, 2859, 2680, 2679, 2649, 206}"
96,1,175,0,0.4910152,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{6 f (c-c \sin (e+f x))^{11/2}}-\frac{a^2 (A-11 B) \cos (e+f x)}{16 c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 (A-11 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{16 \sqrt{2} c^{7/2} f}+\frac{a^2 (A-11 B) \cos ^3(e+f x)}{24 f (c-c \sin (e+f x))^{7/2}}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{6 f (c-c \sin (e+f x))^{11/2}}-\frac{a^2 (A-11 B) \cos (e+f x)}{16 c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 (A-11 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{16 \sqrt{2} c^{7/2} f}+\frac{a^2 (A-11 B) \cos ^3(e+f x)}{24 f (c-c \sin (e+f x))^{7/2}}",1,"(a^2*(A - 11*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(16*Sqrt[2]*c^(7/2)*f) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(6*f*(c - c*Sin[e + f*x])^(11/2)) + (a^2*(A - 11*B)*Cos[e + f*x]^3)/(24*f*(c - c*Sin[e + f*x])^(7/2)) - (a^2*(A - 11*B)*Cos[e + f*x])/(16*c^2*f*(c - c*Sin[e + f*x])^(3/2))","A",6,5,38,0.1316,1,"{2967, 2859, 2680, 2649, 206}"
97,1,222,0,0.5110904,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{9/2}} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(9/2),x]","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{8 f (c-c \sin (e+f x))^{13/2}}+\frac{a^2 (3 A-13 B) \cos (e+f x)}{256 c^3 f (c-c \sin (e+f x))^{3/2}}-\frac{a^2 (3 A-13 B) \cos (e+f x)}{64 c^2 f (c-c \sin (e+f x))^{5/2}}+\frac{a^2 (3 A-13 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{256 \sqrt{2} c^{9/2} f}+\frac{a^2 (3 A-13 B) \cos ^3(e+f x)}{48 f (c-c \sin (e+f x))^{9/2}}","\frac{a^2 c^2 (A+B) \cos ^5(e+f x)}{8 f (c-c \sin (e+f x))^{13/2}}+\frac{a^2 (3 A-13 B) \cos (e+f x)}{256 c^3 f (c-c \sin (e+f x))^{3/2}}-\frac{a^2 (3 A-13 B) \cos (e+f x)}{64 c^2 f (c-c \sin (e+f x))^{5/2}}+\frac{a^2 (3 A-13 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{256 \sqrt{2} c^{9/2} f}+\frac{a^2 (3 A-13 B) \cos ^3(e+f x)}{48 f (c-c \sin (e+f x))^{9/2}}",1,"(a^2*(3*A - 13*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(256*Sqrt[2]*c^(9/2)*f) + (a^2*(A + B)*c^2*Cos[e + f*x]^5)/(8*f*(c - c*Sin[e + f*x])^(13/2)) + (a^2*(3*A - 13*B)*Cos[e + f*x]^3)/(48*f*(c - c*Sin[e + f*x])^(9/2)) - (a^2*(3*A - 13*B)*Cos[e + f*x])/(64*c^2*f*(c - c*Sin[e + f*x])^(5/2)) + (a^2*(3*A - 13*B)*Cos[e + f*x])/(256*c^3*f*(c - c*Sin[e + f*x])^(3/2))","A",7,6,38,0.1579,1,"{2967, 2859, 2680, 2650, 2649, 206}"
98,1,210,0,0.5343928,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","\frac{2 a^3 c^4 (15 A-B) \cos ^7(e+f x)}{195 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a^3 c^5 (15 A-B) \cos ^7(e+f x)}{715 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a^3 c^6 (15 A-B) \cos ^7(e+f x)}{6435 f (c-c \sin (e+f x))^{5/2}}+\frac{256 a^3 c^7 (15 A-B) \cos ^7(e+f x)}{45045 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x) \sqrt{c-c \sin (e+f x)}}{15 f}","\frac{2 a^3 c^4 (15 A-B) \cos ^7(e+f x)}{195 f \sqrt{c-c \sin (e+f x)}}+\frac{8 a^3 c^5 (15 A-B) \cos ^7(e+f x)}{715 f (c-c \sin (e+f x))^{3/2}}+\frac{64 a^3 c^6 (15 A-B) \cos ^7(e+f x)}{6435 f (c-c \sin (e+f x))^{5/2}}+\frac{256 a^3 c^7 (15 A-B) \cos ^7(e+f x)}{45045 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x) \sqrt{c-c \sin (e+f x)}}{15 f}",1,"(256*a^3*(15*A - B)*c^7*Cos[e + f*x]^7)/(45045*f*(c - c*Sin[e + f*x])^(7/2)) + (64*a^3*(15*A - B)*c^6*Cos[e + f*x]^7)/(6435*f*(c - c*Sin[e + f*x])^(5/2)) + (8*a^3*(15*A - B)*c^5*Cos[e + f*x]^7)/(715*f*(c - c*Sin[e + f*x])^(3/2)) + (2*a^3*(15*A - B)*c^4*Cos[e + f*x]^7)/(195*f*Sqrt[c - c*Sin[e + f*x]]) - (2*a^3*B*c^3*Cos[e + f*x]^7*Sqrt[c - c*Sin[e + f*x]])/(15*f)","A",6,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
99,1,161,0,0.4716441,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","\frac{2 a^3 c^4 (13 A+B) \cos ^7(e+f x)}{143 f (c-c \sin (e+f x))^{3/2}}+\frac{16 a^3 c^5 (13 A+B) \cos ^7(e+f x)}{1287 f (c-c \sin (e+f x))^{5/2}}+\frac{64 a^3 c^6 (13 A+B) \cos ^7(e+f x)}{9009 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{13 f \sqrt{c-c \sin (e+f x)}}","\frac{2 a^3 c^4 (13 A+B) \cos ^7(e+f x)}{143 f (c-c \sin (e+f x))^{3/2}}+\frac{16 a^3 c^5 (13 A+B) \cos ^7(e+f x)}{1287 f (c-c \sin (e+f x))^{5/2}}+\frac{64 a^3 c^6 (13 A+B) \cos ^7(e+f x)}{9009 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{13 f \sqrt{c-c \sin (e+f x)}}",1,"(64*a^3*(13*A + B)*c^6*Cos[e + f*x]^7)/(9009*f*(c - c*Sin[e + f*x])^(7/2)) + (16*a^3*(13*A + B)*c^5*Cos[e + f*x]^7)/(1287*f*(c - c*Sin[e + f*x])^(5/2)) + (2*a^3*(13*A + B)*c^4*Cos[e + f*x]^7)/(143*f*(c - c*Sin[e + f*x])^(3/2)) - (2*a^3*B*c^3*Cos[e + f*x]^7)/(13*f*Sqrt[c - c*Sin[e + f*x]])","A",5,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
100,1,124,0,0.4073293,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{2 a^3 c^4 (11 A+3 B) \cos ^7(e+f x)}{99 f (c-c \sin (e+f x))^{5/2}}+\frac{8 a^3 c^5 (11 A+3 B) \cos ^7(e+f x)}{693 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{11 f (c-c \sin (e+f x))^{3/2}}","\frac{2 a^3 c^4 (11 A+3 B) \cos ^7(e+f x)}{99 f (c-c \sin (e+f x))^{5/2}}+\frac{8 a^3 c^5 (11 A+3 B) \cos ^7(e+f x)}{693 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{11 f (c-c \sin (e+f x))^{3/2}}",1,"(8*a^3*(11*A + 3*B)*c^5*Cos[e + f*x]^7)/(693*f*(c - c*Sin[e + f*x])^(7/2)) + (2*a^3*(11*A + 3*B)*c^4*Cos[e + f*x]^7)/(99*f*(c - c*Sin[e + f*x])^(5/2)) - (2*a^3*B*c^3*Cos[e + f*x]^7)/(11*f*(c - c*Sin[e + f*x])^(3/2))","A",4,4,38,0.1053,1,"{2967, 2856, 2674, 2673}"
101,1,81,0,0.3049811,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{2 a^3 c^4 (9 A+5 B) \cos ^7(e+f x)}{63 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{9 f (c-c \sin (e+f x))^{5/2}}","\frac{2 a^3 c^4 (9 A+5 B) \cos ^7(e+f x)}{63 f (c-c \sin (e+f x))^{7/2}}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{9 f (c-c \sin (e+f x))^{5/2}}",1,"(2*a^3*(9*A + 5*B)*c^4*Cos[e + f*x]^7)/(63*f*(c - c*Sin[e + f*x])^(7/2)) - (2*a^3*B*c^3*Cos[e + f*x]^7)/(9*f*(c - c*Sin[e + f*x])^(5/2))","A",3,3,38,0.07895,1,"{2967, 2856, 2673}"
102,1,200,0,0.5212966,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{2 a^3 c^2 (A+B) \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^{5/2}}-\frac{4 a^3 c (A+B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}-\frac{8 a^3 (A+B) \cos (e+f x)}{f \sqrt{c-c \sin (e+f x)}}+\frac{8 \sqrt{2} a^3 (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{7 f (c-c \sin (e+f x))^{7/2}}","-\frac{2 a^3 c^2 (A+B) \cos ^5(e+f x)}{5 f (c-c \sin (e+f x))^{5/2}}-\frac{4 a^3 c (A+B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}-\frac{8 a^3 (A+B) \cos (e+f x)}{f \sqrt{c-c \sin (e+f x)}}+\frac{8 \sqrt{2} a^3 (A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{c} f}-\frac{2 a^3 B c^3 \cos ^7(e+f x)}{7 f (c-c \sin (e+f x))^{7/2}}",1,"(8*Sqrt[2]*a^3*(A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(Sqrt[c]*f) - (2*a^3*B*c^3*Cos[e + f*x]^7)/(7*f*(c - c*Sin[e + f*x])^(7/2)) - (2*a^3*(A + B)*c^2*Cos[e + f*x]^5)/(5*f*(c - c*Sin[e + f*x])^(5/2)) - (4*a^3*(A + B)*c*Cos[e + f*x]^3)/(3*f*(c - c*Sin[e + f*x])^(3/2)) - (8*a^3*(A + B)*Cos[e + f*x])/(f*Sqrt[c - c*Sin[e + f*x]])","A",7,5,38,0.1316,1,"{2967, 2860, 2679, 2649, 206}"
103,1,218,0,0.5461366,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{2 f (c-c \sin (e+f x))^{9/2}}-\frac{2 \sqrt{2} a^3 (5 A+9 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{c^{3/2} f}+\frac{a^3 c (5 A+9 B) \cos ^5(e+f x)}{10 f (c-c \sin (e+f x))^{5/2}}+\frac{a^3 (5 A+9 B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}+\frac{2 a^3 (5 A+9 B) \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{2 f (c-c \sin (e+f x))^{9/2}}-\frac{2 \sqrt{2} a^3 (5 A+9 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{c^{3/2} f}+\frac{a^3 c (5 A+9 B) \cos ^5(e+f x)}{10 f (c-c \sin (e+f x))^{5/2}}+\frac{a^3 (5 A+9 B) \cos ^3(e+f x)}{3 f (c-c \sin (e+f x))^{3/2}}+\frac{2 a^3 (5 A+9 B) \cos (e+f x)}{c f \sqrt{c-c \sin (e+f x)}}",1,"(-2*Sqrt[2]*a^3*(5*A + 9*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(c^(3/2)*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(2*f*(c - c*Sin[e + f*x])^(9/2)) + (a^3*(5*A + 9*B)*c*Cos[e + f*x]^5)/(10*f*(c - c*Sin[e + f*x])^(5/2)) + (a^3*(5*A + 9*B)*Cos[e + f*x]^3)/(3*f*(c - c*Sin[e + f*x])^(3/2)) + (2*a^3*(5*A + 9*B)*Cos[e + f*x])/(c*f*Sqrt[c - c*Sin[e + f*x]])","A",7,5,38,0.1316,1,"{2967, 2859, 2679, 2649, 206}"
104,1,225,0,0.5487249,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{4 f (c-c \sin (e+f x))^{11/2}}-\frac{5 a^3 (3 A+11 B) \cos (e+f x)}{4 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{5 a^3 (3 A+11 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{2 \sqrt{2} c^{5/2} f}-\frac{a^3 c (3 A+11 B) \cos ^5(e+f x)}{8 f (c-c \sin (e+f x))^{7/2}}-\frac{5 a^3 (3 A+11 B) \cos ^3(e+f x)}{24 c f (c-c \sin (e+f x))^{3/2}}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{4 f (c-c \sin (e+f x))^{11/2}}-\frac{5 a^3 (3 A+11 B) \cos (e+f x)}{4 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{5 a^3 (3 A+11 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{2 \sqrt{2} c^{5/2} f}-\frac{a^3 c (3 A+11 B) \cos ^5(e+f x)}{8 f (c-c \sin (e+f x))^{7/2}}-\frac{5 a^3 (3 A+11 B) \cos ^3(e+f x)}{24 c f (c-c \sin (e+f x))^{3/2}}",1,"(5*a^3*(3*A + 11*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(2*Sqrt[2]*c^(5/2)*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(4*f*(c - c*Sin[e + f*x])^(11/2)) - (a^3*(3*A + 11*B)*c*Cos[e + f*x]^5)/(8*f*(c - c*Sin[e + f*x])^(7/2)) - (5*a^3*(3*A + 11*B)*Cos[e + f*x]^3)/(24*c*f*(c - c*Sin[e + f*x])^(3/2)) - (5*a^3*(3*A + 11*B)*Cos[e + f*x])/(4*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",7,6,38,0.1579,1,"{2967, 2859, 2680, 2679, 2649, 206}"
105,1,217,0,0.5493852,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{6 f (c-c \sin (e+f x))^{13/2}}+\frac{5 a^3 (A+13 B) \cos (e+f x)}{16 c^3 f \sqrt{c-c \sin (e+f x)}}-\frac{5 a^3 (A+13 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} c^{7/2} f}-\frac{a^3 c (A+13 B) \cos ^5(e+f x)}{24 f (c-c \sin (e+f x))^{9/2}}+\frac{5 a^3 (A+13 B) \cos ^3(e+f x)}{48 c f (c-c \sin (e+f x))^{5/2}}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{6 f (c-c \sin (e+f x))^{13/2}}+\frac{5 a^3 (A+13 B) \cos (e+f x)}{16 c^3 f \sqrt{c-c \sin (e+f x)}}-\frac{5 a^3 (A+13 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} c^{7/2} f}-\frac{a^3 c (A+13 B) \cos ^5(e+f x)}{24 f (c-c \sin (e+f x))^{9/2}}+\frac{5 a^3 (A+13 B) \cos ^3(e+f x)}{48 c f (c-c \sin (e+f x))^{5/2}}",1,"(-5*a^3*(A + 13*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(8*Sqrt[2]*c^(7/2)*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(6*f*(c - c*Sin[e + f*x])^(13/2)) - (a^3*(A + 13*B)*c*Cos[e + f*x]^5)/(24*f*(c - c*Sin[e + f*x])^(9/2)) + (5*a^3*(A + 13*B)*Cos[e + f*x]^3)/(48*c*f*(c - c*Sin[e + f*x])^(5/2)) + (5*a^3*(A + 13*B)*Cos[e + f*x])/(16*c^3*f*Sqrt[c - c*Sin[e + f*x]])","A",7,6,38,0.1579,1,"{2967, 2859, 2680, 2679, 2649, 206}"
106,1,217,0,0.5572934,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{9/2}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(9/2),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{8 f (c-c \sin (e+f x))^{15/2}}+\frac{5 a^3 (A-15 B) \cos (e+f x)}{128 c^3 f (c-c \sin (e+f x))^{3/2}}-\frac{5 a^3 (A-15 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{128 \sqrt{2} c^{9/2} f}+\frac{a^3 c (A-15 B) \cos ^5(e+f x)}{48 f (c-c \sin (e+f x))^{11/2}}-\frac{5 a^3 (A-15 B) \cos ^3(e+f x)}{192 c f (c-c \sin (e+f x))^{7/2}}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{8 f (c-c \sin (e+f x))^{15/2}}+\frac{5 a^3 (A-15 B) \cos (e+f x)}{128 c^3 f (c-c \sin (e+f x))^{3/2}}-\frac{5 a^3 (A-15 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{128 \sqrt{2} c^{9/2} f}+\frac{a^3 c (A-15 B) \cos ^5(e+f x)}{48 f (c-c \sin (e+f x))^{11/2}}-\frac{5 a^3 (A-15 B) \cos ^3(e+f x)}{192 c f (c-c \sin (e+f x))^{7/2}}",1,"(-5*a^3*(A - 15*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(128*Sqrt[2]*c^(9/2)*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(8*f*(c - c*Sin[e + f*x])^(15/2)) + (a^3*(A - 15*B)*c*Cos[e + f*x]^5)/(48*f*(c - c*Sin[e + f*x])^(11/2)) - (5*a^3*(A - 15*B)*Cos[e + f*x]^3)/(192*c*f*(c - c*Sin[e + f*x])^(7/2)) + (5*a^3*(A - 15*B)*Cos[e + f*x])/(128*c^3*f*(c - c*Sin[e + f*x])^(3/2))","A",7,5,38,0.1316,1,"{2967, 2859, 2680, 2649, 206}"
107,1,266,0,0.5870539,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{11/2}} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(11/2),x]","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{10 f (c-c \sin (e+f x))^{17/2}}-\frac{a^3 (3 A-17 B) \cos (e+f x)}{512 c^4 f (c-c \sin (e+f x))^{3/2}}+\frac{a^3 (3 A-17 B) \cos (e+f x)}{128 c^3 f (c-c \sin (e+f x))^{5/2}}-\frac{a^3 (3 A-17 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{512 \sqrt{2} c^{11/2} f}+\frac{a^3 c (3 A-17 B) \cos ^5(e+f x)}{80 f (c-c \sin (e+f x))^{13/2}}-\frac{a^3 (3 A-17 B) \cos ^3(e+f x)}{96 c f (c-c \sin (e+f x))^{9/2}}","\frac{a^3 c^3 (A+B) \cos ^7(e+f x)}{10 f (c-c \sin (e+f x))^{17/2}}-\frac{a^3 (3 A-17 B) \cos (e+f x)}{512 c^4 f (c-c \sin (e+f x))^{3/2}}+\frac{a^3 (3 A-17 B) \cos (e+f x)}{128 c^3 f (c-c \sin (e+f x))^{5/2}}-\frac{a^3 (3 A-17 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{512 \sqrt{2} c^{11/2} f}+\frac{a^3 c (3 A-17 B) \cos ^5(e+f x)}{80 f (c-c \sin (e+f x))^{13/2}}-\frac{a^3 (3 A-17 B) \cos ^3(e+f x)}{96 c f (c-c \sin (e+f x))^{9/2}}",1,"-(a^3*(3*A - 17*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(512*Sqrt[2]*c^(11/2)*f) + (a^3*(A + B)*c^3*Cos[e + f*x]^7)/(10*f*(c - c*Sin[e + f*x])^(17/2)) + (a^3*(3*A - 17*B)*c*Cos[e + f*x]^5)/(80*f*(c - c*Sin[e + f*x])^(13/2)) - (a^3*(3*A - 17*B)*Cos[e + f*x]^3)/(96*c*f*(c - c*Sin[e + f*x])^(9/2)) + (a^3*(3*A - 17*B)*Cos[e + f*x])/(128*c^3*f*(c - c*Sin[e + f*x])^(5/2)) - (a^3*(3*A - 17*B)*Cos[e + f*x])/(512*c^4*f*(c - c*Sin[e + f*x])^(3/2))","A",8,6,38,0.1579,1,"{2967, 2859, 2680, 2650, 2649, 206}"
108,1,200,0,0.3845754,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2}}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2))/(a + a*Sin[e + f*x]),x]","-\frac{12 c^2 (7 A-9 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{35 a f}-\frac{32 c^3 (7 A-9 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{35 a f}-\frac{128 c^4 (7 A-9 B) \cos (e+f x)}{35 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (7 A-9 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{7 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{9/2}}{a c f}","-\frac{12 c^2 (7 A-9 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{35 a f}-\frac{32 c^3 (7 A-9 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{35 a f}-\frac{128 c^4 (7 A-9 B) \cos (e+f x)}{35 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (7 A-9 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{7 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{9/2}}{a c f}",1,"(-128*(7*A - 9*B)*c^4*Cos[e + f*x])/(35*a*f*Sqrt[c - c*Sin[e + f*x]]) - (32*(7*A - 9*B)*c^3*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(35*a*f) - (12*(7*A - 9*B)*c^2*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(35*a*f) - ((7*A - 9*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(7*a*f) - ((A - B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(9/2))/(a*c*f)","A",6,4,38,0.1053,1,"{2967, 2855, 2647, 2646}"
109,1,159,0,0.3501314,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/(a + a*Sin[e + f*x]),x]","-\frac{8 c^2 (5 A-7 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{15 a f}-\frac{32 c^3 (5 A-7 B) \cos (e+f x)}{15 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (5 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{5 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{a c f}","-\frac{8 c^2 (5 A-7 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{15 a f}-\frac{32 c^3 (5 A-7 B) \cos (e+f x)}{15 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (5 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{5 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{a c f}",1,"(-32*(5*A - 7*B)*c^3*Cos[e + f*x])/(15*a*f*Sqrt[c - c*Sin[e + f*x]]) - (8*(5*A - 7*B)*c^2*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(15*a*f) - ((5*A - 7*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(5*a*f) - ((A - B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(a*c*f)","A",5,4,38,0.1053,1,"{2967, 2855, 2647, 2646}"
110,1,118,0,0.3169231,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/(a + a*Sin[e + f*x]),x]","-\frac{4 c^2 (3 A-5 B) \cos (e+f x)}{3 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (3 A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{a c f}","-\frac{4 c^2 (3 A-5 B) \cos (e+f x)}{3 a f \sqrt{c-c \sin (e+f x)}}-\frac{c (3 A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a f}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{a c f}",1,"(-4*(3*A - 5*B)*c^2*Cos[e + f*x])/(3*a*f*Sqrt[c - c*Sin[e + f*x]]) - ((3*A - 5*B)*c*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(3*a*f) - ((A - B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(a*c*f)","A",4,4,38,0.1053,1,"{2967, 2855, 2647, 2646}"
111,1,73,0,0.2747287,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/(a + a*Sin[e + f*x]),x]","-\frac{c (A-3 B) \cos (e+f x)}{a f \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{a c f}","-\frac{c (A-3 B) \cos (e+f x)}{a f \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{a c f}",1,"-(((A - 3*B)*c*Cos[e + f*x])/(a*f*Sqrt[c - c*Sin[e + f*x]])) - ((A - B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(a*c*f)","A",3,3,38,0.07895,1,"{2967, 2855, 2646}"
112,1,91,0,0.2833676,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]]),x]","\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{2} a \sqrt{c} f}-\frac{(A-B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{a c f}","\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{\sqrt{2} a \sqrt{c} f}-\frac{(A-B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{a c f}",1,"((A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(Sqrt[2]*a*Sqrt[c]*f) - ((A - B)*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a*c*f)","A",4,4,38,0.1053,1,"{2967, 2855, 2649, 206}"
113,1,136,0,0.3304269,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2)),x]","\frac{(3 A-B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} a c^{3/2} f}+\frac{(3 A-B) \cos (e+f x)}{4 a f (c-c \sin (e+f x))^{3/2}}-\frac{(A-B) \sec (e+f x)}{a c f \sqrt{c-c \sin (e+f x)}}","\frac{(3 A-B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} a c^{3/2} f}+\frac{(3 A-B) \cos (e+f x)}{4 a f (c-c \sin (e+f x))^{3/2}}-\frac{(A-B) \sec (e+f x)}{a c f \sqrt{c-c \sin (e+f x)}}",1,"((3*A - B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(4*Sqrt[2]*a*c^(3/2)*f) + ((3*A - B)*Cos[e + f*x])/(4*a*f*(c - c*Sin[e + f*x])^(3/2)) - ((A - B)*Sec[e + f*x])/(a*c*f*Sqrt[c - c*Sin[e + f*x]])","A",5,5,38,0.1316,1,"{2967, 2855, 2650, 2649, 206}"
114,1,180,0,0.4246609,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2)),x]","-\frac{(5 A-3 B) \sec (e+f x)}{8 a c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{3 (5 A-3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{32 \sqrt{2} a c^{5/2} f}+\frac{3 (5 A-3 B) \cos (e+f x)}{32 a c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \sec (e+f x)}{4 a c f (c-c \sin (e+f x))^{3/2}}","-\frac{(5 A-3 B) \sec (e+f x)}{8 a c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{3 (5 A-3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{32 \sqrt{2} a c^{5/2} f}+\frac{3 (5 A-3 B) \cos (e+f x)}{32 a c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \sec (e+f x)}{4 a c f (c-c \sin (e+f x))^{3/2}}",1,"(3*(5*A - 3*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(32*Sqrt[2]*a*c^(5/2)*f) + (3*(5*A - 3*B)*Cos[e + f*x])/(32*a*c*f*(c - c*Sin[e + f*x])^(3/2)) + ((A + B)*Sec[e + f*x])/(4*a*c*f*(c - c*Sin[e + f*x])^(3/2)) - ((5*A - 3*B)*Sec[e + f*x])/(8*a*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",6,6,38,0.1579,1,"{2967, 2859, 2687, 2650, 2649, 206}"
115,1,242,0,0.6507604,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{9/2}}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(9/2))/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{13/2}}{3 a^2 c^2 f}-\frac{64 c^2 (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{105 a^2 f}-\frac{512 c^3 (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{105 a^2 f}+\frac{2048 c^4 (7 A-13 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{105 a^2 f}-\frac{(7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{9/2}}{21 a^2 f}-\frac{16 c (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{105 a^2 f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{13/2}}{3 a^2 c^2 f}-\frac{64 c^2 (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{105 a^2 f}-\frac{512 c^3 (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{105 a^2 f}+\frac{2048 c^4 (7 A-13 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{105 a^2 f}-\frac{(7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{9/2}}{21 a^2 f}-\frac{16 c (7 A-13 B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{105 a^2 f}",1,"(2048*(7*A - 13*B)*c^4*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(105*a^2*f) - (512*(7*A - 13*B)*c^3*Sec[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(105*a^2*f) - (64*(7*A - 13*B)*c^2*Sec[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(105*a^2*f) - (16*(7*A - 13*B)*c*Sec[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(105*a^2*f) - ((7*A - 13*B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(9/2))/(21*a^2*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(13/2))/(3*a^2*c^2*f)","A",7,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
116,1,201,0,0.5582007,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2}}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2))/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{11/2}}{3 a^2 c^2 f}-\frac{32 c^2 (5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^2 f}+\frac{128 c^3 (5 A-11 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{15 a^2 f}-\frac{(5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{15 a^2 f}-\frac{4 c (5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{15 a^2 f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{11/2}}{3 a^2 c^2 f}-\frac{32 c^2 (5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^2 f}+\frac{128 c^3 (5 A-11 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{15 a^2 f}-\frac{(5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{7/2}}{15 a^2 f}-\frac{4 c (5 A-11 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{15 a^2 f}",1,"(128*(5*A - 11*B)*c^3*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(15*a^2*f) - (32*(5*A - 11*B)*c^2*Sec[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(15*a^2*f) - (4*(5*A - 11*B)*c*Sec[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(15*a^2*f) - ((5*A - 11*B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(15*a^2*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(11/2))/(3*a^2*c^2*f)","A",6,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
117,1,154,0,0.4791864,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{3 a^2 c^2 f}+\frac{32 c^2 (A-3 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}-\frac{(A-3 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 f}-\frac{8 c (A-3 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{3 a^2 c^2 f}+\frac{32 c^2 (A-3 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}-\frac{(A-3 B) \sec (e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 f}-\frac{8 c (A-3 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 f}",1,"(32*(A - 3*B)*c^2*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(3*a^2*f) - (8*(A - 3*B)*c*Sec[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(3*a^2*f) - ((A - 3*B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(3*a^2*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(9/2))/(3*a^2*c^2*f)","A",5,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
118,1,115,0,0.4083154,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{3 a^2 c^2 f}-\frac{(A-7 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 f}+\frac{4 c (A-7 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{3 a^2 c^2 f}-\frac{(A-7 B) \sec (e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 f}+\frac{4 c (A-7 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}",1,"(4*(A - 7*B)*c*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(3*a^2*f) - ((A - 7*B)*Sec[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(3*a^2*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(7/2))/(3*a^2*c^2*f)","A",4,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
119,1,78,0,0.3125567,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 c^2 f}-\frac{(A+5 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 c^2 f}-\frac{(A+5 B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 f}",1,"-((A + 5*B)*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(3*a^2*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(3*a^2*c^2*f)","A",3,3,38,0.07895,1,"{2967, 2855, 2673}"
120,1,135,0,0.3536566,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*Sqrt[c - c*Sin[e + f*x]]),x]","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 c^2 f}-\frac{(A+B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a^2 c f}+\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{2 \sqrt{2} a^2 \sqrt{c} f}","-\frac{(A-B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{3 a^2 c^2 f}-\frac{(A+B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a^2 c f}+\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{2 \sqrt{2} a^2 \sqrt{c} f}",1,"((A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(2*Sqrt[2]*a^2*Sqrt[c]*f) - ((A + B)*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(2*a^2*c*f) - ((A - B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(3*a^2*c^2*f)","A",5,5,38,0.1316,1,"{2967, 2855, 2675, 2649, 206}"
121,1,175,0,0.3918881,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^(3/2)),x]","-\frac{(A-B) \sec ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 c^2 f}+\frac{(5 A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} a^2 c^{3/2} f}+\frac{(5 A+B) \cos (e+f x)}{8 a^2 f (c-c \sin (e+f x))^{3/2}}-\frac{(5 A+B) \sec (e+f x)}{6 a^2 c f \sqrt{c-c \sin (e+f x)}}","-\frac{(A-B) \sec ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{3 a^2 c^2 f}+\frac{(5 A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{8 \sqrt{2} a^2 c^{3/2} f}+\frac{(5 A+B) \cos (e+f x)}{8 a^2 f (c-c \sin (e+f x))^{3/2}}-\frac{(5 A+B) \sec (e+f x)}{6 a^2 c f \sqrt{c-c \sin (e+f x)}}",1,"((5*A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(8*Sqrt[2]*a^2*c^(3/2)*f) + ((5*A + B)*Cos[e + f*x])/(8*a^2*f*(c - c*Sin[e + f*x])^(3/2)) - ((5*A + B)*Sec[e + f*x])/(6*a^2*c*f*Sqrt[c - c*Sin[e + f*x]]) - ((A - B)*Sec[e + f*x]^3*Sqrt[c - c*Sin[e + f*x]])/(3*a^2*c^2*f)","A",6,6,38,0.1579,1,"{2967, 2855, 2687, 2650, 2649, 206}"
122,1,225,0,0.4837252,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c - c*Sin[e + f*x])^(5/2)),x]","-\frac{(A-B) \sec ^3(e+f x)}{3 a^2 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{5 (7 A-B) \sec (e+f x)}{48 a^2 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{5 (7 A-B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{64 \sqrt{2} a^2 c^{5/2} f}+\frac{5 (7 A-B) \cos (e+f x)}{64 a^2 c f (c-c \sin (e+f x))^{3/2}}+\frac{(7 A-B) \sec (e+f x)}{24 a^2 c f (c-c \sin (e+f x))^{3/2}}","-\frac{(A-B) \sec ^3(e+f x)}{3 a^2 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{5 (7 A-B) \sec (e+f x)}{48 a^2 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{5 (7 A-B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{64 \sqrt{2} a^2 c^{5/2} f}+\frac{5 (7 A-B) \cos (e+f x)}{64 a^2 c f (c-c \sin (e+f x))^{3/2}}+\frac{(7 A-B) \sec (e+f x)}{24 a^2 c f (c-c \sin (e+f x))^{3/2}}",1,"(5*(7*A - B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(64*Sqrt[2]*a^2*c^(5/2)*f) + (5*(7*A - B)*Cos[e + f*x])/(64*a^2*c*f*(c - c*Sin[e + f*x])^(3/2)) + ((7*A - B)*Sec[e + f*x])/(24*a^2*c*f*(c - c*Sin[e + f*x])^(3/2)) - (5*(7*A - B)*Sec[e + f*x])/(48*a^2*c^2*f*Sqrt[c - c*Sin[e + f*x]]) - ((A - B)*Sec[e + f*x]^3)/(3*a^2*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",7,7,38,0.1842,1,"{2967, 2855, 2681, 2687, 2650, 2649, 206}"
123,1,242,0,0.64716,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{9/2}}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(9/2))/(a + a*Sin[e + f*x])^3,x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{15/2}}{5 a^3 c^3 f}+\frac{512 c^2 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}-\frac{2048 c^3 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}-\frac{(A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{11/2}}{5 a^3 c f}-\frac{16 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{15 a^3 f}-\frac{64 c (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{15/2}}{5 a^3 c^3 f}+\frac{512 c^2 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}-\frac{2048 c^3 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}-\frac{(A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{11/2}}{5 a^3 c f}-\frac{16 (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{15 a^3 f}-\frac{64 c (A-3 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 f}",1,"(-2048*(A - 3*B)*c^3*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(15*a^3*f) + (512*(A - 3*B)*c^2*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(5*a^3*f) - (64*(A - 3*B)*c*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(7/2))/(5*a^3*f) - (16*(A - 3*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(9/2))/(15*a^3*f) - ((A - 3*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(11/2))/(5*a^3*c*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(15/2))/(5*a^3*c^3*f)","A",7,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
124,1,209,0,0.5674346,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2}}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2))/(a + a*Sin[e + f*x])^3,x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{13/2}}{5 a^3 c^3 f}-\frac{128 c^2 (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}-\frac{(3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{15 a^3 c f}-\frac{4 (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 f}+\frac{32 c (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{13/2}}{5 a^3 c^3 f}-\frac{128 c^2 (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}-\frac{(3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{9/2}}{15 a^3 c f}-\frac{4 (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 f}+\frac{32 c (3 A-13 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}",1,"(-128*(3*A - 13*B)*c^2*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(15*a^3*f) + (32*(3*A - 13*B)*c*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(5*a^3*f) - (4*(3*A - 13*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(7/2))/(5*a^3*f) - ((3*A - 13*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(9/2))/(15*a^3*c*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(13/2))/(5*a^3*c^3*f)","A",6,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
125,1,160,0,0.4798437,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/(a + a*Sin[e + f*x])^3,x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{11/2}}{5 a^3 c^3 f}-\frac{(A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 c f}+\frac{8 (A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}-\frac{32 c (A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{11/2}}{5 a^3 c^3 f}-\frac{(A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 c f}+\frac{8 (A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 f}-\frac{32 c (A-11 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}",1,"(-32*(A - 11*B)*c*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(15*a^3*f) + (8*(A - 11*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(5*a^3*f) - ((A - 11*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(7/2))/(5*a^3*c*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(11/2))/(5*a^3*c^3*f)","A",5,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
126,1,121,0,0.4126881,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/(a + a*Sin[e + f*x])^3,x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{9/2}}{5 a^3 c^3 f}-\frac{(A+9 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 c f}+\frac{4 (A+9 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{9/2}}{5 a^3 c^3 f}-\frac{(A+9 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 c f}+\frac{4 (A+9 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 f}",1,"(4*(A + 9*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(15*a^3*f) - ((A + 9*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(5/2))/(5*a^3*c*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(9/2))/(5*a^3*c^3*f)","A",4,4,38,0.1053,1,"{2967, 2855, 2674, 2673}"
127,1,85,0,0.3151977,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/(a + a*Sin[e + f*x])^3,x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 c^3 f}-\frac{(3 A+7 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 c f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{7/2}}{5 a^3 c^3 f}-\frac{(3 A+7 B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{15 a^3 c f}",1,"-((3*A + 7*B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(15*a^3*c*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(7/2))/(5*a^3*c^3*f)","A",3,3,38,0.07895,1,"{2967, 2855, 2673}"
128,1,174,0,0.4378451,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*Sqrt[c - c*Sin[e + f*x]]),x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 c^3 f}-\frac{(A+B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{6 a^3 c^2 f}-\frac{(A+B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{4 a^3 c f}+\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} a^3 \sqrt{c} f}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{5/2}}{5 a^3 c^3 f}-\frac{(A+B) \sec ^3(e+f x) (c-c \sin (e+f x))^{3/2}}{6 a^3 c^2 f}-\frac{(A+B) \sec (e+f x) \sqrt{c-c \sin (e+f x)}}{4 a^3 c f}+\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{4 \sqrt{2} a^3 \sqrt{c} f}",1,"((A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(4*Sqrt[2]*a^3*Sqrt[c]*f) - ((A + B)*Sec[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(4*a^3*c*f) - ((A + B)*Sec[e + f*x]^3*(c - c*Sin[e + f*x])^(3/2))/(6*a^3*c^2*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(5/2))/(5*a^3*c^3*f)","A",6,5,38,0.1316,1,"{2967, 2855, 2675, 2649, 206}"
129,1,224,0,0.4796936,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^(3/2)),x]","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{3/2}}{5 a^3 c^3 f}-\frac{(7 A+3 B) \sec ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{30 a^3 c^2 f}+\frac{(7 A+3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{16 \sqrt{2} a^3 c^{3/2} f}+\frac{(7 A+3 B) \cos (e+f x)}{16 a^3 f (c-c \sin (e+f x))^{3/2}}-\frac{(7 A+3 B) \sec (e+f x)}{12 a^3 c f \sqrt{c-c \sin (e+f x)}}","-\frac{(A-B) \sec ^5(e+f x) (c-c \sin (e+f x))^{3/2}}{5 a^3 c^3 f}-\frac{(7 A+3 B) \sec ^3(e+f x) \sqrt{c-c \sin (e+f x)}}{30 a^3 c^2 f}+\frac{(7 A+3 B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{16 \sqrt{2} a^3 c^{3/2} f}+\frac{(7 A+3 B) \cos (e+f x)}{16 a^3 f (c-c \sin (e+f x))^{3/2}}-\frac{(7 A+3 B) \sec (e+f x)}{12 a^3 c f \sqrt{c-c \sin (e+f x)}}",1,"((7*A + 3*B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(16*Sqrt[2]*a^3*c^(3/2)*f) + ((7*A + 3*B)*Cos[e + f*x])/(16*a^3*f*(c - c*Sin[e + f*x])^(3/2)) - ((7*A + 3*B)*Sec[e + f*x])/(12*a^3*c*f*Sqrt[c - c*Sin[e + f*x]]) - ((7*A + 3*B)*Sec[e + f*x]^3*Sqrt[c - c*Sin[e + f*x]])/(30*a^3*c^2*f) - ((A - B)*Sec[e + f*x]^5*(c - c*Sin[e + f*x])^(3/2))/(5*a^3*c^3*f)","A",7,7,38,0.1842,1,"{2967, 2855, 2675, 2687, 2650, 2649, 206}"
130,1,258,0,0.5550096,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^(5/2)),x]","-\frac{(A-B) \sec ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{5 a^3 c^3 f}-\frac{(9 A+B) \sec ^3(e+f x)}{30 a^3 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{7 (9 A+B) \sec (e+f x)}{96 a^3 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{7 (9 A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{128 \sqrt{2} a^3 c^{5/2} f}+\frac{7 (9 A+B) \cos (e+f x)}{128 a^3 c f (c-c \sin (e+f x))^{3/2}}+\frac{7 (9 A+B) \sec (e+f x)}{240 a^3 c f (c-c \sin (e+f x))^{3/2}}","-\frac{(A-B) \sec ^5(e+f x) \sqrt{c-c \sin (e+f x)}}{5 a^3 c^3 f}-\frac{(9 A+B) \sec ^3(e+f x)}{30 a^3 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{7 (9 A+B) \sec (e+f x)}{96 a^3 c^2 f \sqrt{c-c \sin (e+f x)}}+\frac{7 (9 A+B) \tanh ^{-1}\left(\frac{\sqrt{c} \cos (e+f x)}{\sqrt{2} \sqrt{c-c \sin (e+f x)}}\right)}{128 \sqrt{2} a^3 c^{5/2} f}+\frac{7 (9 A+B) \cos (e+f x)}{128 a^3 c f (c-c \sin (e+f x))^{3/2}}+\frac{7 (9 A+B) \sec (e+f x)}{240 a^3 c f (c-c \sin (e+f x))^{3/2}}",1,"(7*(9*A + B)*ArcTanh[(Sqrt[c]*Cos[e + f*x])/(Sqrt[2]*Sqrt[c - c*Sin[e + f*x]])])/(128*Sqrt[2]*a^3*c^(5/2)*f) + (7*(9*A + B)*Cos[e + f*x])/(128*a^3*c*f*(c - c*Sin[e + f*x])^(3/2)) + (7*(9*A + B)*Sec[e + f*x])/(240*a^3*c*f*(c - c*Sin[e + f*x])^(3/2)) - (7*(9*A + B)*Sec[e + f*x])/(96*a^3*c^2*f*Sqrt[c - c*Sin[e + f*x]]) - ((9*A + B)*Sec[e + f*x]^3)/(30*a^3*c^2*f*Sqrt[c - c*Sin[e + f*x]]) - ((A - B)*Sec[e + f*x]^5*Sqrt[c - c*Sin[e + f*x]])/(5*a^3*c^3*f)","A",8,7,38,0.1842,1,"{2967, 2855, 2687, 2681, 2650, 2649, 206}"
131,1,94,0,0.3393292,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{5 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 f \sqrt{a \sin (e+f x)+a}}","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{5 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 f \sqrt{a \sin (e+f x)+a}}",1,"-(a*(A + B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(4*f*Sqrt[a + a*Sin[e + f*x]]) + (a*B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(9/2))/(5*c*f*Sqrt[a + a*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
132,1,94,0,0.3372086,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 f \sqrt{a \sin (e+f x)+a}}","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 f \sqrt{a \sin (e+f x)+a}}",1,"-(a*(A + B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(3*f*Sqrt[a + a*Sin[e + f*x]]) + (a*B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(4*c*f*Sqrt[a + a*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
133,1,94,0,0.3334728,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}",1,"-(a*(A + B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*f*Sqrt[a + a*Sin[e + f*x]]) + (a*B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(3*c*f*Sqrt[a + a*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
134,1,92,0,0.3086254,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}","\frac{a B \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}",1,"-((a*(A + B)*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]])) + (a*B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*c*f*Sqrt[a + a*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
135,1,100,0,0.3370569,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","\frac{a B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}","\frac{a B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{c f \sqrt{a \sin (e+f x)+a}}-\frac{a (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}",1,"-((a*(A + B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])) + (a*B*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(c*f*Sqrt[a + a*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2971, 2738, 2737, 2667, 31}"
136,1,99,0,0.3578621,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{a (A+B) \cos (e+f x)}{f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{a B \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}","\frac{a (A+B) \cos (e+f x)}{f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{a B \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}",1,"(a*(A + B)*Cos[e + f*x])/(f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + (a*B*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2971, 2737, 2667, 31, 2738}"
137,1,92,0,0.344732,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","\frac{a (A+B) \cos (e+f x)}{2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{a B \cos (e+f x)}{c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}","\frac{a (A+B) \cos (e+f x)}{2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{a B \cos (e+f x)}{c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}",1,"(a*(A + B)*Cos[e + f*x])/(2*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2)) - (a*B*Cos[e + f*x])/(c*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2))","A",3,2,40,0.05000,1,"{2971, 2738}"
138,1,94,0,0.3366195,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{a (A+B) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}-\frac{a B \cos (e+f x)}{2 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}","\frac{a (A+B) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}-\frac{a B \cos (e+f x)}{2 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}",1,"(a*(A + B)*Cos[e + f*x])/(3*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(7/2)) - (a*B*Cos[e + f*x])/(2*c*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2))","A",3,2,40,0.05000,1,"{2971, 2738}"
139,1,146,0,0.358177,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","-\frac{a^2 (3 A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{30 f \sqrt{a \sin (e+f x)+a}}-\frac{a (3 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{15 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{6 f}","-\frac{a^2 (3 A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{30 f \sqrt{a \sin (e+f x)+a}}-\frac{a (3 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{15 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{6 f}",1,"-(a^2*(3*A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(30*f*Sqrt[a + a*Sin[e + f*x]]) - (a*(3*A - B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(7/2))/(15*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(7/2))/(6*f)","A",3,3,40,0.07500,1,"{2973, 2740, 2738}"
140,1,146,0,0.3613135,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","-\frac{a^2 (5 A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{30 f \sqrt{a \sin (e+f x)+a}}-\frac{a (5 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}{20 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}{5 f}","-\frac{a^2 (5 A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{30 f \sqrt{a \sin (e+f x)+a}}-\frac{a (5 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}{20 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}{5 f}",1,"-(a^2*(5*A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(30*f*Sqrt[a + a*Sin[e + f*x]]) - (a*(5*A - B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2))/(20*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(5/2))/(5*f)","A",3,3,40,0.07500,1,"{2973, 2740, 2738}"
141,1,134,0,0.3481951,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","-\frac{a^2 A \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{a A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}{3 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}{4 f}","-\frac{a^2 A \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{a A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}{3 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}{4 f}",1,"-(a^2*A*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(3*f*Sqrt[a + a*Sin[e + f*x]]) - (a*A*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2))/(3*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(3/2))/(4*f)","A",3,3,40,0.07500,1,"{2973, 2740, 2738}"
142,1,96,0,0.3246914,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 a f \sqrt{c-c \sin (e+f x)}}","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 a f \sqrt{c-c \sin (e+f x)}}",1,"((A - B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*f*Sqrt[c - c*Sin[e + f*x]]) + (B*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(3*a*f*Sqrt[c - c*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
143,1,145,0,0.3815689,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{2 a^2 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}","-\frac{2 a^2 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}",1,"(-2*a^2*(A + B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (a*(A + B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(f*Sqrt[c - c*Sin[e + f*x]]) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*f*Sqrt[c - c*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2973, 2740, 2737, 2667, 31}"
144,1,158,0,0.3851505,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{a^2 (A+3 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f (c-c \sin (e+f x))^{3/2}}","\frac{a^2 (A+3 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f (c-c \sin (e+f x))^{3/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*f*(c - c*Sin[e + f*x])^(3/2)) + (a^2*(A + 3*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (a*(A + 3*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(2*c*f*Sqrt[c - c*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
145,1,149,0,0.3870053,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","-\frac{a^2 B \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 f (c-c \sin (e+f x))^{5/2}}-\frac{a B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f (c-c \sin (e+f x))^{3/2}}","-\frac{a^2 B \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 f (c-c \sin (e+f x))^{5/2}}-\frac{a B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f (c-c \sin (e+f x))^{3/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(4*f*(c - c*Sin[e + f*x])^(5/2)) - (a*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c*f*(c - c*Sin[e + f*x])^(3/2)) - (a^2*B*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2972, 2739, 2737, 2667, 31}"
146,1,96,0,0.2745958,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{24 c f (c-c \sin (e+f x))^{5/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{6 f (c-c \sin (e+f x))^{7/2}}","\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{24 c f (c-c \sin (e+f x))^{5/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{6 f (c-c \sin (e+f x))^{7/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(6*f*(c - c*Sin[e + f*x])^(7/2)) + ((A - 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(24*c*f*(c - c*Sin[e + f*x])^(5/2))","A",2,2,40,0.05000,1,"{2972, 2742}"
147,1,146,0,0.3755028,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{9/2}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(9/2),x]","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{96 c^2 f (c-c \sin (e+f x))^{5/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{24 c f (c-c \sin (e+f x))^{7/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{8 f (c-c \sin (e+f x))^{9/2}}","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{96 c^2 f (c-c \sin (e+f x))^{5/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{24 c f (c-c \sin (e+f x))^{7/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{8 f (c-c \sin (e+f x))^{9/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(8*f*(c - c*Sin[e + f*x])^(9/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(24*c*f*(c - c*Sin[e + f*x])^(7/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(96*c^2*f*(c - c*Sin[e + f*x])^(5/2))","A",3,3,40,0.07500,1,"{2972, 2743, 2742}"
148,1,154,0,0.3727953,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{11/2}} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(11/2),x]","-\frac{a^2 (3 A-7 B) \cos (e+f x)}{120 c^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}+\frac{a (3 A-7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{40 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{10 f (c-c \sin (e+f x))^{11/2}}","-\frac{a^2 (3 A-7 B) \cos (e+f x)}{120 c^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}+\frac{a (3 A-7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{40 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{10 f (c-c \sin (e+f x))^{11/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(10*f*(c - c*Sin[e + f*x])^(11/2)) + (a*(3*A - 7*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(40*c*f*(c - c*Sin[e + f*x])^(9/2)) - (a^2*(3*A - 7*B)*Cos[e + f*x])/(120*c^2*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(7/2))","A",3,3,40,0.07500,1,"{2972, 2739, 2738}"
149,1,198,0,0.4761909,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","-\frac{2 a^2 (7 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{105 f}-\frac{a^3 (7 A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{a (7 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{42 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{7/2}}{7 f}","-\frac{2 a^2 (7 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{105 f}-\frac{a^3 (7 A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{a (7 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{42 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{7/2}}{7 f}",1,"-(a^3*(7*A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(105*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a^2*(7*A - B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(7/2))/(105*f) - (a*(7*A - B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(7/2))/(42*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(7/2))/(7*f)","A",4,3,40,0.07500,1,"{2973, 2740, 2738}"
150,1,180,0,0.4658968,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","-\frac{2 a^3 A \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{a^2 A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}{5 f}-\frac{a A \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}{5 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{5/2}}{6 f}","-\frac{2 a^3 A \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{a^2 A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}{5 f}-\frac{a A \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}{5 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{5/2}}{6 f}",1,"(-2*a^3*A*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(15*f*Sqrt[a + a*Sin[e + f*x]]) - (a^2*A*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2))/(5*f) - (a*A*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(5/2))/(5*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(5/2))/(6*f)","A",4,3,40,0.07500,1,"{2973, 2740, 2738}"
151,1,142,0,0.3624239,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{c^2 (5 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{30 f \sqrt{c-c \sin (e+f x)}}+\frac{c (5 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}{20 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{3/2}}{5 f}","\frac{c^2 (5 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{30 f \sqrt{c-c \sin (e+f x)}}+\frac{c (5 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}{20 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{3/2}}{5 f}",1,"((5*A + B)*c^2*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(30*f*Sqrt[c - c*Sin[e + f*x]]) + ((5*A + B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*Sqrt[c - c*Sin[e + f*x]])/(20*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(3/2))/(5*f)","A",3,3,40,0.07500,1,"{2973, 2740, 2738}"
152,1,96,0,0.3182355,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 a f \sqrt{c-c \sin (e+f x)}}","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 a f \sqrt{c-c \sin (e+f x)}}",1,"((A - B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(3*f*Sqrt[c - c*Sin[e + f*x]]) + (B*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(4*a*f*Sqrt[c - c*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
153,1,193,0,0.462769,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{2 a^2 (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{4 a^3 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}","-\frac{2 a^2 (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{4 a^3 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}",1,"(-4*a^3*(A + B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (2*a^2*(A + B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(f*Sqrt[c - c*Sin[e + f*x]]) - (a*(A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*f*Sqrt[c - c*Sin[e + f*x]]) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(3*f*Sqrt[c - c*Sin[e + f*x]])","A",6,5,40,0.1250,1,"{2973, 2740, 2737, 2667, 31}"
154,1,210,0,0.4847634,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{2 a^2 (A+2 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f \sqrt{c-c \sin (e+f x)}}+\frac{4 a^3 (A+2 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (A+2 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{2 f (c-c \sin (e+f x))^{3/2}}","\frac{2 a^2 (A+2 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f \sqrt{c-c \sin (e+f x)}}+\frac{4 a^3 (A+2 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (A+2 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{2 f (c-c \sin (e+f x))^{3/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(2*f*(c - c*Sin[e + f*x])^(3/2)) + (4*a^3*(A + 2*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (2*a^2*(A + 2*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c*f*Sqrt[c - c*Sin[e + f*x]]) + (a*(A + 2*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*c*f*Sqrt[c - c*Sin[e + f*x]])","A",6,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
155,1,212,0,0.489921,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","-\frac{a^2 (A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{a^3 (A+5 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{4 f (c-c \sin (e+f x))^{5/2}}","-\frac{a^2 (A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{a^3 (A+5 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{4 f (c-c \sin (e+f x))^{5/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(4*f*(c - c*Sin[e + f*x])^(5/2)) - (a*(A + 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(4*c*f*(c - c*Sin[e + f*x])^(3/2)) - (a^3*(A + 5*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (a^2*(A + 5*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(2*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",6,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
156,1,196,0,0.4877202,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{a^2 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^3 B \cos (e+f x) \log (1-\sin (e+f x))}{c^3 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{6 f (c-c \sin (e+f x))^{7/2}}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f (c-c \sin (e+f x))^{5/2}}","\frac{a^2 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^3 B \cos (e+f x) \log (1-\sin (e+f x))}{c^3 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{6 f (c-c \sin (e+f x))^{7/2}}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f (c-c \sin (e+f x))^{5/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(6*f*(c - c*Sin[e + f*x])^(7/2)) - (a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*c*f*(c - c*Sin[e + f*x])^(5/2)) + (a^2*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c^2*f*(c - c*Sin[e + f*x])^(3/2)) + (a^3*B*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^3*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",6,5,40,0.1250,1,"{2972, 2739, 2737, 2667, 31}"
157,1,96,0,0.2756958,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{9/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(9/2),x]","\frac{(A-7 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{48 c f (c-c \sin (e+f x))^{7/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{8 f (c-c \sin (e+f x))^{9/2}}","\frac{(A-7 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{48 c f (c-c \sin (e+f x))^{7/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{8 f (c-c \sin (e+f x))^{9/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(8*f*(c - c*Sin[e + f*x])^(9/2)) + ((A - 7*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(48*c*f*(c - c*Sin[e + f*x])^(7/2))","A",2,2,40,0.05000,1,"{2972, 2742}"
158,1,146,0,0.3762711,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{11/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(11/2),x]","\frac{(A-4 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{240 c^2 f (c-c \sin (e+f x))^{7/2}}+\frac{(A-4 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{40 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{10 f (c-c \sin (e+f x))^{11/2}}","\frac{(A-4 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{240 c^2 f (c-c \sin (e+f x))^{7/2}}+\frac{(A-4 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{40 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{10 f (c-c \sin (e+f x))^{11/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(10*f*(c - c*Sin[e + f*x])^(11/2)) + ((A - 4*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(40*c*f*(c - c*Sin[e + f*x])^(9/2)) + ((A - 4*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(240*c^2*f*(c - c*Sin[e + f*x])^(7/2))","A",3,3,40,0.07500,1,"{2972, 2743, 2742}"
159,1,196,0,0.4834593,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{13/2}} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(13/2),x]","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{960 c^3 f (c-c \sin (e+f x))^{7/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{160 c^2 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{40 c f (c-c \sin (e+f x))^{11/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{12 f (c-c \sin (e+f x))^{13/2}}","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{960 c^3 f (c-c \sin (e+f x))^{7/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{160 c^2 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{40 c f (c-c \sin (e+f x))^{11/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{12 f (c-c \sin (e+f x))^{13/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(12*f*(c - c*Sin[e + f*x])^(13/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(40*c*f*(c - c*Sin[e + f*x])^(11/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(160*c^2*f*(c - c*Sin[e + f*x])^(9/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(960*c^3*f*(c - c*Sin[e + f*x])^(7/2))","A",4,3,40,0.07500,1,"{2972, 2743, 2742}"
160,1,250,0,0.5668066,"\int (a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{9/2} \, dx","Int[(a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(9/2),x]","-\frac{a^2 (9 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{9/2}}{84 f}-\frac{a^3 (9 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{9/2}}{126 f}-\frac{a^4 (9 A-B) \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{315 f \sqrt{a \sin (e+f x)+a}}-\frac{a (9 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{9/2}}{72 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{9/2}}{9 f}","-\frac{a^2 (9 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{9/2}}{84 f}-\frac{a^3 (9 A-B) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{9/2}}{126 f}-\frac{a^4 (9 A-B) \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{315 f \sqrt{a \sin (e+f x)+a}}-\frac{a (9 A-B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{9/2}}{72 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{9/2}}{9 f}",1,"-(a^4*(9*A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(9/2))/(315*f*Sqrt[a + a*Sin[e + f*x]]) - (a^3*(9*A - B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(9/2))/(126*f) - (a^2*(9*A - B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(9/2))/(84*f) - (a*(9*A - B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(9/2))/(72*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*(c - c*Sin[e + f*x])^(9/2))/(9*f)","A",5,3,40,0.07500,1,"{2973, 2740, 2738}"
161,1,226,0,0.5590839,"\int (a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2} \, dx","Int[(a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2),x]","-\frac{2 a^4 A \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{35 f \sqrt{a \sin (e+f x)+a}}-\frac{4 a^3 A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{35 f}-\frac{a^2 A \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{7 f}-\frac{a A \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{7/2}}{7 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{7/2}}{8 f}","-\frac{2 a^4 A \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{35 f \sqrt{a \sin (e+f x)+a}}-\frac{4 a^3 A \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{7/2}}{35 f}-\frac{a^2 A \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{7/2}}{7 f}-\frac{a A \cos (e+f x) (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{7/2}}{7 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{7/2}}{8 f}",1,"(-2*a^4*A*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(35*f*Sqrt[a + a*Sin[e + f*x]]) - (4*a^3*A*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(7/2))/(35*f) - (a^2*A*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(7/2))/(7*f) - (a*A*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(7/2))/(7*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*(c - c*Sin[e + f*x])^(7/2))/(8*f)","A",5,3,40,0.07500,1,"{2973, 2740, 2738}"
162,1,192,0,0.4597972,"\int (a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","\frac{2 c^2 (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} \sqrt{c-c \sin (e+f x)}}{105 f}+\frac{c^3 (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{105 f \sqrt{c-c \sin (e+f x)}}+\frac{c (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{3/2}}{42 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{5/2}}{7 f}","\frac{2 c^2 (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} \sqrt{c-c \sin (e+f x)}}{105 f}+\frac{c^3 (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{105 f \sqrt{c-c \sin (e+f x)}}+\frac{c (7 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{3/2}}{42 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{5/2}}{7 f}",1,"((7*A + B)*c^3*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(105*f*Sqrt[c - c*Sin[e + f*x]]) + (2*(7*A + B)*c^2*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*Sqrt[c - c*Sin[e + f*x]])/(105*f) + ((7*A + B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*(c - c*Sin[e + f*x])^(3/2))/(42*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*(c - c*Sin[e + f*x])^(5/2))/(7*f)","A",4,3,40,0.07500,1,"{2973, 2740, 2738}"
163,1,142,0,0.3592937,"\int (a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","\frac{c^2 (3 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{30 f \sqrt{c-c \sin (e+f x)}}+\frac{c (3 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} \sqrt{c-c \sin (e+f x)}}{15 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{3/2}}{6 f}","\frac{c^2 (3 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{30 f \sqrt{c-c \sin (e+f x)}}+\frac{c (3 A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2} \sqrt{c-c \sin (e+f x)}}{15 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2} (c-c \sin (e+f x))^{3/2}}{6 f}",1,"((3*A + B)*c^2*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(30*f*Sqrt[c - c*Sin[e + f*x]]) + ((3*A + B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*Sqrt[c - c*Sin[e + f*x]])/(15*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2)*(c - c*Sin[e + f*x])^(3/2))/(6*f)","A",3,3,40,0.07500,1,"{2973, 2740, 2738}"
164,1,96,0,0.3249368,"\int (a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{9/2}}{5 a f \sqrt{c-c \sin (e+f x)}}","\frac{c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f \sqrt{c-c \sin (e+f x)}}+\frac{B c \cos (e+f x) (a \sin (e+f x)+a)^{9/2}}{5 a f \sqrt{c-c \sin (e+f x)}}",1,"((A - B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(4*f*Sqrt[c - c*Sin[e + f*x]]) + (B*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(9/2))/(5*a*f*Sqrt[c - c*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
165,1,239,0,0.568527,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","-\frac{4 a^3 (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{a^2 (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{f \sqrt{c-c \sin (e+f x)}}-\frac{8 a^4 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f \sqrt{c-c \sin (e+f x)}}","-\frac{4 a^3 (A+B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{f \sqrt{c-c \sin (e+f x)}}-\frac{a^2 (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{f \sqrt{c-c \sin (e+f x)}}-\frac{8 a^4 (A+B) \cos (e+f x) \log (1-\sin (e+f x))}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 f \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f \sqrt{c-c \sin (e+f x)}}",1,"(-8*a^4*(A + B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (4*a^3*(A + B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(f*Sqrt[c - c*Sin[e + f*x]]) - (a^2*(A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(f*Sqrt[c - c*Sin[e + f*x]]) - (a*(A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(3*f*Sqrt[c - c*Sin[e + f*x]]) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(4*f*Sqrt[c - c*Sin[e + f*x]])","A",7,5,40,0.1250,1,"{2973, 2740, 2737, 2667, 31}"
166,1,271,0,0.5930293,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{2 a^3 (3 A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f \sqrt{c-c \sin (e+f x)}}+\frac{a^2 (3 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{4 a^4 (3 A+5 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (3 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{6 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{2 f (c-c \sin (e+f x))^{3/2}}","\frac{2 a^3 (3 A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c f \sqrt{c-c \sin (e+f x)}}+\frac{a^2 (3 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c f \sqrt{c-c \sin (e+f x)}}+\frac{4 a^4 (3 A+5 B) \cos (e+f x) \log (1-\sin (e+f x))}{c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{a (3 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{6 c f \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{2 f (c-c \sin (e+f x))^{3/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(2*f*(c - c*Sin[e + f*x])^(3/2)) + (4*a^4*(3*A + 5*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (2*a^3*(3*A + 5*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c*f*Sqrt[c - c*Sin[e + f*x]]) + (a^2*(3*A + 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*c*f*Sqrt[c - c*Sin[e + f*x]]) + (a*(3*A + 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(6*c*f*Sqrt[c - c*Sin[e + f*x]])","A",7,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
167,1,263,0,0.5952385,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","-\frac{3 a^3 (A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{3 a^2 (A+3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{6 a^4 (A+3 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{2 c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f (c-c \sin (e+f x))^{5/2}}","-\frac{3 a^3 (A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{3 a^2 (A+3 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c^2 f \sqrt{c-c \sin (e+f x)}}-\frac{6 a^4 (A+3 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+3 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{2 c f (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{4 f (c-c \sin (e+f x))^{5/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(4*f*(c - c*Sin[e + f*x])^(5/2)) - (a*(A + 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(2*c*f*(c - c*Sin[e + f*x])^(3/2)) - (6*a^4*(A + 3*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (3*a^3*(A + 3*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c^2*f*Sqrt[c - c*Sin[e + f*x]]) - (3*a^2*(A + 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(4*c^2*f*Sqrt[c - c*Sin[e + f*x]])","A",7,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
168,1,264,0,0.6087634,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{7/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(7/2),x]","\frac{a^3 (A+7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c^3 f \sqrt{c-c \sin (e+f x)}}+\frac{a^2 (A+7 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^4 (A+7 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^3 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+7 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{12 c f (c-c \sin (e+f x))^{5/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{6 f (c-c \sin (e+f x))^{7/2}}","\frac{a^3 (A+7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 c^3 f \sqrt{c-c \sin (e+f x)}}+\frac{a^2 (A+7 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{4 c^2 f (c-c \sin (e+f x))^{3/2}}+\frac{a^4 (A+7 B) \cos (e+f x) \log (1-\sin (e+f x))}{c^3 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{a (A+7 B) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{12 c f (c-c \sin (e+f x))^{5/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{6 f (c-c \sin (e+f x))^{7/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(6*f*(c - c*Sin[e + f*x])^(7/2)) - (a*(A + 7*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(12*c*f*(c - c*Sin[e + f*x])^(5/2)) + (a^2*(A + 7*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(4*c^2*f*(c - c*Sin[e + f*x])^(3/2)) + (a^4*(A + 7*B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^3*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (a^3*(A + 7*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(2*c^3*f*Sqrt[c - c*Sin[e + f*x]])","A",7,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
169,1,247,0,0.5987355,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{9/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(9/2),x]","-\frac{a^3 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^3 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c^2 f (c-c \sin (e+f x))^{5/2}}-\frac{a^4 B \cos (e+f x) \log (1-\sin (e+f x))}{c^4 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{8 f (c-c \sin (e+f x))^{9/2}}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 c f (c-c \sin (e+f x))^{7/2}}","-\frac{a^3 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{c^3 f (c-c \sin (e+f x))^{3/2}}+\frac{a^2 B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 c^2 f (c-c \sin (e+f x))^{5/2}}-\frac{a^4 B \cos (e+f x) \log (1-\sin (e+f x))}{c^4 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{8 f (c-c \sin (e+f x))^{9/2}}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{3 c f (c-c \sin (e+f x))^{7/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(8*f*(c - c*Sin[e + f*x])^(9/2)) - (a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(3*c*f*(c - c*Sin[e + f*x])^(7/2)) + (a^2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*c^2*f*(c - c*Sin[e + f*x])^(5/2)) - (a^3*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(c^3*f*(c - c*Sin[e + f*x])^(3/2)) - (a^4*B*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(c^4*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",7,5,40,0.1250,1,"{2972, 2739, 2737, 2667, 31}"
170,1,96,0,0.2719341,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{11/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(11/2),x]","\frac{(A-9 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{80 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{10 f (c-c \sin (e+f x))^{11/2}}","\frac{(A-9 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{80 c f (c-c \sin (e+f x))^{9/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{10 f (c-c \sin (e+f x))^{11/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(10*f*(c - c*Sin[e + f*x])^(11/2)) + ((A - 9*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(80*c*f*(c - c*Sin[e + f*x])^(9/2))","A",2,2,40,0.05000,1,"{2972, 2742}"
171,1,146,0,0.3789836,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{13/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(13/2),x]","\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{480 c^2 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{60 c f (c-c \sin (e+f x))^{11/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{12 f (c-c \sin (e+f x))^{13/2}}","\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{480 c^2 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-5 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{60 c f (c-c \sin (e+f x))^{11/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{12 f (c-c \sin (e+f x))^{13/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(12*f*(c - c*Sin[e + f*x])^(13/2)) + ((A - 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(60*c*f*(c - c*Sin[e + f*x])^(11/2)) + ((A - 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(480*c^2*f*(c - c*Sin[e + f*x])^(9/2))","A",3,3,40,0.07500,1,"{2972, 2743, 2742}"
172,1,202,0,0.4906604,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{15/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(15/2),x]","\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{6720 c^3 f (c-c \sin (e+f x))^{9/2}}+\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{840 c^2 f (c-c \sin (e+f x))^{11/2}}+\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{168 c f (c-c \sin (e+f x))^{13/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{14 f (c-c \sin (e+f x))^{15/2}}","\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{6720 c^3 f (c-c \sin (e+f x))^{9/2}}+\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{840 c^2 f (c-c \sin (e+f x))^{11/2}}+\frac{(3 A-11 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{168 c f (c-c \sin (e+f x))^{13/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{14 f (c-c \sin (e+f x))^{15/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(14*f*(c - c*Sin[e + f*x])^(15/2)) + ((3*A - 11*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(168*c*f*(c - c*Sin[e + f*x])^(13/2)) + ((3*A - 11*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(840*c^2*f*(c - c*Sin[e + f*x])^(11/2)) + ((3*A - 11*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(6720*c^3*f*(c - c*Sin[e + f*x])^(9/2))","A",4,3,40,0.07500,1,"{2972, 2743, 2742}"
173,1,246,0,0.5908865,"\int \frac{(a+a \sin (e+f x))^{7/2} (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{17/2}} \, dx","Int[((a + a*Sin[e + f*x])^(7/2)*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(17/2),x]","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{8960 c^4 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{1120 c^3 f (c-c \sin (e+f x))^{11/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{224 c^2 f (c-c \sin (e+f x))^{13/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{56 c f (c-c \sin (e+f x))^{15/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{16 f (c-c \sin (e+f x))^{17/2}}","\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{8960 c^4 f (c-c \sin (e+f x))^{9/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{1120 c^3 f (c-c \sin (e+f x))^{11/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{224 c^2 f (c-c \sin (e+f x))^{13/2}}+\frac{(A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{56 c f (c-c \sin (e+f x))^{15/2}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{16 f (c-c \sin (e+f x))^{17/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(16*f*(c - c*Sin[e + f*x])^(17/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(56*c*f*(c - c*Sin[e + f*x])^(15/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(224*c^2*f*(c - c*Sin[e + f*x])^(13/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(1120*c^3*f*(c - c*Sin[e + f*x])^(11/2)) + ((A - 3*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(8960*c^4*f*(c - c*Sin[e + f*x])^(9/2))","A",5,3,40,0.07500,1,"{2972, 2743, 2742}"
174,1,197,0,0.4629337,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/Sqrt[a + a*Sin[e + f*x]],x]","\frac{2 c^2 (A-B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}+\frac{4 c^3 (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 f \sqrt{a \sin (e+f x)+a}}","\frac{2 c^2 (A-B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}+\frac{4 c^3 (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 f \sqrt{a \sin (e+f x)+a}}",1,"(4*(A - B)*c^3*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (2*(A - B)*c^2*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]) + ((A - B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*f*Sqrt[a + a*Sin[e + f*x]]) - (B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(3*f*Sqrt[a + a*Sin[e + f*x]])","A",6,5,40,0.1250,1,"{2973, 2740, 2737, 2667, 31}"
175,1,146,0,0.3653478,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/Sqrt[a + a*Sin[e + f*x]],x]","\frac{2 c^2 (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}","\frac{2 c^2 (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f \sqrt{a \sin (e+f x)+a}}",1,"(2*(A - B)*c^2*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + ((A - B)*c*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]) - (B*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*f*Sqrt[a + a*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2973, 2740, 2737, 2667, 31}"
176,1,96,0,0.3223276,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/Sqrt[a + a*Sin[e + f*x]],x]","\frac{c (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}","\frac{c (A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{B \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{f \sqrt{a \sin (e+f x)+a}}",1,"((A - B)*c*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (B*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(f*Sqrt[a + a*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2971, 2738, 2737, 2667, 31}"
177,1,113,0,0.3635922,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]),x]","\frac{(A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A+B) \cos (e+f x) \log (1-\sin (e+f x))}{2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}","\frac{(A-B) \cos (e+f x) \log (\sin (e+f x)+1)}{2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A+B) \cos (e+f x) \log (1-\sin (e+f x))}{2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}",1,"-((A + B)*Cos[e + f*x]*Log[1 - Sin[e + f*x]])/(2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + ((A - B)*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",7,4,40,0.1000,1,"{2969, 2737, 2667, 31}"
178,1,103,0,0.2519127,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)),x]","\frac{(A+B) \cos (e+f x)}{2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}","\frac{(A+B) \cos (e+f x)}{2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}",1,"((A + B)*Cos[e + f*x])/(2*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + ((A - B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(2*c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",3,3,40,0.07500,1,"{2972, 2741, 3770}"
179,1,153,0,0.3550568,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2)),x]","\frac{(A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{4 c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A-B) \cos (e+f x)}{4 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x)}{4 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}","\frac{(A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{4 c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(A-B) \cos (e+f x)}{4 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(A+B) \cos (e+f x)}{4 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}",1,"((A + B)*Cos[e + f*x])/(4*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2)) + ((A - B)*Cos[e + f*x])/(4*c*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + ((A - B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(4*c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",4,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
180,1,271,0,0.5772645,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2}}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2))/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{2 c^3 (3 A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f \sqrt{a \sin (e+f x)+a}}-\frac{c^2 (3 A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{4 c^4 (3 A-5 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (3 A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{6 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{2 f (a \sin (e+f x)+a)^{3/2}}","-\frac{2 c^3 (3 A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f \sqrt{a \sin (e+f x)+a}}-\frac{c^2 (3 A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{4 c^4 (3 A-5 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (3 A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{6 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{2 f (a \sin (e+f x)+a)^{3/2}}",1,"(-4*(3*A - 5*B)*c^4*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (2*(3*A - 5*B)*c^3*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]) - ((3*A - 5*B)*c^2*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - ((3*A - 5*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(6*a*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",7,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
181,1,210,0,0.4780906,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{2 c^2 (A-2 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f \sqrt{a \sin (e+f x)+a}}-\frac{4 c^3 (A-2 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-2 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{2 f (a \sin (e+f x)+a)^{3/2}}","-\frac{2 c^2 (A-2 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f \sqrt{a \sin (e+f x)+a}}-\frac{4 c^3 (A-2 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-2 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{2 f (a \sin (e+f x)+a)^{3/2}}",1,"(-4*(A - 2*B)*c^3*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) - (2*(A - 2*B)*c^2*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - 2*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",6,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
182,1,159,0,0.3856115,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{c^2 (A-3 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-3 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f (a \sin (e+f x)+a)^{3/2}}","-\frac{c^2 (A-3 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-3 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{2 f (a \sin (e+f x)+a)^{3/2}}",1,"-(((A - 3*B)*c^2*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])) - ((A - 3*B)*c*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",5,5,40,0.1250,1,"{2972, 2740, 2737, 2667, 31}"
183,1,100,0,0.3463026,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/(a + a*Sin[e + f*x])^(3/2),x]","\frac{B c \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}","\frac{B c \cos (e+f x) \log (\sin (e+f x)+1)}{a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{c (A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}",1,"-(((A - B)*c*Cos[e + f*x])/(f*(a + a*Sin[e + f*x])^(3/2)*Sqrt[c - c*Sin[e + f*x]])) + (B*c*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",5,5,40,0.1250,1,"{2971, 2737, 2667, 31, 2738}"
184,1,103,0,0.255653,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*Sqrt[c - c*Sin[e + f*x]]),x]","\frac{(A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}","\frac{(A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 a f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}",1,"-((A - B)*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(3/2)*Sqrt[c - c*Sin[e + f*x]]) + ((A + B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",3,3,40,0.07500,1,"{2972, 2741, 3770}"
185,1,150,0,0.3733412,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(3/2)),x]","-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}+\frac{A \cos (e+f x)}{2 a f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{A \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 a c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}","-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}+\frac{A \cos (e+f x)}{2 a f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{A \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{2 a c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}",1,"-((A - B)*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(3/2)) + (A*Cos[e + f*x])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + (A*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(2*a*c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",4,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
186,1,217,0,0.4793278,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(5/2)),x]","\frac{(3 A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(3 A-B) \cos (e+f x)}{8 a c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(3 A-B) \cos (e+f x)}{8 a f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}","\frac{(3 A-B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{(3 A-B) \cos (e+f x)}{8 a c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(3 A-B) \cos (e+f x)}{8 a f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}",1,"-((A - B)*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(5/2)) + ((3*A - B)*Cos[e + f*x])/(8*a*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2)) + ((3*A - B)*Cos[e + f*x])/(8*a*c*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + ((3*A - B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(8*a*c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",5,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
187,1,323,0,0.7128624,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{9/2}}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(9/2))/(a + a*Sin[e + f*x])^(5/2),x]","\frac{4 c^4 (3 A-7 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^3 (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^2 (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{8 c^5 (3 A-7 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{4 f (a \sin (e+f x)+a)^{5/2}}","\frac{4 c^4 (3 A-7 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^3 (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^2 (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{3 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{8 c^5 (3 A-7 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (3 A-7 B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{9/2}}{4 f (a \sin (e+f x)+a)^{5/2}}",1,"(8*(3*A - 7*B)*c^5*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (4*(3*A - 7*B)*c^4*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]) + ((3*A - 7*B)*c^3*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(a^2*f*Sqrt[a + a*Sin[e + f*x]]) + ((3*A - 7*B)*c^2*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(3*a^2*f*Sqrt[a + a*Sin[e + f*x]]) + ((3*A - 7*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(4*a*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(9/2))/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",8,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
188,1,263,0,0.6073527,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{7/2}}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(7/2))/(a + a*Sin[e + f*x])^(5/2),x]","\frac{3 c^3 (A-3 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{3 c^2 (A-3 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{6 c^4 (A-3 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-3 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{2 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 f (a \sin (e+f x)+a)^{5/2}}","\frac{3 c^3 (A-3 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{3 c^2 (A-3 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{6 c^4 (A-3 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-3 B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{2 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{7/2}}{4 f (a \sin (e+f x)+a)^{5/2}}",1,"(6*(A - 3*B)*c^4*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + (3*(A - 3*B)*c^3*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]) + (3*(A - 3*B)*c^2*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(4*a^2*f*Sqrt[a + a*Sin[e + f*x]]) + ((A - 3*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(2*a*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(7/2))/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",7,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
189,1,211,0,0.4944401,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2}}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2))/(a + a*Sin[e + f*x])^(5/2),x]","\frac{c^2 (A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^3 (A-5 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{4 f (a \sin (e+f x)+a)^{5/2}}","\frac{c^2 (A-5 B) \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{2 a^2 f \sqrt{a \sin (e+f x)+a}}+\frac{c^3 (A-5 B) \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{c (A-5 B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{5/2}}{4 f (a \sin (e+f x)+a)^{5/2}}",1,"((A - 5*B)*c^3*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]]) + ((A - 5*B)*c^2*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(2*a^2*f*Sqrt[a + a*Sin[e + f*x]]) + ((A - 5*B)*c*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(4*a*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(5/2))/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",6,6,40,0.1500,1,"{2972, 2739, 2740, 2737, 2667, 31}"
190,1,149,0,0.3923603,"\int \frac{(A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2}}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2))/(a + a*Sin[e + f*x])^(5/2),x]","-\frac{B c^2 \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{B c \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f (a \sin (e+f x)+a)^{3/2}}","-\frac{B c^2 \cos (e+f x) \log (\sin (e+f x)+1)}{a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x) (c-c \sin (e+f x))^{3/2}}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{B c \cos (e+f x) \sqrt{c-c \sin (e+f x)}}{a f (a \sin (e+f x)+a)^{3/2}}",1,"-((B*c^2*Cos[e + f*x]*Log[1 + Sin[e + f*x]])/(a^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])) - (B*c*Cos[e + f*x]*Sqrt[c - c*Sin[e + f*x]])/(a*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - B)*Cos[e + f*x]*(c - c*Sin[e + f*x])^(3/2))/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",5,5,40,0.1250,1,"{2972, 2739, 2737, 2667, 31}"
191,1,94,0,0.3330823,"\int \frac{(A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)}}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]])/(a + a*Sin[e + f*x])^(5/2),x]","-\frac{c (A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}-\frac{B c \cos (e+f x)}{a f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}","-\frac{c (A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}-\frac{B c \cos (e+f x)}{a f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}",1,"-((A - B)*c*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(5/2)*Sqrt[c - c*Sin[e + f*x]]) - (B*c*Cos[e + f*x])/(a*f*(a + a*Sin[e + f*x])^(3/2)*Sqrt[c - c*Sin[e + f*x]])","A",3,2,40,0.05000,1,"{2971, 2738}"
192,1,151,0,0.3539676,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} \sqrt{c-c \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*Sqrt[c - c*Sin[e + f*x]]),x]","\frac{(A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{4 a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A+B) \cos (e+f x)}{4 a f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}","\frac{(A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{4 a^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(A+B) \cos (e+f x)}{4 a f (a \sin (e+f x)+a)^{3/2} \sqrt{c-c \sin (e+f x)}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} \sqrt{c-c \sin (e+f x)}}",1,"-((A - B)*Cos[e + f*x])/(4*f*(a + a*Sin[e + f*x])^(5/2)*Sqrt[c - c*Sin[e + f*x]]) - ((A + B)*Cos[e + f*x])/(4*a*f*(a + a*Sin[e + f*x])^(3/2)*Sqrt[c - c*Sin[e + f*x]]) + ((A + B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(4*a^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",4,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
193,1,208,0,0.4804425,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} (c-c \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(3/2)),x]","\frac{(3 A+B) \cos (e+f x)}{8 a^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(3 A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a^2 c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(3 A+B) \cos (e+f x)}{8 a f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{3/2}}","\frac{(3 A+B) \cos (e+f x)}{8 a^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{(3 A+B) \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a^2 c f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}-\frac{(3 A+B) \cos (e+f x)}{8 a f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{3/2}}",1,"-((A - B)*Cos[e + f*x])/(4*f*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(3/2)) - ((3*A + B)*Cos[e + f*x])/(8*a*f*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(3/2)) + ((3*A + B)*Cos[e + f*x])/(8*a^2*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + ((3*A + B)*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(8*a^2*c*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",5,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
194,1,245,0,0.5699156,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} (c-c \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(5/2)),x]","\frac{3 A \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a^2 c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{3 A \cos (e+f x)}{8 a^2 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{3 A \cos (e+f x)}{8 a^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{5/2}}-\frac{A \cos (e+f x)}{2 a f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}","\frac{3 A \cos (e+f x) \tanh ^{-1}(\sin (e+f x))}{8 a^2 c^2 f \sqrt{a \sin (e+f x)+a} \sqrt{c-c \sin (e+f x)}}+\frac{3 A \cos (e+f x)}{8 a^2 c f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{3/2}}+\frac{3 A \cos (e+f x)}{8 a^2 f \sqrt{a \sin (e+f x)+a} (c-c \sin (e+f x))^{5/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2} (c-c \sin (e+f x))^{5/2}}-\frac{A \cos (e+f x)}{2 a f (a \sin (e+f x)+a)^{3/2} (c-c \sin (e+f x))^{5/2}}",1,"-((A - B)*Cos[e + f*x])/(4*f*(a + a*Sin[e + f*x])^(5/2)*(c - c*Sin[e + f*x])^(5/2)) - (A*Cos[e + f*x])/(2*a*f*(a + a*Sin[e + f*x])^(3/2)*(c - c*Sin[e + f*x])^(5/2)) + (3*A*Cos[e + f*x])/(8*a^2*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(5/2)) + (3*A*Cos[e + f*x])/(8*a^2*c*f*Sqrt[a + a*Sin[e + f*x]]*(c - c*Sin[e + f*x])^(3/2)) + (3*A*ArcTanh[Sin[e + f*x]]*Cos[e + f*x])/(8*a^2*c^2*f*Sqrt[a + a*Sin[e + f*x]]*Sqrt[c - c*Sin[e + f*x]])","A",6,4,40,0.1000,1,"{2972, 2743, 2741, 3770}"
195,1,174,0,0.3145605,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^n \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^n,x]","\frac{c 2^{n+\frac{1}{2}} (A (m+n+1)+B (m-n)) \cos (e+f x) (1-\sin (e+f x))^{\frac{1}{2}-n} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (1-2 n);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) (m+n+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^n}{f (m+n+1)}","\frac{c 2^{n+\frac{1}{2}} (A (m+n+1)+B (m-n)) \cos (e+f x) (1-\sin (e+f x))^{\frac{1}{2}-n} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{n-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (1-2 n);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) (m+n+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^n}{f (m+n+1)}",1,"(2^(1/2 + n)*c*(B*(m - n) + A*(1 + m + n))*Cos[e + f*x]*Hypergeometric2F1[(1 + 2*m)/2, (1 - 2*n)/2, (3 + 2*m)/2, (1 + Sin[e + f*x])/2]*(1 - Sin[e + f*x])^(1/2 - n)*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 + n))/(f*(1 + 2*m)*(1 + m + n)) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^n)/(f*(1 + m + n))","A",5,5,36,0.1389,1,"{2973, 2745, 2689, 70, 69}"
196,1,145,0,0.3418066,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^3,x]","\frac{a^4 c^3 2^{m+\frac{1}{2}} (B (3-m)-A (m+4)) \cos ^7(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-4} \, _2F_1\left(\frac{7}{2},\frac{1}{2}-m;\frac{9}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{7 f (m+4)}-\frac{a^3 B c^3 \cos ^7(e+f x) (a \sin (e+f x)+a)^{m-3}}{f (m+4)}","\frac{a^4 c^3 2^{m+\frac{1}{2}} (B (3-m)-A (m+4)) \cos ^7(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-4} \, _2F_1\left(\frac{7}{2},\frac{1}{2}-m;\frac{9}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{7 f (m+4)}-\frac{a^3 B c^3 \cos ^7(e+f x) (a \sin (e+f x)+a)^{m-3}}{f (m+4)}",1,"(2^(1/2 + m)*a^4*c^3*(B*(3 - m) - A*(4 + m))*Cos[e + f*x]^7*Hypergeometric2F1[7/2, 1/2 - m, 9/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^(-4 + m))/(7*f*(4 + m)) - (a^3*B*c^3*Cos[e + f*x]^7*(a + a*Sin[e + f*x])^(-3 + m))/(f*(4 + m))","A",5,5,36,0.1389,1,"{2967, 2860, 2689, 70, 69}"
197,1,145,0,0.334866,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^2,x]","\frac{a^3 c^2 2^{m+\frac{1}{2}} (B (2-m)-A (m+3)) \cos ^5(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-3} \, _2F_1\left(\frac{5}{2},\frac{1}{2}-m;\frac{7}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{5 f (m+3)}-\frac{a^2 B c^2 \cos ^5(e+f x) (a \sin (e+f x)+a)^{m-2}}{f (m+3)}","\frac{a^3 c^2 2^{m+\frac{1}{2}} (B (2-m)-A (m+3)) \cos ^5(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-3} \, _2F_1\left(\frac{5}{2},\frac{1}{2}-m;\frac{7}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{5 f (m+3)}-\frac{a^2 B c^2 \cos ^5(e+f x) (a \sin (e+f x)+a)^{m-2}}{f (m+3)}",1,"(2^(1/2 + m)*a^3*c^2*(B*(2 - m) - A*(3 + m))*Cos[e + f*x]^5*Hypergeometric2F1[5/2, 1/2 - m, 7/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^(-3 + m))/(5*f*(3 + m)) - (a^2*B*c^2*Cos[e + f*x]^5*(a + a*Sin[e + f*x])^(-2 + m))/(f*(3 + m))","A",5,5,36,0.1389,1,"{2967, 2860, 2689, 70, 69}"
198,1,139,0,0.2891084,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x]),x]","\frac{a^2 c 2^{m+\frac{1}{2}} (B (1-m)-A (m+2)) \cos ^3(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-2} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-m;\frac{5}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{3 f (m+2)}-\frac{a B c \cos ^3(e+f x) (a \sin (e+f x)+a)^{m-1}}{f (m+2)}","\frac{a^2 c 2^{m+\frac{1}{2}} (B (1-m)-A (m+2)) \cos ^3(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m-2} \, _2F_1\left(\frac{3}{2},\frac{1}{2}-m;\frac{5}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{3 f (m+2)}-\frac{a B c \cos ^3(e+f x) (a \sin (e+f x)+a)^{m-1}}{f (m+2)}",1,"(2^(1/2 + m)*a^2*c*(B*(1 - m) - A*(2 + m))*Cos[e + f*x]^3*Hypergeometric2F1[3/2, 1/2 - m, 5/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^(-2 + m))/(3*f*(2 + m)) - (a*B*c*Cos[e + f*x]^3*(a + a*Sin[e + f*x])^(-1 + m))/(f*(2 + m))","A",5,5,34,0.1471,1,"{2967, 2860, 2689, 70, 69}"
199,1,117,0,0.0817716,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]),x]","-\frac{2^{m+\frac{1}{2}} (A m+A+B m) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1)}","-\frac{2^{m+\frac{1}{2}} (A m+A+B m) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1)}",1,"-((B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + m))) - (2^(1/2 + m)*(A + A*m + B*m)*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m))","A",3,3,23,0.1304,1,"{2751, 2652, 2651}"
200,1,123,0,0.3031417,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{c-c \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x]),x]","\frac{2^{m+\frac{1}{2}} (A m+B m+B) \sec (e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^m \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-m;\frac{1}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{c f m}-\frac{B \sec (e+f x) (a \sin (e+f x)+a)^{m+1}}{a c f m}","\frac{2^{m+\frac{1}{2}} (A m+B m+B) \sec (e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^m \, _2F_1\left(-\frac{1}{2},\frac{1}{2}-m;\frac{1}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{c f m}-\frac{B \sec (e+f x) (a \sin (e+f x)+a)^{m+1}}{a c f m}",1,"(2^(1/2 + m)*(B + A*m + B*m)*Hypergeometric2F1[-1/2, 1/2 - m, 1/2, (1 - Sin[e + f*x])/2]*Sec[e + f*x]*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^m)/(c*f*m) - (B*Sec[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*c*f*m)","A",5,5,36,0.1389,1,"{2967, 2860, 2689, 70, 69}"
201,1,148,0,0.3301382,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c-c \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^2,x]","\frac{B \sec ^3(e+f x) (a \sin (e+f x)+a)^{m+2}}{a^2 c^2 f (1-m)}+\frac{2^{m+\frac{1}{2}} (A (1-m)-B (m+2)) \sec ^3(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2}-m;-\frac{1}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{3 a c^2 f (1-m)}","\frac{B \sec ^3(e+f x) (a \sin (e+f x)+a)^{m+2}}{a^2 c^2 f (1-m)}+\frac{2^{m+\frac{1}{2}} (A (1-m)-B (m+2)) \sec ^3(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{1}{2}-m;-\frac{1}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{3 a c^2 f (1-m)}",1,"(2^(1/2 + m)*(A*(1 - m) - B*(2 + m))*Hypergeometric2F1[-3/2, 1/2 - m, -1/2, (1 - Sin[e + f*x])/2]*Sec[e + f*x]^3*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^(1 + m))/(3*a*c^2*f*(1 - m)) + (B*Sec[e + f*x]^3*(a + a*Sin[e + f*x])^(2 + m))/(a^2*c^2*f*(1 - m))","A",5,5,36,0.1389,1,"{2967, 2860, 2689, 70, 69}"
202,1,148,0,0.3317813,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c-c \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^3,x]","\frac{2^{m+\frac{1}{2}} (A (2-m)-B (m+3)) \sec ^5(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{1}{2}-m;-\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{5 a^2 c^3 f (2-m)}+\frac{B \sec ^5(e+f x) (a \sin (e+f x)+a)^{m+3}}{a^3 c^3 f (2-m)}","\frac{2^{m+\frac{1}{2}} (A (2-m)-B (m+3)) \sec ^5(e+f x) (\sin (e+f x)+1)^{\frac{1}{2}-m} (a \sin (e+f x)+a)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{1}{2}-m;-\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{5 a^2 c^3 f (2-m)}+\frac{B \sec ^5(e+f x) (a \sin (e+f x)+a)^{m+3}}{a^3 c^3 f (2-m)}",1,"(2^(1/2 + m)*(A*(2 - m) - B*(3 + m))*Hypergeometric2F1[-5/2, 1/2 - m, -3/2, (1 - Sin[e + f*x])/2]*Sec[e + f*x]^5*(1 + Sin[e + f*x])^(1/2 - m)*(a + a*Sin[e + f*x])^(2 + m))/(5*a^2*c^3*f*(2 - m)) + (B*Sec[e + f*x]^5*(a + a*Sin[e + f*x])^(3 + m))/(a^3*c^3*f*(2 - m))","A",5,5,36,0.1389,1,"{2967, 2860, 2689, 70, 69}"
203,1,118,0,0.2944325,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}",1,"(-2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]]) + ((A + B)*Cos[e + f*x]*Hypergeometric2F1[1, 1/2 + m, 3/2 + m, (1 + Sin[e + f*x])/2]*(a + a*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2973, 2745, 2667, 68}"
204,1,118,0,0.2881174,"\int \frac{(A+B \sin (e+f x)) (c+c \sin (e+f x))^m}{\sqrt{a-a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c + c*Sin[e + f*x])^m)/Sqrt[a - a*Sin[e + f*x]],x]","\frac{(A+B) \cos (e+f x) (c \sin (e+f x)+c)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{a-a \sin (e+f x)}}-\frac{2 B \cos (e+f x) (c \sin (e+f x)+c)^m}{f (2 m+1) \sqrt{a-a \sin (e+f x)}}","\frac{(A+B) \cos (e+f x) (c \sin (e+f x)+c)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{a-a \sin (e+f x)}}-\frac{2 B \cos (e+f x) (c \sin (e+f x)+c)^m}{f (2 m+1) \sqrt{a-a \sin (e+f x)}}",1,"(-2*B*Cos[e + f*x]*(c + c*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[a - a*Sin[e + f*x]]) + ((A + B)*Cos[e + f*x]*Hypergeometric2F1[1, 1/2 + m, 3/2 + m, (1 + Sin[e + f*x])/2]*(c + c*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[a - a*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2973, 2745, 2667, 68}"
205,1,275,0,0.5034577,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{5/2} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(5/2),x]","-\frac{16 c^2 (B (5-2 m)-A (2 m+7)) \cos (e+f x) \sqrt{c-c \sin (e+f x)} (a \sin (e+f x)+a)^m}{f (2 m+7) \left(4 m^2+16 m+15\right)}-\frac{64 c^3 (B (5-2 m)-A (2 m+7)) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+5) (2 m+7) \left(4 m^2+8 m+3\right) \sqrt{c-c \sin (e+f x)}}-\frac{2 c (B (5-2 m)-A (2 m+7)) \cos (e+f x) (c-c \sin (e+f x))^{3/2} (a \sin (e+f x)+a)^m}{f (2 m+5) (2 m+7)}-\frac{2 B \cos (e+f x) (c-c \sin (e+f x))^{5/2} (a \sin (e+f x)+a)^m}{f (2 m+7)}","-\frac{16 c^2 (B (5-2 m)-A (2 m+7)) \cos (e+f x) \sqrt{c-c \sin (e+f x)} (a \sin (e+f x)+a)^m}{f (2 m+7) \left(4 m^2+16 m+15\right)}-\frac{64 c^3 (B (5-2 m)-A (2 m+7)) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+5) (2 m+7) \left(4 m^2+8 m+3\right) \sqrt{c-c \sin (e+f x)}}-\frac{2 c (B (5-2 m)-A (2 m+7)) \cos (e+f x) (c-c \sin (e+f x))^{3/2} (a \sin (e+f x)+a)^m}{f (2 m+5) (2 m+7)}-\frac{2 B \cos (e+f x) (c-c \sin (e+f x))^{5/2} (a \sin (e+f x)+a)^m}{f (2 m+7)}",1,"(-64*c^3*(B*(5 - 2*m) - A*(7 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(5 + 2*m)*(7 + 2*m)*(3 + 8*m + 4*m^2)*Sqrt[c - c*Sin[e + f*x]]) - (16*c^2*(B*(5 - 2*m) - A*(7 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[c - c*Sin[e + f*x]])/(f*(7 + 2*m)*(15 + 16*m + 4*m^2)) - (2*c*(B*(5 - 2*m) - A*(7 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(3/2))/(f*(5 + 2*m)*(7 + 2*m)) - (2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(5/2))/(f*(7 + 2*m))","A",4,3,38,0.07895,1,"{2973, 2740, 2738}"
206,1,192,0,0.3540948,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(3/2),x]","-\frac{8 c^2 (B (3-2 m)-A (2 m+5)) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+5) \left(4 m^2+8 m+3\right) \sqrt{c-c \sin (e+f x)}}-\frac{2 c (B (3-2 m)-A (2 m+5)) \cos (e+f x) \sqrt{c-c \sin (e+f x)} (a \sin (e+f x)+a)^m}{f (2 m+3) (2 m+5)}-\frac{2 B \cos (e+f x) (c-c \sin (e+f x))^{3/2} (a \sin (e+f x)+a)^m}{f (2 m+5)}","-\frac{2 B c^2 \cos (e+f x) (a \sin (e+f x)+a)^{m+2}}{a^2 f (2 m+5) \sqrt{c-c \sin (e+f x)}}+\frac{4 c^2 (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}-\frac{2 c^2 (A-3 B) \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (2 m+3) \sqrt{c-c \sin (e+f x)}}",1,"(-8*c^2*(B*(3 - 2*m) - A*(5 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(5 + 2*m)*(3 + 8*m + 4*m^2)*Sqrt[c - c*Sin[e + f*x]]) - (2*c*(B*(3 - 2*m) - A*(5 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[c - c*Sin[e + f*x]])/(f*(3 + 2*m)*(5 + 2*m)) - (2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(3/2))/(f*(5 + 2*m))","A",3,3,38,0.07895,1,"{2973, 2740, 2738}"
207,1,104,0,0.2821081,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \sqrt{c-c \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*Sqrt[c - c*Sin[e + f*x]],x]","\frac{2 c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{2 B c \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (2 m+3) \sqrt{c-c \sin (e+f x)}}","\frac{2 c (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{2 B c \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (2 m+3) \sqrt{c-c \sin (e+f x)}}",1,"(2*(A - B)*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]]) + (2*B*c*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*f*(3 + 2*m)*Sqrt[c - c*Sin[e + f*x]])","A",3,2,38,0.05263,1,"{2971, 2738}"
208,1,118,0,0.2821204,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{\sqrt{c-c \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/Sqrt[c - c*Sin[e + f*x]],x]","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (2 m+1) \sqrt{c-c \sin (e+f x)}}",1,"(-2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]]) + ((A + B)*Cos[e + f*x]*Hypergeometric2F1[1, 1/2 + m, 3/2 + m, (1 + Sin[e + f*x])/2]*(a + a*Sin[e + f*x])^m)/(f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2973, 2745, 2667, 68}"
209,1,134,0,0.2997696,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(3/2),x]","\frac{(A (1-2 m)-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{4 c f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m}{2 f (c-c \sin (e+f x))^{3/2}}","\frac{(A (1-2 m)-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(1,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{4 c f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m}{2 f (c-c \sin (e+f x))^{3/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(2*f*(c - c*Sin[e + f*x])^(3/2)) + ((A*(1 - 2*m) - B*(3 + 2*m))*Cos[e + f*x]*Hypergeometric2F1[1, 1/2 + m, 3/2 + m, (1 + Sin[e + f*x])/2]*(a + a*Sin[e + f*x])^m)/(4*c*f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2972, 2745, 2667, 68}"
210,1,134,0,0.3323243,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c-c \sin (e+f x))^{5/2}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^(5/2),x]","\frac{(A (3-2 m)-B (2 m+5)) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(2,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{16 c^2 f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m}{4 f (c-c \sin (e+f x))^{5/2}}","\frac{(A (3-2 m)-B (2 m+5)) \cos (e+f x) (a \sin (e+f x)+a)^m \, _2F_1\left(2,m+\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1)\right)}{16 c^2 f (2 m+1) \sqrt{c-c \sin (e+f x)}}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m}{4 f (c-c \sin (e+f x))^{5/2}}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(4*f*(c - c*Sin[e + f*x])^(5/2)) + ((A*(3 - 2*m) - B*(5 + 2*m))*Cos[e + f*x]*Hypergeometric2F1[2, 1/2 + m, 3/2 + m, (1 + Sin[e + f*x])/2]*(a + a*Sin[e + f*x])^m)/(16*c^2*f*(1 + 2*m)*Sqrt[c - c*Sin[e + f*x]])","A",4,4,38,0.1053,1,"{2972, 2745, 2667, 68}"
211,1,267,0,0.4268697,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{-4-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(-4 - m),x]","\frac{2 (3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{c^2 f (2 m+7) \left(4 m^2+16 m+15\right)}+\frac{2 (3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c^3 f (2 m+5) (2 m+7) \left(4 m^2+8 m+3\right)}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-4}}{f (2 m+7)}+\frac{(3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-3}}{c f (2 m+5) (2 m+7)}","\frac{2 (3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{c^2 f (2 m+7) \left(4 m^2+16 m+15\right)}+\frac{2 (3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c^3 f (2 m+5) (2 m+7) \left(4 m^2+8 m+3\right)}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-4}}{f (2 m+7)}+\frac{(3 A-2 B (m+2)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-3}}{c f (2 m+5) (2 m+7)}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-4 - m))/(f*(7 + 2*m)) + ((3*A - 2*B*(2 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-3 - m))/(c*f*(5 + 2*m)*(7 + 2*m)) + (2*(3*A - 2*B*(2 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-2 - m))/(c^2*f*(7 + 2*m)*(15 + 16*m + 4*m^2)) + (2*(3*A - 2*B*(2 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(c^3*f*(5 + 2*m)*(7 + 2*m)*(3 + 8*m + 4*m^2))","A",4,3,40,0.07500,1,"{2972, 2743, 2742}"
212,1,191,0,0.3096812,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{-3-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(-3 - m),x]","\frac{(2 A-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c^2 f (2 m+5) \left(4 m^2+8 m+3\right)}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-3}}{f (2 m+5)}+\frac{(2 A-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{c f (2 m+3) (2 m+5)}","\frac{(2 A-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c^2 f (2 m+5) \left(4 m^2+8 m+3\right)}+\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-3}}{f (2 m+5)}+\frac{(2 A-B (2 m+3)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{c f (2 m+3) (2 m+5)}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-3 - m))/(f*(5 + 2*m)) + ((2*A - B*(3 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-2 - m))/(c*f*(3 + 2*m)*(5 + 2*m)) + ((2*A - B*(3 + 2*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(c^2*f*(5 + 2*m)*(3 + 8*m + 4*m^2))","A",3,3,40,0.07500,1,"{2972, 2743, 2742}"
213,1,114,0,0.2216476,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{-2-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(-2 - m),x]","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{f (2 m+3)}+\frac{(A-2 B (m+1)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c f (2 m+1) (2 m+3)}","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-2}}{f (2 m+3)}+\frac{(A-2 B (m+1)) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{c f (2 m+1) (2 m+3)}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-2 - m))/(f*(3 + 2*m)) + ((A - 2*B*(1 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(c*f*(1 + 2*m)*(3 + 2*m))","A",2,2,40,0.05000,1,"{2972, 2742}"
214,1,163,0,0.3090104,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{-1-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(-1 - m),x]","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{f (2 m+1)}-\frac{B 2^{\frac{1}{2}-m} \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}","\frac{(A+B) \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1}}{f (2 m+1)}-\frac{B 2^{\frac{1}{2}-m} \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}",1,"((A + B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(f*(1 + 2*m)) - (2^(1/2 - m)*B*Cos[e + f*x]*Hypergeometric2F1[(1 + 2*m)/2, (1 + 2*m)/2, (3 + 2*m)/2, (1 + Sin[e + f*x])/2]*(1 - Sin[e + f*x])^(1/2 + m)*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(f*(1 + 2*m))","A",5,5,40,0.1250,1,"{2972, 2745, 2689, 70, 69}"
215,1,158,0,0.2681441,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{-m} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c - c*Sin[e + f*x])^m,x]","\frac{c 2^{\frac{1}{2}-m} (A+2 B m) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m}}{f}","\frac{c 2^{\frac{1}{2}-m} (A+2 B m) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m+1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m}}{f}",1,"(2^(1/2 - m)*c*(A + 2*B*m)*Cos[e + f*x]*Hypergeometric2F1[(1 + 2*m)/2, (1 + 2*m)/2, (3 + 2*m)/2, (1 + Sin[e + f*x])/2]*(1 - Sin[e + f*x])^(1/2 + m)*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(f*(1 + 2*m)) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(c - c*Sin[e + f*x])^m)","A",5,5,38,0.1316,1,"{2973, 2745, 2689, 70, 69}"
216,1,170,0,0.3286505,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{1-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(1 - m),x]","\frac{c^2 2^{\frac{1}{2}-m} (2 A-B (1-2 m)) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m-1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{1-m}}{2 f}","\frac{c^2 2^{\frac{1}{2}-m} (2 A-B (1-2 m)) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m-1),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{1-m}}{2 f}",1,"(2^(1/2 - m)*c^2*(2*A - B*(1 - 2*m))*Cos[e + f*x]*Hypergeometric2F1[(-1 + 2*m)/2, (1 + 2*m)/2, (3 + 2*m)/2, (1 + Sin[e + f*x])/2]*(1 - Sin[e + f*x])^(1/2 + m)*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(f*(1 + 2*m)) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(1 - m))/(2*f)","A",5,5,40,0.1250,1,"{2973, 2745, 2689, 70, 69}"
217,1,173,0,0.3361362,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c-c \sin (e+f x))^{2-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c - c*Sin[e + f*x])^(2 - m),x]","\frac{c^3 2^{\frac{5}{2}-m} (3 A-2 B (1-m)) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m-3),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{3 f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{2-m}}{3 f}","\frac{c^3 2^{\frac{5}{2}-m} (3 A-2 B (1-m)) \cos (e+f x) (1-\sin (e+f x))^{m+\frac{1}{2}} (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{-m-1} \, _2F_1\left(\frac{1}{2} (2 m-3),\frac{1}{2} (2 m+1);\frac{1}{2} (2 m+3);\frac{1}{2} (\sin (e+f x)+1)\right)}{3 f (2 m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^{2-m}}{3 f}",1,"(2^(5/2 - m)*c^3*(3*A - 2*B*(1 - m))*Cos[e + f*x]*Hypergeometric2F1[(-3 + 2*m)/2, (1 + 2*m)/2, (3 + 2*m)/2, (1 + Sin[e + f*x])/2]*(1 - Sin[e + f*x])^(1/2 + m)*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(-1 - m))/(3*f*(1 + 2*m)) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^(2 - m))/(3*f)","A",5,5,40,0.1250,1,"{2973, 2745, 2689, 70, 69}"
218,1,34,0,0.2739131,"\int (a+a \sin (e+f x))^3 (c-c \sin (e+f x))^n (B (3-n)-B (4+n) \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^3*(c - c*Sin[e + f*x])^n*(B*(3 - n) - B*(4 + n)*Sin[e + f*x]),x]","\frac{a^3 B c^3 \cos ^7(e+f x) (c-c \sin (e+f x))^{n-3}}{f}","\frac{a^3 B c^3 \cos ^7(e+f x) (c-c \sin (e+f x))^{n-3}}{f}",1,"(a^3*B*c^3*Cos[e + f*x]^7*(c - c*Sin[e + f*x])^(-3 + n))/f","A",2,2,46,0.04348,1,"{2967, 2854}"
219,1,34,0,0.2383535,"\int (a-a \sin (e+f x))^3 (c+c \sin (e+f x))^n (B (3-n)+B (4+n) \sin (e+f x)) \, dx","Int[(a - a*Sin[e + f*x])^3*(c + c*Sin[e + f*x])^n*(B*(3 - n) + B*(4 + n)*Sin[e + f*x]),x]","-\frac{a^3 B c^3 \cos ^7(e+f x) (c \sin (e+f x)+c)^{n-3}}{f}","-\frac{a^3 B c^3 \cos ^7(e+f x) (c \sin (e+f x)+c)^{n-3}}{f}",1,"-((a^3*B*c^3*Cos[e + f*x]^7*(c + c*Sin[e + f*x])^(-3 + n))/f)","A",2,2,45,0.04444,1,"{2967, 2854}"
220,1,33,0,0.2374852,"\int (a+a \sin (e+f x))^m (c-c \sin (e+f x))^3 (B (-3+m)-B (4+m) \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^3*(B*(-3 + m) - B*(4 + m)*Sin[e + f*x]),x]","\frac{a^3 B c^3 \cos ^7(e+f x) (a \sin (e+f x)+a)^{m-3}}{f}","\frac{a^3 B c^3 \cos ^7(e+f x) (a \sin (e+f x)+a)^{m-3}}{f}",1,"(a^3*B*c^3*Cos[e + f*x]^7*(a + a*Sin[e + f*x])^(-3 + m))/f","A",2,2,44,0.04545,1,"{2967, 2854}"
221,1,35,0,0.2383967,"\int (a-a \sin (e+f x))^m (c+c \sin (e+f x))^3 (B (-3+m)+B (4+m) \sin (e+f x)) \, dx","Int[(a - a*Sin[e + f*x])^m*(c + c*Sin[e + f*x])^3*(B*(-3 + m) + B*(4 + m)*Sin[e + f*x]),x]","-\frac{a^3 B c^3 \cos ^7(e+f x) (a-a \sin (e+f x))^{m-3}}{f}","-\frac{a^3 B c^3 \cos ^7(e+f x) (a-a \sin (e+f x))^{m-3}}{f}",1,"-((a^3*B*c^3*Cos[e + f*x]^7*(a - a*Sin[e + f*x])^(-3 + m))/f)","A",2,2,43,0.04651,1,"{2967, 2854}"
222,1,36,0,0.1318276,"\int (a+a \sin (e+f x))^m (c-c \sin (e+f x))^n (B (m-n)-B (1+m+n) \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^n*(B*(m - n) - B*(1 + m + n)*Sin[e + f*x]),x]","\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^n}{f}","\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c-c \sin (e+f x))^n}{f}",1,"(B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c - c*Sin[e + f*x])^n)/f","A",1,1,47,0.02128,1,"{2970}"
223,1,37,0,0.1234548,"\int (a-a \sin (e+f x))^m (c+c \sin (e+f x))^n (B (m-n)+B (1+m+n) \sin (e+f x)) \, dx","Int[(a - a*Sin[e + f*x])^m*(c + c*Sin[e + f*x])^n*(B*(m - n) + B*(1 + m + n)*Sin[e + f*x]),x]","-\frac{B \cos (e+f x) (a-a \sin (e+f x))^m (c \sin (e+f x)+c)^n}{f}","-\frac{B \cos (e+f x) (a-a \sin (e+f x))^m (c \sin (e+f x)+c)^n}{f}",1,"-((B*Cos[e + f*x]*(a - a*Sin[e + f*x])^m*(c + c*Sin[e + f*x])^n)/f)","A",1,1,46,0.02174,1,"{2970}"
224,1,140,0,0.1859631,"\int \sin ^3(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Sin[c + d*x]^3*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{a^3 A \cos ^7(c+d x)}{7 d}+\frac{3 a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^5(c+d x) \cos (c+d x)}{3 d}-\frac{a^3 A \sin ^3(c+d x) \cos (c+d x)}{12 d}-\frac{a^3 A \sin (c+d x) \cos (c+d x)}{8 d}+\frac{1}{8} a^3 A x","-\frac{a^3 A \cos ^7(c+d x)}{7 d}+\frac{3 a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^5(c+d x) \cos (c+d x)}{3 d}-\frac{a^3 A \sin ^3(c+d x) \cos (c+d x)}{12 d}-\frac{a^3 A \sin (c+d x) \cos (c+d x)}{8 d}+\frac{1}{8} a^3 A x",1,"(a^3*A*x)/8 - (2*a^3*A*Cos[c + d*x]^3)/(3*d) + (3*a^3*A*Cos[c + d*x]^5)/(5*d) - (a^3*A*Cos[c + d*x]^7)/(7*d) - (a^3*A*Cos[c + d*x]*Sin[c + d*x])/(8*d) - (a^3*A*Cos[c + d*x]*Sin[c + d*x]^3)/(12*d) + (a^3*A*Cos[c + d*x]*Sin[c + d*x]^5)/(3*d)","A",13,4,32,0.1250,1,"{2966, 2633, 2635, 8}"
225,1,121,0,0.1680422,"\int \sin ^2(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Sin[c + d*x]^2*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","\frac{2 a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^5(c+d x) \cos (c+d x)}{6 d}+\frac{5 a^3 A \sin ^3(c+d x) \cos (c+d x)}{24 d}-\frac{3 a^3 A \sin (c+d x) \cos (c+d x)}{16 d}+\frac{3}{16} a^3 A x","\frac{2 a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^5(c+d x) \cos (c+d x)}{6 d}+\frac{5 a^3 A \sin ^3(c+d x) \cos (c+d x)}{24 d}-\frac{3 a^3 A \sin (c+d x) \cos (c+d x)}{16 d}+\frac{3}{16} a^3 A x",1,"(3*a^3*A*x)/16 - (2*a^3*A*Cos[c + d*x]^3)/(3*d) + (2*a^3*A*Cos[c + d*x]^5)/(5*d) - (3*a^3*A*Cos[c + d*x]*Sin[c + d*x])/(16*d) + (5*a^3*A*Cos[c + d*x]*Sin[c + d*x]^3)/(24*d) + (a^3*A*Cos[c + d*x]*Sin[c + d*x]^5)/(6*d)","A",12,4,32,0.1250,1,"{2966, 2635, 8, 2633}"
226,1,96,0,0.1164725,"\int \sin (c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Sin[c + d*x]*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","\frac{a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^3(c+d x) \cos (c+d x)}{2 d}-\frac{a^3 A \sin (c+d x) \cos (c+d x)}{4 d}+\frac{1}{4} a^3 A x","\frac{a^3 A \cos ^5(c+d x)}{5 d}-\frac{2 a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \sin ^3(c+d x) \cos (c+d x)}{2 d}-\frac{a^3 A \sin (c+d x) \cos (c+d x)}{4 d}+\frac{1}{4} a^3 A x",1,"(a^3*A*x)/4 - (2*a^3*A*Cos[c + d*x]^3)/(3*d) + (a^3*A*Cos[c + d*x]^5)/(5*d) - (a^3*A*Cos[c + d*x]*Sin[c + d*x])/(4*d) + (a^3*A*Cos[c + d*x]*Sin[c + d*x]^3)/(2*d)","A",10,5,30,0.1667,1,"{2966, 2638, 2635, 8, 2633}"
227,1,82,0,0.1058927,"\int (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{5 a^3 A \cos ^3(c+d x)}{12 d}-\frac{A \cos ^3(c+d x) \left(a^3 \sin (c+d x)+a^3\right)}{4 d}+\frac{5 a^3 A \sin (c+d x) \cos (c+d x)}{8 d}+\frac{5}{8} a^3 A x","-\frac{5 a^3 A \cos ^3(c+d x)}{12 d}-\frac{A \cos ^3(c+d x) \left(a^3 \sin (c+d x)+a^3\right)}{4 d}+\frac{5 a^3 A \sin (c+d x) \cos (c+d x)}{8 d}+\frac{5}{8} a^3 A x",1,"(5*a^3*A*x)/8 - (5*a^3*A*Cos[c + d*x]^3)/(12*d) + (5*a^3*A*Cos[c + d*x]*Sin[c + d*x])/(8*d) - (A*Cos[c + d*x]^3*(a^3 + a^3*Sin[c + d*x]))/(4*d)","A",5,5,24,0.2083,1,"{2736, 2678, 2669, 2635, 8}"
228,1,76,0,0.1041529,"\int \csc (c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \cos (c+d x)}{d}+\frac{a^3 A \sin (c+d x) \cos (c+d x)}{d}-\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{d}+a^3 A x","-\frac{a^3 A \cos ^3(c+d x)}{3 d}+\frac{a^3 A \cos (c+d x)}{d}+\frac{a^3 A \sin (c+d x) \cos (c+d x)}{d}-\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{d}+a^3 A x",1,"a^3*A*x - (a^3*A*ArcTanh[Cos[c + d*x]])/d + (a^3*A*Cos[c + d*x])/d - (a^3*A*Cos[c + d*x]^3)/(3*d) + (a^3*A*Cos[c + d*x]*Sin[c + d*x])/d","A",7,5,30,0.1667,1,"{2966, 3770, 2635, 8, 2633}"
229,1,79,0,0.1789118,"\int \csc ^2(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^2*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","\frac{2 a^3 A \cos (c+d x)}{d}-\frac{a^3 A \cot (c+d x)}{d}+\frac{a^3 A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{2 a^3 A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{1}{2} a^3 A x","\frac{2 a^3 A \cos (c+d x)}{d}-\frac{a^3 A \cot (c+d x)}{d}+\frac{a^3 A \sin (c+d x) \cos (c+d x)}{2 d}-\frac{2 a^3 A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{1}{2} a^3 A x",1,"-(a^3*A*x)/2 - (2*a^3*A*ArcTanh[Cos[c + d*x]])/d + (2*a^3*A*Cos[c + d*x])/d - (a^3*A*Cot[c + d*x])/d + (a^3*A*Cos[c + d*x]*Sin[c + d*x])/(2*d)","A",9,7,32,0.2188,1,"{2950, 2709, 3770, 3767, 8, 2638, 2635}"
230,1,78,0,0.120552,"\int \csc ^3(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^3*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","\frac{a^3 A \cos (c+d x)}{d}-\frac{2 a^3 A \cot (c+d x)}{d}-\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a^3 A \cot (c+d x) \csc (c+d x)}{2 d}-2 a^3 A x","\frac{a^3 A \cos (c+d x)}{d}-\frac{2 a^3 A \cot (c+d x)}{d}-\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{2 d}-\frac{a^3 A \cot (c+d x) \csc (c+d x)}{2 d}-2 a^3 A x",1,"-2*a^3*A*x - (a^3*A*ArcTanh[Cos[c + d*x]])/(2*d) + (a^3*A*Cos[c + d*x])/d - (2*a^3*A*Cot[c + d*x])/d - (a^3*A*Cot[c + d*x]*Csc[c + d*x])/(2*d)","A",7,6,32,0.1875,1,"{2966, 3767, 8, 3768, 3770, 2638}"
231,1,78,0,0.1307121,"\int \csc ^4(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^4*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{a^3 A \cot ^3(c+d x)}{3 d}-\frac{a^3 A \cot (c+d x)}{d}+\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a^3 A \cot (c+d x) \csc (c+d x)}{d}-a^3 A x","-\frac{a^3 A \cot ^3(c+d x)}{3 d}-\frac{a^3 A \cot (c+d x)}{d}+\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{d}-\frac{a^3 A \cot (c+d x) \csc (c+d x)}{d}-a^3 A x",1,"-(a^3*A*x) + (a^3*A*ArcTanh[Cos[c + d*x]])/d - (a^3*A*Cot[c + d*x])/d - (a^3*A*Cot[c + d*x]^3)/(3*d) - (a^3*A*Cot[c + d*x]*Csc[c + d*x])/d","A",7,4,32,0.1250,1,"{2966, 3770, 3768, 3767}"
232,1,86,0,0.147784,"\int \csc ^5(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^5*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{5 a^3 A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a^3 A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{3 a^3 A \cot (c+d x) \csc (c+d x)}{8 d}","-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{5 a^3 A \tanh ^{-1}(\cos (c+d x))}{8 d}-\frac{a^3 A \cot (c+d x) \csc ^3(c+d x)}{4 d}-\frac{3 a^3 A \cot (c+d x) \csc (c+d x)}{8 d}",1,"(5*a^3*A*ArcTanh[Cos[c + d*x]])/(8*d) - (2*a^3*A*Cot[c + d*x]^3)/(3*d) - (3*a^3*A*Cot[c + d*x]*Csc[c + d*x])/(8*d) - (a^3*A*Cot[c + d*x]*Csc[c + d*x]^3)/(4*d)","A",10,5,32,0.1562,1,"{2966, 3770, 3767, 8, 3768}"
233,1,105,0,0.234037,"\int \csc ^6(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^6*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{a^3 A \cot ^5(c+d x)}{5 d}-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{4 d}-\frac{a^3 A \cot (c+d x) \csc ^3(c+d x)}{2 d}+\frac{a^3 A \cot (c+d x) \csc (c+d x)}{4 d}","-\frac{a^3 A \cot ^5(c+d x)}{5 d}-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{a^3 A \tanh ^{-1}(\cos (c+d x))}{4 d}-\frac{a^3 A \cot (c+d x) \csc ^3(c+d x)}{2 d}+\frac{a^3 A \cot (c+d x) \csc (c+d x)}{4 d}",1,"(a^3*A*ArcTanh[Cos[c + d*x]])/(4*d) - (2*a^3*A*Cot[c + d*x]^3)/(3*d) - (a^3*A*Cot[c + d*x]^5)/(5*d) + (a^3*A*Cot[c + d*x]*Csc[c + d*x])/(4*d) - (a^3*A*Cot[c + d*x]*Csc[c + d*x]^3)/(2*d)","A",12,6,32,0.1875,1,"{2950, 2709, 3767, 8, 3768, 3770}"
234,1,130,0,0.1966503,"\int \csc ^7(c+d x) (a+a \sin (c+d x))^3 (A-A \sin (c+d x)) \, dx","Int[Csc[c + d*x]^7*(a + a*Sin[c + d*x])^3*(A - A*Sin[c + d*x]),x]","-\frac{2 a^3 A \cot ^5(c+d x)}{5 d}-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{3 a^3 A \tanh ^{-1}(\cos (c+d x))}{16 d}-\frac{a^3 A \cot (c+d x) \csc ^5(c+d x)}{6 d}-\frac{5 a^3 A \cot (c+d x) \csc ^3(c+d x)}{24 d}+\frac{3 a^3 A \cot (c+d x) \csc (c+d x)}{16 d}","-\frac{2 a^3 A \cot ^5(c+d x)}{5 d}-\frac{2 a^3 A \cot ^3(c+d x)}{3 d}+\frac{3 a^3 A \tanh ^{-1}(\cos (c+d x))}{16 d}-\frac{a^3 A \cot (c+d x) \csc ^5(c+d x)}{6 d}-\frac{5 a^3 A \cot (c+d x) \csc ^3(c+d x)}{24 d}+\frac{3 a^3 A \cot (c+d x) \csc (c+d x)}{16 d}",1,"(3*a^3*A*ArcTanh[Cos[c + d*x]])/(16*d) - (2*a^3*A*Cot[c + d*x]^3)/(3*d) - (2*a^3*A*Cot[c + d*x]^5)/(5*d) + (3*a^3*A*Cot[c + d*x]*Csc[c + d*x])/(16*d) - (5*a^3*A*Cot[c + d*x]*Csc[c + d*x]^3)/(24*d) - (a^3*A*Cot[c + d*x]*Csc[c + d*x]^5)/(6*d)","A",12,4,32,0.1250,1,"{2966, 3768, 3770, 3767}"
235,1,129,0,0.2081719,"\int \frac{\sin ^4(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Sin[c + d*x]^4*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","-\frac{4 A \cos (c+d x)}{a^3 d}+\frac{A \sin (c+d x) \cos (c+d x)}{2 a^3 d}-\frac{199 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}+\frac{41 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{19 A x}{2 a^3}","-\frac{4 A \cos (c+d x)}{a^3 d}+\frac{A \sin (c+d x) \cos (c+d x)}{2 a^3 d}-\frac{199 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}+\frac{41 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{19 A x}{2 a^3}",1,"(-19*A*x)/(2*a^3) - (4*A*Cos[c + d*x])/(a^3*d) + (A*Cos[c + d*x]*Sin[c + d*x])/(2*a^3*d) - (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) + (41*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x])^2) - (199*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x]))","A",11,6,32,0.1875,1,"{2966, 2638, 2635, 8, 2650, 2648}"
236,1,103,0,0.1877401,"\int \frac{\sin ^3(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Sin[c + d*x]^3*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","\frac{A \cos (c+d x)}{a^3 d}+\frac{104 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}-\frac{31 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}+\frac{4 A x}{a^3}","\frac{A \cos (c+d x)}{a^3 d}+\frac{104 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}-\frac{31 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}+\frac{4 A x}{a^3}",1,"(4*A*x)/a^3 + (A*Cos[c + d*x])/(a^3*d) + (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) - (31*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x])^2) + (104*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x]))","A",9,4,32,0.1250,1,"{2966, 2638, 2650, 2648}"
237,1,89,0,0.1730791,"\int \frac{\sin ^2(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Sin[c + d*x]^2*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","-\frac{13 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}+\frac{7 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{A x}{a^3}","-\frac{13 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}+\frac{7 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{A x}{a^3}",1,"-((A*x)/a^3) - (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) + (7*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^2) - (13*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x]))","A",8,3,32,0.09375,1,"{2966, 2650, 2648}"
238,1,82,0,0.1380054,"\int \frac{\sin (c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Sin[c + d*x]*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","\frac{4 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}-\frac{11 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}","\frac{4 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}-\frac{11 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}",1,"(2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) - (11*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x])^2) + (4*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x]))","A",8,3,30,0.1000,1,"{2966, 2650, 2648}"
239,1,58,0,0.1143676,"\int \frac{A-A \sin (c+d x)}{(a+a \sin (c+d x))^3} \, dx","Int[(A - A*Sin[c + d*x])/(a + a*Sin[c + d*x])^3,x]","-\frac{A \cos ^3(c+d x)}{15 d (a \sin (c+d x)+a)^3}-\frac{a A \cos ^3(c+d x)}{5 d (a \sin (c+d x)+a)^4}","-\frac{A \cos ^3(c+d x)}{15 d (a \sin (c+d x)+a)^3}-\frac{a A \cos ^3(c+d x)}{5 d (a \sin (c+d x)+a)^4}",1,"-(a*A*Cos[c + d*x]^3)/(5*d*(a + a*Sin[c + d*x])^4) - (A*Cos[c + d*x]^3)/(15*d*(a + a*Sin[c + d*x])^3)","A",3,3,24,0.1250,1,"{2736, 2672, 2671}"
240,1,98,0,0.1644679,"\int \frac{\csc (c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Csc[c + d*x]*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","\frac{8 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}+\frac{3 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{A \tanh ^{-1}(\cos (c+d x))}{a^3 d}","\frac{8 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}+\frac{3 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{A \tanh ^{-1}(\cos (c+d x))}{a^3 d}",1,"-((A*ArcTanh[Cos[c + d*x]])/(a^3*d)) + (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) + (3*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^2) + (8*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x]))","A",9,4,30,0.1333,1,"{2966, 3770, 2650, 2648}"
241,1,113,0,0.3982753,"\int \frac{\csc ^2(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Csc[c + d*x]^2*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","-\frac{A \cot (c+d x)}{a^3 d}+\frac{4 A \tanh ^{-1}(\cos (c+d x))}{a^3 d}-\frac{104 A \cot (c+d x)}{15 a^3 d (\csc (c+d x)+1)}+\frac{31 A \cot (c+d x)}{15 a^3 d (\csc (c+d x)+1)^2}-\frac{2 A \cot (c+d x)}{5 a^3 d (\csc (c+d x)+1)^3}","-\frac{A \cot (c+d x)}{a^3 d}+\frac{4 A \tanh ^{-1}(\cos (c+d x))}{a^3 d}-\frac{104 A \cot (c+d x)}{15 a^3 d (\csc (c+d x)+1)}+\frac{31 A \cot (c+d x)}{15 a^3 d (\csc (c+d x)+1)^2}-\frac{2 A \cot (c+d x)}{5 a^3 d (\csc (c+d x)+1)^3}",1,"(4*A*ArcTanh[Cos[c + d*x]])/(a^3*d) - (A*Cot[c + d*x])/(a^3*d) - (2*A*Cot[c + d*x])/(5*a^3*d*(1 + Csc[c + d*x])^3) + (31*A*Cot[c + d*x])/(15*a^3*d*(1 + Csc[c + d*x])^2) - (104*A*Cot[c + d*x])/(15*a^3*d*(1 + Csc[c + d*x]))","A",15,9,32,0.2812,1,"{2950, 2709, 3770, 3767, 8, 3777, 3922, 3919, 3794}"
242,1,138,0,0.2246902,"\int \frac{\csc ^3(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Csc[c + d*x]^3*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","\frac{4 A \cot (c+d x)}{a^3 d}+\frac{164 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}+\frac{29 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{19 A \tanh ^{-1}(\cos (c+d x))}{2 a^3 d}-\frac{A \cot (c+d x) \csc (c+d x)}{2 a^3 d}","\frac{4 A \cot (c+d x)}{a^3 d}+\frac{164 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)}+\frac{29 A \cos (c+d x)}{15 a^3 d (\sin (c+d x)+1)^2}+\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}-\frac{19 A \tanh ^{-1}(\cos (c+d x))}{2 a^3 d}-\frac{A \cot (c+d x) \csc (c+d x)}{2 a^3 d}",1,"(-19*A*ArcTanh[Cos[c + d*x]])/(2*a^3*d) + (4*A*Cot[c + d*x])/(a^3*d) - (A*Cot[c + d*x]*Csc[c + d*x])/(2*a^3*d) + (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) + (29*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x])^2) + (164*A*Cos[c + d*x])/(15*a^3*d*(1 + Sin[c + d*x]))","A",13,7,32,0.2188,1,"{2966, 3770, 3767, 8, 3768, 2650, 2648}"
243,1,153,0,0.2464709,"\int \frac{\csc ^4(c+d x) (A-A \sin (c+d x))}{(a+a \sin (c+d x))^3} \, dx","Int[(Csc[c + d*x]^4*(A - A*Sin[c + d*x]))/(a + a*Sin[c + d*x])^3,x]","-\frac{A \cot ^3(c+d x)}{3 a^3 d}-\frac{10 A \cot (c+d x)}{a^3 d}-\frac{93 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}-\frac{13 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}+\frac{18 A \tanh ^{-1}(\cos (c+d x))}{a^3 d}+\frac{2 A \cot (c+d x) \csc (c+d x)}{a^3 d}","-\frac{A \cot ^3(c+d x)}{3 a^3 d}-\frac{10 A \cot (c+d x)}{a^3 d}-\frac{93 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)}-\frac{13 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^2}-\frac{2 A \cos (c+d x)}{5 a^3 d (\sin (c+d x)+1)^3}+\frac{18 A \tanh ^{-1}(\cos (c+d x))}{a^3 d}+\frac{2 A \cot (c+d x) \csc (c+d x)}{a^3 d}",1,"(18*A*ArcTanh[Cos[c + d*x]])/(a^3*d) - (10*A*Cot[c + d*x])/(a^3*d) - (A*Cot[c + d*x]^3)/(3*a^3*d) + (2*A*Cot[c + d*x]*Csc[c + d*x])/(a^3*d) - (2*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^3) - (13*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x])^2) - (93*A*Cos[c + d*x])/(5*a^3*d*(1 + Sin[c + d*x]))","A",15,7,32,0.2188,1,"{2966, 3770, 3767, 8, 3768, 2650, 2648}"
244,1,327,0,0.5790648,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","-\frac{a \left(5 A d \left(16 c^2 d+3 c^3+12 c d^2+4 d^3\right)-B \left(-52 c^2 d^2-15 c^3 d+3 c^4-60 c d^3-16 d^4\right)\right) \cos (e+f x)}{30 d f}-\frac{a \left(5 A d \left(6 c^2+20 c d+9 d^2\right)-B \left(-30 c^2 d+6 c^3-71 c d^2-45 d^3\right)\right) \sin (e+f x) \cos (e+f x)}{120 f}+\frac{1}{8} a x \left(A \left(12 c^2 d+8 c^3+12 c d^2+3 d^3\right)+B \left(12 c^2 d+4 c^3+9 c d^2+3 d^3\right)\right)-\frac{a \left(4 d^2 (5 A+4 B)-3 c (B c-5 d (A+B))\right) \cos (e+f x) (c+d \sin (e+f x))^2}{60 d f}+\frac{a (B c-5 d (A+B)) \cos (e+f x) (c+d \sin (e+f x))^3}{20 d f}-\frac{a B \cos (e+f x) (c+d \sin (e+f x))^4}{5 d f}","-\frac{a \left(5 A d \left(16 c^2 d+3 c^3+12 c d^2+4 d^3\right)-B \left(-52 c^2 d^2-15 c^3 d+3 c^4-60 c d^3-16 d^4\right)\right) \cos (e+f x)}{30 d f}-\frac{a \left(5 A d \left(6 c^2+20 c d+9 d^2\right)-B \left(-30 c^2 d+6 c^3-71 c d^2-45 d^3\right)\right) \sin (e+f x) \cos (e+f x)}{120 f}+\frac{1}{8} a x \left(A \left(12 c^2 d+8 c^3+12 c d^2+3 d^3\right)+B \left(12 c^2 d+4 c^3+9 c d^2+3 d^3\right)\right)-\frac{a \left(4 d^2 (5 A+4 B)-3 c (B c-5 d (A+B))\right) \cos (e+f x) (c+d \sin (e+f x))^2}{60 d f}+\frac{a (B c-5 d (A+B)) \cos (e+f x) (c+d \sin (e+f x))^3}{20 d f}-\frac{a B \cos (e+f x) (c+d \sin (e+f x))^4}{5 d f}",1,"(a*(B*(4*c^3 + 12*c^2*d + 9*c*d^2 + 3*d^3) + A*(8*c^3 + 12*c^2*d + 12*c*d^2 + 3*d^3))*x)/8 - (a*(5*A*d*(3*c^3 + 16*c^2*d + 12*c*d^2 + 4*d^3) - B*(3*c^4 - 15*c^3*d - 52*c^2*d^2 - 60*c*d^3 - 16*d^4))*Cos[e + f*x])/(30*d*f) - (a*(5*A*d*(6*c^2 + 20*c*d + 9*d^2) - B*(6*c^3 - 30*c^2*d - 71*c*d^2 - 45*d^3))*Cos[e + f*x]*Sin[e + f*x])/(120*f) - (a*(4*(5*A + 4*B)*d^2 - 3*c*(B*c - 5*(A + B)*d))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(60*d*f) + (a*(B*c - 5*(A + B)*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(20*d*f) - (a*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(5*d*f)","A",5,4,33,0.1212,1,"{2968, 3023, 2753, 2734}"
245,1,213,0,0.3604042,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","-\frac{a \left(4 A d \left(c^2+3 c d+d^2\right)-B \left(-4 c^2 d+c^3-8 c d^2-4 d^3\right)\right) \cos (e+f x)}{6 d f}+\frac{a \left(-8 c d (A+B)-3 d^2 (4 A+3 B)+2 B c^2\right) \sin (e+f x) \cos (e+f x)}{24 f}+\frac{1}{8} a x \left(4 A \left(2 c^2+2 c d+d^2\right)+B \left(4 c^2+8 c d+3 d^2\right)\right)+\frac{a (B c-4 d (A+B)) \cos (e+f x) (c+d \sin (e+f x))^2}{12 d f}-\frac{a B \cos (e+f x) (c+d \sin (e+f x))^3}{4 d f}","-\frac{a \left(4 A d \left(c^2+3 c d+d^2\right)-B \left(-4 c^2 d+c^3-8 c d^2-4 d^3\right)\right) \cos (e+f x)}{6 d f}+\frac{1}{8} a x \left(4 A \left(2 c^2+2 c d+d^2\right)+B \left(4 c^2+8 c d+3 d^2\right)\right)-\frac{a \left(3 d^2 (4 A+3 B)-2 c (B c-4 d (A+B))\right) \sin (e+f x) \cos (e+f x)}{24 f}+\frac{a (B c-4 d (A+B)) \cos (e+f x) (c+d \sin (e+f x))^2}{12 d f}-\frac{a B \cos (e+f x) (c+d \sin (e+f x))^3}{4 d f}",1,"(a*(4*A*(2*c^2 + 2*c*d + d^2) + B*(4*c^2 + 8*c*d + 3*d^2))*x)/8 - (a*(4*A*d*(c^2 + 3*c*d + d^2) - B*(c^3 - 4*c^2*d - 8*c*d^2 - 4*d^3))*Cos[e + f*x])/(6*d*f) + (a*(2*B*c^2 - 8*(A + B)*c*d - 3*(4*A + 3*B)*d^2)*Cos[e + f*x]*Sin[e + f*x])/(24*f) + (a*(B*c - 4*(A + B)*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(12*d*f) - (a*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(4*d*f)","A",4,4,33,0.1212,1,"{2968, 3023, 2753, 2734}"
246,1,111,0,0.1567403,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{a (3 A (c+d)+B (3 c+d)) \cos (e+f x)}{3 f}-\frac{a (3 A d+3 B c-B d) \sin (e+f x) \cos (e+f x)}{6 f}+\frac{1}{2} a x (A (2 c+d)+B (c+d))-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^2}{3 a f}","-\frac{a (3 A (c+d)+B (3 c+d)) \cos (e+f x)}{3 f}-\frac{a (3 A d+3 B c-B d) \sin (e+f x) \cos (e+f x)}{6 f}+\frac{1}{2} a x (A (2 c+d)+B (c+d))-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^2}{3 a f}",1,"(a*(B*(c + d) + A*(2*c + d))*x)/2 - (a*(3*A*(c + d) + B*(3*c + d))*Cos[e + f*x])/(3*f) - (a*(3*B*c + 3*A*d - B*d)*Cos[e + f*x]*Sin[e + f*x])/(6*f) - (B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(3*a*f)","A",3,3,31,0.09677,1,"{2968, 3023, 2734}"
247,1,48,0,0.0231044,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]),x]","-\frac{a (A+B) \cos (e+f x)}{f}+\frac{1}{2} a x (2 A+B)-\frac{a B \sin (e+f x) \cos (e+f x)}{2 f}","-\frac{a (A+B) \cos (e+f x)}{f}+\frac{1}{2} a x (2 A+B)-\frac{a B \sin (e+f x) \cos (e+f x)}{2 f}",1,"(a*(2*A + B)*x)/2 - (a*(A + B)*Cos[e + f*x])/f - (a*B*Cos[e + f*x]*Sin[e + f*x])/(2*f)","A",1,1,21,0.04762,1,"{2734}"
248,1,98,0,0.2730269,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","\frac{2 a (c-d) (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^2 f \sqrt{c^2-d^2}}-\frac{a x (B c-d (A+B))}{d^2}-\frac{a B \cos (e+f x)}{d f}","\frac{2 a (c-d) (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^2 f \sqrt{c^2-d^2}}-\frac{a x (B c-d (A+B))}{d^2}-\frac{a B \cos (e+f x)}{d f}",1,"-((a*(B*c - (A + B)*d)*x)/d^2) + (2*a*(c - d)*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^2*Sqrt[c^2 - d^2]*f) - (a*B*Cos[e + f*x])/(d*f)","A",6,6,33,0.1818,1,"{2968, 3023, 2735, 2660, 618, 204}"
249,1,124,0,0.3251467,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","\frac{2 a \left(d^2 (A+B) (c-d)-B c \left(c^2-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^2 f \left(c^2-d^2\right)^{3/2}}+\frac{a (B c-A d) \cos (e+f x)}{d f (c+d) (c+d \sin (e+f x))}+\frac{a B x}{d^2}","\frac{2 a \left(d^2 (A+B) (c-d)-B c \left(c^2-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^2 f \left(c^2-d^2\right)^{3/2}}+\frac{a (B c-A d) \cos (e+f x)}{d f (c+d) (c+d \sin (e+f x))}+\frac{a B x}{d^2}",1,"(a*B*x)/d^2 + (2*a*((A + B)*(c - d)*d^2 - B*c*(c^2 - d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^2*(c^2 - d^2)^(3/2)*f) + (a*(B*c - A*d)*Cos[e + f*x])/(d*(c + d)*f*(c + d*Sin[e + f*x]))","A",6,6,33,0.1818,1,"{2968, 3021, 2735, 2660, 618, 204}"
250,1,176,0,0.4209816,"\int \frac{(a+a \sin (e+f x)) (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","\frac{a (2 A c-A d+B c-2 B d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{f (c+d) \left(c^2-d^2\right)^{3/2}}-\frac{a \left(A d (c-2 d)+B \left(c^2+2 c d-2 d^2\right)\right) \cos (e+f x)}{2 d f (c-d) (c+d)^2 (c+d \sin (e+f x))}+\frac{a (B c-A d) \cos (e+f x)}{2 d f (c+d) (c+d \sin (e+f x))^2}","\frac{a (2 A c-A d+B c-2 B d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{f (c+d) \left(c^2-d^2\right)^{3/2}}-\frac{a \left(A d (c-2 d)+B \left(c^2+2 c d-2 d^2\right)\right) \cos (e+f x)}{2 d f (c-d) (c+d)^2 (c+d \sin (e+f x))}+\frac{a (B c-A d) \cos (e+f x)}{2 d f (c+d) (c+d \sin (e+f x))^2}",1,"(a*(2*A*c + B*c - A*d - 2*B*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/((c + d)*(c^2 - d^2)^(3/2)*f) + (a*(B*c - A*d)*Cos[e + f*x])/(2*d*(c + d)*f*(c + d*Sin[e + f*x])^2) - (a*(A*(c - 2*d)*d + B*(c^2 + 2*c*d - 2*d^2))*Cos[e + f*x])/(2*(c - d)*d*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",7,7,33,0.2121,1,"{2968, 3021, 2754, 12, 2660, 618, 204}"
251,1,464,0,0.95209,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","\frac{a^2 \left(6 A d \left(-44 c^2 d^2-10 c^3 d+c^4-40 c d^3-12 d^4\right)-B \left(47 c^3 d^2+208 c^2 d^3-12 c^4 d+2 c^5+216 c d^4+64 d^5\right)\right) \cos (e+f x)}{60 d^2 f}+\frac{a^2 \left(6 A d (c-10 d)-B \left(2 c^2-12 c d+55 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{120 d^2 f}+\frac{a^2 \left(6 A d \left(c^2-10 c d-12 d^2\right)-B \left(-12 c^2 d+2 c^3+51 c d^2+64 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{120 d^2 f}+\frac{a^2 \left(6 A d \left(-20 c^2 d+2 c^3-57 c d^2-30 d^3\right)-B \left(96 c^2 d^2-24 c^3 d+4 c^4+284 c d^3+165 d^4\right)\right) \sin (e+f x) \cos (e+f x)}{240 d f}+\frac{1}{16} a^2 x \left(6 A \left(8 c^2 d+4 c^3+7 c d^2+2 d^3\right)+B \left(42 c^2 d+16 c^3+36 c d^2+11 d^3\right)\right)+\frac{a^2 (-6 A d+2 B c-7 B d) \cos (e+f x) (c+d \sin (e+f x))^4}{30 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (c+d \sin (e+f x))^4}{6 d f}","\frac{a^2 \left(6 A d \left(-44 c^2 d^2-10 c^3 d+c^4-40 c d^3-12 d^4\right)-B \left(47 c^3 d^2+208 c^2 d^3-12 c^4 d+2 c^5+216 c d^4+64 d^5\right)\right) \cos (e+f x)}{60 d^2 f}+\frac{a^2 \left(6 A d (c-10 d)-B \left(2 c^2-12 c d+55 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{120 d^2 f}+\frac{a^2 \left(6 A d \left(c^2-10 c d-12 d^2\right)-B \left(-12 c^2 d+2 c^3+51 c d^2+64 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{120 d^2 f}+\frac{a^2 \left(6 A d \left(-20 c^2 d+2 c^3-57 c d^2-30 d^3\right)-B \left(96 c^2 d^2-24 c^3 d+4 c^4+284 c d^3+165 d^4\right)\right) \sin (e+f x) \cos (e+f x)}{240 d f}+\frac{1}{16} a^2 x \left(6 A \left(8 c^2 d+4 c^3+7 c d^2+2 d^3\right)+B \left(42 c^2 d+16 c^3+36 c d^2+11 d^3\right)\right)+\frac{a^2 (-6 A d+2 B c-7 B d) \cos (e+f x) (c+d \sin (e+f x))^4}{30 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (c+d \sin (e+f x))^4}{6 d f}",1,"(a^2*(6*A*(4*c^3 + 8*c^2*d + 7*c*d^2 + 2*d^3) + B*(16*c^3 + 42*c^2*d + 36*c*d^2 + 11*d^3))*x)/16 + (a^2*(6*A*d*(c^4 - 10*c^3*d - 44*c^2*d^2 - 40*c*d^3 - 12*d^4) - B*(2*c^5 - 12*c^4*d + 47*c^3*d^2 + 208*c^2*d^3 + 216*c*d^4 + 64*d^5))*Cos[e + f*x])/(60*d^2*f) + (a^2*(6*A*d*(2*c^3 - 20*c^2*d - 57*c*d^2 - 30*d^3) - B*(4*c^4 - 24*c^3*d + 96*c^2*d^2 + 284*c*d^3 + 165*d^4))*Cos[e + f*x]*Sin[e + f*x])/(240*d*f) + (a^2*(6*A*d*(c^2 - 10*c*d - 12*d^2) - B*(2*c^3 - 12*c^2*d + 51*c*d^2 + 64*d^3))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(120*d^2*f) + (a^2*(6*A*(c - 10*d)*d - B*(2*c^2 - 12*c*d + 55*d^2))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(120*d^2*f) + (a^2*(2*B*c - 6*A*d - 7*B*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(30*d^2*f) - (B*Cos[e + f*x]*(a^2 + a^2*Sin[e + f*x])*(c + d*Sin[e + f*x])^4)/(6*d*f)","A",6,5,35,0.1429,1,"{2976, 2968, 3023, 2753, 2734}"
252,1,336,0,0.7030946,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","\frac{a^2 \left(5 A d \left(-8 c^2 d+c^3-20 c d^2-8 d^3\right)-2 B \left(16 c^2 d^2-5 c^3 d+c^4+40 c d^3+18 d^4\right)\right) \cos (e+f x)}{30 d^2 f}+\frac{a^2 \left(5 A d (c-8 d)-2 B \left(c^2-5 c d+18 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{60 d^2 f}+\frac{a^2 \left(5 A d \left(2 c^2-16 c d-21 d^2\right)-B \left(-20 c^2 d+4 c^3+66 c d^2+90 d^3\right)\right) \sin (e+f x) \cos (e+f x)}{120 d f}+\frac{1}{8} a^2 x \left(12 A c^2+16 A c d+7 A d^2+8 B c^2+14 B c d+6 B d^2\right)+\frac{a^2 (2 B (c-3 d)-5 A d) \cos (e+f x) (c+d \sin (e+f x))^3}{20 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (c+d \sin (e+f x))^3}{5 d f}","\frac{a^2 \left(5 A d \left(-8 c^2 d+c^3-20 c d^2-8 d^3\right)-2 B \left(16 c^2 d^2-5 c^3 d+c^4+40 c d^3+18 d^4\right)\right) \cos (e+f x)}{30 d^2 f}+\frac{a^2 \left(5 A d (c-8 d)-2 B \left(c^2-5 c d+18 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{60 d^2 f}+\frac{a^2 \left(5 A d \left(2 c^2-16 c d-21 d^2\right)-B \left(-20 c^2 d+4 c^3+66 c d^2+90 d^3\right)\right) \sin (e+f x) \cos (e+f x)}{120 d f}+\frac{1}{8} a^2 x \left(12 A c^2+16 A c d+7 A d^2+8 B c^2+14 B c d+6 B d^2\right)+\frac{a^2 (2 B (c-3 d)-5 A d) \cos (e+f x) (c+d \sin (e+f x))^3}{20 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right) (c+d \sin (e+f x))^3}{5 d f}",1,"(a^2*(12*A*c^2 + 8*B*c^2 + 16*A*c*d + 14*B*c*d + 7*A*d^2 + 6*B*d^2)*x)/8 + (a^2*(5*A*d*(c^3 - 8*c^2*d - 20*c*d^2 - 8*d^3) - 2*B*(c^4 - 5*c^3*d + 16*c^2*d^2 + 40*c*d^3 + 18*d^4))*Cos[e + f*x])/(30*d^2*f) + (a^2*(5*A*d*(2*c^2 - 16*c*d - 21*d^2) - B*(4*c^3 - 20*c^2*d + 66*c*d^2 + 90*d^3))*Cos[e + f*x]*Sin[e + f*x])/(120*d*f) + (a^2*(5*A*(c - 8*d)*d - 2*B*(c^2 - 5*c*d + 18*d^2))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(60*d^2*f) + (a^2*(2*B*(c - 3*d) - 5*A*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(20*d^2*f) - (B*Cos[e + f*x]*(a^2 + a^2*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(5*d*f)","A",5,5,35,0.1429,1,"{2976, 2968, 3023, 2753, 2734}"
253,1,166,0,0.2707381,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{a^2 (12 A c+8 A d+8 B c+7 B d) \cos (e+f x)}{6 f}-\frac{a^2 (12 A c+8 A d+8 B c+7 B d) \sin (e+f x) \cos (e+f x)}{24 f}+\frac{1}{8} a^2 x (12 A c+8 A d+8 B c+7 B d)-\frac{(4 A d+4 B c-B d) \cos (e+f x) (a \sin (e+f x)+a)^2}{12 f}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^3}{4 a f}","-\frac{a^2 (12 A c+8 A d+8 B c+7 B d) \cos (e+f x)}{6 f}-\frac{a^2 (12 A c+8 A d+8 B c+7 B d) \sin (e+f x) \cos (e+f x)}{24 f}+\frac{1}{8} a^2 x (12 A c+8 A d+8 B c+7 B d)-\frac{(4 A d+4 B c-B d) \cos (e+f x) (a \sin (e+f x)+a)^2}{12 f}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^3}{4 a f}",1,"(a^2*(12*A*c + 8*B*c + 8*A*d + 7*B*d)*x)/8 - (a^2*(12*A*c + 8*B*c + 8*A*d + 7*B*d)*Cos[e + f*x])/(6*f) - (a^2*(12*A*c + 8*B*c + 8*A*d + 7*B*d)*Cos[e + f*x]*Sin[e + f*x])/(24*f) - ((4*B*c + 4*A*d - B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(12*f) - (B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^3)/(4*a*f)","A",4,4,33,0.1212,1,"{2968, 3023, 2751, 2644}"
254,1,94,0,0.0607967,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]),x]","-\frac{2 a^2 (3 A+2 B) \cos (e+f x)}{3 f}-\frac{a^2 (3 A+2 B) \sin (e+f x) \cos (e+f x)}{6 f}+\frac{1}{2} a^2 x (3 A+2 B)-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^2}{3 f}","-\frac{2 a^2 (3 A+2 B) \cos (e+f x)}{3 f}-\frac{a^2 (3 A+2 B) \sin (e+f x) \cos (e+f x)}{6 f}+\frac{1}{2} a^2 x (3 A+2 B)-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^2}{3 f}",1,"(a^2*(3*A + 2*B)*x)/2 - (2*a^2*(3*A + 2*B)*Cos[e + f*x])/(3*f) - (a^2*(3*A + 2*B)*Cos[e + f*x]*Sin[e + f*x])/(6*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(3*f)","A",2,2,23,0.08696,1,"{2751, 2644}"
255,1,171,0,0.52178,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","-\frac{2 a^2 (c-d)^2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f \sqrt{c^2-d^2}}-\frac{a^2 x \left(2 A d (c-2 d)-B \left(2 c^2-4 c d+3 d^2\right)\right)}{2 d^3}+\frac{a^2 (-2 A d+2 B c-3 B d) \cos (e+f x)}{2 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{2 d f}","-\frac{2 a^2 (c-d)^2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f \sqrt{c^2-d^2}}-\frac{a^2 x \left(2 A d (c-2 d)-B \left(2 c^2-4 c d+3 d^2\right)\right)}{2 d^3}+\frac{a^2 (-2 A d+2 B c-3 B d) \cos (e+f x)}{2 d^2 f}-\frac{B \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{2 d f}",1,"-(a^2*(2*A*(c - 2*d)*d - B*(2*c^2 - 4*c*d + 3*d^2))*x)/(2*d^3) - (2*a^2*(c - d)^2*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^3*Sqrt[c^2 - d^2]*f) + (a^2*(2*B*c - 2*A*d - 3*B*d)*Cos[e + f*x])/(2*d^2*f) - (B*Cos[e + f*x]*(a^2 + a^2*Sin[e + f*x]))/(2*d*f)","A",7,7,35,0.2000,1,"{2976, 2968, 3023, 2735, 2660, 618, 204}"
256,1,198,0,0.5808263,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","-\frac{2 a^2 (c-d) \left(A d (c+2 d)-B \left(2 c^2+2 c d-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f (c+d) \sqrt{c^2-d^2}}+\frac{a^2 (A d-B (2 c+d)) \cos (e+f x)}{d^2 f (c+d)}-\frac{a^2 x (-A d+2 B c-2 B d)}{d^3}+\frac{(B c-A d) \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{d f (c+d) (c+d \sin (e+f x))}","-\frac{2 a^2 (c-d) \left(A d (c+2 d)-B \left(2 c^2+2 c d-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f (c+d) \sqrt{c^2-d^2}}+\frac{a^2 (A d-B (2 c+d)) \cos (e+f x)}{d^2 f (c+d)}-\frac{a^2 x (-A d+2 B c-2 B d)}{d^3}+\frac{(B c-A d) \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{d f (c+d) (c+d \sin (e+f x))}",1,"-((a^2*(2*B*c - A*d - 2*B*d)*x)/d^3) - (2*a^2*(c - d)*(A*d*(c + 2*d) - B*(2*c^2 + 2*c*d - d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^3*(c + d)*Sqrt[c^2 - d^2]*f) + (a^2*(A*d - B*(2*c + d))*Cos[e + f*x])/(d^2*(c + d)*f) + ((B*c - A*d)*Cos[e + f*x]*(a^2 + a^2*Sin[e + f*x]))/(d*(c + d)*f*(c + d*Sin[e + f*x]))","A",7,7,35,0.2000,1,"{2975, 2968, 3023, 2735, 2660, 618, 204}"
257,1,215,0,0.6225925,"\int \frac{(a+a \sin (e+f x))^2 (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","\frac{a^2 \left(3 A d^3-B \left(4 c^2 d+2 c^3+c d^2-4 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f (c+d)^2 \sqrt{c^2-d^2}}-\frac{a^2 \left(3 A d^2-B \left(2 c^2+3 c d-2 d^2\right)\right) \cos (e+f x)}{2 d^2 f (c+d)^2 (c+d \sin (e+f x))}+\frac{(B c-A d) \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{2 d f (c+d) (c+d \sin (e+f x))^2}+\frac{a^2 B x}{d^3}","\frac{a^2 \left(3 A d^3-B \left(4 c^2 d+2 c^3+c d^2-4 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f (c+d)^2 \sqrt{c^2-d^2}}-\frac{a^2 \left(3 A d^2-B \left(2 c^2+3 c d-2 d^2\right)\right) \cos (e+f x)}{2 d^2 f (c+d)^2 (c+d \sin (e+f x))}+\frac{(B c-A d) \cos (e+f x) \left(a^2 \sin (e+f x)+a^2\right)}{2 d f (c+d) (c+d \sin (e+f x))^2}+\frac{a^2 B x}{d^3}",1,"(a^2*B*x)/d^3 + (a^2*(3*A*d^3 - B*(2*c^3 + 4*c^2*d + c*d^2 - 4*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^3*(c + d)^2*Sqrt[c^2 - d^2]*f) + ((B*c - A*d)*Cos[e + f*x]*(a^2 + a^2*Sin[e + f*x]))/(2*d*(c + d)*f*(c + d*Sin[e + f*x])^2) - (a^2*(3*A*d^2 - B*(2*c^2 + 3*c*d - 2*d^2))*Cos[e + f*x])/(2*d^2*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",7,7,35,0.2000,1,"{2975, 2968, 3021, 2735, 2660, 618, 204}"
258,1,604,0,1.4857913,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","-\frac{a^3 \left(7 A d \left(107 c^3 d^2+472 c^2 d^3-18 c^4 d+2 c^5+456 c d^4+136 d^5\right)-3 B \left(51 c^4 d^2-189 c^3 d^3-920 c^2 d^4-14 c^5 d+2 c^6-952 c d^5-288 d^6\right)\right) \cos (e+f x)}{420 d^3 f}-\frac{a^3 \left(-14 A c d+91 A d^2+6 B c^2-27 B c d+87 B d^2\right) \cos (e+f x) (c+d \sin (e+f x))^4}{210 d^3 f}-\frac{a^3 \left(7 A d \left(2 c^2-18 c d+115 d^2\right)-B \left(-42 c^2 d+6 c^3+177 c d^2-735 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{840 d^3 f}-\frac{a^3 \left(7 A d \left(-18 c^2 d+2 c^3+111 c d^2+136 d^3\right)-B \left(165 c^2 d^2-42 c^3 d+6 c^4-651 c d^3-864 d^4\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{840 d^3 f}-\frac{a^3 \left(7 A d \left(216 c^2 d^2-36 c^3 d+4 c^4+626 c d^3+345 d^4\right)-3 B \left(104 c^3 d^2-392 c^2 d^3-28 c^4 d+4 c^5-1263 c d^4-735 d^5\right)\right) \sin (e+f x) \cos (e+f x)}{1680 d^2 f}+\frac{1}{16} a^3 x \left(A \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right)+3 B \left(26 c^2 d+10 c^3+23 c d^2+7 d^3\right)\right)+\frac{(3 B (c-3 d)-7 A d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^4}{42 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^4}{7 d f}","-\frac{a^3 \left(7 A d \left(107 c^3 d^2+472 c^2 d^3-18 c^4 d+2 c^5+456 c d^4+136 d^5\right)-3 B \left(51 c^4 d^2-189 c^3 d^3-920 c^2 d^4-14 c^5 d+2 c^6-952 c d^5-288 d^6\right)\right) \cos (e+f x)}{420 d^3 f}-\frac{a^3 \left(-14 A c d+91 A d^2+6 B c^2-27 B c d+87 B d^2\right) \cos (e+f x) (c+d \sin (e+f x))^4}{210 d^3 f}-\frac{a^3 \left(7 A d \left(2 c^2-18 c d+115 d^2\right)-B \left(-42 c^2 d+6 c^3+177 c d^2-735 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{840 d^3 f}-\frac{a^3 \left(7 A d \left(-18 c^2 d+2 c^3+111 c d^2+136 d^3\right)-B \left(165 c^2 d^2-42 c^3 d+6 c^4-651 c d^3-864 d^4\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{840 d^3 f}-\frac{a^3 \left(7 A d \left(216 c^2 d^2-36 c^3 d+4 c^4+626 c d^3+345 d^4\right)-3 B \left(104 c^3 d^2-392 c^2 d^3-28 c^4 d+4 c^5-1263 c d^4-735 d^5\right)\right) \sin (e+f x) \cos (e+f x)}{1680 d^2 f}+\frac{1}{16} a^3 x \left(A \left(90 c^2 d+40 c^3+78 c d^2+23 d^3\right)+3 B \left(26 c^2 d+10 c^3+23 c d^2+7 d^3\right)\right)+\frac{(3 B (c-3 d)-7 A d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^4}{42 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^4}{7 d f}",1,"(a^3*(3*B*(10*c^3 + 26*c^2*d + 23*c*d^2 + 7*d^3) + A*(40*c^3 + 90*c^2*d + 78*c*d^2 + 23*d^3))*x)/16 - (a^3*(7*A*d*(2*c^5 - 18*c^4*d + 107*c^3*d^2 + 472*c^2*d^3 + 456*c*d^4 + 136*d^5) - 3*B*(2*c^6 - 14*c^5*d + 51*c^4*d^2 - 189*c^3*d^3 - 920*c^2*d^4 - 952*c*d^5 - 288*d^6))*Cos[e + f*x])/(420*d^3*f) - (a^3*(7*A*d*(4*c^4 - 36*c^3*d + 216*c^2*d^2 + 626*c*d^3 + 345*d^4) - 3*B*(4*c^5 - 28*c^4*d + 104*c^3*d^2 - 392*c^2*d^3 - 1263*c*d^4 - 735*d^5))*Cos[e + f*x]*Sin[e + f*x])/(1680*d^2*f) - (a^3*(7*A*d*(2*c^3 - 18*c^2*d + 111*c*d^2 + 136*d^3) - B*(6*c^4 - 42*c^3*d + 165*c^2*d^2 - 651*c*d^3 - 864*d^4))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(840*d^3*f) - (a^3*(7*A*d*(2*c^2 - 18*c*d + 115*d^2) - B*(6*c^3 - 42*c^2*d + 177*c*d^2 - 735*d^3))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(840*d^3*f) - (a^3*(6*B*c^2 - 14*A*c*d - 27*B*c*d + 91*A*d^2 + 87*B*d^2)*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(210*d^3*f) - (a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^4)/(7*d*f) + ((3*B*(c - 3*d) - 7*A*d)*Cos[e + f*x]*(a^3 + a^3*Sin[e + f*x])*(c + d*Sin[e + f*x])^4)/(42*d^2*f)","A",7,5,35,0.1429,1,"{2976, 2968, 3023, 2753, 2734}"
259,1,463,0,1.1279983,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","-\frac{a^3 \left(2 A d \left(72 c^2 d^2-15 c^3 d+2 c^4+180 c d^3+76 d^4\right)-B \left(37 c^3 d^2-112 c^2 d^3-12 c^4 d+2 c^5-304 c d^4-136 d^5\right)\right) \cos (e+f x)}{60 d^3 f}+\frac{a^3 \left(2 A d (2 c-11 d)-B \left(2 c^2-8 c d+21 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{40 d^3 f}-\frac{a^3 \left(2 A d \left(2 c^2-15 c d+76 d^2\right)-B \left(-12 c^2 d+2 c^3+41 c d^2-136 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{120 d^3 f}-\frac{a^3 \left(2 A d \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right)-B \left(76 c^2 d^2-24 c^3 d+4 c^4-236 c d^3-345 d^4\right)\right) \sin (e+f x) \cos (e+f x)}{240 d^2 f}+\frac{1}{16} a^3 x \left(A \left(40 c^2+60 c d+26 d^2\right)+B \left(30 c^2+52 c d+23 d^2\right)\right)+\frac{(-6 A d+3 B c-8 B d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^3}{30 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^3}{6 d f}","-\frac{a^3 \left(2 A d \left(72 c^2 d^2-15 c^3 d+2 c^4+180 c d^3+76 d^4\right)-B \left(37 c^3 d^2-112 c^2 d^3-12 c^4 d+2 c^5-304 c d^4-136 d^5\right)\right) \cos (e+f x)}{60 d^3 f}+\frac{a^3 \left(2 A d (2 c-11 d)-B \left(2 c^2-8 c d+21 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{40 d^3 f}-\frac{a^3 \left(2 A d \left(2 c^2-15 c d+76 d^2\right)-B \left(-12 c^2 d+2 c^3+41 c d^2-136 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^2}{120 d^3 f}-\frac{a^3 \left(2 A d \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right)-B \left(76 c^2 d^2-24 c^3 d+4 c^4-236 c d^3-345 d^4\right)\right) \sin (e+f x) \cos (e+f x)}{240 d^2 f}+\frac{1}{16} a^3 x \left(A \left(40 c^2+60 c d+26 d^2\right)+B \left(30 c^2+52 c d+23 d^2\right)\right)+\frac{(-6 A d+3 B c-8 B d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^3}{30 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^3}{6 d f}",1,"(a^3*(B*(30*c^2 + 52*c*d + 23*d^2) + A*(40*c^2 + 60*c*d + 26*d^2))*x)/16 - (a^3*(2*A*d*(2*c^4 - 15*c^3*d + 72*c^2*d^2 + 180*c*d^3 + 76*d^4) - B*(2*c^5 - 12*c^4*d + 37*c^3*d^2 - 112*c^2*d^3 - 304*c*d^4 - 136*d^5))*Cos[e + f*x])/(60*d^3*f) - (a^3*(2*A*d*(4*c^3 - 30*c^2*d + 146*c*d^2 + 195*d^3) - B*(4*c^4 - 24*c^3*d + 76*c^2*d^2 - 236*c*d^3 - 345*d^4))*Cos[e + f*x]*Sin[e + f*x])/(240*d^2*f) - (a^3*(2*A*d*(2*c^2 - 15*c*d + 76*d^2) - B*(2*c^3 - 12*c^2*d + 41*c*d^2 - 136*d^3))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(120*d^3*f) + (a^3*(2*A*(2*c - 11*d)*d - B*(2*c^2 - 8*c*d + 21*d^2))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(40*d^3*f) - (a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^3)/(6*d*f) + ((3*B*c - 6*A*d - 8*B*d)*Cos[e + f*x]*(a^3 + a^3*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(30*d^2*f)","A",6,5,35,0.1429,1,"{2976, 2968, 3023, 2753, 2734}"
260,1,201,0,0.3349709,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","\frac{a^3 (20 A c+15 A d+15 B c+13 B d) \cos ^3(e+f x)}{60 f}-\frac{a^3 (20 A c+15 A d+15 B c+13 B d) \cos (e+f x)}{5 f}-\frac{3 a^3 (20 A c+15 A d+15 B c+13 B d) \sin (e+f x) \cos (e+f x)}{40 f}+\frac{1}{8} a^3 x (20 A c+15 A d+15 B c+13 B d)-\frac{(5 A d+5 B c-B d) \cos (e+f x) (a \sin (e+f x)+a)^3}{20 f}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^4}{5 a f}","\frac{a^3 (20 A c+15 A d+15 B c+13 B d) \cos ^3(e+f x)}{60 f}-\frac{a^3 (20 A c+15 A d+15 B c+13 B d) \cos (e+f x)}{5 f}-\frac{3 a^3 (20 A c+15 A d+15 B c+13 B d) \sin (e+f x) \cos (e+f x)}{40 f}+\frac{1}{8} a^3 x (20 A c+15 A d+15 B c+13 B d)-\frac{(5 A d+5 B c-B d) \cos (e+f x) (a \sin (e+f x)+a)^3}{20 f}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^4}{5 a f}",1,"(a^3*(20*A*c + 15*B*c + 15*A*d + 13*B*d)*x)/8 - (a^3*(20*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x])/(5*f) + (a^3*(20*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x]^3)/(60*f) - (3*a^3*(20*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x]*Sin[e + f*x])/(40*f) - ((5*B*c + 5*A*d - B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^3)/(20*f) - (B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^4)/(5*a*f)","A",10,8,33,0.2424,1,"{2968, 3023, 2751, 2645, 2638, 2635, 8, 2633}"
261,1,117,0,0.1005617,"\int (a+a \sin (e+f x))^3 (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]),x]","\frac{a^3 (4 A+3 B) \cos ^3(e+f x)}{12 f}-\frac{a^3 (4 A+3 B) \cos (e+f x)}{f}-\frac{3 a^3 (4 A+3 B) \sin (e+f x) \cos (e+f x)}{8 f}+\frac{5}{8} a^3 x (4 A+3 B)-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^3}{4 f}","-\frac{5 a^3 (4 A+3 B) \cos (e+f x)}{6 f}-\frac{5 a^3 (4 A+3 B) \sin (e+f x) \cos (e+f x)}{24 f}+\frac{5}{8} a^3 x (4 A+3 B)-\frac{a (4 A+3 B) \cos (e+f x) (a \sin (e+f x)+a)^2}{12 f}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^3}{4 f}",1,"(5*a^3*(4*A + 3*B)*x)/8 - (a^3*(4*A + 3*B)*Cos[e + f*x])/f + (a^3*(4*A + 3*B)*Cos[e + f*x]^3)/(12*f) - (3*a^3*(4*A + 3*B)*Cos[e + f*x]*Sin[e + f*x])/(8*f) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^3)/(4*f)","A",8,6,23,0.2609,1,"{2751, 2645, 2638, 2635, 8, 2633}"
262,1,246,0,0.8952512,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","\frac{a^3 \left(A d (2 c-5 d)-B \left(2 c^2-5 c d+5 d^2\right)\right) \cos (e+f x)}{2 d^3 f}+\frac{2 a^3 (c-d)^3 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f \sqrt{c^2-d^2}}+\frac{a^3 x \left(A d \left(2 c^2-6 c d+7 d^2\right)-B \left(-6 c^2 d+2 c^3+7 c d^2-5 d^3\right)\right)}{2 d^4}+\frac{(-3 A d+3 B c-5 B d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{6 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2}{3 d f}","\frac{a^3 \left(A d (2 c-5 d)-B \left(2 c^2-5 c d+5 d^2\right)\right) \cos (e+f x)}{2 d^3 f}+\frac{2 a^3 (c-d)^3 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f \sqrt{c^2-d^2}}+\frac{a^3 x \left(A d \left(2 c^2-6 c d+7 d^2\right)-B \left(-6 c^2 d+2 c^3+7 c d^2-5 d^3\right)\right)}{2 d^4}+\frac{(-3 A d+3 B c-5 B d) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{6 d^2 f}-\frac{a B \cos (e+f x) (a \sin (e+f x)+a)^2}{3 d f}",1,"(a^3*(A*d*(2*c^2 - 6*c*d + 7*d^2) - B*(2*c^3 - 6*c^2*d + 7*c*d^2 - 5*d^3))*x)/(2*d^4) + (2*a^3*(c - d)^3*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^4*Sqrt[c^2 - d^2]*f) + (a^3*(A*(2*c - 5*d)*d - B*(2*c^2 - 5*c*d + 5*d^2))*Cos[e + f*x])/(2*d^3*f) - (a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(3*d*f) + ((3*B*c - 3*A*d - 5*B*d)*Cos[e + f*x]*(a^3 + a^3*Sin[e + f*x]))/(6*d^2*f)","A",8,7,35,0.2000,1,"{2976, 2968, 3023, 2735, 2660, 618, 204}"
263,1,283,0,0.941206,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","-\frac{a^3 \left(4 A c d-B \left(6 c^2-3 c d-5 d^2\right)\right) \cos (e+f x)}{2 d^3 f (c+d)}+\frac{2 a^3 (c-d)^2 \left(A d (2 c+3 d)-B \left(3 c^2+3 c d-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f (c+d) \sqrt{c^2-d^2}}-\frac{a^3 x \left(2 A d (2 c-3 d)-B \left(6 c^2-12 c d+7 d^2\right)\right)}{2 d^4}+\frac{(2 A d-B (3 c+d)) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{2 d^2 f (c+d)}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^2}{d f (c+d) (c+d \sin (e+f x))}","-\frac{a^3 \left(4 A c d-B \left(6 c^2-3 c d-5 d^2\right)\right) \cos (e+f x)}{2 d^3 f (c+d)}+\frac{2 a^3 (c-d)^2 \left(A d (2 c+3 d)-B \left(3 c^2+3 c d-d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f (c+d) \sqrt{c^2-d^2}}-\frac{a^3 x \left(2 A d (2 c-3 d)-B \left(6 c^2-12 c d+7 d^2\right)\right)}{2 d^4}+\frac{(2 A d-B (3 c+d)) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{2 d^2 f (c+d)}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^2}{d f (c+d) (c+d \sin (e+f x))}",1,"-(a^3*(2*A*(2*c - 3*d)*d - B*(6*c^2 - 12*c*d + 7*d^2))*x)/(2*d^4) + (2*a^3*(c - d)^2*(A*d*(2*c + 3*d) - B*(3*c^2 + 3*c*d - d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^4*(c + d)*Sqrt[c^2 - d^2]*f) - (a^3*(4*A*c*d - B*(6*c^2 - 3*c*d - 5*d^2))*Cos[e + f*x])/(2*d^3*(c + d)*f) + ((2*A*d - B*(3*c + d))*Cos[e + f*x]*(a^3 + a^3*Sin[e + f*x]))/(2*d^2*(c + d)*f) + (a*(B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(d*(c + d)*f*(c + d*Sin[e + f*x]))","A",8,8,35,0.2286,1,"{2975, 2976, 2968, 3023, 2735, 2660, 618, 204}"
264,1,305,0,0.93441,"\int \frac{(a+a \sin (e+f x))^3 (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^3*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","-\frac{a^3 (c-d) \left(A d \left(2 c^2+6 c d+7 d^2\right)-3 B \left(4 c^2 d+2 c^3+c d^2-2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f (c+d)^2 \sqrt{c^2-d^2}}-\frac{\left(A d (c+4 d)-B \left(3 c^2+4 c d-2 d^2\right)\right) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{2 d^2 f (c+d)^2 (c+d \sin (e+f x))}-\frac{a^3 (3 B c (2 c+3 d)-A d (2 c+5 d)) \cos (e+f x)}{2 d^3 f (c+d)^2}-\frac{a^3 x (-A d+3 B c-3 B d)}{d^4}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^2}{2 d f (c+d) (c+d \sin (e+f x))^2}","-\frac{a^3 (c-d) \left(A d \left(2 c^2+6 c d+7 d^2\right)-3 B \left(4 c^2 d+2 c^3+c d^2-2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^4 f (c+d)^2 \sqrt{c^2-d^2}}-\frac{\left(A d (c+4 d)-B \left(3 c^2+4 c d-2 d^2\right)\right) \cos (e+f x) \left(a^3 \sin (e+f x)+a^3\right)}{2 d^2 f (c+d)^2 (c+d \sin (e+f x))}-\frac{a^3 (3 B c (2 c+3 d)-A d (2 c+5 d)) \cos (e+f x)}{2 d^3 f (c+d)^2}-\frac{a^3 x (-A d+3 B c-3 B d)}{d^4}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^2}{2 d f (c+d) (c+d \sin (e+f x))^2}",1,"-((a^3*(3*B*c - A*d - 3*B*d)*x)/d^4) - (a^3*(c - d)*(A*d*(2*c^2 + 6*c*d + 7*d^2) - 3*B*(2*c^3 + 4*c^2*d + c*d^2 - 2*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^4*(c + d)^2*Sqrt[c^2 - d^2]*f) - (a^3*(3*B*c*(2*c + 3*d) - A*d*(2*c + 5*d))*Cos[e + f*x])/(2*d^3*(c + d)^2*f) + (a*(B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^2)/(2*d*(c + d)*f*(c + d*Sin[e + f*x])^2) - ((A*d*(c + 4*d) - B*(3*c^2 + 4*c*d - 2*d^2))*Cos[e + f*x]*(a^3 + a^3*Sin[e + f*x]))/(2*d^2*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",8,7,35,0.2000,1,"{2975, 2968, 3023, 2735, 2660, 618, 204}"
265,1,220,0,0.3611714,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(a + a*Sin[e + f*x]),x]","\frac{2 d \left(3 A \left(c^2-3 c d+d^2\right)-B \left(7 c^2-9 c d+4 d^2\right)\right) \cos (e+f x)}{3 a f}+\frac{x \left(3 A d \left(2 c^2-2 c d+d^2\right)+B \left(-6 c^2 d+2 c^3+9 c d^2-3 d^3\right)\right)}{2 a}+\frac{d^2 (6 A c-9 A d-11 B c+9 B d) \sin (e+f x) \cos (e+f x)}{6 a f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{f (a \sin (e+f x)+a)}+\frac{d (3 A-4 B) \cos (e+f x) (c+d \sin (e+f x))^2}{3 a f}","\frac{2 d \left(3 A \left(c^2-3 c d+d^2\right)-B \left(7 c^2-9 c d+4 d^2\right)\right) \cos (e+f x)}{3 a f}+\frac{x \left(3 A d \left(2 c^2-2 c d+d^2\right)+B \left(-6 c^2 d+2 c^3+9 c d^2-3 d^3\right)\right)}{2 a}+\frac{d^2 (6 A c-9 A d-11 B c+9 B d) \sin (e+f x) \cos (e+f x)}{6 a f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{f (a \sin (e+f x)+a)}+\frac{d (3 A-4 B) \cos (e+f x) (c+d \sin (e+f x))^2}{3 a f}",1,"((3*A*d*(2*c^2 - 2*c*d + d^2) + B*(2*c^3 - 6*c^2*d + 9*c*d^2 - 3*d^3))*x)/(2*a) + (2*d*(3*A*(c^2 - 3*c*d + d^2) - B*(7*c^2 - 9*c*d + 4*d^2))*Cos[e + f*x])/(3*a*f) + (d^2*(6*A*c - 11*B*c - 9*A*d + 9*B*d)*Cos[e + f*x]*Sin[e + f*x])/(6*a*f) + ((3*A - 4*B)*d*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(3*a*f) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(f*(a + a*Sin[e + f*x]))","A",3,3,35,0.08571,1,"{2977, 2753, 2734}"
266,1,141,0,0.2057081,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/(a + a*Sin[e + f*x]),x]","\frac{x \left(d^2 (-(2 A-3 B))+4 A c d+2 B c (c-2 d)\right)}{2 a}+\frac{2 d (A (c-d)-B (2 c-d)) \cos (e+f x)}{a f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{f (a \sin (e+f x)+a)}+\frac{d^2 (2 A-3 B) \sin (e+f x) \cos (e+f x)}{2 a f}","\frac{x \left(2 A d (2 c-d)+B \left(2 c^2-4 c d+3 d^2\right)\right)}{2 a}+\frac{2 d (A (c-d)-B (2 c-d)) \cos (e+f x)}{a f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{f (a \sin (e+f x)+a)}+\frac{d^2 (2 A-3 B) \sin (e+f x) \cos (e+f x)}{2 a f}",1,"((2*B*c*(c - 2*d) + 4*A*c*d - (2*A - 3*B)*d^2)*x)/(2*a) + (2*(A*(c - d) - B*(2*c - d))*d*Cos[e + f*x])/(a*f) + ((2*A - 3*B)*d^2*Cos[e + f*x]*Sin[e + f*x])/(2*a*f) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(f*(a + a*Sin[e + f*x]))","A",2,2,35,0.05714,1,"{2977, 2734}"
267,1,67,0,0.2032304,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/(a + a*Sin[e + f*x]),x]","-\frac{(A-B) (c-d) \cos (e+f x)}{a f (\sin (e+f x)+1)}+\frac{x (A d+B (c-d))}{a}-\frac{B d \cos (e+f x)}{a f}","-\frac{(A-B) (c-d) \cos (e+f x)}{a f (\sin (e+f x)+1)}+\frac{x (A d+B (c-d))}{a}-\frac{B d \cos (e+f x)}{a f}",1,"((B*(c - d) + A*d)*x)/a - (B*d*Cos[e + f*x])/(a*f) - ((A - B)*(c - d)*Cos[e + f*x])/(a*f*(1 + Sin[e + f*x]))","A",4,4,33,0.1212,1,"{2968, 3023, 2735, 2648}"
268,1,35,0,0.0485771,"\int \frac{A+B \sin (e+f x)}{a+a \sin (e+f x)} \, dx","Int[(A + B*Sin[e + f*x])/(a + a*Sin[e + f*x]),x]","\frac{B x}{a}-\frac{(A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)}","\frac{B x}{a}-\frac{(A-B) \cos (e+f x)}{f (a \sin (e+f x)+a)}",1,"(B*x)/a - ((A - B)*Cos[e + f*x])/(f*(a + a*Sin[e + f*x]))","A",2,2,23,0.08696,1,"{2735, 2648}"
269,1,101,0,0.1702179,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c + d*Sin[e + f*x])),x]","\frac{2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \sqrt{c^2-d^2}}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a)}","\frac{2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \sqrt{c^2-d^2}}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a)}",1,"(2*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a*(c - d)*Sqrt[c^2 - d^2]*f) - ((A - B)*Cos[e + f*x])/((c - d)*f*(a + a*Sin[e + f*x]))","A",5,5,35,0.1429,1,"{2978, 12, 2660, 618, 204}"
270,1,181,0,0.3494433,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c + d*Sin[e + f*x])^2),x]","-\frac{2 \left(A d (2 c+d)-B \left(c^2+c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \left(c^2-d^2\right)^{3/2}}+\frac{d (B (2 c+d)-A (c+2 d)) \cos (e+f x)}{a f (c-d)^2 (c+d) (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a) (c+d \sin (e+f x))}","-\frac{2 \left(A d (2 c+d)-B \left(c^2+c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \left(c^2-d^2\right)^{3/2}}+\frac{d (B (2 c+d)-A (c+2 d)) \cos (e+f x)}{a f (c-d)^2 (c+d) (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a) (c+d \sin (e+f x))}",1,"(-2*(A*d*(2*c + d) - B*(c^2 + c*d + d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a*(c - d)*(c^2 - d^2)^(3/2)*f) + (d*(B*(2*c + d) - A*(c + 2*d))*Cos[e + f*x])/(a*(c - d)^2*(c + d)*f*(c + d*Sin[e + f*x])) - ((A - B)*Cos[e + f*x])/((c - d)*f*(a + a*Sin[e + f*x])*(c + d*Sin[e + f*x]))","A",6,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
271,1,283,0,0.5503169,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x)) (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])*(c + d*Sin[e + f*x])^3),x]","-\frac{\left(3 A d \left(2 c^2+2 c d+d^2\right)-B \left(4 c^2 d+2 c^3+7 c d^2+2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \left(c^2-d^2\right)^{5/2}}-\frac{d \left(2 A c^2+9 A c d+4 A d^2-5 B c^2-6 B c d-4 B d^2\right) \cos (e+f x)}{2 a f (c-d)^3 (c+d)^2 (c+d \sin (e+f x))}-\frac{d (2 A c+3 A d-3 B c-2 B d) \cos (e+f x)}{2 a f (c-d)^2 (c+d) (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a) (c+d \sin (e+f x))^2}","-\frac{\left(3 A d \left(2 c^2+2 c d+d^2\right)-B \left(4 c^2 d+2 c^3+7 c d^2+2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a f (c-d) \left(c^2-d^2\right)^{5/2}}-\frac{d \left(2 A c^2+9 A c d+4 A d^2-5 B c^2-6 B c d-4 B d^2\right) \cos (e+f x)}{2 a f (c-d)^3 (c+d)^2 (c+d \sin (e+f x))}-\frac{d (2 A c+3 A d-3 B c-2 B d) \cos (e+f x)}{2 a f (c-d)^2 (c+d) (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{f (c-d) (a \sin (e+f x)+a) (c+d \sin (e+f x))^2}",1,"-(((3*A*d*(2*c^2 + 2*c*d + d^2) - B*(2*c^3 + 4*c^2*d + 7*c*d^2 + 2*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a*(c - d)*(c^2 - d^2)^(5/2)*f)) - (d*(2*A*c - 3*B*c + 3*A*d - 2*B*d)*Cos[e + f*x])/(2*a*(c - d)^2*(c + d)*f*(c + d*Sin[e + f*x])^2) - ((A - B)*Cos[e + f*x])/((c - d)*f*(a + a*Sin[e + f*x])*(c + d*Sin[e + f*x])^2) - (d*(2*A*c^2 - 5*B*c^2 + 9*A*c*d - 6*B*c*d + 4*A*d^2 - 4*B*d^2)*Cos[e + f*x])/(2*a*(c - d)^3*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",7,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
272,1,228,0,0.5232749,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^2,x]","\frac{2 d \left(A \left(c^2+6 c d-5 d^2\right)+B \left(2 c^2-15 c d+8 d^2\right)\right) \cos (e+f x)}{3 a^2 f}+\frac{d x \left(2 A d (3 c-2 d)+B \left(6 c^2-12 c d+7 d^2\right)\right)}{2 a^2}+\frac{d^2 (2 A (c+6 d)+B (4 c-21 d)) \sin (e+f x) \cos (e+f x)}{6 a^2 f}-\frac{(A (c+5 d)+2 B (c-4 d)) \cos (e+f x) (c+d \sin (e+f x))^2}{3 a^2 f (\sin (e+f x)+1)}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{3 f (a \sin (e+f x)+a)^2}","\frac{2 d \left(A \left(c^2+6 c d-5 d^2\right)+B \left(2 c^2-15 c d+8 d^2\right)\right) \cos (e+f x)}{3 a^2 f}+\frac{d x \left(2 A d (3 c-2 d)+B \left(6 c^2-12 c d+7 d^2\right)\right)}{2 a^2}+\frac{d^2 (2 A (c+6 d)+B (4 c-21 d)) \sin (e+f x) \cos (e+f x)}{6 a^2 f}-\frac{(A (c+5 d)+2 B (c-4 d)) \cos (e+f x) (c+d \sin (e+f x))^2}{3 a^2 f (\sin (e+f x)+1)}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{3 f (a \sin (e+f x)+a)^2}",1,"(d*(2*A*(3*c - 2*d)*d + B*(6*c^2 - 12*c*d + 7*d^2))*x)/(2*a^2) + (2*d*(A*(c^2 + 6*c*d - 5*d^2) + B*(2*c^2 - 15*c*d + 8*d^2))*Cos[e + f*x])/(3*a^2*f) + (d^2*(B*(4*c - 21*d) + 2*A*(c + 6*d))*Cos[e + f*x]*Sin[e + f*x])/(6*a^2*f) - ((2*B*(c - 4*d) + A*(c + 5*d))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(3*a^2*f*(1 + Sin[e + f*x])) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(3*f*(a + a*Sin[e + f*x])^2)","A",3,2,35,0.05714,1,"{2977, 2734}"
273,1,132,0,0.5097241,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^2,x]","-\frac{(c-d) (A (c+3 d)+2 B (c-3 d)) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}+\frac{d x (A d+2 B (c-d))}{a^2}+\frac{d^2 (A-4 B) \cos (e+f x)}{3 a^2 f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{3 f (a \sin (e+f x)+a)^2}","-\frac{(c-d) (A (c+3 d)+2 B (c-3 d)) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}+\frac{d x (A d+2 B (c-d))}{a^2}+\frac{d^2 (A-4 B) \cos (e+f x)}{3 a^2 f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{3 f (a \sin (e+f x)+a)^2}",1,"(d*(2*B*(c - d) + A*d)*x)/a^2 + ((A - 4*B)*d^2*Cos[e + f*x])/(3*a^2*f) - ((c - d)*(2*B*(c - 3*d) + A*(c + 3*d))*Cos[e + f*x])/(3*a^2*f*(1 + Sin[e + f*x])) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(3*f*(a + a*Sin[e + f*x])^2)","A",5,5,35,0.1429,1,"{2977, 2968, 3023, 2735, 2648}"
274,1,85,0,0.2108148,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/(a + a*Sin[e + f*x])^2,x]","-\frac{(A c+2 A d+2 B c-5 B d) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}+\frac{B d x}{a^2}-\frac{(A-B) (c-d) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}","-\frac{(A c+2 A d+2 B c-5 B d) \cos (e+f x)}{3 a^2 f (\sin (e+f x)+1)}+\frac{B d x}{a^2}-\frac{(A-B) (c-d) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}",1,"(B*d*x)/a^2 - ((A*c + 2*B*c + 2*A*d - 5*B*d)*Cos[e + f*x])/(3*a^2*f*(1 + Sin[e + f*x])) - ((A - B)*(c - d)*Cos[e + f*x])/(3*f*(a + a*Sin[e + f*x])^2)","A",4,4,33,0.1212,1,"{2968, 3019, 2735, 2648}"
275,1,65,0,0.0517211,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/(a + a*Sin[e + f*x])^2,x]","-\frac{(A+2 B) \cos (e+f x)}{3 f \left(a^2 \sin (e+f x)+a^2\right)}-\frac{(A-B) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}","-\frac{(A+2 B) \cos (e+f x)}{3 f \left(a^2 \sin (e+f x)+a^2\right)}-\frac{(A-B) \cos (e+f x)}{3 f (a \sin (e+f x)+a)^2}",1,"-((A - B)*Cos[e + f*x])/(3*f*(a + a*Sin[e + f*x])^2) - ((A + 2*B)*Cos[e + f*x])/(3*f*(a^2 + a^2*Sin[e + f*x]))","A",2,2,23,0.08696,1,"{2750, 2648}"
276,1,152,0,0.4192582,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])),x]","-\frac{2 d (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^2 \sqrt{c^2-d^2}}-\frac{(A (c-4 d)+B (2 c+d)) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1)}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2}","-\frac{2 d (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^2 \sqrt{c^2-d^2}}-\frac{(A (c-4 d)+B (2 c+d)) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1)}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2}",1,"(-2*d*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^2*(c - d)^2*Sqrt[c^2 - d^2]*f) - ((A*(c - 4*d) + B*(2*c + d))*Cos[e + f*x])/(3*a^2*(c - d)^2*f*(1 + Sin[e + f*x])) - ((A - B)*Cos[e + f*x])/(3*(c - d)*f*(a + a*Sin[e + f*x])^2)","A",6,5,35,0.1429,1,"{2978, 12, 2660, 618, 204}"
277,1,275,0,0.6722154,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^2),x]","\frac{2 d \left(A d (3 c+2 d)-B \left(2 c^2+2 c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^3 (c+d) \sqrt{c^2-d^2}}-\frac{d \left(A \left(c^2-6 c d-10 d^2\right)+B \left(2 c^2+9 c d+4 d^2\right)\right) \cos (e+f x)}{3 a^2 f (c-d)^3 (c+d) (c+d \sin (e+f x))}-\frac{(A c-6 A d+2 B c+3 B d) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1) (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))}","\frac{2 d \left(A d (3 c+2 d)-B \left(2 c^2+2 c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^3 (c+d) \sqrt{c^2-d^2}}-\frac{d \left(A \left(c^2-6 c d-10 d^2\right)+B \left(2 c^2+9 c d+4 d^2\right)\right) \cos (e+f x)}{3 a^2 f (c-d)^3 (c+d) (c+d \sin (e+f x))}-\frac{(A c-6 A d+2 B c+3 B d) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1) (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))}",1,"(2*d*(A*d*(3*c + 2*d) - B*(2*c^2 + 2*c*d + d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^2*(c - d)^3*(c + d)*Sqrt[c^2 - d^2]*f) - (d*(A*(c^2 - 6*c*d - 10*d^2) + B*(2*c^2 + 9*c*d + 4*d^2))*Cos[e + f*x])/(3*a^2*(c - d)^3*(c + d)*f*(c + d*Sin[e + f*x])) - ((A*c + 2*B*c - 6*A*d + 3*B*d)*Cos[e + f*x])/(3*a^2*(c - d)^2*f*(1 + Sin[e + f*x])*(c + d*Sin[e + f*x])) - ((A - B)*Cos[e + f*x])/(3*(c - d)*f*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x]))","A",7,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
278,1,386,0,0.9613311,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^2 (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^3),x]","\frac{d \left(A d \left(12 c^2+16 c d+7 d^2\right)-B \left(12 c^2 d+6 c^3+13 c d^2+4 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^4 (c+d)^2 \sqrt{c^2-d^2}}-\frac{d \left(A \left(-16 c^2 d+2 c^3-59 c d^2-32 d^3\right)+B \left(37 c^2 d+4 c^3+44 c d^2+20 d^3\right)\right) \cos (e+f x)}{6 a^2 f (c-d)^4 (c+d)^2 (c+d \sin (e+f x))}-\frac{d \left(A \left(2 c^2-16 c d-21 d^2\right)+B \left(4 c^2+19 c d+12 d^2\right)\right) \cos (e+f x)}{6 a^2 f (c-d)^3 (c+d) (c+d \sin (e+f x))^2}-\frac{(A c-8 A d+2 B c+5 B d) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1) (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^2}","\frac{d \left(A d \left(12 c^2+16 c d+7 d^2\right)-B \left(12 c^2 d+6 c^3+13 c d^2+4 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^2 f (c-d)^4 (c+d)^2 \sqrt{c^2-d^2}}-\frac{d \left(A \left(-16 c^2 d+2 c^3-59 c d^2-32 d^3\right)+B \left(37 c^2 d+4 c^3+44 c d^2+20 d^3\right)\right) \cos (e+f x)}{6 a^2 f (c-d)^4 (c+d)^2 (c+d \sin (e+f x))}-\frac{d \left(A \left(2 c^2-16 c d-21 d^2\right)+B \left(4 c^2+19 c d+12 d^2\right)\right) \cos (e+f x)}{6 a^2 f (c-d)^3 (c+d) (c+d \sin (e+f x))^2}-\frac{(A c-8 A d+2 B c+5 B d) \cos (e+f x)}{3 a^2 f (c-d)^2 (\sin (e+f x)+1) (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{3 f (c-d) (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^2}",1,"(d*(A*d*(12*c^2 + 16*c*d + 7*d^2) - B*(6*c^3 + 12*c^2*d + 13*c*d^2 + 4*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^2*(c - d)^4*(c + d)^2*Sqrt[c^2 - d^2]*f) - (d*(A*(2*c^2 - 16*c*d - 21*d^2) + B*(4*c^2 + 19*c*d + 12*d^2))*Cos[e + f*x])/(6*a^2*(c - d)^3*(c + d)*f*(c + d*Sin[e + f*x])^2) - ((A*c + 2*B*c - 8*A*d + 5*B*d)*Cos[e + f*x])/(3*a^2*(c - d)^2*f*(1 + Sin[e + f*x])*(c + d*Sin[e + f*x])^2) - ((A - B)*Cos[e + f*x])/(3*(c - d)*f*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^2) - (d*(A*(2*c^3 - 16*c^2*d - 59*c*d^2 - 32*d^3) + B*(4*c^3 + 37*c^2*d + 44*c*d^2 + 20*d^3))*Cos[e + f*x])/(6*a^2*(c - d)^4*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",8,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
279,1,225,0,0.8093072,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^3,x]","-\frac{(c-d) \left(A \left(2 c^2+7 c d+15 d^2\right)+3 B \left(c^2+6 c d-15 d^2\right)\right) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{d^2 (A (2 c+7 d)+3 B (c-9 d)) \cos (e+f x)}{15 a^3 f}+\frac{d^2 x (A d+3 B (c-d))}{a^3}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{5 f (a \sin (e+f x)+a)^3}-\frac{(2 A (c+2 d)+3 B (c-3 d)) \cos (e+f x) (c+d \sin (e+f x))^2}{15 a f (a \sin (e+f x)+a)^2}","-\frac{(c-d) \left(A \left(2 c^2+7 c d+15 d^2\right)+3 B \left(c^2+6 c d-15 d^2\right)\right) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{d^2 (A (2 c+7 d)+3 B (c-9 d)) \cos (e+f x)}{15 a^3 f}+\frac{d^2 x (A d+3 B (c-d))}{a^3}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{5 f (a \sin (e+f x)+a)^3}-\frac{(2 A (c+2 d)+3 B (c-3 d)) \cos (e+f x) (c+d \sin (e+f x))^2}{15 a f (a \sin (e+f x)+a)^2}",1,"(d^2*(3*B*(c - d) + A*d)*x)/a^3 + (d^2*(3*B*(c - 9*d) + A*(2*c + 7*d))*Cos[e + f*x])/(15*a^3*f) - ((c - d)*(3*B*(c^2 + 6*c*d - 15*d^2) + A*(2*c^2 + 7*c*d + 15*d^2))*Cos[e + f*x])/(15*f*(a^3 + a^3*Sin[e + f*x])) - ((3*B*(c - 3*d) + 2*A*(c + 2*d))*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(15*a*f*(a + a*Sin[e + f*x])^2) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(5*f*(a + a*Sin[e + f*x])^3)","A",6,5,35,0.1429,1,"{2977, 2968, 3023, 2735, 2648}"
280,1,164,0,0.4610745,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^3,x]","-\frac{\left(2 A \left(c^2+3 c d+2 d^2\right)+B \left(3 c^2+14 c d-29 d^2\right)\right) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{B d^2 x}{a^3}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{5 f (a \sin (e+f x)+a)^3}-\frac{(c-d) (2 A (c+d)+B (3 c-7 d)) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}","-\frac{\left(2 A \left(c^2+3 c d+2 d^2\right)+B \left(3 c^2+14 c d-29 d^2\right)\right) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}+\frac{B d^2 x}{a^3}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{5 f (a \sin (e+f x)+a)^3}-\frac{(c-d) (2 A (c+d)+B (3 c-7 d)) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}",1,"(B*d^2*x)/a^3 - ((c - d)*(B*(3*c - 7*d) + 2*A*(c + d))*Cos[e + f*x])/(15*a*f*(a + a*Sin[e + f*x])^2) - ((B*(3*c^2 + 14*c*d - 29*d^2) + 2*A*(c^2 + 3*c*d + 2*d^2))*Cos[e + f*x])/(15*f*(a^3 + a^3*Sin[e + f*x])) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(5*f*(a + a*Sin[e + f*x])^3)","A",5,5,35,0.1429,1,"{2977, 2968, 3019, 2735, 2648}"
281,1,127,0,0.2265322,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{(a+a \sin (e+f x))^3} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/(a + a*Sin[e + f*x])^3,x]","-\frac{(2 A c+3 A d+3 B c+7 B d) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A c+3 A d+3 B c-8 B d) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}-\frac{(A-B) (c-d) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}","-\frac{(2 A c+3 A d+3 B c+7 B d) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A c+3 A d+3 B c-8 B d) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}-\frac{(A-B) (c-d) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}",1,"-((A - B)*(c - d)*Cos[e + f*x])/(5*f*(a + a*Sin[e + f*x])^3) - ((2*A*c + 3*B*c + 3*A*d - 8*B*d)*Cos[e + f*x])/(15*a*f*(a + a*Sin[e + f*x])^2) - ((2*A*c + 3*B*c + 3*A*d + 7*B*d)*Cos[e + f*x])/(15*f*(a^3 + a^3*Sin[e + f*x]))","A",4,4,33,0.1212,1,"{2968, 3019, 2750, 2648}"
282,1,102,0,0.0750472,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/(a + a*Sin[e + f*x])^3,x]","-\frac{(2 A+3 B) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A+3 B) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}-\frac{(A-B) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}","-\frac{(2 A+3 B) \cos (e+f x)}{15 f \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A+3 B) \cos (e+f x)}{15 a f (a \sin (e+f x)+a)^2}-\frac{(A-B) \cos (e+f x)}{5 f (a \sin (e+f x)+a)^3}",1,"-((A - B)*Cos[e + f*x])/(5*f*(a + a*Sin[e + f*x])^3) - ((2*A + 3*B)*Cos[e + f*x])/(15*a*f*(a + a*Sin[e + f*x])^2) - ((2*A + 3*B)*Cos[e + f*x])/(15*f*(a^3 + a^3*Sin[e + f*x]))","A",3,3,23,0.1304,1,"{2750, 2650, 2648}"
283,1,229,0,0.7239707,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c + d*Sin[e + f*x])),x]","\frac{2 d^2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^3 \sqrt{c^2-d^2}}-\frac{\left(A \left(2 c^2-9 c d+22 d^2\right)+B \left(3 c^2-16 c d-2 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A c-7 A d+3 B c+2 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3}","\frac{2 d^2 (B c-A d) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^3 \sqrt{c^2-d^2}}-\frac{\left(A \left(2 c^2-9 c d+22 d^2\right)+B \left(3 c^2-16 c d-2 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right)}-\frac{(2 A c-7 A d+3 B c+2 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3}",1,"(2*d^2*(B*c - A*d)*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^3*(c - d)^3*Sqrt[c^2 - d^2]*f) - ((A - B)*Cos[e + f*x])/(5*(c - d)*f*(a + a*Sin[e + f*x])^3) - ((2*A*c + 3*B*c - 7*A*d + 2*B*d)*Cos[e + f*x])/(15*a*(c - d)^2*f*(a + a*Sin[e + f*x])^2) - ((B*(3*c^2 - 16*c*d - 2*d^2) + A*(2*c^2 - 9*c*d + 22*d^2))*Cos[e + f*x])/(15*(c - d)^3*f*(a^3 + a^3*Sin[e + f*x]))","A",7,5,35,0.1429,1,"{2978, 12, 2660, 618, 204}"
284,1,381,0,1.0810594,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c + d*Sin[e + f*x])^2),x]","-\frac{2 d^2 \left(A d (4 c+3 d)-B \left(3 c^2+3 c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^4 (c+d) \sqrt{c^2-d^2}}-\frac{d \left(A \left(-12 c^2 d+2 c^3+43 c d^2+72 d^3\right)+B \left(-23 c^2 d+3 c^3-63 c d^2-22 d^3\right)\right) \cos (e+f x)}{15 a^3 f (c-d)^4 (c+d) (c+d \sin (e+f x))}-\frac{\left(A \left(2 c^2-12 c d+45 d^2\right)+B \left(3 c^2-23 c d-15 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))}-\frac{(2 A c-9 A d+3 B c+4 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3 (c+d \sin (e+f x))}","-\frac{2 d^2 \left(A d (4 c+3 d)-B \left(3 c^2+3 c d+d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^4 (c+d) \sqrt{c^2-d^2}}-\frac{d \left(A \left(-12 c^2 d+2 c^3+43 c d^2+72 d^3\right)+B \left(-23 c^2 d+3 c^3-63 c d^2-22 d^3\right)\right) \cos (e+f x)}{15 a^3 f (c-d)^4 (c+d) (c+d \sin (e+f x))}-\frac{\left(A \left(2 c^2-12 c d+45 d^2\right)+B \left(3 c^2-23 c d-15 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))}-\frac{(2 A c-9 A d+3 B c+4 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3 (c+d \sin (e+f x))}",1,"(-2*d^2*(A*d*(4*c + 3*d) - B*(3*c^2 + 3*c*d + d^2))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^3*(c - d)^4*(c + d)*Sqrt[c^2 - d^2]*f) - (d*(B*(3*c^3 - 23*c^2*d - 63*c*d^2 - 22*d^3) + A*(2*c^3 - 12*c^2*d + 43*c*d^2 + 72*d^3))*Cos[e + f*x])/(15*a^3*(c - d)^4*(c + d)*f*(c + d*Sin[e + f*x])) - ((A - B)*Cos[e + f*x])/(5*(c - d)*f*(a + a*Sin[e + f*x])^3*(c + d*Sin[e + f*x])) - ((2*A*c + 3*B*c - 9*A*d + 4*B*d)*Cos[e + f*x])/(15*a*(c - d)^2*f*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])) - ((B*(3*c^2 - 23*c*d - 15*d^2) + A*(2*c^2 - 12*c*d + 45*d^2))*Cos[e + f*x])/(15*(c - d)^3*f*(a^3 + a^3*Sin[e + f*x])*(c + d*Sin[e + f*x]))","A",8,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
285,1,508,0,1.4465588,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^3 (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^3*(c + d*Sin[e + f*x])^3),x]","-\frac{d^2 \left(A d \left(20 c^2+30 c d+13 d^2\right)-3 B \left(8 c^2 d+4 c^3+7 c d^2+2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^5 (c+d)^2 \sqrt{c^2-d^2}}-\frac{d \left(A \left(142 c^2 d^2-30 c^3 d+4 c^4+525 c d^3+304 d^4\right)+3 B \left(-119 c^2 d^2-20 c^3 d+2 c^4-130 c d^3-48 d^4\right)\right) \cos (e+f x)}{30 a^3 f (c-d)^5 (c+d)^2 (c+d \sin (e+f x))}-\frac{d \left(A \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right)+3 B \left(-20 c^2 d+2 c^3-57 c d^2-30 d^3\right)\right) \cos (e+f x)}{30 a^3 f (c-d)^4 (c+d) (c+d \sin (e+f x))^2}-\frac{\left(A \left(2 c^2-15 c d+76 d^2\right)+3 B \left(c^2-10 c d-12 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^2}-\frac{(2 A c-11 A d+3 B c+6 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3 (c+d \sin (e+f x))^2}","-\frac{d^2 \left(A d \left(20 c^2+30 c d+13 d^2\right)-3 B \left(8 c^2 d+4 c^3+7 c d^2+2 d^3\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{a^3 f (c-d)^5 (c+d)^2 \sqrt{c^2-d^2}}-\frac{d \left(A \left(142 c^2 d^2-30 c^3 d+4 c^4+525 c d^3+304 d^4\right)+3 B \left(-119 c^2 d^2-20 c^3 d+2 c^4-130 c d^3-48 d^4\right)\right) \cos (e+f x)}{30 a^3 f (c-d)^5 (c+d)^2 (c+d \sin (e+f x))}-\frac{d \left(A \left(-30 c^2 d+4 c^3+146 c d^2+195 d^3\right)+3 B \left(-20 c^2 d+2 c^3-57 c d^2-30 d^3\right)\right) \cos (e+f x)}{30 a^3 f (c-d)^4 (c+d) (c+d \sin (e+f x))^2}-\frac{\left(A \left(2 c^2-15 c d+76 d^2\right)+3 B \left(c^2-10 c d-12 d^2\right)\right) \cos (e+f x)}{15 f (c-d)^3 \left(a^3 \sin (e+f x)+a^3\right) (c+d \sin (e+f x))^2}-\frac{(2 A c-11 A d+3 B c+6 B d) \cos (e+f x)}{15 a f (c-d)^2 (a \sin (e+f x)+a)^2 (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{5 f (c-d) (a \sin (e+f x)+a)^3 (c+d \sin (e+f x))^2}",1,"-((d^2*(A*d*(20*c^2 + 30*c*d + 13*d^2) - 3*B*(4*c^3 + 8*c^2*d + 7*c*d^2 + 2*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(a^3*(c - d)^5*(c + d)^2*Sqrt[c^2 - d^2]*f)) - (d*(3*B*(2*c^3 - 20*c^2*d - 57*c*d^2 - 30*d^3) + A*(4*c^3 - 30*c^2*d + 146*c*d^2 + 195*d^3))*Cos[e + f*x])/(30*a^3*(c - d)^4*(c + d)*f*(c + d*Sin[e + f*x])^2) - ((A - B)*Cos[e + f*x])/(5*(c - d)*f*(a + a*Sin[e + f*x])^3*(c + d*Sin[e + f*x])^2) - ((2*A*c + 3*B*c - 11*A*d + 6*B*d)*Cos[e + f*x])/(15*a*(c - d)^2*f*(a + a*Sin[e + f*x])^2*(c + d*Sin[e + f*x])^2) - ((3*B*(c^2 - 10*c*d - 12*d^2) + A*(2*c^2 - 15*c*d + 76*d^2))*Cos[e + f*x])/(15*(c - d)^3*f*(a^3 + a^3*Sin[e + f*x])*(c + d*Sin[e + f*x])^2) - (d*(3*B*(2*c^4 - 20*c^3*d - 119*c^2*d^2 - 130*c*d^3 - 48*d^4) + A*(4*c^4 - 30*c^3*d + 142*c^2*d^2 + 525*c*d^3 + 304*d^4))*Cos[e + f*x])/(30*a^3*(c - d)^5*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",9,6,35,0.1714,1,"{2978, 2754, 12, 2660, 618, 204}"
286,1,256,0,0.4599777,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","\frac{4 a (c+d) \left(15 c^2+10 c d+7 d^2\right) (-9 A d+B c-8 B d) \cos (e+f x)}{315 d f \sqrt{a \sin (e+f x)+a}}+\frac{2 a (-9 A d+B c-8 B d) \cos (e+f x) (c+d \sin (e+f x))^3}{63 d f \sqrt{a \sin (e+f x)+a}}+\frac{4 d (c+d) (-9 A d+B c-8 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 a f}+\frac{8 (5 c-d) (c+d) (-9 A d+B c-8 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 f}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^4}{9 d f \sqrt{a \sin (e+f x)+a}}","\frac{4 a (c+d) \left(15 c^2+10 c d+7 d^2\right) (-9 A d+B c-8 B d) \cos (e+f x)}{315 d f \sqrt{a \sin (e+f x)+a}}+\frac{2 a (-9 A d+B c-8 B d) \cos (e+f x) (c+d \sin (e+f x))^3}{63 d f \sqrt{a \sin (e+f x)+a}}+\frac{4 d (c+d) (-9 A d+B c-8 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 a f}+\frac{8 (5 c-d) (c+d) (-9 A d+B c-8 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 f}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^4}{9 d f \sqrt{a \sin (e+f x)+a}}",1,"(4*a*(c + d)*(B*c - 9*A*d - 8*B*d)*(15*c^2 + 10*c*d + 7*d^2)*Cos[e + f*x])/(315*d*f*Sqrt[a + a*Sin[e + f*x]]) + (8*(5*c - d)*(c + d)*(B*c - 9*A*d - 8*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(315*f) + (4*d*(c + d)*(B*c - 9*A*d - 8*B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(105*a*f) + (2*a*(B*c - 9*A*d - 8*B*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(63*d*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(9*d*f*Sqrt[a + a*Sin[e + f*x]])","A",5,5,37,0.1351,1,"{2981, 2770, 2761, 2751, 2646}"
287,1,192,0,0.3393425,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","\frac{2 a \left(15 c^2+10 c d+7 d^2\right) (-7 A d+B c-6 B d) \cos (e+f x)}{105 d f \sqrt{a \sin (e+f x)+a}}+\frac{2 d (-7 A d+B c-6 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 a f}+\frac{4 (5 c-d) (-7 A d+B c-6 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^3}{7 d f \sqrt{a \sin (e+f x)+a}}","\frac{2 a \left(15 c^2+10 c d+7 d^2\right) (-7 A d+B c-6 B d) \cos (e+f x)}{105 d f \sqrt{a \sin (e+f x)+a}}+\frac{2 d (-7 A d+B c-6 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 a f}+\frac{4 (5 c-d) (-7 A d+B c-6 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^3}{7 d f \sqrt{a \sin (e+f x)+a}}",1,"(2*a*(B*c - 7*A*d - 6*B*d)*(15*c^2 + 10*c*d + 7*d^2)*Cos[e + f*x])/(105*d*f*Sqrt[a + a*Sin[e + f*x]]) + (4*(5*c - d)*(B*c - 7*A*d - 6*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(105*f) + (2*d*(B*c - 7*A*d - 6*B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(35*a*f) - (2*a*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(7*d*f*Sqrt[a + a*Sin[e + f*x]])","A",4,4,37,0.1081,1,"{2981, 2761, 2751, 2646}"
288,1,118,0,0.2490477,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{2 (5 A d+5 B c-2 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 f}-\frac{2 a (15 A c+5 A d+5 B c+7 B d) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 a f}","-\frac{2 (5 A d+5 B c-2 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 f}-\frac{2 a (15 A c+5 A d+5 B c+7 B d) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 a f}",1,"(-2*a*(15*A*c + 5*B*c + 5*A*d + 7*B*d)*Cos[e + f*x])/(15*f*Sqrt[a + a*Sin[e + f*x]]) - (2*(5*B*c + 5*A*d - 2*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(15*f) - (2*B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(5*a*f)","A",4,4,35,0.1143,1,"{2968, 3023, 2751, 2646}"
289,1,62,0,0.0576309,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]),x]","-\frac{2 a (3 A+B) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 f}","-\frac{2 a (3 A+B) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 f}",1,"(-2*a*(3*A + B)*Cos[e + f*x])/(3*f*Sqrt[a + a*Sin[e + f*x]]) - (2*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3*f)","A",2,2,25,0.08000,1,"{2751, 2646}"
290,1,100,0,0.2457285,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","\frac{2 \sqrt{a} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{3/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x)}{d f \sqrt{a \sin (e+f x)+a}}","\frac{2 \sqrt{a} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{3/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x)}{d f \sqrt{a \sin (e+f x)+a}}",1,"(2*Sqrt[a]*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(3/2)*Sqrt[c + d]*f) - (2*a*B*Cos[e + f*x])/(d*f*Sqrt[a + a*Sin[e + f*x]])","A",3,3,37,0.08108,1,"{2981, 2773, 208}"
291,1,126,0,0.2617332,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","\frac{a (B c-A d) \cos (e+f x)}{d f (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{\sqrt{a} (A d+B (c+2 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{3/2} f (c+d)^{3/2}}","\frac{a (B c-A d) \cos (e+f x)}{d f (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{\sqrt{a} (A d+B (c+2 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{3/2} f (c+d)^{3/2}}",1,"-((Sqrt[a]*(A*d + B*(c + 2*d))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(3/2)*(c + d)^(3/2)*f)) + (a*(B*c - A*d)*Cos[e + f*x])/(d*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",3,3,37,0.08108,1,"{2980, 2773, 208}"
292,1,192,0,0.3703787,"\int \frac{\sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[(Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","-\frac{\sqrt{a} (3 A d+B (c+4 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{3/2} f (c+d)^{5/2}}-\frac{a (3 A d+B (c+4 d)) \cos (e+f x)}{4 d f (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{a (B c-A d) \cos (e+f x)}{2 d f (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}","-\frac{\sqrt{a} (3 A d+B (c+4 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{3/2} f (c+d)^{5/2}}-\frac{a (3 A d+B (c+4 d)) \cos (e+f x)}{4 d f (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{a (B c-A d) \cos (e+f x)}{2 d f (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}",1,"-(Sqrt[a]*(3*A*d + B*(c + 4*d))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*d^(3/2)*(c + d)^(5/2)*f) + (a*(B*c - A*d)*Cos[e + f*x])/(2*d*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^2) - (a*(3*A*d + B*(c + 4*d))*Cos[e + f*x])/(4*d*(c + d)^2*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",4,4,37,0.1081,1,"{2980, 2772, 2773, 208}"
293,1,374,0,0.9202417,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","\frac{2 a^2 \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{693 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{4 a^2 (c+d) \left(15 c^2+10 c d+7 d^2\right) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x)}{3465 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (3 B (c-4 d)-11 A d) \cos (e+f x) (c+d \sin (e+f x))^4}{99 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{4 (c+d) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{1155 f}+\frac{8 a (5 c-d) (c+d) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3465 d f}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^4}{11 d f}","\frac{2 a^2 \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{693 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{4 a^2 (c+d) \left(15 c^2+10 c d+7 d^2\right) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x)}{3465 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (3 B (c-4 d)-11 A d) \cos (e+f x) (c+d \sin (e+f x))^4}{99 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{4 (c+d) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{1155 f}+\frac{8 a (5 c-d) (c+d) \left(11 A d (c-17 d)-3 B \left(c^2-9 c d+56 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3465 d f}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^4}{11 d f}",1,"(4*a^2*(c + d)*(15*c^2 + 10*c*d + 7*d^2)*(11*A*(c - 17*d)*d - 3*B*(c^2 - 9*c*d + 56*d^2))*Cos[e + f*x])/(3465*d^2*f*Sqrt[a + a*Sin[e + f*x]]) + (8*a*(5*c - d)*(c + d)*(11*A*(c - 17*d)*d - 3*B*(c^2 - 9*c*d + 56*d^2))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3465*d*f) + (4*(c + d)*(11*A*(c - 17*d)*d - 3*B*(c^2 - 9*c*d + 56*d^2))*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(1155*f) + (2*a^2*(11*A*(c - 17*d)*d - 3*B*(c^2 - 9*c*d + 56*d^2))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(693*d^2*f*Sqrt[a + a*Sin[e + f*x]]) + (2*a^2*(3*B*(c - 4*d) - 11*A*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(99*d^2*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^4)/(11*d*f)","A",6,6,37,0.1622,1,"{2976, 2981, 2770, 2761, 2751, 2646}"
294,1,294,0,0.7119035,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","\frac{2 a^2 \left(15 c^2+10 c d+7 d^2\right) \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x)}{315 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-9 A d+3 B c-10 B d) \cos (e+f x) (c+d \sin (e+f x))^3}{63 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 f}+\frac{4 a (5 c-d) \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 d f}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^3}{9 d f}","\frac{2 a^2 \left(15 c^2+10 c d+7 d^2\right) \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x)}{315 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-9 A d+3 B c-10 B d) \cos (e+f x) (c+d \sin (e+f x))^3}{63 d^2 f \sqrt{a \sin (e+f x)+a}}+\frac{2 \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 f}+\frac{4 a (5 c-d) \left(3 A d (c-13 d)-B \left(c^2-7 c d+34 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 d f}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^3}{9 d f}",1,"(2*a^2*(15*c^2 + 10*c*d + 7*d^2)*(3*A*(c - 13*d)*d - B*(c^2 - 7*c*d + 34*d^2))*Cos[e + f*x])/(315*d^2*f*Sqrt[a + a*Sin[e + f*x]]) + (4*a*(5*c - d)*(3*A*(c - 13*d)*d - B*(c^2 - 7*c*d + 34*d^2))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(315*d*f) + (2*(3*A*(c - 13*d)*d - B*(c^2 - 7*c*d + 34*d^2))*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(105*f) + (2*a^2*(3*B*c - 9*A*d - 10*B*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(63*d^2*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^3)/(9*d*f)","A",5,5,37,0.1351,1,"{2976, 2981, 2761, 2751, 2646}"
295,1,165,0,0.3156326,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{8 a^2 (35 A c+21 A d+21 B c+19 B d) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (7 A d+7 B c-2 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 f}-\frac{2 a (35 A c+21 A d+21 B c+19 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{7 a f}","-\frac{8 a^2 (35 A c+21 A d+21 B c+19 B d) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (7 A d+7 B c-2 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 f}-\frac{2 a (35 A c+21 A d+21 B c+19 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{7 a f}",1,"(-8*a^2*(35*A*c + 21*B*c + 21*A*d + 19*B*d)*Cos[e + f*x])/(105*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*(35*A*c + 21*B*c + 21*A*d + 19*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(105*f) - (2*(7*B*c + 7*A*d - 2*B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(35*f) - (2*B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(7*a*f)","A",5,5,35,0.1429,1,"{2968, 3023, 2751, 2647, 2646}"
296,1,101,0,0.0868601,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]),x]","-\frac{8 a^2 (5 A+3 B) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a (5 A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 f}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 f}","-\frac{8 a^2 (5 A+3 B) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a (5 A+3 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 f}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 f}",1,"(-8*a^2*(5*A + 3*B)*Cos[e + f*x])/(15*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*(5*A + 3*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(15*f) - (2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(5*f)","A",3,3,25,0.1200,1,"{2751, 2647, 2646}"
297,1,153,0,0.5028245,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","\frac{2 a^2 (-3 A d+3 B c-4 B d) \cos (e+f x)}{3 d^2 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^{3/2} (c-d) (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{5/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 d f}","\frac{2 a^2 (-3 A d+3 B c-4 B d) \cos (e+f x)}{3 d^2 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^{3/2} (c-d) (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{5/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 d f}",1,"(-2*a^(3/2)*(c - d)*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(5/2)*Sqrt[c + d]*f) + (2*a^2*(3*B*c - 3*A*d - 4*B*d)*Cos[e + f*x])/(3*d^2*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3*d*f)","A",4,4,37,0.1081,1,"{2976, 2981, 2773, 208}"
298,1,191,0,0.5522183,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","-\frac{a^{3/2} \left(A d (c+3 d)-B \left(3 c^2+3 c d-2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{5/2} f (c+d)^{3/2}}-\frac{a^2 (-A d+3 B c+2 B d) \cos (e+f x)}{d^2 f (c+d) \sqrt{a \sin (e+f x)+a}}+\frac{a (B c-A d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{d f (c+d) (c+d \sin (e+f x))}","-\frac{a^{3/2} \left(A d (c+3 d)-B \left(3 c^2+3 c d-2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{5/2} f (c+d)^{3/2}}-\frac{a^2 (-A d+3 B c+2 B d) \cos (e+f x)}{d^2 f (c+d) \sqrt{a \sin (e+f x)+a}}+\frac{a (B c-A d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{d f (c+d) (c+d \sin (e+f x))}",1,"-((a^(3/2)*(A*d*(c + 3*d) - B*(3*c^2 + 3*c*d - 2*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(5/2)*(c + d)^(3/2)*f)) - (a^2*(3*B*c - A*d + 2*B*d)*Cos[e + f*x])/(d^2*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]) + (a*(B*c - A*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(d*(c + d)*f*(c + d*Sin[e + f*x]))","A",4,4,37,0.1081,1,"{2975, 2981, 2773, 208}"
299,1,221,0,0.6095101,"\int \frac{(a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","\frac{a^2 \left(A d (c-5 d)+B \left(3 c^2+5 c d-4 d^2\right)\right) \cos (e+f x)}{4 d^2 f (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{a^{3/2} \left(A d (c+7 d)+3 B \left(c^2+3 c d+4 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{5/2} f (c+d)^{5/2}}+\frac{a (B c-A d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 d f (c+d) (c+d \sin (e+f x))^2}","\frac{a^2 \left(A d (c-5 d)+B \left(3 c^2+5 c d-4 d^2\right)\right) \cos (e+f x)}{4 d^2 f (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{a^{3/2} \left(A d (c+7 d)+3 B \left(c^2+3 c d+4 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{5/2} f (c+d)^{5/2}}+\frac{a (B c-A d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{2 d f (c+d) (c+d \sin (e+f x))^2}",1,"-(a^(3/2)*(A*d*(c + 7*d) + 3*B*(c^2 + 3*c*d + 4*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*d^(5/2)*(c + d)^(5/2)*f) + (a*(B*c - A*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(2*d*(c + d)*f*(c + d*Sin[e + f*x])^2) + (a^2*(A*(c - 5*d)*d + B*(3*c^2 + 5*c*d - 4*d^2))*Cos[e + f*x])/(4*d^2*(c + d)^2*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",4,4,37,0.1081,1,"{2975, 2980, 2773, 208}"
300,1,534,0,1.2030594,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c+d \sin (e+f x))^3 \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3,x]","-\frac{2 a^3 \left(-39 A c d+299 A d^2+15 B c^2-75 B c d+280 B d^2\right) \cos (e+f x) (c+d \sin (e+f x))^4}{1287 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{9009 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{8 a^2 (5 c-d) (c+d) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{45045 d^2 f}-\frac{4 a^3 (c+d) \left(15 c^2+10 c d+7 d^2\right) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x)}{45045 d^3 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-13 A d+5 B c-16 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^4}{143 d^2 f}-\frac{4 a (c+d) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{15015 d f}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^4}{13 d f}","-\frac{2 a^3 \left(-39 A c d+299 A d^2+15 B c^2-75 B c d+280 B d^2\right) \cos (e+f x) (c+d \sin (e+f x))^4}{1287 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{9009 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{8 a^2 (5 c-d) (c+d) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{45045 d^2 f}-\frac{4 a^3 (c+d) \left(15 c^2+10 c d+7 d^2\right) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x)}{45045 d^3 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-13 A d+5 B c-16 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^4}{143 d^2 f}-\frac{4 a (c+d) \left(13 A d \left(3 c^2-38 c d+355 d^2\right)-B \left(-150 c^2 d+15 c^3+799 c d^2-4184 d^3\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{15015 d f}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^4}{13 d f}",1,"(-4*a^3*(c + d)*(15*c^2 + 10*c*d + 7*d^2)*(13*A*d*(3*c^2 - 38*c*d + 355*d^2) - B*(15*c^3 - 150*c^2*d + 799*c*d^2 - 4184*d^3))*Cos[e + f*x])/(45045*d^3*f*Sqrt[a + a*Sin[e + f*x]]) - (8*a^2*(5*c - d)*(c + d)*(13*A*d*(3*c^2 - 38*c*d + 355*d^2) - B*(15*c^3 - 150*c^2*d + 799*c*d^2 - 4184*d^3))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(45045*d^2*f) - (4*a*(c + d)*(13*A*d*(3*c^2 - 38*c*d + 355*d^2) - B*(15*c^3 - 150*c^2*d + 799*c*d^2 - 4184*d^3))*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(15015*d*f) - (2*a^3*(13*A*d*(3*c^2 - 38*c*d + 355*d^2) - B*(15*c^3 - 150*c^2*d + 799*c*d^2 - 4184*d^3))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(9009*d^3*f*Sqrt[a + a*Sin[e + f*x]]) - (2*a^3*(15*B*c^2 - 39*A*c*d - 75*B*c*d + 299*A*d^2 + 280*B*d^2)*Cos[e + f*x]*(c + d*Sin[e + f*x])^4)/(1287*d^3*f*Sqrt[a + a*Sin[e + f*x]]) + (2*a^2*(5*B*c - 13*A*d - 16*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^4)/(143*d^2*f) - (2*a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^4)/(13*d*f)","A",7,6,37,0.1622,1,"{2976, 2981, 2770, 2761, 2751, 2646}"
301,1,429,0,1.0657619,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","\frac{2 a^3 \left(11 A d (3 c-19 d)-B \left(15 c^2-65 c d+194 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{693 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(15 c^2+10 c d+7 d^2\right) \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x)}{3465 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{4 a^2 (5 c-d) \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3465 d^2 f}+\frac{2 a^2 (-11 A d+5 B c-14 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^3}{99 d^2 f}-\frac{2 a \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{1155 d f}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^3}{11 d f}","\frac{2 a^3 \left(11 A d (3 c-19 d)-B \left(15 c^2-65 c d+194 d^2\right)\right) \cos (e+f x) (c+d \sin (e+f x))^3}{693 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{2 a^3 \left(15 c^2+10 c d+7 d^2\right) \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x)}{3465 d^3 f \sqrt{a \sin (e+f x)+a}}-\frac{4 a^2 (5 c-d) \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3465 d^2 f}+\frac{2 a^2 (-11 A d+5 B c-14 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^3}{99 d^2 f}-\frac{2 a \left(11 A d \left(c^2-10 c d+73 d^2\right)-B \left(-40 c^2 d+5 c^3+169 c d^2-710 d^3\right)\right) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{1155 d f}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^3}{11 d f}",1,"(-2*a^3*(15*c^2 + 10*c*d + 7*d^2)*(11*A*d*(c^2 - 10*c*d + 73*d^2) - B*(5*c^3 - 40*c^2*d + 169*c*d^2 - 710*d^3))*Cos[e + f*x])/(3465*d^3*f*Sqrt[a + a*Sin[e + f*x]]) - (4*a^2*(5*c - d)*(11*A*d*(c^2 - 10*c*d + 73*d^2) - B*(5*c^3 - 40*c^2*d + 169*c*d^2 - 710*d^3))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3465*d^2*f) - (2*a*(11*A*d*(c^2 - 10*c*d + 73*d^2) - B*(5*c^3 - 40*c^2*d + 169*c*d^2 - 710*d^3))*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(1155*d*f) + (2*a^3*(11*A*(3*c - 19*d)*d - B*(15*c^2 - 65*c*d + 194*d^2))*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(693*d^3*f*Sqrt[a + a*Sin[e + f*x]]) + (2*a^2*(5*B*c - 11*A*d - 14*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^3)/(99*d^2*f) - (2*a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^3)/(11*d*f)","A",6,5,37,0.1351,1,"{2976, 2981, 2761, 2751, 2646}"
302,1,212,0,0.3676513,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{16 a^2 (21 A c+15 A d+15 B c+13 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 f}-\frac{64 a^3 (21 A c+15 A d+15 B c+13 B d) \cos (e+f x)}{315 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (9 A d+9 B c-2 B d) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{63 f}-\frac{2 a (21 A c+15 A d+15 B c+13 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 f}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{9 a f}","-\frac{16 a^2 (21 A c+15 A d+15 B c+13 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{315 f}-\frac{64 a^3 (21 A c+15 A d+15 B c+13 B d) \cos (e+f x)}{315 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (9 A d+9 B c-2 B d) \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{63 f}-\frac{2 a (21 A c+15 A d+15 B c+13 B d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{105 f}-\frac{2 B d \cos (e+f x) (a \sin (e+f x)+a)^{7/2}}{9 a f}",1,"(-64*a^3*(21*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x])/(315*f*Sqrt[a + a*Sin[e + f*x]]) - (16*a^2*(21*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(315*f) - (2*a*(21*A*c + 15*B*c + 15*A*d + 13*B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(105*f) - (2*(9*B*c + 9*A*d - 2*B*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(63*f) - (2*B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^(7/2))/(9*a*f)","A",6,5,35,0.1429,1,"{2968, 3023, 2751, 2647, 2646}"
303,1,138,0,0.1124033,"\int (a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]),x]","-\frac{64 a^3 (7 A+5 B) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{16 a^2 (7 A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 a (7 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 f}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{7 f}","-\frac{64 a^3 (7 A+5 B) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{16 a^2 (7 A+5 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 f}-\frac{2 a (7 A+5 B) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{35 f}-\frac{2 B \cos (e+f x) (a \sin (e+f x)+a)^{5/2}}{7 f}",1,"(-64*a^3*(7*A + 5*B)*Cos[e + f*x])/(105*f*Sqrt[a + a*Sin[e + f*x]]) - (16*a^2*(7*A + 5*B)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(105*f) - (2*a*(7*A + 5*B)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(35*f) - (2*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(5/2))/(7*f)","A",4,3,25,0.1200,1,"{2751, 2647, 2646}"
304,1,218,0,0.8846463,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","\frac{2 a^3 \left(5 A d (3 c-7 d)-B \left(15 c^2-35 c d+32 d^2\right)\right) \cos (e+f x)}{15 d^3 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-5 A d+5 B c-8 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 d^2 f}+\frac{2 a^{5/2} (c-d)^2 (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{7/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 d f}","\frac{2 a^3 \left(5 A d (3 c-7 d)-B \left(15 c^2-35 c d+32 d^2\right)\right) \cos (e+f x)}{15 d^3 f \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 (-5 A d+5 B c-8 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 d^2 f}+\frac{2 a^{5/2} (c-d)^2 (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{7/2} f \sqrt{c+d}}-\frac{2 a B \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{5 d f}",1,"(2*a^(5/2)*(c - d)^2*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(7/2)*Sqrt[c + d]*f) + (2*a^3*(5*A*(3*c - 7*d)*d - B*(15*c^2 - 35*c*d + 32*d^2))*Cos[e + f*x])/(15*d^3*f*Sqrt[a + a*Sin[e + f*x]]) + (2*a^2*(5*B*c - 5*A*d - 8*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(15*d^2*f) - (2*a*B*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(5*d*f)","A",5,4,37,0.1081,1,"{2976, 2981, 2773, 208}"
305,1,265,0,0.9378348,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","-\frac{a^3 \left(3 A d (3 c+d)-B \left(15 c^2-5 c d-14 d^2\right)\right) \cos (e+f x)}{3 d^3 f (c+d) \sqrt{a \sin (e+f x)+a}}+\frac{a^{5/2} (c-d) \left(A d (3 c+5 d)-B \left(5 c^2+5 c d-2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{7/2} f (c+d)^{3/2}}-\frac{a^2 (-3 A d+5 B c+2 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 d^2 f (c+d)}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{d f (c+d) (c+d \sin (e+f x))}","-\frac{a^3 \left(3 A d (3 c+d)-B \left(15 c^2-5 c d-14 d^2\right)\right) \cos (e+f x)}{3 d^3 f (c+d) \sqrt{a \sin (e+f x)+a}}+\frac{a^{5/2} (c-d) \left(A d (3 c+5 d)-B \left(5 c^2+5 c d-2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{d^{7/2} f (c+d)^{3/2}}-\frac{a^2 (-3 A d+5 B c+2 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 d^2 f (c+d)}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{d f (c+d) (c+d \sin (e+f x))}",1,"(a^(5/2)*(c - d)*(A*d*(3*c + 5*d) - B*(5*c^2 + 5*c*d - 2*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(d^(7/2)*(c + d)^(3/2)*f) - (a^3*(3*A*d*(3*c + d) - B*(15*c^2 - 5*c*d - 14*d^2))*Cos[e + f*x])/(3*d^3*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]) - (a^2*(5*B*c - 3*A*d + 2*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3*d^2*(c + d)*f) + (a*(B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(d*(c + d)*f*(c + d*Sin[e + f*x]))","A",5,5,37,0.1351,1,"{2975, 2976, 2981, 2773, 208}"
306,1,308,0,0.9719299,"\int \frac{(a+a \sin (e+f x))^{5/2} (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^(5/2)*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","\frac{a^3 \left(3 A d (c+3 d)-B \left(15 c^2+25 c d+4 d^2\right)\right) \cos (e+f x)}{4 d^3 f (c+d)^2 \sqrt{a \sin (e+f x)+a}}-\frac{a^2 \left(A d (c+7 d)-B \left(5 c^2+7 c d-4 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{4 d^2 f (c+d)^2 (c+d \sin (e+f x))}-\frac{a^{5/2} \left(A d \left(3 c^2+10 c d+19 d^2\right)-B \left(30 c^2 d+15 c^3+7 c d^2-20 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{7/2} f (c+d)^{5/2}}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 d f (c+d) (c+d \sin (e+f x))^2}","\frac{a^3 \left(3 A d (c+3 d)-B \left(15 c^2+25 c d+4 d^2\right)\right) \cos (e+f x)}{4 d^3 f (c+d)^2 \sqrt{a \sin (e+f x)+a}}-\frac{a^2 \left(A d (c+7 d)-B \left(5 c^2+7 c d-4 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{4 d^2 f (c+d)^2 (c+d \sin (e+f x))}-\frac{a^{5/2} \left(A d \left(3 c^2+10 c d+19 d^2\right)-B \left(30 c^2 d+15 c^3+7 c d^2-20 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 d^{7/2} f (c+d)^{5/2}}+\frac{a (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^{3/2}}{2 d f (c+d) (c+d \sin (e+f x))^2}",1,"-(a^(5/2)*(A*d*(3*c^2 + 10*c*d + 19*d^2) - B*(15*c^3 + 30*c^2*d + 7*c*d^2 - 20*d^3))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*d^(7/2)*(c + d)^(5/2)*f) + (a^3*(3*A*d*(c + 3*d) - B*(15*c^2 + 25*c*d + 4*d^2))*Cos[e + f*x])/(4*d^3*(c + d)^2*f*Sqrt[a + a*Sin[e + f*x]]) + (a*(B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^(3/2))/(2*d*(c + d)*f*(c + d*Sin[e + f*x])^2) - (a^2*(A*d*(c + 7*d) - B*(5*c^2 + 7*c*d - 4*d^2))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(4*d^2*(c + d)^2*f*(c + d*Sin[e + f*x]))","A",5,4,37,0.1081,1,"{2975, 2981, 2773, 208}"
307,1,284,0,1.0014436,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{2 d \left(7 A d (9 c-d)+B \left(24 c^2-15 c d+31 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 a f}-\frac{4 \left(7 A d \left(21 c^2-12 c d+7 d^2\right)+B \left(-63 c^2 d+36 c^3+144 c d^2-37 d^3\right)\right) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (7 A d+6 B c-B d) \cos (e+f x) (c+d \sin (e+f x))^2}{35 f \sqrt{a \sin (e+f x)+a}}-\frac{\sqrt{2} (A-B) (c-d)^3 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^3}{7 f \sqrt{a \sin (e+f x)+a}}","-\frac{2 d \left(7 A d (9 c-d)+B \left(24 c^2-15 c d+31 d^2\right)\right) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{105 a f}-\frac{4 \left(7 A d \left(21 c^2-12 c d+7 d^2\right)+B \left(-63 c^2 d+36 c^3+144 c d^2-37 d^3\right)\right) \cos (e+f x)}{105 f \sqrt{a \sin (e+f x)+a}}-\frac{2 (7 A d+6 B c-B d) \cos (e+f x) (c+d \sin (e+f x))^2}{35 f \sqrt{a \sin (e+f x)+a}}-\frac{\sqrt{2} (A-B) (c-d)^3 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^3}{7 f \sqrt{a \sin (e+f x)+a}}",1,"-((Sqrt[2]*(A - B)*(c - d)^3*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*f)) - (4*(7*A*d*(21*c^2 - 12*c*d + 7*d^2) + B*(36*c^3 - 63*c^2*d + 144*c*d^2 - 37*d^3))*Cos[e + f*x])/(105*f*Sqrt[a + a*Sin[e + f*x]]) - (2*d*(7*A*(9*c - d)*d + B*(24*c^2 - 15*c*d + 31*d^2))*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(105*a*f) - (2*(6*B*c + 7*A*d - B*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(35*f*Sqrt[a + a*Sin[e + f*x]]) - (2*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(7*f*Sqrt[a + a*Sin[e + f*x]])","A",7,6,37,0.1622,1,"{2983, 2968, 3023, 2751, 2649, 206}"
308,1,200,0,0.584511,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{4 \left(5 A d (3 c-d)+B \left(6 c^2-7 c d+7 d^2\right)\right) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 d (5 A d+4 B c-B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 a f}-\frac{\sqrt{2} (A-B) (c-d)^2 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^2}{5 f \sqrt{a \sin (e+f x)+a}}","-\frac{4 \left(5 A d (3 c-d)+B \left(6 c^2-7 c d+7 d^2\right)\right) \cos (e+f x)}{15 f \sqrt{a \sin (e+f x)+a}}-\frac{2 d (5 A d+4 B c-B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{15 a f}-\frac{\sqrt{2} (A-B) (c-d)^2 \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^2}{5 f \sqrt{a \sin (e+f x)+a}}",1,"-((Sqrt[2]*(A - B)*(c - d)^2*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*f)) - (4*(5*A*(3*c - d)*d + B*(6*c^2 - 7*c*d + 7*d^2))*Cos[e + f*x])/(15*f*Sqrt[a + a*Sin[e + f*x]]) - (2*d*(4*B*c + 5*A*d - B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(15*a*f) - (2*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(5*f*Sqrt[a + a*Sin[e + f*x]])","A",6,6,37,0.1622,1,"{2983, 2968, 3023, 2751, 2649, 206}"
309,1,130,0,0.2699644,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{2 (3 A d+3 B c-2 B d) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{\sqrt{2} (A-B) (c-d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B d \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 a f}","-\frac{2 (3 A d+3 B c-2 B d) \cos (e+f x)}{3 f \sqrt{a \sin (e+f x)+a}}-\frac{\sqrt{2} (A-B) (c-d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B d \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{3 a f}",1,"-((Sqrt[2]*(A - B)*(c - d)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*f)) - (2*(3*B*c + 3*A*d - 2*B*d)*Cos[e + f*x])/(3*f*Sqrt[a + a*Sin[e + f*x]]) - (2*B*d*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(3*a*f)","A",5,5,35,0.1429,1,"{2968, 3023, 2751, 2649, 206}"
310,1,79,0,0.0703238,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x)}{f \sqrt{a \sin (e+f x)+a}}","-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f}-\frac{2 B \cos (e+f x)}{f \sqrt{a \sin (e+f x)+a}}",1,"-((Sqrt[2]*(A - B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*f)) - (2*B*Cos[e + f*x])/(f*Sqrt[a + a*Sin[e + f*x]])","A",3,3,25,0.1200,1,"{2751, 2649, 206}"
311,1,136,0,0.2827827,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])),x]","-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}-\frac{2 (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d) \sqrt{c+d}}","-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)}-\frac{2 (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d) \sqrt{c+d}}",1,"-((Sqrt[2]*(A - B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*(c - d)*f)) - (2*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*(c - d)*Sqrt[d]*Sqrt[c + d]*f)","A",5,5,37,0.1351,1,"{2985, 2649, 206, 2773, 208}"
312,1,207,0,0.6169851,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^2),x]","-\frac{(B c-A d) \cos (e+f x)}{f \left(c^2-d^2\right) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{\left(A d (3 c+d)-B \left(c^2+c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d)^2 (c+d)^{3/2}}-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)^2}","-\frac{(B c-A d) \cos (e+f x)}{f \left(c^2-d^2\right) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{\left(A d (3 c+d)-B \left(c^2+c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} \sqrt{d} f (c-d)^2 (c+d)^{3/2}}-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)^2}",1,"-((Sqrt[2]*(A - B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*(c - d)^2*f)) + ((A*d*(3*c + d) - B*(c^2 + c*d + 2*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*(c - d)^2*Sqrt[d]*(c + d)^(3/2)*f) - ((B*c - A*d)*Cos[e + f*x])/((c^2 - d^2)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",6,6,37,0.1622,1,"{2984, 2985, 2649, 206, 2773, 208}"
313,1,309,0,1.054172,"\int \frac{A+B \sin (e+f x)}{\sqrt{a+a \sin (e+f x)} (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/(Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^3),x]","\frac{\left(A d (7 c+d)-B \left(3 c^2+c d+4 d^2\right)\right) \cos (e+f x)}{4 f \left(c^2-d^2\right)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{(B c-A d) \cos (e+f x)}{2 f \left(c^2-d^2\right) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}+\frac{\left(A d \left(15 c^2+10 c d+7 d^2\right)-B \left(6 c^2 d+3 c^3+19 c d^2+4 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 \sqrt{a} \sqrt{d} f (c-d)^3 (c+d)^{5/2}}-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)^3}","\frac{\left(A d (7 c+d)-B \left(3 c^2+c d+4 d^2\right)\right) \cos (e+f x)}{4 f \left(c^2-d^2\right)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{(B c-A d) \cos (e+f x)}{2 f \left(c^2-d^2\right) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}+\frac{\left(A d \left(15 c^2+10 c d+7 d^2\right)-B \left(6 c^2 d+3 c^3+19 c d^2+4 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 \sqrt{a} \sqrt{d} f (c-d)^3 (c+d)^{5/2}}-\frac{\sqrt{2} (A-B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{\sqrt{a} f (c-d)^3}",1,"-((Sqrt[2]*(A - B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(Sqrt[a]*(c - d)^3*f)) + ((A*d*(15*c^2 + 10*c*d + 7*d^2) - B*(3*c^3 + 6*c^2*d + 19*c*d^2 + 4*d^3))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*Sqrt[a]*(c - d)^3*Sqrt[d]*(c + d)^(5/2)*f) - ((B*c - A*d)*Cos[e + f*x])/(2*(c^2 - d^2)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^2) + ((A*d*(7*c + d) - B*(3*c^2 + c*d + 4*d^2))*Cos[e + f*x])/(4*(c^2 - d^2)^2*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",7,6,37,0.1622,1,"{2984, 2985, 2649, 206, 2773, 208}"
314,1,283,0,0.9997278,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^(3/2),x]","\frac{d^2 (15 A c-35 A d-51 B c+39 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{30 a^2 f}-\frac{(c-d)^2 (A (c+11 d)+3 B (c-5 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{d \left(15 A c^2-120 A c d+65 A d^2-99 B c^2+168 B c d-93 B d^2\right) \cos (e+f x)}{15 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{2 f (a \sin (e+f x)+a)^{3/2}}+\frac{d (5 A-9 B) \cos (e+f x) (c+d \sin (e+f x))^2}{10 a f \sqrt{a \sin (e+f x)+a}}","\frac{d^2 (15 A c-35 A d-51 B c+39 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{30 a^2 f}-\frac{(c-d)^2 (A (c+11 d)+3 B (c-5 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{d \left(15 A c^2-120 A c d+65 A d^2-99 B c^2+168 B c d-93 B d^2\right) \cos (e+f x)}{15 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{2 f (a \sin (e+f x)+a)^{3/2}}+\frac{d (5 A-9 B) \cos (e+f x) (c+d \sin (e+f x))^2}{10 a f \sqrt{a \sin (e+f x)+a}}",1,"-((c - d)^2*(3*B*(c - 5*d) + A*(c + 11*d))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*f) + (d*(15*A*c^2 - 99*B*c^2 - 120*A*c*d + 168*B*c*d + 65*A*d^2 - 93*B*d^2)*Cos[e + f*x])/(15*a*f*Sqrt[a + a*Sin[e + f*x]]) + (d^2*(15*A*c - 51*B*c - 35*A*d + 39*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(30*a^2*f) + ((5*A - 9*B)*d*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(10*a*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",7,7,37,0.1892,1,"{2977, 2983, 2968, 3023, 2751, 2649, 206}"
315,1,203,0,0.5753661,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{(c-d) (A c+7 A d+3 B c-11 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{d^2 (3 A-7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{6 a^2 f}+\frac{d (3 A c-9 A d-15 B c+13 B d) \cos (e+f x)}{3 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{2 f (a \sin (e+f x)+a)^{3/2}}","-\frac{(c-d) (A c+7 A d+3 B c-11 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}+\frac{d^2 (3 A-7 B) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{6 a^2 f}+\frac{d (3 A c-9 A d-15 B c+13 B d) \cos (e+f x)}{3 a f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{2 f (a \sin (e+f x)+a)^{3/2}}",1,"-((c - d)*(A*c + 3*B*c + 7*A*d - 11*B*d)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*f) + (d*(3*A*c - 15*B*c - 9*A*d + 13*B*d)*Cos[e + f*x])/(3*a*f*Sqrt[a + a*Sin[e + f*x]]) + ((3*A - 7*B)*d^2*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(6*a^2*f) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",6,6,37,0.1622,1,"{2977, 2968, 3023, 2751, 2649, 206}"
316,1,133,0,0.2790381,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{(A c+3 A d+3 B c-7 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(A-B) (c-d) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2}}-\frac{2 B d \cos (e+f x)}{a f \sqrt{a \sin (e+f x)+a}}","-\frac{(A c+3 A d+3 B c-7 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(A-B) (c-d) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2}}-\frac{2 B d \cos (e+f x)}{a f \sqrt{a \sin (e+f x)+a}}",1,"-((A*c + 3*B*c + 3*A*d - 7*B*d)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*f) - ((A - B)*(c - d)*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(3/2)) - (2*B*d*Cos[e + f*x])/(a*f*Sqrt[a + a*Sin[e + f*x]])","A",5,5,35,0.1429,1,"{2968, 3019, 2751, 2649, 206}"
317,1,87,0,0.0777001,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/(a + a*Sin[e + f*x])^(3/2),x]","-\frac{(A+3 B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2}}","-\frac{(A+3 B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f}-\frac{(A-B) \cos (e+f x)}{2 f (a \sin (e+f x)+a)^{3/2}}",1,"-((A + 3*B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*f) - ((A - B)*Cos[e + f*x])/(2*f*(a + a*Sin[e + f*x])^(3/2))","A",3,3,25,0.1200,1,"{2750, 2649, 206}"
318,1,187,0,0.5898679,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])),x]","-\frac{(A (c-5 d)+B (3 c+d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^2}+\frac{2 \sqrt{d} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{3/2} f (c-d)^2 \sqrt{c+d}}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2}}","-\frac{(A (c-5 d)+B (3 c+d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^2}+\frac{2 \sqrt{d} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{3/2} f (c-d)^2 \sqrt{c+d}}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2}}",1,"-((A*(c - 5*d) + B*(3*c + d))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*(c - d)^2*f) + (2*Sqrt[d]*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(a^(3/2)*(c - d)^2*Sqrt[c + d]*f) - ((A - B)*Cos[e + f*x])/(2*(c - d)*f*(a + a*Sin[e + f*x])^(3/2))","A",6,6,37,0.1622,1,"{2978, 2985, 2649, 206, 2773, 208}"
319,1,292,0,1.0175037,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^2),x]","-\frac{\sqrt{d} \left(A d (5 c+3 d)-B \left(3 c^2+3 c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{3/2} f (c-d)^3 (c+d)^{3/2}}-\frac{(A c-9 A d+3 B c+5 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^3}+\frac{d (B (3 c+d)-A (c+3 d)) \cos (e+f x)}{2 a f (c-d)^2 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))}","-\frac{\sqrt{d} \left(A d (5 c+3 d)-B \left(3 c^2+3 c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{3/2} f (c-d)^3 (c+d)^{3/2}}-\frac{(A c-9 A d+3 B c+5 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^3}+\frac{d (B (3 c+d)-A (c+3 d)) \cos (e+f x)}{2 a f (c-d)^2 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))}",1,"-((A*c + 3*B*c - 9*A*d + 5*B*d)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*(c - d)^3*f) - (Sqrt[d]*(A*d*(5*c + 3*d) - B*(3*c^2 + 3*c*d + 2*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(a^(3/2)*(c - d)^3*(c + d)^(3/2)*f) - ((A - B)*Cos[e + f*x])/(2*(c - d)*f*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])) + (d*(B*(3*c + d) - A*(c + 3*d))*Cos[e + f*x])/(2*a*(c - d)^2*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",7,7,37,0.1892,1,"{2978, 2984, 2985, 2649, 206, 2773, 208}"
320,1,402,0,1.5620899,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{3/2} (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^3),x]","-\frac{\sqrt{d} \left(A d \left(35 c^2+42 c d+19 d^2\right)-3 B \left(10 c^2 d+5 c^3+13 c d^2+4 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 a^{3/2} f (c-d)^4 (c+d)^{5/2}}-\frac{(A (c-13 d)+3 B (c+3 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^4}+\frac{d \left(3 B \left(3 c^2+3 c d+2 d^2\right)-A \left(2 c^2+15 c d+7 d^2\right)\right) \cos (e+f x)}{4 a f (c-d)^3 (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{d (B (2 c+d)-A (c+2 d)) \cos (e+f x)}{2 a f (c-d)^2 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^2}","-\frac{\sqrt{d} \left(A d \left(35 c^2+42 c d+19 d^2\right)-3 B \left(10 c^2 d+5 c^3+13 c d^2+4 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 a^{3/2} f (c-d)^4 (c+d)^{5/2}}-\frac{(A (c-13 d)+3 B (c+3 d)) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{2 \sqrt{2} a^{3/2} f (c-d)^4}+\frac{d \left(3 B \left(3 c^2+3 c d+2 d^2\right)-A \left(2 c^2+15 c d+7 d^2\right)\right) \cos (e+f x)}{4 a f (c-d)^3 (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{d (B (2 c+d)-A (c+2 d)) \cos (e+f x)}{2 a f (c-d)^2 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{2 f (c-d) (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^2}",1,"-((A*(c - 13*d) + 3*B*(c + 3*d))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(2*Sqrt[2]*a^(3/2)*(c - d)^4*f) - (Sqrt[d]*(A*d*(35*c^2 + 42*c*d + 19*d^2) - 3*B*(5*c^3 + 10*c^2*d + 13*c*d^2 + 4*d^3))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*a^(3/2)*(c - d)^4*(c + d)^(5/2)*f) - ((A - B)*Cos[e + f*x])/(2*(c - d)*f*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^2) + (d*(B*(2*c + d) - A*(c + 2*d))*Cos[e + f*x])/(2*a*(c - d)^2*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^2) + (d*(3*B*(3*c^2 + 3*c*d + 2*d^2) - A*(2*c^2 + 15*c*d + 7*d^2))*Cos[e + f*x])/(4*a*(c - d)^3*(c + d)^2*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",8,7,37,0.1892,1,"{2978, 2984, 2985, 2649, 206, 2773, 208}"
321,1,308,0,1.0591858,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^3}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^3)/(a + a*Sin[e + f*x])^(5/2),x]","\frac{d \left(A \left(9 c^2+36 c d-93 d^2\right)+B \left(15 c^2-228 c d+197 d^2\right)\right) \cos (e+f x)}{24 a^2 f \sqrt{a \sin (e+f x)+a}}-\frac{(c-d) \left(3 A \left(c^2+6 c d+25 d^2\right)+B \left(5 c^2+62 c d-163 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}+\frac{d^2 (9 A c+39 A d+15 B c-95 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{48 a^3 f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{(3 A c+9 A d+5 B c-17 B d) \cos (e+f x) (c+d \sin (e+f x))^2}{16 a f (a \sin (e+f x)+a)^{3/2}}","\frac{d \left(A \left(9 c^2+36 c d-93 d^2\right)+B \left(15 c^2-228 c d+197 d^2\right)\right) \cos (e+f x)}{24 a^2 f \sqrt{a \sin (e+f x)+a}}-\frac{(c-d) \left(3 A \left(c^2+6 c d+25 d^2\right)+B \left(5 c^2+62 c d-163 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}+\frac{d^2 (9 A c+39 A d+15 B c-95 B d) \cos (e+f x) \sqrt{a \sin (e+f x)+a}}{48 a^3 f}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^3}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{(3 A c+9 A d+5 B c-17 B d) \cos (e+f x) (c+d \sin (e+f x))^2}{16 a f (a \sin (e+f x)+a)^{3/2}}",1,"-((c - d)*(B*(5*c^2 + 62*c*d - 163*d^2) + 3*A*(c^2 + 6*c*d + 25*d^2))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*f) + (d*(A*(9*c^2 + 36*c*d - 93*d^2) + B*(15*c^2 - 228*c*d + 197*d^2))*Cos[e + f*x])/(24*a^2*f*Sqrt[a + a*Sin[e + f*x]]) + (d^2*(9*A*c + 15*B*c + 39*A*d - 95*B*d)*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]])/(48*a^3*f) - ((3*A*c + 5*B*c + 9*A*d - 17*B*d)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(16*a*f*(a + a*Sin[e + f*x])^(3/2)) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^3)/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",7,6,37,0.1622,1,"{2977, 2968, 3023, 2751, 2649, 206}"
322,1,219,0,0.5786709,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^2}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2)/(a + a*Sin[e + f*x])^(5/2),x]","-\frac{\left(A \left(3 c^2+10 c d+19 d^2\right)+B \left(5 c^2+38 c d-75 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}+\frac{d^2 (A-9 B) \cos (e+f x)}{4 a^2 f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{(c-d) (3 A c+5 A d+5 B c-13 B d) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}","-\frac{\left(A \left(3 c^2+10 c d+19 d^2\right)+B \left(5 c^2+38 c d-75 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}+\frac{d^2 (A-9 B) \cos (e+f x)}{4 a^2 f \sqrt{a \sin (e+f x)+a}}-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^2}{4 f (a \sin (e+f x)+a)^{5/2}}-\frac{(c-d) (3 A c+5 A d+5 B c-13 B d) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}",1,"-((B*(5*c^2 + 38*c*d - 75*d^2) + A*(3*c^2 + 10*c*d + 19*d^2))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*f) - ((c - d)*(3*A*c + 5*B*c + 5*A*d - 13*B*d)*Cos[e + f*x])/(16*a*f*(a + a*Sin[e + f*x])^(3/2)) + ((A - 9*B)*d^2*Cos[e + f*x])/(4*a^2*f*Sqrt[a + a*Sin[e + f*x]]) - ((A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^2)/(4*f*(a + a*Sin[e + f*x])^(5/2))","A",6,6,37,0.1622,1,"{2977, 2968, 3019, 2751, 2649, 206}"
323,1,151,0,0.2874604,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]))/(a + a*Sin[e + f*x])^(5/2),x]","-\frac{(3 A c+5 A d+5 B c+19 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}-\frac{(3 A c+5 A d+5 B c-13 B d) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) (c-d) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2}}","-\frac{(3 A c+5 A d+5 B c+19 B d) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}-\frac{(3 A c+5 A d+5 B c-13 B d) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) (c-d) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2}}",1,"-((3*A*c + 5*B*c + 5*A*d + 19*B*d)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*f) - ((A - B)*(c - d)*Cos[e + f*x])/(4*f*(a + a*Sin[e + f*x])^(5/2)) - ((3*A*c + 5*B*c + 5*A*d - 13*B*d)*Cos[e + f*x])/(16*a*f*(a + a*Sin[e + f*x])^(3/2))","A",5,5,35,0.1429,1,"{2968, 3019, 2750, 2649, 206}"
324,1,126,0,0.1072496,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/(a + a*Sin[e + f*x])^(5/2),x]","-\frac{(3 A+5 B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}-\frac{(3 A+5 B) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2}}","-\frac{(3 A+5 B) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f}-\frac{(3 A+5 B) \cos (e+f x)}{16 a f (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (a \sin (e+f x)+a)^{5/2}}",1,"-((3*A + 5*B)*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*f) - ((A - B)*Cos[e + f*x])/(4*f*(a + a*Sin[e + f*x])^(5/2)) - ((3*A + 5*B)*Cos[e + f*x])/(16*a*f*(a + a*Sin[e + f*x])^(3/2))","A",4,4,25,0.1600,1,"{2750, 2650, 2649, 206}"
325,1,261,0,0.9840719,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} (c+d \sin (e+f x))} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*(c + d*Sin[e + f*x])),x]","-\frac{\left(A \left(3 c^2-14 c d+43 d^2\right)+B \left(5 c^2-34 c d-3 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^3}-\frac{2 d^{3/2} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{5/2} f (c-d)^3 \sqrt{c+d}}-\frac{(3 A c-11 A d+5 B c+3 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2}}","-\frac{\left(A \left(3 c^2-14 c d+43 d^2\right)+B \left(5 c^2-34 c d-3 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^3}-\frac{2 d^{3/2} (B c-A d) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{5/2} f (c-d)^3 \sqrt{c+d}}-\frac{(3 A c-11 A d+5 B c+3 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2}}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2}}",1,"-((B*(5*c^2 - 34*c*d - 3*d^2) + A*(3*c^2 - 14*c*d + 43*d^2))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*(c - d)^3*f) - (2*d^(3/2)*(B*c - A*d)*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(a^(5/2)*(c - d)^3*Sqrt[c + d]*f) - ((A - B)*Cos[e + f*x])/(4*(c - d)*f*(a + a*Sin[e + f*x])^(5/2)) - ((3*A*c + 5*B*c - 11*A*d + 3*B*d)*Cos[e + f*x])/(16*a*(c - d)^2*f*(a + a*Sin[e + f*x])^(3/2))","A",7,6,37,0.1622,1,"{2978, 2985, 2649, 206, 2773, 208}"
326,1,395,0,1.5357121,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} (c+d \sin (e+f x))^2} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*(c + d*Sin[e + f*x])^2),x]","-\frac{d \left(A \left(3 c^2-16 c d-35 d^2\right)+B \left(5 c^2+32 c d+11 d^2\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^3 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{d^{3/2} \left(A d (7 c+5 d)-B \left(5 c^2+5 c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{5/2} f (c-d)^4 (c+d)^{3/2}}-\frac{\left(A \left(3 c^2-22 c d+115 d^2\right)+B \left(5 c^2-58 c d-43 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^4}-\frac{(3 A c-15 A d+5 B c+7 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2} (c+d \sin (e+f x))}","-\frac{d \left(A \left(3 c^2-16 c d-35 d^2\right)+B \left(5 c^2+32 c d+11 d^2\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^3 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}+\frac{d^{3/2} \left(A d (7 c+5 d)-B \left(5 c^2+5 c d+2 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{a^{5/2} f (c-d)^4 (c+d)^{3/2}}-\frac{\left(A \left(3 c^2-22 c d+115 d^2\right)+B \left(5 c^2-58 c d-43 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^4}-\frac{(3 A c-15 A d+5 B c+7 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2} (c+d \sin (e+f x))}",1,"-((B*(5*c^2 - 58*c*d - 43*d^2) + A*(3*c^2 - 22*c*d + 115*d^2))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*(c - d)^4*f) + (d^(3/2)*(A*d*(7*c + 5*d) - B*(5*c^2 + 5*c*d + 2*d^2))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(a^(5/2)*(c - d)^4*(c + d)^(3/2)*f) - ((A - B)*Cos[e + f*x])/(4*(c - d)*f*(a + a*Sin[e + f*x])^(5/2)*(c + d*Sin[e + f*x])) - ((3*A*c + 5*B*c - 15*A*d + 7*B*d)*Cos[e + f*x])/(16*a*(c - d)^2*f*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])) - (d*(A*(3*c^2 - 16*c*d - 35*d^2) + B*(5*c^2 + 32*c*d + 11*d^2))*Cos[e + f*x])/(16*a^2*(c - d)^3*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",8,7,37,0.1892,1,"{2978, 2984, 2985, 2649, 206, 2773, 208}"
327,1,519,0,2.1522762,"\int \frac{A+B \sin (e+f x)}{(a+a \sin (e+f x))^{5/2} (c+d \sin (e+f x))^3} \, dx","Int[(A + B*Sin[e + f*x])/((a + a*Sin[e + f*x])^(5/2)*(c + d*Sin[e + f*x])^3),x]","-\frac{d \left(3 A \left(-7 c^2 d+c^3-37 c d^2-21 d^3\right)+B \left(73 c^2 d+5 c^3+79 c d^2+35 d^3\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^4 (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{d \left(A \left(3 c^2-20 c d-31 d^2\right)+B \left(5 c^2+28 c d+15 d^2\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^3 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}+\frac{d^{3/2} \left(3 A d \left(21 c^2+30 c d+13 d^2\right)-B \left(70 c^2 d+35 c^3+67 c d^2+20 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 a^{5/2} f (c-d)^5 (c+d)^{5/2}}-\frac{\left(3 A \left(c^2-10 c d+73 d^2\right)+B \left(5 c^2-82 c d-115 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^5}-\frac{(3 A c-19 A d+5 B c+11 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2} (c+d \sin (e+f x))^2}","-\frac{d \left(3 A \left(-7 c^2 d+c^3-37 c d^2-21 d^3\right)+B \left(73 c^2 d+5 c^3+79 c d^2+35 d^3\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^4 (c+d)^2 \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))}-\frac{d \left(A \left(3 c^2-20 c d-31 d^2\right)+B \left(5 c^2+28 c d+15 d^2\right)\right) \cos (e+f x)}{16 a^2 f (c-d)^3 (c+d) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^2}+\frac{d^{3/2} \left(3 A d \left(21 c^2+30 c d+13 d^2\right)-B \left(70 c^2 d+35 c^3+67 c d^2+20 d^3\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d} \cos (e+f x)}{\sqrt{c+d} \sqrt{a \sin (e+f x)+a}}\right)}{4 a^{5/2} f (c-d)^5 (c+d)^{5/2}}-\frac{\left(3 A \left(c^2-10 c d+73 d^2\right)+B \left(5 c^2-82 c d-115 d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt{a} \cos (e+f x)}{\sqrt{2} \sqrt{a \sin (e+f x)+a}}\right)}{16 \sqrt{2} a^{5/2} f (c-d)^5}-\frac{(3 A c-19 A d+5 B c+11 B d) \cos (e+f x)}{16 a f (c-d)^2 (a \sin (e+f x)+a)^{3/2} (c+d \sin (e+f x))^2}-\frac{(A-B) \cos (e+f x)}{4 f (c-d) (a \sin (e+f x)+a)^{5/2} (c+d \sin (e+f x))^2}",1,"-((B*(5*c^2 - 82*c*d - 115*d^2) + 3*A*(c^2 - 10*c*d + 73*d^2))*ArcTanh[(Sqrt[a]*Cos[e + f*x])/(Sqrt[2]*Sqrt[a + a*Sin[e + f*x]])])/(16*Sqrt[2]*a^(5/2)*(c - d)^5*f) + (d^(3/2)*(3*A*d*(21*c^2 + 30*c*d + 13*d^2) - B*(35*c^3 + 70*c^2*d + 67*c*d^2 + 20*d^3))*ArcTanh[(Sqrt[a]*Sqrt[d]*Cos[e + f*x])/(Sqrt[c + d]*Sqrt[a + a*Sin[e + f*x]])])/(4*a^(5/2)*(c - d)^5*(c + d)^(5/2)*f) - ((A - B)*Cos[e + f*x])/(4*(c - d)*f*(a + a*Sin[e + f*x])^(5/2)*(c + d*Sin[e + f*x])^2) - ((3*A*c + 5*B*c - 19*A*d + 11*B*d)*Cos[e + f*x])/(16*a*(c - d)^2*f*(a + a*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^2) - (d*(A*(3*c^2 - 20*c*d - 31*d^2) + B*(5*c^2 + 28*c*d + 15*d^2))*Cos[e + f*x])/(16*a^2*(c - d)^3*(c + d)*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^2) - (d*(3*A*(c^3 - 7*c^2*d - 37*c*d^2 - 21*d^3) + B*(5*c^3 + 73*c^2*d + 79*c*d^2 + 35*d^3))*Cos[e + f*x])/(16*a^2*(c - d)^4*(c + d)^2*f*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x]))","A",9,7,37,0.1892,1,"{2978, 2984, 2985, 2649, 206, 2773, 208}"
328,1,221,0,0.3379473,"\int (a+a \sin (e+f x))^2 (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[(a + a*Sin[e + f*x])^2*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","-\frac{4 \sqrt{2} a^2 (A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{8 \sqrt{2} a^2 B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{5}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}","-\frac{4 \sqrt{2} a^2 (A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{8 \sqrt{2} a^2 B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{5}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}",1,"(-8*Sqrt[2]*a^2*B*AppellF1[1/2, -5/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n) - (4*Sqrt[2]*a^2*(A - B)*AppellF1[1/2, -3/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",7,4,35,0.1143,1,"{2987, 2784, 139, 138}"
329,1,217,0,0.3004437,"\int (a+a \sin (e+f x)) (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[(a + a*Sin[e + f*x])*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","-\frac{2 \sqrt{2} a (A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} a B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}","-\frac{2 \sqrt{2} a (A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}-\frac{4 \sqrt{2} a B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};-\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{\sin (e+f x)+1}}",1,"(-4*Sqrt[2]*a*B*AppellF1[1/2, -3/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n) - (2*Sqrt[2]*a*(A - B)*AppellF1[1/2, -1/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",8,6,33,0.1818,1,"{2968, 3017, 2755, 139, 138, 2784}"
330,1,221,0,0.304206,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^n}{a+a \sin (e+f x)} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n)/(a + a*Sin[e + f*x]),x]","-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{\sqrt{2} a f \sqrt{\sin (e+f x)+1}}-\frac{\sqrt{2} B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{a f \sqrt{\sin (e+f x)+1}}","-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{\sqrt{2} a f \sqrt{\sin (e+f x)+1}}-\frac{\sqrt{2} B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{1}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{a f \sqrt{\sin (e+f x)+1}}",1,"-((Sqrt[2]*B*AppellF1[1/2, 1/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(a*f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)) - ((A - B)*AppellF1[1/2, 3/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(Sqrt[2]*a*f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",7,5,35,0.1429,1,"{2987, 2784, 139, 138, 2665}"
331,1,223,0,0.341262,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^n}{(a+a \sin (e+f x))^2} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n)/(a + a*Sin[e + f*x])^2,x]","-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{5}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{2 \sqrt{2} a^2 f \sqrt{\sin (e+f x)+1}}-\frac{B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{\sqrt{2} a^2 f \sqrt{\sin (e+f x)+1}}","-\frac{(A-B) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{5}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{2 \sqrt{2} a^2 f \sqrt{\sin (e+f x)+1}}-\frac{B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} F_1\left(\frac{1}{2};\frac{3}{2},-n;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x)),\frac{d (1-\sin (e+f x))}{c+d}\right)}{\sqrt{2} a^2 f \sqrt{\sin (e+f x)+1}}",1,"-((B*AppellF1[1/2, 3/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(Sqrt[2]*a^2*f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)) - ((A - B)*AppellF1[1/2, 5/2, -n, 3/2, (1 - Sin[e + f*x])/2, (d*(1 - Sin[e + f*x]))/(c + d)]*Cos[e + f*x]*(c + d*Sin[e + f*x])^n)/(2*Sqrt[2]*a^2*f*Sqrt[1 + Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",7,4,35,0.1143,1,"{2987, 2784, 139, 138}"
332,1,427,0,0.914932,"\int (a+a \sin (e+f x))^{3/2} (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[(a + a*Sin[e + f*x])^(3/2)*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","\frac{2 a^2 (A-B) (c-d (4 n+5)) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A-B) \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 B \left(3 c^2-2 c d (4 n+7)+d^2 \left(16 n^2+56 n+43\right)\right) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d^2 f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 B (3 c-d (4 n+11)) \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d^2 f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^{n+1}}{d f (2 n+5)}","\frac{2 a^2 (A-B) (c-d (4 n+5)) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 (A-B) \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a^2 B \left(3 c^2-2 c d (4 n+7)+d^2 \left(16 n^2+56 n+43\right)\right) \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d^2 f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}+\frac{2 a^2 B (3 c-d (4 n+11)) \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d^2 f (2 n+3) (2 n+5) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) \sqrt{a \sin (e+f x)+a} (c+d \sin (e+f x))^{n+1}}{d f (2 n+5)}",1,"(-2*a^2*(A - B)*Cos[e + f*x]*(c + d*Sin[e + f*x])^(1 + n))/(d*f*(3 + 2*n)*Sqrt[a + a*Sin[e + f*x]]) + (2*a^2*B*(3*c - d*(11 + 4*n))*Cos[e + f*x]*(c + d*Sin[e + f*x])^(1 + n))/(d^2*f*(3 + 2*n)*(5 + 2*n)*Sqrt[a + a*Sin[e + f*x]]) - (2*a*B*Cos[e + f*x]*Sqrt[a + a*Sin[e + f*x]]*(c + d*Sin[e + f*x])^(1 + n))/(d*f*(5 + 2*n)) + (2*a^2*(A - B)*(c - d*(5 + 4*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, (d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^n)/(d*f*(3 + 2*n)*Sqrt[a + a*Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n) - (2*a^2*B*(3*c^2 - 2*c*d*(7 + 4*n) + d^2*(43 + 56*n + 16*n^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, (d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^n)/(d^2*f*(3 + 2*n)*(5 + 2*n)*Sqrt[a + a*Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",11,7,37,0.1892,1,"{2987, 2763, 21, 2776, 70, 69, 2981}"
333,1,167,0,0.2648298,"\int \sqrt{a+a \sin (e+f x)} (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[Sqrt[a + a*Sin[e + f*x]]*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","\frac{2 a \cos (e+f x) (-A d (2 n+3)+B c-2 B d (n+1)) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}","-\frac{2 a \cos (e+f x) (A d (2 n+3)-B (c-2 d (n+1))) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}-\frac{2 a B \cos (e+f x) (c+d \sin (e+f x))^{n+1}}{d f (2 n+3) \sqrt{a \sin (e+f x)+a}}",1,"(-2*a*B*Cos[e + f*x]*(c + d*Sin[e + f*x])^(1 + n))/(d*f*(3 + 2*n)*Sqrt[a + a*Sin[e + f*x]]) + (2*a*(B*c - 2*B*d*(1 + n) - A*d*(3 + 2*n))*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, (d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^n)/(d*f*(3 + 2*n)*Sqrt[a + a*Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",4,4,37,0.1081,1,"{2981, 2776, 70, 69}"
334,1,220,0,0.4027288,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^n}{\sqrt{a+a \sin (e+f x)}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n)/Sqrt[a + a*Sin[e + f*x]],x]","-\frac{(A-B) \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},1;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{f (n+1) (c-d) (1-\sin (e+f x)) \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{a \sin (e+f x)+a}}","-\frac{(A-B) \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},1;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{f (n+1) (c-d) (1-\sin (e+f x)) \sqrt{a \sin (e+f x)+a}}-\frac{2 B \cos (e+f x) (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c+d}\right)^{-n} \, _2F_1\left(\frac{1}{2},-n;\frac{3}{2};\frac{d (1-\sin (e+f x))}{c+d}\right)}{f \sqrt{a \sin (e+f x)+a}}",1,"-(((A - B)*AppellF1[1 + n, 1/2, 1, 2 + n, (c + d*Sin[e + f*x])/(c + d), (c + d*Sin[e + f*x])/(c - d)]*Cos[e + f*x]*Sqrt[(d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^(1 + n))/((c - d)*f*(1 + n)*(1 - Sin[e + f*x])*Sqrt[a + a*Sin[e + f*x]])) - (2*B*Cos[e + f*x]*Hypergeometric2F1[1/2, -n, 3/2, (d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^n)/(f*Sqrt[a + a*Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c + d))^n)","A",7,7,37,0.1892,1,"{2987, 2788, 137, 136, 2776, 70, 69}"
335,1,269,0,0.4698832,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^n}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n)/(a + a*Sin[e + f*x])^(3/2),x]","\frac{d (A-B) \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},2;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{f (n+1) (c-d)^2 (a-a \sin (e+f x)) \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},1;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{a f (n+1) (c-d) (1-\sin (e+f x)) \sqrt{a \sin (e+f x)+a}}","\frac{d (A-B) \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},2;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{f (n+1) (c-d)^2 (a-a \sin (e+f x)) \sqrt{a \sin (e+f x)+a}}-\frac{B \cos (e+f x) \sqrt{\frac{d (1-\sin (e+f x))}{c+d}} (c+d \sin (e+f x))^{n+1} F_1\left(n+1;\frac{1}{2},1;n+2;\frac{c+d \sin (e+f x)}{c+d},\frac{c+d \sin (e+f x)}{c-d}\right)}{a f (n+1) (c-d) (1-\sin (e+f x)) \sqrt{a \sin (e+f x)+a}}",1,"-((B*AppellF1[1 + n, 1/2, 1, 2 + n, (c + d*Sin[e + f*x])/(c + d), (c + d*Sin[e + f*x])/(c - d)]*Cos[e + f*x]*Sqrt[(d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^(1 + n))/(a*(c - d)*f*(1 + n)*(1 - Sin[e + f*x])*Sqrt[a + a*Sin[e + f*x]])) + ((A - B)*d*AppellF1[1 + n, 1/2, 2, 2 + n, (c + d*Sin[e + f*x])/(c + d), (c + d*Sin[e + f*x])/(c - d)]*Cos[e + f*x]*Sqrt[(d*(1 - Sin[e + f*x]))/(c + d)]*(c + d*Sin[e + f*x])^(1 + n))/((c - d)^2*f*(1 + n)*(a - a*Sin[e + f*x])*Sqrt[a + a*Sin[e + f*x]])","A",7,4,37,0.1081,1,"{2987, 2788, 137, 136}"
336,1,351,0,0.9867976,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^2 \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^2,x]","-\frac{2^{m+\frac{1}{2}} \cos (e+f x) \left(A (m+3) \left(c^2 \left(m^2+3 m+2\right)+2 c d m (m+2)+d^2 \left(m^2+m+1\right)\right)+B \left(c^2 m \left(m^2+5 m+6\right)+2 c d \left(m^3+4 m^2+4 m+3\right)+d^2 m \left(m^2+3 m+5\right)\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2) (m+3)}+\frac{\cos (e+f x) \left(d (A d (m+3)+B (2 c+d m))-2 (m+2) \left(A c d (m+3)+B \left(c^2+c d m+d^2\right)\right)\right) (a \sin (e+f x)+a)^m}{f (m+1) (m+2) (m+3)}-\frac{d \cos (e+f x) (A d (m+3)+B (2 c+d m)) (a \sin (e+f x)+a)^{m+1}}{a f (m+2) (m+3)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^2}{f (m+3)}","-\frac{2^{m+\frac{1}{2}} \cos (e+f x) \left(A (m+3) \left(c^2 \left(m^2+3 m+2\right)+2 c d m (m+2)+d^2 \left(m^2+m+1\right)\right)+B \left(c^2 m \left(m^2+5 m+6\right)+2 c d \left(m^3+4 m^2+4 m+3\right)+d^2 m \left(m^2+3 m+5\right)\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2) (m+3)}+\frac{\cos (e+f x) \left(d (A d (m+3)+B (2 c+d m))-2 (m+2) \left(A c d (m+3)+B \left(c^2+c d m+d^2\right)\right)\right) (a \sin (e+f x)+a)^m}{f (m+1) (m+2) (m+3)}-\frac{d \cos (e+f x) (A d (m+3)+B (2 c+d m)) (a \sin (e+f x)+a)^{m+1}}{a f (m+2) (m+3)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^2}{f (m+3)}",1,"((d*(A*d*(3 + m) + B*(2*c + d*m)) - 2*(2 + m)*(A*c*d*(3 + m) + B*(c^2 + d^2 + c*d*m)))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)*(3 + m)) - (2^(1/2 + m)*(A*(3 + m)*(2*c*d*m*(2 + m) + d^2*(1 + m + m^2) + c^2*(2 + 3*m + m^2)) + B*(d^2*m*(5 + 3*m + m^2) + c^2*m*(6 + 5*m + m^2) + 2*c*d*(3 + 4*m + 4*m^2 + m^3)))*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)*(3 + m)) - (d*(A*d*(3 + m) + B*(2*c + d*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*f*(2 + m)*(3 + m)) - (B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^2)/(f*(3 + m))","A",6,6,35,0.1714,1,"{2983, 2968, 3023, 2751, 2652, 2651}"
337,1,198,0,0.3617583,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x]),x]","-\frac{2^{m+\frac{1}{2}} \cos (e+f x) \left(A (m+2) (c m+c+d m)+B c m (m+2)+B d \left(m^2+m+1\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{\cos (e+f x) (B d-(m+2) (A d+B c)) (a \sin (e+f x)+a)^m}{f (m+1) (m+2)}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (m+2)}","-\frac{2^{m+\frac{1}{2}} \cos (e+f x) \left(A (m+2) (c m+c+d m)+B \left(c m (m+2)+d \left(m^2+m+1\right)\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1) (m+2)}+\frac{\cos (e+f x) (B d-(m+2) (A d+B c)) (a \sin (e+f x)+a)^m}{f (m+1) (m+2)}-\frac{B d \cos (e+f x) (a \sin (e+f x)+a)^{m+1}}{a f (m+2)}",1,"((B*d - (B*c + A*d)*(2 + m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)) - (2^(1/2 + m)*(B*c*m*(2 + m) + A*(2 + m)*(c + c*m + d*m) + B*d*(1 + m + m^2))*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m)*(2 + m)) - (B*d*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m))/(a*f*(2 + m))","A",5,5,33,0.1515,1,"{2968, 3023, 2751, 2652, 2651}"
338,1,117,0,0.0809615,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]),x]","-\frac{2^{m+\frac{1}{2}} (A m+A+B m) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1)}","-\frac{2^{m+\frac{1}{2}} (A m+A+B m) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{f (m+1)}-\frac{B \cos (e+f x) (a \sin (e+f x)+a)^m}{f (m+1)}",1,"-((B*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(f*(1 + m))) - (2^(1/2 + m)*(A + A*m + B*m)*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(f*(1 + m))","A",3,3,23,0.1304,1,"{2751, 2652, 2651}"
339,1,191,0,0.2915159,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{c+d \sin (e+f x)} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x]),x]","-\frac{\sqrt{2} (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{d f (2 m+1) (c-d) \sqrt{1-\sin (e+f x)}}-\frac{B 2^{m+\frac{1}{2}} \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f}","-\frac{\sqrt{2} (B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{d f (2 m+1) (c-d) \sqrt{1-\sin (e+f x)}}-\frac{B 2^{m+\frac{1}{2}} \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f}",1,"-((Sqrt[2]*(B*c - A*d)*AppellF1[1/2 + m, 1/2, 1, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/((c - d)*d*f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]])) - (2^(1/2 + m)*B*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(d*f)","A",6,6,35,0.1714,1,"{2986, 2652, 2651, 2788, 137, 136}"
340,1,293,0,0.6181402,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","\frac{\sqrt{2} \cos (e+f x) \left(A d (c (1-m)-d m)-B \left(c^2 (-m)-c d m+d^2\right)\right) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{d f (2 m+1) (c-d)^2 (c+d) \sqrt{1-\sin (e+f x)}}+\frac{2^{m+\frac{1}{2}} m (B c-A d) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f \left(c^2-d^2\right)}-\frac{(B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m}{f \left(c^2-d^2\right) (c+d \sin (e+f x))}","\frac{\sqrt{2} \cos (e+f x) \left(A d (c (1-m)-d m)-B \left(c^2 (-m)-c d m+d^2\right)\right) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{d f (2 m+1) (c-d)^2 (c+d) \sqrt{1-\sin (e+f x)}}+\frac{2^{m+\frac{1}{2}} m (B c-A d) \cos (e+f x) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f \left(c^2-d^2\right)}-\frac{(B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m}{f \left(c^2-d^2\right) (c+d \sin (e+f x))}",1,"(Sqrt[2]*(A*d*(c*(1 - m) - d*m) - B*(d^2 - c^2*m - c*d*m))*AppellF1[1/2 + m, 1/2, 1, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/((c - d)^2*d*(c + d)*f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]) + (2^(1/2 + m)*(B*c - A*d)*m*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(d*(c^2 - d^2)*f) - ((B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/((c^2 - d^2)*f*(c + d*Sin[e + f*x]))","A",7,7,35,0.2000,1,"{2984, 2986, 2652, 2651, 2788, 137, 136}"
341,1,467,0,1.3469609,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c+d \sin (e+f x))^3} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^3,x]","\frac{\cos (e+f x) \left(B \left(2 c^2 d (1-m) m+c^3 (1-m) m-c d^2 \left(m^2-3 m+3\right)+2 d^3 m\right)-A d \left(c^2 \left(-\left(m^2-3 m+2\right)\right)+2 c d (2-m) m-d^2 \left(m^2-m+1\right)\right)\right) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{\sqrt{2} d f (2 m+1) (c-d)^3 (c+d)^2 \sqrt{1-\sin (e+f x)}}-\frac{2^{m-\frac{1}{2}} m \cos (e+f x) \left(A d (c (3-m)-d m)-B \left(c^2 (1-m)-c d m+2 d^2\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f \left(c^2-d^2\right)^2}+\frac{\cos (e+f x) \left(A d (c (3-m)-d m)-B \left(c^2 (1-m)-c d m+2 d^2\right)\right) (a \sin (e+f x)+a)^m}{2 f \left(c^2-d^2\right)^2 (c+d \sin (e+f x))}-\frac{(B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m}{2 f \left(c^2-d^2\right) (c+d \sin (e+f x))^2}","\frac{\cos (e+f x) \left(B \left(2 c^2 d (1-m) m+c^3 (1-m) m-c d^2 \left(m^2-3 m+3\right)+2 d^3 m\right)-A d \left(c^2 \left(-\left(m^2-3 m+2\right)\right)+2 c d (2-m) m-d^2 \left(m^2-m+1\right)\right)\right) (a \sin (e+f x)+a)^m F_1\left(m+\frac{1}{2};\frac{1}{2},1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{\sqrt{2} d f (2 m+1) (c-d)^3 (c+d)^2 \sqrt{1-\sin (e+f x)}}-\frac{2^{m-\frac{1}{2}} m \cos (e+f x) \left(A d (c (3-m)-d m)-B \left(c^2 (1-m)-c d m+2 d^2\right)\right) (\sin (e+f x)+1)^{-m-\frac{1}{2}} (a \sin (e+f x)+a)^m \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{1}{2} (1-\sin (e+f x))\right)}{d f \left(c^2-d^2\right)^2}+\frac{\cos (e+f x) \left(A d (c (3-m)-d m)-B \left(c^2 (1-m)-c d m+2 d^2\right)\right) (a \sin (e+f x)+a)^m}{2 f \left(c^2-d^2\right)^2 (c+d \sin (e+f x))}-\frac{(B c-A d) \cos (e+f x) (a \sin (e+f x)+a)^m}{2 f \left(c^2-d^2\right) (c+d \sin (e+f x))^2}",1,"((B*(2*d^3*m + c^3*(1 - m)*m + 2*c^2*d*(1 - m)*m - c*d^2*(3 - 3*m + m^2)) - A*d*(2*c*d*(2 - m)*m - c^2*(2 - 3*m + m^2) - d^2*(1 - m + m^2)))*AppellF1[1/2 + m, 1/2, 1, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(Sqrt[2]*(c - d)^3*d*(c + d)^2*f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]) - (2^(-1/2 + m)*m*(A*d*(c*(3 - m) - d*m) - B*(2*d^2 + c^2*(1 - m) - c*d*m))*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (1 - Sin[e + f*x])/2]*(1 + Sin[e + f*x])^(-1/2 - m)*(a + a*Sin[e + f*x])^m)/(d*(c^2 - d^2)^2*f) - ((B*c - A*d)*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(2*(c^2 - d^2)*f*(c + d*Sin[e + f*x])^2) + ((A*d*(c*(3 - m) - d*m) - B*(2*d^2 + c^2*(1 - m) - c*d*m))*Cos[e + f*x]*(a + a*Sin[e + f*x])^m)/(2*(c^2 - d^2)^2*f*(c + d*Sin[e + f*x]))","A",8,7,35,0.2000,1,"{2984, 2986, 2652, 2651, 2788, 137, 136}"
342,1,284,0,0.6279227,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^{3/2} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^(3/2),x]","\frac{\sqrt{2} (A-B) (c-d) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{1}{2};\frac{1}{2},-\frac{3}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}+\frac{\sqrt{2} B (c-d) \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{3}{2};\frac{1}{2},-\frac{3}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}","\frac{\sqrt{2} (A-B) (c-d) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{1}{2};\frac{1}{2},-\frac{3}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}+\frac{\sqrt{2} B (c-d) \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{3}{2};\frac{1}{2},-\frac{3}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}",1,"(Sqrt[2]*(A - B)*(c - d)*AppellF1[1/2 + m, 1/2, -3/2, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[c + d*Sin[e + f*x]])/(f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[(c + d*Sin[e + f*x])/(c - d)]) + (Sqrt[2]*B*(c - d)*AppellF1[3/2 + m, 1/2, -3/2, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*Sqrt[c + d*Sin[e + f*x]])/(a*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[(c + d*Sin[e + f*x])/(c - d)])","A",9,5,37,0.1351,1,"{2987, 2788, 140, 139, 138}"
343,1,274,0,0.554948,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) \sqrt{c+d \sin (e+f x)} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*Sqrt[c + d*Sin[e + f*x]],x]","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{1}{2};\frac{1}{2},-\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{3}{2};\frac{1}{2},-\frac{1}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{1}{2};\frac{1}{2},-\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{c+d \sin (e+f x)} F_1\left(m+\frac{3}{2};\frac{1}{2},-\frac{1}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{\frac{c+d \sin (e+f x)}{c-d}}}",1,"(Sqrt[2]*(A - B)*AppellF1[1/2 + m, 1/2, -1/2, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[c + d*Sin[e + f*x]])/(f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[(c + d*Sin[e + f*x])/(c - d)]) + (Sqrt[2]*B*AppellF1[3/2 + m, 1/2, -1/2, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*Sqrt[c + d*Sin[e + f*x]])/(a*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[(c + d*Sin[e + f*x])/(c - d)])","A",9,5,37,0.1351,1,"{2987, 2788, 140, 139, 138}"
344,1,274,0,0.5435004,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{\sqrt{c+d \sin (e+f x)}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/Sqrt[c + d*Sin[e + f*x]],x]","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{1}{2};\frac{1}{2},\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{3}{2};\frac{1}{2},\frac{1}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{1}{2};\frac{1}{2},\frac{1}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{3}{2};\frac{1}{2},\frac{1}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}",1,"(Sqrt[2]*(A - B)*AppellF1[1/2 + m, 1/2, 1/2, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[(c + d*Sin[e + f*x])/(c - d)])/(f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[c + d*Sin[e + f*x]]) + (Sqrt[2]*B*AppellF1[3/2 + m, 1/2, 1/2, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*Sqrt[(c + d*Sin[e + f*x])/(c - d)])/(a*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[c + d*Sin[e + f*x]])","A",9,5,37,0.1351,1,"{2987, 2788, 140, 139, 138}"
345,1,288,0,0.5454621,"\int \frac{(a+a \sin (e+f x))^m (A+B \sin (e+f x))}{(c+d \sin (e+f x))^{3/2}} \, dx","Int[((a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^(3/2),x]","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{1}{2};\frac{1}{2},\frac{3}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) (c-d) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{3}{2};\frac{1}{2},\frac{3}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) (c-d) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{1}{2};\frac{1}{2},\frac{3}{2};m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) (c-d) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} \sqrt{\frac{c+d \sin (e+f x)}{c-d}} F_1\left(m+\frac{3}{2};\frac{1}{2},\frac{3}{2};m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) (c-d) \sqrt{1-\sin (e+f x)} \sqrt{c+d \sin (e+f x)}}",1,"(Sqrt[2]*(A - B)*AppellF1[1/2 + m, 1/2, 3/2, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*Sqrt[(c + d*Sin[e + f*x])/(c - d)])/((c - d)*f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[c + d*Sin[e + f*x]]) + (Sqrt[2]*B*AppellF1[3/2 + m, 1/2, 3/2, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*Sqrt[(c + d*Sin[e + f*x])/(c - d)])/(a*(c - d)*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*Sqrt[c + d*Sin[e + f*x]])","A",9,5,37,0.1351,1,"{2987, 2788, 140, 139, 138}"
346,1,270,0,0.4295053,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{1}{2};\frac{1}{2},-n;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{3}{2};\frac{1}{2},-n;m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)}}","\frac{\sqrt{2} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{1}{2};\frac{1}{2},-n;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) \sqrt{1-\sin (e+f x)}}+\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{3}{2};\frac{1}{2},-n;m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) \sqrt{1-\sin (e+f x)}}",1,"(Sqrt[2]*(A - B)*AppellF1[1/2 + m, 1/2, -n, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^n)/(f*(1 + 2*m)*Sqrt[1 - Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c - d))^n) + (Sqrt[2]*B*AppellF1[3/2 + m, 1/2, -n, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*(c + d*Sin[e + f*x])^n)/(a*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*((c + d*Sin[e + f*x])/(c - d))^n)","A",9,5,35,0.1429,1,"{2987, 2788, 140, 139, 138}"
347,1,277,0,0.482663,"\int (a+a \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^{-1-m} \, dx","Int[(a + a*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^(-1 - m),x]","\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^{-m} \left(\frac{c+d \sin (e+f x)}{c-d}\right)^m F_1\left(m+\frac{3}{2};\frac{1}{2},m+1;m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) (c-d) \sqrt{1-\sin (e+f x)}}-\frac{a 2^{m+\frac{1}{2}} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{m-1} \left(\frac{(c+d) (\sin (e+f x)+1)}{c+d \sin (e+f x)}\right)^{\frac{1}{2}-m} (c+d \sin (e+f x))^{-m} \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{(c-d) (1-\sin (e+f x))}{2 (c+d \sin (e+f x))}\right)}{f (c+d)}","\frac{\sqrt{2} B \cos (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^{-m} \left(\frac{c+d \sin (e+f x)}{c-d}\right)^m F_1\left(m+\frac{3}{2};\frac{1}{2},m+1;m+\frac{5}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{a f (2 m+3) (c-d) \sqrt{1-\sin (e+f x)}}-\frac{a 2^{m+\frac{1}{2}} (A-B) \cos (e+f x) (a \sin (e+f x)+a)^{m-1} \left(\frac{(c+d) (\sin (e+f x)+1)}{c+d \sin (e+f x)}\right)^{\frac{1}{2}-m} (c+d \sin (e+f x))^{-m} \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{(c-d) (1-\sin (e+f x))}{2 (c+d \sin (e+f x))}\right)}{f (c+d)}",1,"-((2^(1/2 + m)*a*(A - B)*Cos[e + f*x]*Hypergeometric2F1[1/2, 1/2 - m, 3/2, ((c - d)*(1 - Sin[e + f*x]))/(2*(c + d*Sin[e + f*x]))]*(a + a*Sin[e + f*x])^(-1 + m)*(((c + d)*(1 + Sin[e + f*x]))/(c + d*Sin[e + f*x]))^(1/2 - m))/((c + d)*f*(c + d*Sin[e + f*x])^m)) + (Sqrt[2]*B*AppellF1[3/2 + m, 1/2, 1 + m, 5/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Cos[e + f*x]*(a + a*Sin[e + f*x])^(1 + m)*((c + d*Sin[e + f*x])/(c - d))^m)/(a*(c - d)*f*(3 + 2*m)*Sqrt[1 - Sin[e + f*x]]*(c + d*Sin[e + f*x])^m)","A",7,6,39,0.1538,1,"{2987, 2788, 132, 140, 139, 138}"
348,1,132,0,0.2003233,"\int (a-a \sin (e+f x)) (a+a \sin (e+f x))^m (c+d \sin (e+f x))^n \, dx","Int[(a - a*Sin[e + f*x])*(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^n,x]","\frac{2 \sqrt{2} \sqrt{1-\sin (e+f x)} \sec (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{1}{2};-\frac{1}{2},-n;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1)}","\frac{2 \sqrt{2} \sqrt{1-\sin (e+f x)} \sec (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^n \left(\frac{c+d \sin (e+f x)}{c-d}\right)^{-n} F_1\left(m+\frac{1}{2};-\frac{1}{2},-n;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1)}",1,"(2*Sqrt[2]*AppellF1[1/2 + m, -1/2, -n, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Sec[e + f*x]*Sqrt[1 - Sin[e + f*x]]*(a + a*Sin[e + f*x])^(1 + m)*(c + d*Sin[e + f*x])^n)/(f*(1 + 2*m)*((c + d*Sin[e + f*x])/(c - d))^n)","A",4,4,36,0.1111,1,"{3008, 140, 139, 138}"
349,1,139,0,0.2301916,"\int (a-a \sin (e+f x)) (a+a \sin (e+f x))^m (c+d \sin (e+f x))^{-1-m} \, dx","Int[(a - a*Sin[e + f*x])*(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^(-1 - m),x]","\frac{2 \sqrt{2} \sqrt{1-\sin (e+f x)} \sec (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^{-m} \left(\frac{c+d \sin (e+f x)}{c-d}\right)^m F_1\left(m+\frac{1}{2};-\frac{1}{2},m+1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) (c-d)}","\frac{2 \sqrt{2} \sqrt{1-\sin (e+f x)} \sec (e+f x) (a \sin (e+f x)+a)^{m+1} (c+d \sin (e+f x))^{-m} \left(\frac{c+d \sin (e+f x)}{c-d}\right)^m F_1\left(m+\frac{1}{2};-\frac{1}{2},m+1;m+\frac{3}{2};\frac{1}{2} (\sin (e+f x)+1),-\frac{d (\sin (e+f x)+1)}{c-d}\right)}{f (2 m+1) (c-d)}",1,"(2*Sqrt[2]*AppellF1[1/2 + m, -1/2, 1 + m, 3/2 + m, (1 + Sin[e + f*x])/2, -((d*(1 + Sin[e + f*x]))/(c - d))]*Sec[e + f*x]*Sqrt[1 - Sin[e + f*x]]*(a + a*Sin[e + f*x])^(1 + m)*((c + d*Sin[e + f*x])/(c - d))^m)/((c - d)*f*(1 + 2*m)*(c + d*Sin[e + f*x])^m)","A",4,4,40,0.1000,1,"{3008, 140, 139, 138}"
350,1,39,0,0.1717875,"\int (a+a \sin (e+f x))^m (c+d \sin (e+f x))^{-2-m} (d-(c-d) m+(c+(c-d) m) \sin (e+f x)) \, dx","Int[(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^(-2 - m)*(d - (c - d)*m + (c + (c - d)*m)*Sin[e + f*x]),x]","-\frac{\cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^{-m-1}}{f}","-\frac{\cos (e+f x) (a \sin (e+f x)+a)^m (c+d \sin (e+f x))^{-m-1}}{f}",1,"-((Cos[e + f*x]*(a + a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^(-1 - m))/f)","A",1,1,55,0.01818,1,"{2974}"
351,1,40,0,0.171891,"\int (a-a \sin (e+f x))^m (c+d \sin (e+f x))^{-2-m} (d+(c+d) m+(c+(c+d) m) \sin (e+f x)) \, dx","Int[(a - a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^(-2 - m)*(d + (c + d)*m + (c + (c + d)*m)*Sin[e + f*x]),x]","-\frac{\cos (e+f x) (a-a \sin (e+f x))^m (c+d \sin (e+f x))^{-m-1}}{f}","-\frac{\cos (e+f x) (a-a \sin (e+f x))^m (c+d \sin (e+f x))^{-m-1}}{f}",1,"-((Cos[e + f*x]*(a - a*Sin[e + f*x])^m*(c + d*Sin[e + f*x])^(-1 - m))/f)","A",1,1,51,0.01961,1,"{2974}"
352,1,199,0,0.5802759,"\int \frac{(a+b \sin (e+f x))^2 (A+B \sin (e+f x))}{(c+d \sin (e+f x))^2} \, dx","Int[((a + b*Sin[e + f*x])^2*(A + B*Sin[e + f*x]))/(c + d*Sin[e + f*x])^2,x]","-\frac{2 (b c-a d) \left(a d^2 (A c-B d)-b \left(-A c^2 d+2 A d^3+2 B c^3-3 B c d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f \left(c^2-d^2\right)^{3/2}}-\frac{(b c-a d)^2 (B c-A d) \cos (e+f x)}{d^2 f \left(c^2-d^2\right) (c+d \sin (e+f x))}-\frac{b x (-2 a B d-A b d+2 b B c)}{d^3}-\frac{b^2 B \cos (e+f x)}{d^2 f}","-\frac{2 (b c-a d) \left(a d^2 (A c-B d)-b \left(-A c^2 d+2 A d^3+2 B c^3-3 B c d^2\right)\right) \tan ^{-1}\left(\frac{c \tan \left(\frac{1}{2} (e+f x)\right)+d}{\sqrt{c^2-d^2}}\right)}{d^3 f \left(c^2-d^2\right)^{3/2}}-\frac{(b c-a d)^2 (B c-A d) \cos (e+f x)}{d^2 f \left(c^2-d^2\right) (c+d \sin (e+f x))}-\frac{b x (-2 a B d-A b d+2 b B c)}{d^3}-\frac{b^2 B \cos (e+f x)}{d^2 f}",1,"-((b*(2*b*B*c - A*b*d - 2*a*B*d)*x)/d^3) - (2*(b*c - a*d)*(a*d^2*(A*c - B*d) - b*(2*B*c^3 - A*c^2*d - 3*B*c*d^2 + 2*A*d^3))*ArcTan[(d + c*Tan[(e + f*x)/2])/Sqrt[c^2 - d^2]])/(d^3*(c^2 - d^2)^(3/2)*f) - (b^2*B*Cos[e + f*x])/(d^2*f) - ((b*c - a*d)^2*(B*c - A*d)*Cos[e + f*x])/(d^2*(c^2 - d^2)*f*(c + d*Sin[e + f*x]))","A",6,6,35,0.1714,1,"{2988, 3023, 2735, 2660, 618, 204}"
353,1,840,0,3.1559234,"\int \frac{(A+B \sin (e+f x)) (c+d \sin (e+f x))^{3/2}}{(a+b \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^(3/2))/(a + b*Sin[e + f*x])^(3/2),x]","\frac{2 (A b-a B) (b c-a d) \sqrt{c+d \sin (e+f x)} \cos (e+f x)}{b \left(a^2-b^2\right) f \sqrt{a+b \sin (e+f x)}}-\frac{\left(2 A b (b c-a d)-B \left(-3 d a^2+2 b c a+b^2 d\right)\right) \sqrt{c+d \sin (e+f x)} \cos (e+f x)}{b \left(a^2-b^2\right) f \sqrt{a+b \sin (e+f x)}}+\frac{(c-d) \sqrt{c+d} \left(3 B d a^2-2 b B c a-2 A b d a+2 A b^2 c-b^2 B d\right) E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right) \sec (e+f x) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} (a+b \sin (e+f x))}{(a-b) b^2 \sqrt{a+b} (b c-a d) f}+\frac{\sqrt{c+d} (3 b B c+2 A b d-3 a B d) \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right) \sec (e+f x) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} (a+b \sin (e+f x))}{b^3 \sqrt{a+b} f}+\frac{\sqrt{a+b} \left(2 A b (b (c-2 d)+a d)-B \left(3 d a^2-6 b d a+b^2 (2 c+d)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{(a-b) b^3 \sqrt{c+d} f}","\frac{2 (A b-a B) (b c-a d) \sqrt{c+d \sin (e+f x)} \cos (e+f x)}{b \left(a^2-b^2\right) f \sqrt{a+b \sin (e+f x)}}-\frac{\left(2 A b (b c-a d)-B \left(-3 d a^2+2 b c a+b^2 d\right)\right) \sqrt{c+d \sin (e+f x)} \cos (e+f x)}{b \left(a^2-b^2\right) f \sqrt{a+b \sin (e+f x)}}+\frac{(c-d) \sqrt{c+d} \left(3 B d a^2-2 b B c a-2 A b d a+2 A b^2 c-b^2 B d\right) E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right) \sec (e+f x) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} (a+b \sin (e+f x))}{(a-b) b^2 \sqrt{a+b} (b c-a d) f}+\frac{\sqrt{c+d} (3 b B c+2 A b d-3 a B d) \Pi \left(\frac{b (c+d)}{(a+b) d};\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right) \sec (e+f x) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} (a+b \sin (e+f x))}{b^3 \sqrt{a+b} f}+\frac{\sqrt{a+b} \left(2 A b (b (c-2 d)+a d)-B \left(3 d a^2-6 b d a+b^2 (2 c+d)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{(a-b) b^3 \sqrt{c+d} f}",1,"((c - d)*Sqrt[c + d]*(2*A*b^2*c - 2*a*b*B*c - 2*a*A*b*d + 3*a^2*B*d - b^2*B*d)*EllipticE[ArcSin[(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])/(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])], ((a - b)*(c + d))/((a + b)*(c - d))]*Sec[e + f*x]*Sqrt[-(((b*c - a*d)*(1 - Sin[e + f*x]))/((c + d)*(a + b*Sin[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sin[e + f*x]))/((c - d)*(a + b*Sin[e + f*x]))]*(a + b*Sin[e + f*x]))/((a - b)*b^2*Sqrt[a + b]*(b*c - a*d)*f) + (Sqrt[c + d]*(3*b*B*c + 2*A*b*d - 3*a*B*d)*EllipticPi[(b*(c + d))/((a + b)*d), ArcSin[(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])/(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])], ((a - b)*(c + d))/((a + b)*(c - d))]*Sec[e + f*x]*Sqrt[-(((b*c - a*d)*(1 - Sin[e + f*x]))/((c + d)*(a + b*Sin[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sin[e + f*x]))/((c - d)*(a + b*Sin[e + f*x]))]*(a + b*Sin[e + f*x]))/(b^3*Sqrt[a + b]*f) + (2*(A*b - a*B)*(b*c - a*d)*Cos[e + f*x]*Sqrt[c + d*Sin[e + f*x]])/(b*(a^2 - b^2)*f*Sqrt[a + b*Sin[e + f*x]]) - ((2*A*b*(b*c - a*d) - B*(2*a*b*c - 3*a^2*d + b^2*d))*Cos[e + f*x]*Sqrt[c + d*Sin[e + f*x]])/(b*(a^2 - b^2)*f*Sqrt[a + b*Sin[e + f*x]]) + (Sqrt[a + b]*(2*A*b*(b*(c - 2*d) + a*d) - B*(3*a^2*d - 6*a*b*d + b^2*(2*c + d)))*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/((a - b)*b^3*Sqrt[c + d]*f)","A",7,7,39,0.1795,1,"{2989, 3061, 3053, 2811, 2998, 2818, 2996}"
354,1,630,0,0.8863124,"\int \frac{(A+B \sin (e+f x)) \sqrt{c+d \sin (e+f x)}}{(a+b \sin (e+f x))^{3/2}} \, dx","Int[((A + B*Sin[e + f*x])*Sqrt[c + d*Sin[e + f*x]])/(a + b*Sin[e + f*x])^(3/2),x]","\frac{2 \sqrt{a+b} (c-d) (A b-a B) \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b f (a-b) \sqrt{c+d} (b c-a d)}+\frac{2 (c-d) \sqrt{c+d} (A b-a B) \sec (e+f x) (a+b \sin (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{b f (a-b) \sqrt{a+b} (b c-a d)}+\frac{2 B \sqrt{a+b} \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} \Pi \left(\frac{(a+b) d}{b (c+d)};\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b^2 f \sqrt{c+d}}","\frac{2 \sqrt{a+b} (c-d) (A b-a B) \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b f (a-b) \sqrt{c+d} (b c-a d)}+\frac{2 (c-d) \sqrt{c+d} (A b-a B) \sec (e+f x) (a+b \sin (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{b f (a-b) \sqrt{a+b} (b c-a d)}+\frac{2 B \sqrt{a+b} \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} \Pi \left(\frac{(a+b) d}{b (c+d)};\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{b^2 f \sqrt{c+d}}",1,"(2*(A*b - a*B)*(c - d)*Sqrt[c + d]*EllipticE[ArcSin[(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])/(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])], ((a - b)*(c + d))/((a + b)*(c - d))]*Sec[e + f*x]*Sqrt[-(((b*c - a*d)*(1 - Sin[e + f*x]))/((c + d)*(a + b*Sin[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sin[e + f*x]))/((c - d)*(a + b*Sin[e + f*x]))]*(a + b*Sin[e + f*x]))/((a - b)*b*Sqrt[a + b]*(b*c - a*d)*f) + (2*Sqrt[a + b]*(A*b - a*B)*(c - d)*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/((a - b)*b*Sqrt[c + d]*(b*c - a*d)*f) + (2*Sqrt[a + b]*B*EllipticPi[((a + b)*d)/(b*(c + d)), ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/(b^2*Sqrt[c + d]*f)","A",5,5,39,0.1282,1,"{2992, 2811, 2795, 2818, 2996}"
355,1,417,0,0.5374945,"\int \frac{A+B \sin (e+f x)}{(a+b \sin (e+f x))^{3/2} \sqrt{c+d \sin (e+f x)}} \, dx","Int[(A + B*Sin[e + f*x])/((a + b*Sin[e + f*x])^(3/2)*Sqrt[c + d*Sin[e + f*x]]),x]","\frac{2 \sqrt{a+b} (A-B) \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f (a-b) \sqrt{c+d} (b c-a d)}+\frac{2 (c-d) \sqrt{c+d} (A b-a B) \sec (e+f x) (a+b \sin (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{f (a-b) \sqrt{a+b} (b c-a d)^2}","\frac{2 \sqrt{a+b} (A-B) \sec (e+f x) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f (a-b) \sqrt{c+d} (b c-a d)}+\frac{2 (c-d) \sqrt{c+d} (A b-a B) \sec (e+f x) (a+b \sin (e+f x)) \sqrt{-\frac{(b c-a d) (1-\sin (e+f x))}{(c+d) (a+b \sin (e+f x))}} \sqrt{\frac{(b c-a d) (\sin (e+f x)+1)}{(c-d) (a+b \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}\right)|\frac{(a-b) (c+d)}{(a+b) (c-d)}\right)}{f (a-b) \sqrt{a+b} (b c-a d)^2}",1,"(2*(A*b - a*B)*(c - d)*Sqrt[c + d]*EllipticE[ArcSin[(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])/(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])], ((a - b)*(c + d))/((a + b)*(c - d))]*Sec[e + f*x]*Sqrt[-(((b*c - a*d)*(1 - Sin[e + f*x]))/((c + d)*(a + b*Sin[e + f*x])))]*Sqrt[((b*c - a*d)*(1 + Sin[e + f*x]))/((c - d)*(a + b*Sin[e + f*x]))]*(a + b*Sin[e + f*x]))/((a - b)*Sqrt[a + b]*(b*c - a*d)^2*f) + (2*Sqrt[a + b]*(A - B)*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/((a - b)*Sqrt[c + d]*(b*c - a*d)*f)","A",3,3,39,0.07692,1,"{2998, 2818, 2996}"
356,1,544,0,1.3767464,"\int \frac{A+B \sin (e+f x)}{(a+b \sin (e+f x))^{3/2} (c+d \sin (e+f x))^{3/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + b*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^(3/2)),x]","\frac{2 \sec (e+f x) \left(a^2 (-A) d^2+a^2 B c d+a b B \left(c^2-d^2\right)-A b^2 \left(c^2-2 d^2\right)-b^2 B c d\right) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{a+b} (c-d) \sqrt{c+d} (b c-a d)^3}+\frac{2 b (A b-a B) \cos (e+f x)}{f \left(a^2-b^2\right) (b c-a d) \sqrt{a+b \sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{2 \sec (e+f x) (-a A d+a B d+A b c-2 A b d+b B c) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{a+b} (c-d) \sqrt{c+d} (b c-a d)^2}","-\frac{2 \sec (e+f x) \left(A \left(a^2 d^2+b^2 \left(c^2-2 d^2\right)\right)-B \left(a^2 c d+a b \left(c^2-d^2\right)-b^2 c d\right)\right) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} E\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{a+b} (c-d) \sqrt{c+d} (b c-a d)^3}+\frac{2 b (A b-a B) \cos (e+f x)}{f \left(a^2-b^2\right) (b c-a d) \sqrt{a+b \sin (e+f x)} \sqrt{c+d \sin (e+f x)}}+\frac{2 \sec (e+f x) (-a A d+a B d+A b c-2 A b d+b B c) (c+d \sin (e+f x)) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right)}{f \sqrt{a+b} (c-d) \sqrt{c+d} (b c-a d)^2}",1,"(2*b*(A*b - a*B)*Cos[e + f*x])/((a^2 - b^2)*(b*c - a*d)*f*Sqrt[a + b*Sin[e + f*x]]*Sqrt[c + d*Sin[e + f*x]]) + (2*(a^2*B*c*d - b^2*B*c*d - a^2*A*d^2 - A*b^2*(c^2 - 2*d^2) + a*b*B*(c^2 - d^2))*EllipticE[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/(Sqrt[a + b]*(c - d)*Sqrt[c + d]*(b*c - a*d)^3*f) + (2*(A*b*c + b*B*c - a*A*d - 2*A*b*d + a*B*d)*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/(Sqrt[a + b]*(c - d)*Sqrt[c + d]*(b*c - a*d)^2*f)","A",4,4,39,0.1026,1,"{3000, 2998, 2818, 2996}"
357,1,858,0,2.6162764,"\int \frac{A+B \sin (e+f x)}{(a+b \sin (e+f x))^{3/2} (c+d \sin (e+f x))^{5/2}} \, dx","Int[(A + B*Sin[e + f*x])/((a + b*Sin[e + f*x])^(3/2)*(c + d*Sin[e + f*x])^(5/2)),x]","\frac{2 d \left(A \left(\left(3 c^2-4 d^2\right) b^2+a^2 d^2\right)-B \left(c d a^2+3 b \left(c^2-d^2\right) a-b^2 c d\right)\right) \sqrt{a+b \sin (e+f x)} \cos (e+f x)}{3 \left(a^2-b^2\right) (b c-a d)^2 \left(c^2-d^2\right) f (c+d \sin (e+f x))^{3/2}}+\frac{2 b (A b-a B) \cos (e+f x)}{\left(a^2-b^2\right) (b c-a d) f \sqrt{a+b \sin (e+f x)} (c+d \sin (e+f x))^{3/2}}+\frac{2 \left(B \left(-d^2 \left(c^2+3 d^2\right) a^3+2 b c d \left(3 c^2-d^2\right) a^2+b^2 \left(3 c^4-5 d^2 c^2+6 d^4\right) a-2 b^3 c d \left(3 c^2-d^2\right)\right)+A \left(-\left(3 c^4-15 d^2 c^2+8 d^4\right) b^3-4 a c d^3 b^2-a^2 d^2 \left(9 c^2-5 d^2\right) b+4 a^3 c d^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{3 \sqrt{a+b} (c-d)^2 (c+d)^{3/2} (b c-a d)^4 f}-\frac{2 \left(B \left(-c \left(3 c^2+3 d c-2 d^2\right) b^2-6 a d \left(c^2-d^2\right) b+a^2 d^2 (c+3 d)\right)-A \left(\left(3 c^3-9 d c^2-6 d^2 c+8 d^3\right) b^2-6 a d \left(c^2-d^2\right) b+a^2 d^2 (3 c+d)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{3 \sqrt{a+b} (c-d)^2 (c+d)^{3/2} (b c-a d)^3 f}","\frac{2 d \left(A \left(\left(3 c^2-4 d^2\right) b^2+a^2 d^2\right)-B \left(c d a^2+3 b \left(c^2-d^2\right) a-b^2 c d\right)\right) \sqrt{a+b \sin (e+f x)} \cos (e+f x)}{3 \left(a^2-b^2\right) (b c-a d)^2 \left(c^2-d^2\right) f (c+d \sin (e+f x))^{3/2}}+\frac{2 b (A b-a B) \cos (e+f x)}{\left(a^2-b^2\right) (b c-a d) f \sqrt{a+b \sin (e+f x)} (c+d \sin (e+f x))^{3/2}}+\frac{2 \left(B \left(-d^2 \left(c^2+3 d^2\right) a^3+2 b c d \left(3 c^2-d^2\right) a^2+b^2 \left(3 c^4-5 d^2 c^2+6 d^4\right) a-2 b^3 c d \left(3 c^2-d^2\right)\right)+A \left(-\left(3 c^4-15 d^2 c^2+8 d^4\right) b^3-4 a c d^3 b^2-a^2 d^2 \left(9 c^2-5 d^2\right) b+4 a^3 c d^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{3 \sqrt{a+b} (c-d)^2 (c+d)^{3/2} (b c-a d)^4 f}-\frac{2 \left(B \left(-c \left(3 c^2+3 d c-2 d^2\right) b^2-6 a d \left(c^2-d^2\right) b+a^2 d^2 (c+3 d)\right)-A \left(\left(3 c^3-9 d c^2-6 d^2 c+8 d^3\right) b^2-6 a d \left(c^2-d^2\right) b+a^2 d^2 (3 c+d)\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c+d} \sqrt{a+b \sin (e+f x)}}{\sqrt{a+b} \sqrt{c+d \sin (e+f x)}}\right)|\frac{(a+b) (c-d)}{(a-b) (c+d)}\right) \sec (e+f x) \sqrt{\frac{(b c-a d) (1-\sin (e+f x))}{(a+b) (c+d \sin (e+f x))}} \sqrt{-\frac{(b c-a d) (\sin (e+f x)+1)}{(a-b) (c+d \sin (e+f x))}} (c+d \sin (e+f x))}{3 \sqrt{a+b} (c-d)^2 (c+d)^{3/2} (b c-a d)^3 f}",1,"(2*b*(A*b - a*B)*Cos[e + f*x])/((a^2 - b^2)*(b*c - a*d)*f*Sqrt[a + b*Sin[e + f*x]]*(c + d*Sin[e + f*x])^(3/2)) + (2*d*(A*(a^2*d^2 + b^2*(3*c^2 - 4*d^2)) - B*(a^2*c*d - b^2*c*d + 3*a*b*(c^2 - d^2)))*Cos[e + f*x]*Sqrt[a + b*Sin[e + f*x]])/(3*(a^2 - b^2)*(b*c - a*d)^2*(c^2 - d^2)*f*(c + d*Sin[e + f*x])^(3/2)) + (2*(B*(2*a^2*b*c*d*(3*c^2 - d^2) - 2*b^3*c*d*(3*c^2 - d^2) - a^3*d^2*(c^2 + 3*d^2) + a*b^2*(3*c^4 - 5*c^2*d^2 + 6*d^4)) + A*(4*a^3*c*d^3 - 4*a*b^2*c*d^3 - a^2*b*d^2*(9*c^2 - 5*d^2) - b^3*(3*c^4 - 15*c^2*d^2 + 8*d^4)))*EllipticE[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/(3*Sqrt[a + b]*(c - d)^2*(c + d)^(3/2)*(b*c - a*d)^4*f) - (2*(B*(a^2*d^2*(c + 3*d) - b^2*c*(3*c^2 + 3*c*d - 2*d^2) - 6*a*b*d*(c^2 - d^2)) - A*(a^2*d^2*(3*c + d) - 6*a*b*d*(c^2 - d^2) + b^2*(3*c^3 - 9*c^2*d - 6*c*d^2 + 8*d^3)))*EllipticF[ArcSin[(Sqrt[c + d]*Sqrt[a + b*Sin[e + f*x]])/(Sqrt[a + b]*Sqrt[c + d*Sin[e + f*x]])], ((a + b)*(c - d))/((a - b)*(c + d))]*Sec[e + f*x]*Sqrt[((b*c - a*d)*(1 - Sin[e + f*x]))/((a + b)*(c + d*Sin[e + f*x]))]*Sqrt[-(((b*c - a*d)*(1 + Sin[e + f*x]))/((a - b)*(c + d*Sin[e + f*x])))]*(c + d*Sin[e + f*x]))/(3*Sqrt[a + b]*(c - d)^2*(c + d)^(3/2)*(b*c - a*d)^3*f)","A",5,5,39,0.1282,1,"{3000, 3055, 2998, 2818, 2996}"
358,0,0,0,0.0929466,"\int (a+b \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","Int[(a + b*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n,x]","\int (a+b \sin (e+f x))^m (A+B \sin (e+f x)) (c+d \sin (e+f x))^n \, dx","\text{Int}\left((A+B \sin (e+f x)) (a+b \sin (e+f x))^m (c+d \sin (e+f x))^n,x\right)",0,"Defer[Int][(a + b*Sin[e + f*x])^m*(A + B*Sin[e + f*x])*(c + d*Sin[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"