1,1,92,0,0.0914089,"\int (c+d x)^4 \sin (a+b x) \, dx","Int[(c + d*x)^4*Sin[a + b*x],x]","-\frac{24 d^3 (c+d x) \sin (a+b x)}{b^4}+\frac{12 d^2 (c+d x)^2 \cos (a+b x)}{b^3}+\frac{4 d (c+d x)^3 \sin (a+b x)}{b^2}-\frac{24 d^4 \cos (a+b x)}{b^5}-\frac{(c+d x)^4 \cos (a+b x)}{b}","-\frac{24 d^3 (c+d x) \sin (a+b x)}{b^4}+\frac{12 d^2 (c+d x)^2 \cos (a+b x)}{b^3}+\frac{4 d (c+d x)^3 \sin (a+b x)}{b^2}-\frac{24 d^4 \cos (a+b x)}{b^5}-\frac{(c+d x)^4 \cos (a+b x)}{b}",1,"(-24*d^4*Cos[a + b*x])/b^5 + (12*d^2*(c + d*x)^2*Cos[a + b*x])/b^3 - ((c + d*x)^4*Cos[a + b*x])/b - (24*d^3*(c + d*x)*Sin[a + b*x])/b^4 + (4*d*(c + d*x)^3*Sin[a + b*x])/b^2","A",5,2,14,0.1429,1,"{3296, 2638}"
2,1,71,0,0.0652611,"\int (c+d x)^3 \sin (a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x],x]","\frac{6 d^2 (c+d x) \cos (a+b x)}{b^3}+\frac{3 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{6 d^3 \sin (a+b x)}{b^4}-\frac{(c+d x)^3 \cos (a+b x)}{b}","\frac{6 d^2 (c+d x) \cos (a+b x)}{b^3}+\frac{3 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{6 d^3 \sin (a+b x)}{b^4}-\frac{(c+d x)^3 \cos (a+b x)}{b}",1,"(6*d^2*(c + d*x)*Cos[a + b*x])/b^3 - ((c + d*x)^3*Cos[a + b*x])/b - (6*d^3*Sin[a + b*x])/b^4 + (3*d*(c + d*x)^2*Sin[a + b*x])/b^2","A",4,2,14,0.1429,1,"{3296, 2637}"
3,1,50,0,0.0389583,"\int (c+d x)^2 \sin (a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x],x]","\frac{2 d (c+d x) \sin (a+b x)}{b^2}+\frac{2 d^2 \cos (a+b x)}{b^3}-\frac{(c+d x)^2 \cos (a+b x)}{b}","\frac{2 d (c+d x) \sin (a+b x)}{b^2}+\frac{2 d^2 \cos (a+b x)}{b^3}-\frac{(c+d x)^2 \cos (a+b x)}{b}",1,"(2*d^2*Cos[a + b*x])/b^3 - ((c + d*x)^2*Cos[a + b*x])/b + (2*d*(c + d*x)*Sin[a + b*x])/b^2","A",3,2,14,0.1429,1,"{3296, 2638}"
4,1,28,0,0.0162482,"\int (c+d x) \sin (a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x],x]","\frac{d \sin (a+b x)}{b^2}-\frac{(c+d x) \cos (a+b x)}{b}","\frac{d \sin (a+b x)}{b^2}-\frac{(c+d x) \cos (a+b x)}{b}",1,"-(((c + d*x)*Cos[a + b*x])/b) + (d*Sin[a + b*x])/b^2","A",2,2,12,0.1667,1,"{3296, 2637}"
5,1,51,0,0.0982246,"\int \frac{\sin (a+b x)}{c+d x} \, dx","Int[Sin[a + b*x]/(c + d*x),x]","\frac{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}","\frac{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}",1,"(CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d + (Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d","A",3,3,14,0.2143,1,"{3303, 3299, 3302}"
6,1,72,0,0.1087484,"\int \frac{\sin (a+b x)}{(c+d x)^2} \, dx","Int[Sin[a + b*x]/(c + d*x)^2,x]","\frac{b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{\sin (a+b x)}{d (c+d x)}","\frac{b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{\sin (a+b x)}{d (c+d x)}",1,"(b*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d^2 - Sin[a + b*x]/(d*(c + d*x)) - (b*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^2","A",4,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
7,1,104,0,0.1390314,"\int \frac{\sin (a+b x)}{(c+d x)^3} \, dx","Int[Sin[a + b*x]/(c + d*x)^3,x]","-\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b \cos (a+b x)}{2 d^2 (c+d x)}-\frac{\sin (a+b x)}{2 d (c+d x)^2}","-\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b \cos (a+b x)}{2 d^2 (c+d x)}-\frac{\sin (a+b x)}{2 d (c+d x)^2}",1,"-(b*Cos[a + b*x])/(2*d^2*(c + d*x)) - (b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(2*d^3) - Sin[a + b*x]/(2*d*(c + d*x)^2) - (b^2*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(2*d^3)","A",5,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
8,1,161,0,0.1028005,"\int (c+d x)^4 \sin ^2(a+b x) \, dx","Int[(c + d*x)^4*Sin[a + b*x]^2,x]","-\frac{3 d^3 (c+d x) \sin ^2(a+b x)}{2 b^4}+\frac{3 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b^3}+\frac{d (c+d x)^3 \sin ^2(a+b x)}{b^2}-\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{4 b^5}-\frac{(c+d x)^4 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}+\frac{3 d^4 x}{4 b^4}+\frac{(c+d x)^5}{10 d}","-\frac{3 d^3 (c+d x) \sin ^2(a+b x)}{2 b^4}+\frac{3 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b^3}+\frac{d (c+d x)^3 \sin ^2(a+b x)}{b^2}-\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{4 b^5}-\frac{(c+d x)^4 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}+\frac{3 d^4 x}{4 b^4}+\frac{(c+d x)^5}{10 d}",1,"(3*d^4*x)/(4*b^4) - (d*(c + d*x)^3)/(2*b^2) + (c + d*x)^5/(10*d) - (3*d^4*Cos[a + b*x]*Sin[a + b*x])/(4*b^5) + (3*d^2*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(2*b^3) - ((c + d*x)^4*Cos[a + b*x]*Sin[a + b*x])/(2*b) - (3*d^3*(c + d*x)*Sin[a + b*x]^2)/(2*b^4) + (d*(c + d*x)^3*Sin[a + b*x]^2)/b^2","A",6,4,16,0.2500,1,"{3311, 32, 2635, 8}"
9,1,134,0,0.0742275,"\int (c+d x)^3 \sin ^2(a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x]^2,x]","\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \sin ^2(a+b x)}{4 b^2}-\frac{3 d^3 \sin ^2(a+b x)}{8 b^4}-\frac{(c+d x)^3 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 c d^2 x}{4 b^2}-\frac{3 d^3 x^2}{8 b^2}+\frac{(c+d x)^4}{8 d}","\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \sin ^2(a+b x)}{4 b^2}-\frac{3 d^3 \sin ^2(a+b x)}{8 b^4}-\frac{(c+d x)^3 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 c d^2 x}{4 b^2}-\frac{3 d^3 x^2}{8 b^2}+\frac{(c+d x)^4}{8 d}",1,"(-3*c*d^2*x)/(4*b^2) - (3*d^3*x^2)/(8*b^2) + (c + d*x)^4/(8*d) + (3*d^2*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(4*b^3) - ((c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/(2*b) - (3*d^3*Sin[a + b*x]^2)/(8*b^4) + (3*d*(c + d*x)^2*Sin[a + b*x]^2)/(4*b^2)","A",4,3,16,0.1875,1,"{3311, 32, 3310}"
10,1,95,0,0.0538203,"\int (c+d x)^2 \sin ^2(a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x]^2,x]","\frac{d (c+d x) \sin ^2(a+b x)}{2 b^2}+\frac{d^2 \sin (a+b x) \cos (a+b x)}{4 b^3}-\frac{(c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d^2 x}{4 b^2}+\frac{(c+d x)^3}{6 d}","\frac{d (c+d x) \sin ^2(a+b x)}{2 b^2}+\frac{d^2 \sin (a+b x) \cos (a+b x)}{4 b^3}-\frac{(c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d^2 x}{4 b^2}+\frac{(c+d x)^3}{6 d}",1,"-(d^2*x)/(4*b^2) + (c + d*x)^3/(6*d) + (d^2*Cos[a + b*x]*Sin[a + b*x])/(4*b^3) - ((c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(2*b) + (d*(c + d*x)*Sin[a + b*x]^2)/(2*b^2)","A",4,4,16,0.2500,1,"{3311, 32, 2635, 8}"
11,1,55,0,0.0268548,"\int (c+d x) \sin ^2(a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x]^2,x]","\frac{d \sin ^2(a+b x)}{4 b^2}-\frac{(c+d x) \sin (a+b x) \cos (a+b x)}{2 b}+\frac{c x}{2}+\frac{d x^2}{4}","\frac{d \sin ^2(a+b x)}{4 b^2}-\frac{(c+d x) \sin (a+b x) \cos (a+b x)}{2 b}+\frac{c x}{2}+\frac{d x^2}{4}",1,"(c*x)/2 + (d*x^2)/4 - ((c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b) + (d*Sin[a + b*x]^2)/(4*b^2)","A",2,1,14,0.07143,1,"{3310}"
12,1,78,0,0.1682391,"\int \frac{\sin ^2(a+b x)}{c+d x} \, dx","Int[Sin[a + b*x]^2/(c + d*x),x]","-\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\log (c+d x)}{2 d}","-\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\log (c+d x)}{2 d}",1,"-(Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(2*d) + Log[c + d*x]/(2*d) + (Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d)","A",5,4,16,0.2500,1,"{3312, 3303, 3299, 3302}"
13,1,81,0,0.1394087,"\int \frac{\sin ^2(a+b x)}{(c+d x)^2} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^2,x]","\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}+\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\sin ^2(a+b x)}{d (c+d x)}","\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}+\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\sin ^2(a+b x)}{d (c+d x)}",1,"(b*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/d^2 - Sin[a + b*x]^2/(d*(c + d*x)) + (b*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2","A",5,5,16,0.3125,1,"{3313, 12, 3303, 3299, 3302}"
14,1,113,0,0.1918133,"\int \frac{\sin ^2(a+b x)}{(c+d x)^3} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^3,x]","\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b \sin (a+b x) \cos (a+b x)}{d^2 (c+d x)}-\frac{\sin ^2(a+b x)}{2 d (c+d x)^2}","\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b \sin (a+b x) \cos (a+b x)}{d^2 (c+d x)}-\frac{\sin ^2(a+b x)}{2 d (c+d x)^2}",1,"(b^2*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^3 - (b*Cos[a + b*x]*Sin[a + b*x])/(d^2*(c + d*x)) - Sin[a + b*x]^2/(2*d*(c + d*x)^2) - (b^2*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^3","A",7,6,16,0.3750,1,"{3314, 31, 3312, 3303, 3299, 3302}"
15,1,162,0,0.180895,"\int \frac{\sin ^2(a+b x)}{(c+d x)^4} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^4,x]","-\frac{2 b^3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}-\frac{2 b^3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}+\frac{2 b^2 \sin ^2(a+b x)}{3 d^3 (c+d x)}-\frac{b \sin (a+b x) \cos (a+b x)}{3 d^2 (c+d x)^2}-\frac{\sin ^2(a+b x)}{3 d (c+d x)^3}-\frac{b^2}{3 d^3 (c+d x)}","-\frac{2 b^3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}-\frac{2 b^3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}+\frac{2 b^2 \sin ^2(a+b x)}{3 d^3 (c+d x)}-\frac{b \sin (a+b x) \cos (a+b x)}{3 d^2 (c+d x)^2}-\frac{\sin ^2(a+b x)}{3 d (c+d x)^3}-\frac{b^2}{3 d^3 (c+d x)}",1,"-b^2/(3*d^3*(c + d*x)) - (2*b^3*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(3*d^4) - (b*Cos[a + b*x]*Sin[a + b*x])/(3*d^2*(c + d*x)^2) - Sin[a + b*x]^2/(3*d*(c + d*x)^3) + (2*b^2*Sin[a + b*x]^2)/(3*d^3*(c + d*x)) - (2*b^3*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(3*d^4)","A",7,7,16,0.4375,1,"{3314, 32, 3313, 12, 3303, 3299, 3302}"
16,1,225,0,0.2500752,"\int (c+d x)^4 \sin ^3(a+b x) \, dx","Int[(c + d*x)^4*Sin[a + b*x]^3,x]","-\frac{8 d^3 (c+d x) \sin ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \sin (a+b x)}{9 b^4}+\frac{80 d^2 (c+d x)^2 \cos (a+b x)}{9 b^3}+\frac{4 d^2 (c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{9 b^3}+\frac{4 d (c+d x)^3 \sin ^3(a+b x)}{9 b^2}+\frac{8 d (c+d x)^3 \sin (a+b x)}{3 b^2}+\frac{8 d^4 \cos ^3(a+b x)}{81 b^5}-\frac{488 d^4 \cos (a+b x)}{27 b^5}-\frac{2 (c+d x)^4 \cos (a+b x)}{3 b}-\frac{(c+d x)^4 \sin ^2(a+b x) \cos (a+b x)}{3 b}","-\frac{8 d^3 (c+d x) \sin ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \sin (a+b x)}{9 b^4}+\frac{80 d^2 (c+d x)^2 \cos (a+b x)}{9 b^3}+\frac{4 d^2 (c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{9 b^3}+\frac{4 d (c+d x)^3 \sin ^3(a+b x)}{9 b^2}+\frac{8 d (c+d x)^3 \sin (a+b x)}{3 b^2}+\frac{8 d^4 \cos ^3(a+b x)}{81 b^5}-\frac{488 d^4 \cos (a+b x)}{27 b^5}-\frac{2 (c+d x)^4 \cos (a+b x)}{3 b}-\frac{(c+d x)^4 \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(-488*d^4*Cos[a + b*x])/(27*b^5) + (80*d^2*(c + d*x)^2*Cos[a + b*x])/(9*b^3) - (2*(c + d*x)^4*Cos[a + b*x])/(3*b) + (8*d^4*Cos[a + b*x]^3)/(81*b^5) - (160*d^3*(c + d*x)*Sin[a + b*x])/(9*b^4) + (8*d*(c + d*x)^3*Sin[a + b*x])/(3*b^2) + (4*d^2*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^2)/(9*b^3) - ((c + d*x)^4*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) - (8*d^3*(c + d*x)*Sin[a + b*x]^3)/(27*b^4) + (4*d*(c + d*x)^3*Sin[a + b*x]^3)/(9*b^2)","A",12,4,16,0.2500,1,"{3311, 3296, 2638, 2633}"
17,1,175,0,0.1587035,"\int (c+d x)^3 \sin ^3(a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x]^3,x]","\frac{40 d^2 (c+d x) \cos (a+b x)}{9 b^3}+\frac{2 d^2 (c+d x) \sin ^2(a+b x) \cos (a+b x)}{9 b^3}+\frac{d (c+d x)^2 \sin ^3(a+b x)}{3 b^2}+\frac{2 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{2 d^3 \sin ^3(a+b x)}{27 b^4}-\frac{40 d^3 \sin (a+b x)}{9 b^4}-\frac{2 (c+d x)^3 \cos (a+b x)}{3 b}-\frac{(c+d x)^3 \sin ^2(a+b x) \cos (a+b x)}{3 b}","\frac{40 d^2 (c+d x) \cos (a+b x)}{9 b^3}+\frac{2 d^2 (c+d x) \sin ^2(a+b x) \cos (a+b x)}{9 b^3}+\frac{d (c+d x)^2 \sin ^3(a+b x)}{3 b^2}+\frac{2 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{2 d^3 \sin ^3(a+b x)}{27 b^4}-\frac{40 d^3 \sin (a+b x)}{9 b^4}-\frac{2 (c+d x)^3 \cos (a+b x)}{3 b}-\frac{(c+d x)^3 \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(40*d^2*(c + d*x)*Cos[a + b*x])/(9*b^3) - (2*(c + d*x)^3*Cos[a + b*x])/(3*b) - (40*d^3*Sin[a + b*x])/(9*b^4) + (2*d*(c + d*x)^2*Sin[a + b*x])/b^2 + (2*d^2*(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^2)/(9*b^3) - ((c + d*x)^3*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) - (2*d^3*Sin[a + b*x]^3)/(27*b^4) + (d*(c + d*x)^2*Sin[a + b*x]^3)/(3*b^2)","A",8,4,16,0.2500,1,"{3311, 3296, 2637, 3310}"
18,1,123,0,0.0960181,"\int (c+d x)^2 \sin ^3(a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x]^3,x]","\frac{2 d (c+d x) \sin ^3(a+b x)}{9 b^2}+\frac{4 d (c+d x) \sin (a+b x)}{3 b^2}-\frac{2 d^2 \cos ^3(a+b x)}{27 b^3}+\frac{14 d^2 \cos (a+b x)}{9 b^3}-\frac{2 (c+d x)^2 \cos (a+b x)}{3 b}-\frac{(c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{3 b}","\frac{2 d (c+d x) \sin ^3(a+b x)}{9 b^2}+\frac{4 d (c+d x) \sin (a+b x)}{3 b^2}-\frac{2 d^2 \cos ^3(a+b x)}{27 b^3}+\frac{14 d^2 \cos (a+b x)}{9 b^3}-\frac{2 (c+d x)^2 \cos (a+b x)}{3 b}-\frac{(c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(14*d^2*Cos[a + b*x])/(9*b^3) - (2*(c + d*x)^2*Cos[a + b*x])/(3*b) - (2*d^2*Cos[a + b*x]^3)/(27*b^3) + (4*d*(c + d*x)*Sin[a + b*x])/(3*b^2) - ((c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) + (2*d*(c + d*x)*Sin[a + b*x]^3)/(9*b^2)","A",6,4,16,0.2500,1,"{3311, 3296, 2638, 2633}"
19,1,75,0,0.0418427,"\int (c+d x) \sin ^3(a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x]^3,x]","\frac{d \sin ^3(a+b x)}{9 b^2}+\frac{2 d \sin (a+b x)}{3 b^2}-\frac{2 (c+d x) \cos (a+b x)}{3 b}-\frac{(c+d x) \sin ^2(a+b x) \cos (a+b x)}{3 b}","\frac{d \sin ^3(a+b x)}{9 b^2}+\frac{2 d \sin (a+b x)}{3 b^2}-\frac{2 (c+d x) \cos (a+b x)}{3 b}-\frac{(c+d x) \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(-2*(c + d*x)*Cos[a + b*x])/(3*b) + (2*d*Sin[a + b*x])/(3*b^2) - ((c + d*x)*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) + (d*Sin[a + b*x]^3)/(9*b^2)","A",3,3,14,0.2143,1,"{3310, 3296, 2637}"
20,1,121,0,0.2451829,"\int \frac{\sin ^3(a+b x)}{c+d x} \, dx","Int[Sin[a + b*x]^3/(c + d*x),x]","-\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}+\frac{3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}","-\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}+\frac{3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}",1,"-(CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(4*d) + (3*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(4*d) + (3*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(4*d) - (Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(4*d)","A",8,4,16,0.2500,1,"{3312, 3303, 3299, 3302}"
21,1,145,0,0.2423828,"\int \frac{\sin ^3(a+b x)}{(c+d x)^2} \, dx","Int[Sin[a + b*x]^3/(c + d*x)^2,x]","\frac{3 b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d^2}-\frac{3 b \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{3 b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\sin ^3(a+b x)}{d (c+d x)}","\frac{3 b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d^2}-\frac{3 b \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{3 b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\sin ^3(a+b x)}{d (c+d x)}",1,"(3*b*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(4*d^2) - (3*b*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(4*d^2) - Sin[a + b*x]^3/(d*(c + d*x)) - (3*b*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(4*d^2) + (3*b*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(4*d^2)","A",8,4,16,0.2500,1,"{3313, 3303, 3299, 3302}"
22,1,184,0,0.3536426,"\int \frac{\sin ^3(a+b x)}{(c+d x)^3} \, dx","Int[Sin[a + b*x]^3/(c + d*x)^3,x]","\frac{9 b^2 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{3 b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^3}+\frac{9 b^2 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b \sin ^2(a+b x) \cos (a+b x)}{2 d^2 (c+d x)}-\frac{\sin ^3(a+b x)}{2 d (c+d x)^2}","\frac{9 b^2 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{3 b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^3}+\frac{9 b^2 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b \sin ^2(a+b x) \cos (a+b x)}{2 d^2 (c+d x)}-\frac{\sin ^3(a+b x)}{2 d (c+d x)^2}",1,"(9*b^2*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(8*d^3) - (3*b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(8*d^3) - (3*b*Cos[a + b*x]*Sin[a + b*x]^2)/(2*d^2*(c + d*x)) - Sin[a + b*x]^3/(2*d*(c + d*x)^2) - (3*b^2*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d^3) + (9*b^2*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(8*d^3)","A",12,5,16,0.3125,1,"{3314, 3303, 3299, 3302, 3312}"
23,1,185,0,0.1369876,"\int (c+d x)^3 \csc (a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x],x]","-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b + ((3*I)*d*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((3*I)*d*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^2 - (6*d^2*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (6*d^2*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((6*I)*d^3*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((6*I)*d^3*PolyLog[4, E^(I*(a + b*x))])/b^4","A",9,5,14,0.3571,1,"{4183, 2531, 6609, 2282, 6589}"
24,1,123,0,0.0882635,"\int (c+d x)^2 \csc (a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x],x]","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b + ((2*I)*d*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^2 - (2*d^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (2*d^2*PolyLog[3, E^(I*(a + b*x))])/b^3","A",7,4,14,0.2857,1,"{4183, 2531, 2282, 6589}"
25,1,67,0,0.0394014,"\int (c+d x) \csc (a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b + (I*d*PolyLog[2, -E^(I*(a + b*x))])/b^2 - (I*d*PolyLog[2, E^(I*(a + b*x))])/b^2","A",5,3,12,0.2500,1,"{4183, 2279, 2391}"
26,0,0,0,0.0221008,"\int \frac{\csc (a+b x)}{c+d x} \, dx","Int[Csc[a + b*x]/(c + d*x),x]","\int \frac{\csc (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc (a+b x)}{c+d x},x\right)",0,"Defer[Int][Csc[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
27,0,0,0,0.0214692,"\int \frac{\csc (a+b x)}{(c+d x)^2} \, dx","Int[Csc[a + b*x]/(c + d*x)^2,x]","\int \frac{\csc (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Csc[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
28,1,113,0,0.213008,"\int (c+d x)^3 \csc ^2(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^2,x]","-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^3 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 d (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \cot (a+b x)}{b}-\frac{i (c+d x)^3}{b}","-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^3 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 d (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \cot (a+b x)}{b}-\frac{i (c+d x)^3}{b}",1,"((-I)*(c + d*x)^3)/b - ((c + d*x)^3*Cot[a + b*x])/b + (3*d*(c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b^2 - ((3*I)*d^2*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^3 + (3*d^3*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^4)","A",6,6,16,0.3750,1,"{4184, 3717, 2190, 2531, 2282, 6589}"
29,1,83,0,0.1359605,"\int (c+d x)^2 \csc ^2(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^2,x]","-\frac{i d^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 d (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \cot (a+b x)}{b}-\frac{i (c+d x)^2}{b}","-\frac{i d^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 d (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \cot (a+b x)}{b}-\frac{i (c+d x)^2}{b}",1,"((-I)*(c + d*x)^2)/b - ((c + d*x)^2*Cot[a + b*x])/b + (2*d*(c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b^2 - (I*d^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^3","A",5,5,16,0.3125,1,"{4184, 3717, 2190, 2279, 2391}"
30,1,29,0,0.0276419,"\int (c+d x) \csc ^2(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^2,x]","\frac{d \log (\sin (a+b x))}{b^2}-\frac{(c+d x) \cot (a+b x)}{b}","\frac{d \log (\sin (a+b x))}{b^2}-\frac{(c+d x) \cot (a+b x)}{b}",1,"-(((c + d*x)*Cot[a + b*x])/b) + (d*Log[Sin[a + b*x]])/b^2","A",2,2,14,0.1429,1,"{4184, 3475}"
31,0,0,0,0.0402203,"\int \frac{\csc ^2(a+b x)}{c+d x} \, dx","Int[Csc[a + b*x]^2/(c + d*x),x]","\int \frac{\csc ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Csc[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
32,0,0,0,0.0374365,"\int \frac{\csc ^2(a+b x)}{(c+d x)^2} \, dx","Int[Csc[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\csc ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Csc[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
33,1,309,0,0.2262423,"\int (c+d x)^3 \csc ^3(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \csc (a+b x)}{2 b^2}-\frac{(c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \cot (a+b x) \csc (a+b x)}{2 b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \csc (a+b x)}{2 b^2}-\frac{(c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \cot (a+b x) \csc (a+b x)}{2 b}",1,"(-6*d^2*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b^3 - ((c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b - (3*d*(c + d*x)^2*Csc[a + b*x])/(2*b^2) - ((c + d*x)^3*Cot[a + b*x]*Csc[a + b*x])/(2*b) + ((3*I)*d^3*PolyLog[2, -E^(I*(a + b*x))])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((3*I)*d^3*PolyLog[2, E^(I*(a + b*x))])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (3*d^2*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((3*I)*d^3*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((3*I)*d^3*PolyLog[4, E^(I*(a + b*x))])/b^4","A",15,8,16,0.5000,1,"{4186, 4183, 2279, 2391, 2531, 6609, 2282, 6589}"
34,1,180,0,0.1360066,"\int (c+d x)^2 \csc ^3(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^3,x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \csc (a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}-\frac{(c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \cot (a+b x) \csc (a+b x)}{2 b}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \csc (a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}-\frac{(c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \cot (a+b x) \csc (a+b x)}{2 b}",1,"-(((c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b) - (d^2*ArcTanh[Cos[a + b*x]])/b^3 - (d*(c + d*x)*Csc[a + b*x])/b^2 - ((c + d*x)^2*Cot[a + b*x]*Csc[a + b*x])/(2*b) + (I*d*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^2 - (I*d*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (d^2*PolyLog[3, E^(I*(a + b*x))])/b^3","A",9,6,16,0.3750,1,"{4186, 3770, 4183, 2531, 2282, 6589}"
35,1,109,0,0.0666484,"\int (c+d x) \csc ^3(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^3,x]","\frac{i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{d \csc (a+b x)}{2 b^2}-\frac{(c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x) \cot (a+b x) \csc (a+b x)}{2 b}","\frac{i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{d \csc (a+b x)}{2 b^2}-\frac{(c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x) \cot (a+b x) \csc (a+b x)}{2 b}",1,"-(((c + d*x)*ArcTanh[E^(I*(a + b*x))])/b) - (d*Csc[a + b*x])/(2*b^2) - ((c + d*x)*Cot[a + b*x]*Csc[a + b*x])/(2*b) + ((I/2)*d*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((I/2)*d*PolyLog[2, E^(I*(a + b*x))])/b^2","A",6,4,14,0.2857,1,"{4185, 4183, 2279, 2391}"
36,0,0,0,0.0390921,"\int \frac{\csc ^3(a+b x)}{c+d x} \, dx","Int[Csc[a + b*x]^3/(c + d*x),x]","\int \frac{\csc ^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][Csc[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
37,0,0,0,0.0376024,"\int \frac{\csc ^3(a+b x)}{(c+d x)^2} \, dx","Int[Csc[a + b*x]^3/(c + d*x)^2,x]","\int \frac{\csc ^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Csc[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
38,1,195,0,0.4341072,"\int (c+d x)^{5/2} \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Sin[a + b*x],x]","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{4 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{2 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{b}","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{4 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{2 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(4*b^3) - ((c + d*x)^(5/2)*Cos[a + b*x])/b - (15*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(4*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x])/(2*b^2)","A",8,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
39,1,170,0,0.2420415,"\int (c+d x)^{3/2} \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Sin[a + b*x],x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{2 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{2 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{b}",1,"-(((c + d*x)^(3/2)*Cos[a + b*x])/b) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(2*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(2*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[a + b*x])/(2*b^2)","A",7,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
40,1,142,0,0.175986,"\int \sqrt{c+d x} \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Sin[a + b*x],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{b}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{b}",1,"-((Sqrt[c + d*x]*Cos[a + b*x])/b) + (Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/b^(3/2) - (Sqrt[d]*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/b^(3/2)","A",6,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
41,1,117,0,0.1325186,"\int \frac{\sin (a+b x)}{\sqrt{c+d x}} \, dx","Int[Sin[a + b*x]/Sqrt[c + d*x],x]","\frac{\sqrt{2 \pi } \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}+\frac{\sqrt{2 \pi } \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}","\frac{\sqrt{2 \pi } \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}+\frac{\sqrt{2 \pi } \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}",1,"(Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(Sqrt[b]*Sqrt[d]) + (Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(Sqrt[b]*Sqrt[d])","A",5,5,16,0.3125,1,"{3306, 3305, 3351, 3304, 3352}"
42,1,139,0,0.2043756,"\int \frac{\sin (a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sin[a + b*x]/(c + d*x)^(3/2),x]","\frac{2 \sqrt{2 \pi } \sqrt{b} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{2 \pi } \sqrt{b} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin (a+b x)}{d \sqrt{c+d x}}","\frac{2 \sqrt{2 \pi } \sqrt{b} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{2 \pi } \sqrt{b} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin (a+b x)}{d \sqrt{c+d x}}",1,"(2*Sqrt[b]*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (2*Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(3/2) - (2*Sin[a + b*x])/(d*Sqrt[c + d*x])","A",6,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
43,1,168,0,0.2383126,"\int \frac{\sin (a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sin[a + b*x]/(c + d*x)^(5/2),x]","-\frac{4 \sqrt{2 \pi } b^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 \sqrt{2 \pi } b^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 b \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sin (a+b x)}{3 d (c+d x)^{3/2}}","-\frac{4 \sqrt{2 \pi } b^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 \sqrt{2 \pi } b^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 b \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sin (a+b x)}{3 d (c+d x)^{3/2}}",1,"(-4*b*Cos[a + b*x])/(3*d^2*Sqrt[c + d*x]) - (4*b^(3/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) - (4*b^(3/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(3*d^(5/2)) - (2*Sin[a + b*x])/(3*d*(c + d*x)^(3/2))","A",7,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
44,1,193,0,0.2968318,"\int \frac{\sin (a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sin[a + b*x]/(c + d*x)^(7/2),x]","-\frac{8 \sqrt{2 \pi } b^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 b^2 \sin (a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{4 b \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sin (a+b x)}{5 d (c+d x)^{5/2}}","-\frac{8 \sqrt{2 \pi } b^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 b^2 \sin (a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{4 b \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sin (a+b x)}{5 d (c+d x)^{5/2}}",1,"(-4*b*Cos[a + b*x])/(15*d^2*(c + d*x)^(3/2)) - (8*b^(5/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) + (8*b^(5/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(15*d^(7/2)) - (2*Sin[a + b*x])/(5*d*(c + d*x)^(5/2)) + (8*b^2*Sin[a + b*x])/(15*d^3*Sqrt[c + d*x])","A",8,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
45,1,231,0,0.442284,"\int (c+d x)^{5/2} \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Sin[a + b*x]^2,x]","-\frac{15 \sqrt{\pi } d^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{128 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin ^2(a+b x)}{8 b^2}-\frac{(c+d x)^{5/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{5 d (c+d x)^{3/2}}{16 b^2}+\frac{(c+d x)^{7/2}}{7 d}","-\frac{15 \sqrt{\pi } d^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{128 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin ^2(a+b x)}{8 b^2}-\frac{(c+d x)^{5/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{5 d (c+d x)^{3/2}}{16 b^2}+\frac{(c+d x)^{7/2}}{7 d}",1,"(-5*d*(c + d*x)^(3/2))/(16*b^2) + (c + d*x)^(7/2)/(7*d) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(7/2)) - ((c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x])/(2*b) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x]^2)/(8*b^2) + (15*d^2*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(64*b^3)","A",10,9,18,0.5000,1,"{3311, 32, 3312, 3296, 3306, 3305, 3351, 3304, 3352}"
46,1,203,0,0.3597437,"\int (c+d x)^{3/2} \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Sin[a + b*x]^2,x]","\frac{3 \sqrt{\pi } d^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin ^2(a+b x)}{8 b^2}-\frac{(c+d x)^{3/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 d \sqrt{c+d x}}{16 b^2}+\frac{(c+d x)^{5/2}}{5 d}","\frac{3 \sqrt{\pi } d^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin ^2(a+b x)}{8 b^2}-\frac{(c+d x)^{3/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 d \sqrt{c+d x}}{16 b^2}+\frac{(c+d x)^{5/2}}{5 d}",1,"(-3*d*Sqrt[c + d*x])/(16*b^2) + (c + d*x)^(5/2)/(5*d) + (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(32*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(32*b^(5/2)) - ((c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x])/(2*b) + (3*d*Sqrt[c + d*x]*Sin[a + b*x]^2)/(8*b^2)","A",9,8,18,0.4444,1,"{3311, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
47,1,158,0,0.2846611,"\int \sqrt{c+d x} \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Sin[a + b*x]^2,x]","\frac{\sqrt{\pi } \sqrt{d} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{8 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \sin (2 a+2 b x)}{4 b}+\frac{(c+d x)^{3/2}}{3 d}","\frac{\sqrt{\pi } \sqrt{d} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{8 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \sin (2 a+2 b x)}{4 b}+\frac{(c+d x)^{3/2}}{3 d}",1,"(c + d*x)^(3/2)/(3*d) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(8*b^(3/2)) + (Sqrt[d]*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(8*b^(3/2)) - (Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(4*b)","A",8,7,18,0.3889,1,"{3312, 3296, 3306, 3305, 3351, 3304, 3352}"
48,1,130,0,0.2342672,"\int \frac{\sin ^2(a+b x)}{\sqrt{c+d x}} \, dx","Int[Sin[a + b*x]^2/Sqrt[c + d*x],x]","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{c+d x}}{d}","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{c+d x}}{d}",1,"Sqrt[c + d*x]/d - (Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(2*Sqrt[b]*Sqrt[d]) + (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(2*Sqrt[b]*Sqrt[d])","A",7,6,18,0.3333,1,"{3312, 3306, 3305, 3351, 3304, 3352}"
49,1,135,0,0.2539506,"\int \frac{\sin ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^(3/2),x]","\frac{2 \sqrt{\pi } \sqrt{b} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{d^{3/2}}+\frac{2 \sqrt{\pi } \sqrt{b} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{d^{3/2}}-\frac{2 \sin ^2(a+b x)}{d \sqrt{c+d x}}","\frac{2 \sqrt{\pi } \sqrt{b} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{d^{3/2}}+\frac{2 \sqrt{\pi } \sqrt{b} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{d^{3/2}}-\frac{2 \sin ^2(a+b x)}{d \sqrt{c+d x}}",1,"(2*Sqrt[b]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/d^(3/2) + (2*Sqrt[b]*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/d^(3/2) - (2*Sin[a + b*x]^2)/(d*Sqrt[c + d*x])","A",7,7,18,0.3889,1,"{3313, 12, 3306, 3305, 3351, 3304, 3352}"
50,1,170,0,0.3282343,"\int \frac{\sin ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^(5/2),x]","\frac{8 \sqrt{\pi } b^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{3 d^{5/2}}-\frac{8 \sqrt{\pi } b^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{3 d^{5/2}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sin ^2(a+b x)}{3 d (c+d x)^{3/2}}","\frac{8 \sqrt{\pi } b^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{3 d^{5/2}}-\frac{8 \sqrt{\pi } b^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{3 d^{5/2}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sin ^2(a+b x)}{3 d (c+d x)^{3/2}}",1,"(8*b^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(3*d^(5/2)) - (8*b^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(3*d^(5/2)) - (8*b*Cos[a + b*x]*Sin[a + b*x])/(3*d^2*Sqrt[c + d*x]) - (2*Sin[a + b*x]^2)/(3*d*(c + d*x)^(3/2))","A",9,8,18,0.4444,1,"{3314, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
51,1,216,0,0.3357689,"\int \frac{\sin ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^(7/2),x]","-\frac{32 \sqrt{\pi } b^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{15 d^{7/2}}-\frac{32 \sqrt{\pi } b^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{15 d^{7/2}}+\frac{32 b^2 \sin ^2(a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sin ^2(a+b x)}{5 d (c+d x)^{5/2}}-\frac{16 b^2}{15 d^3 \sqrt{c+d x}}","-\frac{32 \sqrt{\pi } b^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{15 d^{7/2}}-\frac{32 \sqrt{\pi } b^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{15 d^{7/2}}+\frac{32 b^2 \sin ^2(a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sin ^2(a+b x)}{5 d (c+d x)^{5/2}}-\frac{16 b^2}{15 d^3 \sqrt{c+d x}}",1,"(-16*b^2)/(15*d^3*Sqrt[c + d*x]) - (32*b^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(15*d^(7/2)) - (32*b^(5/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(15*d^(7/2)) - (8*b*Cos[a + b*x]*Sin[a + b*x])/(15*d^2*(c + d*x)^(3/2)) - (2*Sin[a + b*x]^2)/(5*d*(c + d*x)^(5/2)) + (32*b^2*Sin[a + b*x]^2)/(15*d^3*Sqrt[c + d*x])","A",9,9,18,0.5000,1,"{3314, 32, 3313, 12, 3306, 3305, 3351, 3304, 3352}"
52,1,247,0,0.419004,"\int \frac{\sin ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Int[Sin[a + b*x]^2/(c + d*x)^(9/2),x]","-\frac{128 \sqrt{\pi } b^{7/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{105 d^{9/2}}+\frac{128 \sqrt{\pi } b^{7/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{105 d^{9/2}}+\frac{32 b^2 \sin ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}+\frac{128 b^3 \sin (a+b x) \cos (a+b x)}{105 d^4 \sqrt{c+d x}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \sin ^2(a+b x)}{7 d (c+d x)^{7/2}}-\frac{16 b^2}{105 d^3 (c+d x)^{3/2}}","-\frac{128 \sqrt{\pi } b^{7/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{105 d^{9/2}}+\frac{128 \sqrt{\pi } b^{7/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{105 d^{9/2}}+\frac{32 b^2 \sin ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}+\frac{128 b^3 \sin (a+b x) \cos (a+b x)}{105 d^4 \sqrt{c+d x}}-\frac{8 b \sin (a+b x) \cos (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \sin ^2(a+b x)}{7 d (c+d x)^{7/2}}-\frac{16 b^2}{105 d^3 (c+d x)^{3/2}}",1,"(-16*b^2)/(105*d^3*(c + d*x)^(3/2)) - (128*b^(7/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(105*d^(9/2)) + (128*b^(7/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(105*d^(9/2)) - (8*b*Cos[a + b*x]*Sin[a + b*x])/(35*d^2*(c + d*x)^(5/2)) + (128*b^3*Cos[a + b*x]*Sin[a + b*x])/(105*d^4*Sqrt[c + d*x]) - (2*Sin[a + b*x]^2)/(7*d*(c + d*x)^(7/2)) + (32*b^2*Sin[a + b*x]^2)/(105*d^3*(c + d*x)^(3/2))","A",11,8,18,0.4444,1,"{3314, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
53,1,410,0,1.1265767,"\int (c+d x)^{5/2} \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Sin[a + b*x]^3,x]","-\frac{45 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{144 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{144 b^{7/2}}+\frac{45 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (a+b x)}{16 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \sin ^3(a+b x)}{18 b^2}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{3 b^2}-\frac{2 (c+d x)^{5/2} \cos (a+b x)}{3 b}-\frac{(c+d x)^{5/2} \sin ^2(a+b x) \cos (a+b x)}{3 b}","-\frac{45 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{144 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{144 b^{7/2}}+\frac{45 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (a+b x)}{16 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \sin ^3(a+b x)}{18 b^2}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{3 b^2}-\frac{2 (c+d x)^{5/2} \cos (a+b x)}{3 b}-\frac{(c+d x)^{5/2} \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(45*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(16*b^3) - (2*(c + d*x)^(5/2)*Cos[a + b*x])/(3*b) - (5*d^2*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(144*b^3) - (45*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(7/2)) + (5*d^(5/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(144*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(144*b^(7/2)) + (45*d^(5/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(16*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x])/(3*b^2) - ((c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x]^3)/(18*b^2)","A",23,8,18,0.4444,1,"{3311, 3296, 3306, 3305, 3351, 3304, 3352, 3312}"
54,1,354,0,0.97218,"\int (c+d x)^{3/2} \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Sin[a + b*x]^3,x]","\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{24 b^{5/2}}-\frac{9 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}-\frac{9 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{24 b^{5/2}}+\frac{d \sqrt{c+d x} \sin ^3(a+b x)}{6 b^2}+\frac{d \sqrt{c+d x} \sin (a+b x)}{b^2}-\frac{2 (c+d x)^{3/2} \cos (a+b x)}{3 b}-\frac{(c+d x)^{3/2} \sin ^2(a+b x) \cos (a+b x)}{3 b}","\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{24 b^{5/2}}-\frac{9 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}-\frac{9 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{24 b^{5/2}}+\frac{d \sqrt{c+d x} \sin ^3(a+b x)}{6 b^2}+\frac{d \sqrt{c+d x} \sin (a+b x)}{b^2}-\frac{2 (c+d x)^{3/2} \cos (a+b x)}{3 b}-\frac{(c+d x)^{3/2} \sin ^2(a+b x) \cos (a+b x)}{3 b}",1,"(-2*(c + d*x)^(3/2)*Cos[a + b*x])/(3*b) - (9*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(8*b^(5/2)) + (d^(3/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(24*b^(5/2)) + (d^(3/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(24*b^(5/2)) - (9*d^(3/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(8*b^(5/2)) + (d*Sqrt[c + d*x]*Sin[a + b*x])/b^2 - ((c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b) + (d*Sqrt[c + d*x]*Sin[a + b*x]^3)/(6*b^2)","A",20,8,18,0.4444,1,"{3311, 3296, 3306, 3305, 3351, 3304, 3352, 3312}"
55,1,304,0,0.4977792,"\int \sqrt{c+d x} \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Sin[a + b*x]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{12 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{12 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (a+b x)}{4 b}+\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 b}","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{12 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{12 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (a+b x)}{4 b}+\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 b}",1,"(-3*Sqrt[c + d*x]*Cos[a + b*x])/(4*b) + (Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(12*b) + (3*Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(12*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(12*b^(3/2)) - (3*Sqrt[d]*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(4*b^(3/2))","A",14,7,18,0.3889,1,"{3312, 3296, 3306, 3305, 3351, 3304, 3352}"
56,1,257,0,0.4049878,"\int \frac{\sin ^3(a+b x)}{\sqrt{c+d x}} \, dx","Int[Sin[a + b*x]^3/Sqrt[c + d*x],x]","-\frac{\sqrt{\frac{\pi }{6}} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{3 \sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{3 \sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\frac{\pi }{6}} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}","-\frac{\sqrt{\frac{\pi }{6}} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{3 \sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{3 \sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\frac{\pi }{6}} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}",1,"(3*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d]) - (Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d]) - (Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(2*Sqrt[b]*Sqrt[d]) + (3*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(2*Sqrt[b]*Sqrt[d])","A",12,6,18,0.3333,1,"{3312, 3306, 3305, 3351, 3304, 3352}"
57,1,270,0,0.5638337,"\int \frac{\sin ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sin[a + b*x]^3/(c + d*x)^(3/2),x]","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin ^3(a+b x)}{d \sqrt{c+d x}}","\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin ^3(a+b x)}{d \sqrt{c+d x}}",1,"(3*Sqrt[b]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (Sqrt[b]*Sqrt[(3*Pi)/2]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) + (Sqrt[b]*Sqrt[(3*Pi)/2]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/d^(3/2) - (3*Sqrt[b]*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(3/2) - (2*Sin[a + b*x]^3)/(d*Sqrt[c + d*x])","A",12,6,18,0.3333,1,"{3313, 3306, 3305, 3351, 3304, 3352}"
58,1,292,0,0.7103837,"\int \frac{\sin ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sin[a + b*x]^3/(c + d*x)^(5/2),x]","\frac{\sqrt{6 \pi } b^{3/2} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{\sqrt{2 \pi } b^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{\sqrt{2 \pi } b^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}+\frac{\sqrt{6 \pi } b^{3/2} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{4 b \sin ^2(a+b x) \cos (a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \sin ^3(a+b x)}{3 d (c+d x)^{3/2}}","\frac{\sqrt{6 \pi } b^{3/2} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{\sqrt{2 \pi } b^{3/2} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{\sqrt{2 \pi } b^{3/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}+\frac{\sqrt{6 \pi } b^{3/2} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{5/2}}-\frac{4 b \sin ^2(a+b x) \cos (a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \sin ^3(a+b x)}{3 d (c+d x)^{3/2}}",1,"-((b^(3/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(5/2)) + (b^(3/2)*Sqrt[6*Pi]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(5/2) + (b^(3/2)*Sqrt[6*Pi]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/d^(5/2) - (b^(3/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(5/2) - (4*b*Cos[a + b*x]*Sin[a + b*x]^2)/(d^2*Sqrt[c + d*x]) - (2*Sin[a + b*x]^3)/(3*d*(c + d*x)^(3/2))","A",18,7,18,0.3889,1,"{3314, 3306, 3305, 3351, 3304, 3352, 3312}"
59,1,356,0,0.796731,"\int \frac{\sin ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sin[a + b*x]^3/(c + d*x)^(7/2),x]","-\frac{2 \sqrt{2 \pi } b^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{6 \sqrt{6 \pi } b^{5/2} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{6 \sqrt{6 \pi } b^{5/2} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{24 b^2 \sin ^3(a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{16 b^2 \sin (a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{4 b \sin ^2(a+b x) \cos (a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \sin ^3(a+b x)}{5 d (c+d x)^{5/2}}","-\frac{2 \sqrt{2 \pi } b^{5/2} \cos \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{6 \sqrt{6 \pi } b^{5/2} \cos \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{6 \sqrt{6 \pi } b^{5/2} \sin \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{5/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{24 b^2 \sin ^3(a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{16 b^2 \sin (a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{4 b \sin ^2(a+b x) \cos (a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \sin ^3(a+b x)}{5 d (c+d x)^{5/2}}",1,"(-2*b^(5/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) + (6*b^(5/2)*Sqrt[6*Pi]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) - (6*b^(5/2)*Sqrt[6*Pi]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(5*d^(7/2)) + (2*b^(5/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(5*d^(7/2)) - (16*b^2*Sin[a + b*x])/(5*d^3*Sqrt[c + d*x]) - (4*b*Cos[a + b*x]*Sin[a + b*x]^2)/(5*d^2*(c + d*x)^(3/2)) - (2*Sin[a + b*x]^3)/(5*d*(c + d*x)^(5/2)) + (24*b^2*Sin[a + b*x]^3)/(5*d^3*Sqrt[c + d*x])","A",19,8,18,0.4444,1,"{3314, 3297, 3306, 3305, 3351, 3304, 3352, 3313}"
60,1,87,0,0.1092949,"\int (d x)^{3/2} \sin (f x) \, dx","Int[(d*x)^(3/2)*Sin[f*x],x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{2 f^{5/2}}+\frac{3 d \sqrt{d x} \sin (f x)}{2 f^2}-\frac{(d x)^{3/2} \cos (f x)}{f}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{2 f^{5/2}}+\frac{3 d \sqrt{d x} \sin (f x)}{2 f^2}-\frac{(d x)^{3/2} \cos (f x)}{f}",1,"-(((d*x)^(3/2)*Cos[f*x])/f) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[f]*Sqrt[2/Pi]*Sqrt[d*x])/Sqrt[d]])/(2*f^(5/2)) + (3*d*Sqrt[d*x]*Sin[f*x])/(2*f^2)","A",4,3,12,0.2500,1,"{3296, 3305, 3351}"
61,1,65,0,0.0579075,"\int \sqrt{d x} \sin (f x) \, dx","Int[Sqrt[d*x]*Sin[f*x],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{f^{3/2}}-\frac{\sqrt{d x} \cos (f x)}{f}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{f^{3/2}}-\frac{\sqrt{d x} \cos (f x)}{f}",1,"-((Sqrt[d*x]*Cos[f*x])/f) + (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(Sqrt[f]*Sqrt[2/Pi]*Sqrt[d*x])/Sqrt[d]])/f^(3/2)","A",3,3,12,0.2500,1,"{3296, 3304, 3352}"
62,1,46,0,0.0344381,"\int \frac{\sin (f x)}{\sqrt{d x}} \, dx","Int[Sin[f*x]/Sqrt[d*x],x]","\frac{\sqrt{2 \pi } S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{f}}","\frac{\sqrt{2 \pi } S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{f}}",1,"(Sqrt[2*Pi]*FresnelS[(Sqrt[f]*Sqrt[2/Pi]*Sqrt[d*x])/Sqrt[d]])/(Sqrt[d]*Sqrt[f])","A",2,2,12,0.1667,1,"{3305, 3351}"
63,1,64,0,0.0649724,"\int \frac{\sin (f x)}{(d x)^{3/2}} \, dx","Int[Sin[f*x]/(d*x)^(3/2),x]","\frac{2 \sqrt{2 \pi } \sqrt{f} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin (f x)}{d \sqrt{d x}}","\frac{2 \sqrt{2 \pi } \sqrt{f} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sin (f x)}{d \sqrt{d x}}",1,"(2*Sqrt[f]*Sqrt[2*Pi]*FresnelC[(Sqrt[f]*Sqrt[2/Pi]*Sqrt[d*x])/Sqrt[d]])/d^(3/2) - (2*Sin[f*x])/(d*Sqrt[d*x])","A",3,3,12,0.2500,1,"{3297, 3304, 3352}"
64,1,87,0,0.0926116,"\int \frac{\sin (f x)}{(d x)^{5/2}} \, dx","Int[Sin[f*x]/(d*x)^(5/2),x]","-\frac{4 \sqrt{2 \pi } f^{3/2} S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 f \cos (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \sin (f x)}{3 d (d x)^{3/2}}","-\frac{4 \sqrt{2 \pi } f^{3/2} S\left(\frac{\sqrt{f} \sqrt{\frac{2}{\pi }} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 f \cos (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \sin (f x)}{3 d (d x)^{3/2}}",1,"(-4*f*Cos[f*x])/(3*d^2*Sqrt[d*x]) - (4*f^(3/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[f]*Sqrt[2/Pi]*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (2*Sin[f*x])/(3*d*(d*x)^(3/2))","A",4,3,12,0.2500,1,"{3297, 3305, 3351}"
65,0,0,0,0.0310791,"\int \sqrt{c+d x} \csc (a+b x) \, dx","Int[Sqrt[c + d*x]*Csc[a + b*x],x]","\int \sqrt{c+d x} \csc (a+b x) \, dx","\text{Int}\left(\sqrt{c+d x} \csc (a+b x),x\right)",0,"Defer[Int][Sqrt[c + d*x]*Csc[a + b*x], x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0310664,"\int \frac{\csc (a+b x)}{\sqrt{c+d x}} \, dx","Int[Csc[a + b*x]/Sqrt[c + d*x],x]","\int \frac{\csc (a+b x)}{\sqrt{c+d x}} \, dx","\text{Int}\left(\frac{\csc (a+b x)}{\sqrt{c+d x}},x\right)",0,"Defer[Int][Csc[a + b*x]/Sqrt[c + d*x], x]","A",0,0,0,0,-1,"{}"
67,1,38,0,0.0613543,"\int \left(\frac{x}{\sin ^{\frac{3}{2}}(e+f x)}+x \sqrt{\sin (e+f x)}\right) \, dx","Int[x/Sin[e + f*x]^(3/2) + x*Sqrt[Sin[e + f*x]],x]","\frac{4 \sqrt{\sin (e+f x)}}{f^2}-\frac{2 x \cos (e+f x)}{f \sqrt{\sin (e+f x)}}","\frac{4 \sqrt{\sin (e+f x)}}{f^2}-\frac{2 x \cos (e+f x)}{f \sqrt{\sin (e+f x)}}",1,"(-2*x*Cos[e + f*x])/(f*Sqrt[Sin[e + f*x]]) + (4*Sqrt[Sin[e + f*x]])/f^2","A",2,1,25,0.04000,1,"{3315}"
68,1,62,0,0.106662,"\int \left(\frac{x^2}{\sin ^{\frac{3}{2}}(e+f x)}+x^2 \sqrt{\sin (e+f x)}\right) \, dx","Int[x^2/Sin[e + f*x]^(3/2) + x^2*Sqrt[Sin[e + f*x]],x]","\frac{8 x \sqrt{\sin (e+f x)}}{f^2}-\frac{16 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f^3}-\frac{2 x^2 \cos (e+f x)}{f \sqrt{\sin (e+f x)}}","\frac{8 x \sqrt{\sin (e+f x)}}{f^2}-\frac{16 E\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{f^3}-\frac{2 x^2 \cos (e+f x)}{f \sqrt{\sin (e+f x)}}",1,"(-16*EllipticE[(e - Pi/2 + f*x)/2, 2])/f^3 - (2*x^2*Cos[e + f*x])/(f*Sqrt[Sin[e + f*x]]) + (8*x*Sqrt[Sin[e + f*x]])/f^2","A",3,2,29,0.06897,1,"{3316, 2639}"
69,1,42,0,0.0603062,"\int \left(\frac{x}{\sin ^{\frac{5}{2}}(e+f x)}-\frac{x}{3 \sqrt{\sin (e+f x)}}\right) \, dx","Int[x/Sin[e + f*x]^(5/2) - x/(3*Sqrt[Sin[e + f*x]]),x]","-\frac{4}{3 f^2 \sqrt{\sin (e+f x)}}-\frac{2 x \cos (e+f x)}{3 f \sin ^{\frac{3}{2}}(e+f x)}","-\frac{4}{3 f^2 \sqrt{\sin (e+f x)}}-\frac{2 x \cos (e+f x)}{3 f \sin ^{\frac{3}{2}}(e+f x)}",1,"(-2*x*Cos[e + f*x])/(3*f*Sin[e + f*x]^(3/2)) - 4/(3*f^2*Sqrt[Sin[e + f*x]])","A",2,1,28,0.03571,1,"{3315}"
70,1,83,0,0.0858376,"\int \left(\frac{x}{\sin ^{\frac{7}{2}}(e+f x)}+\frac{3}{5} x \sqrt{\sin (e+f x)}\right) \, dx","Int[x/Sin[e + f*x]^(7/2) + (3*x*Sqrt[Sin[e + f*x]])/5,x]","-\frac{4}{15 f^2 \sin ^{\frac{3}{2}}(e+f x)}+\frac{12 \sqrt{\sin (e+f x)}}{5 f^2}-\frac{2 x \cos (e+f x)}{5 f \sin ^{\frac{5}{2}}(e+f x)}-\frac{6 x \cos (e+f x)}{5 f \sqrt{\sin (e+f x)}}","-\frac{4}{15 f^2 \sin ^{\frac{3}{2}}(e+f x)}+\frac{12 \sqrt{\sin (e+f x)}}{5 f^2}-\frac{2 x \cos (e+f x)}{5 f \sin ^{\frac{5}{2}}(e+f x)}-\frac{6 x \cos (e+f x)}{5 f \sqrt{\sin (e+f x)}}",1,"(-2*x*Cos[e + f*x])/(5*f*Sin[e + f*x]^(5/2)) - 4/(15*f^2*Sin[e + f*x]^(3/2)) - (6*x*Cos[e + f*x])/(5*f*Sqrt[Sin[e + f*x]]) + (12*Sqrt[Sin[e + f*x]])/(5*f^2)","A",3,1,28,0.03571,1,"{3315}"
71,0,0,0,0.0418718,"\int (c+d x)^m (b \sin (e+f x))^n \, dx","Int[(c + d*x)^m*(b*Sin[e + f*x])^n,x]","\int (c+d x)^m (b \sin (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (b \sin (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(b*Sin[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
72,1,267,0,0.3030632,"\int (c+d x)^m \sin ^3(a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x]^3,x]","-\frac{3 e^{i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i b (c+d x)}{d}\right)}{8 b}+\frac{3^{-m-1} e^{3 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i b (c+d x)}{d}\right)}{8 b}-\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i b (c+d x)}{d}\right)}{8 b}+\frac{3^{-m-1} e^{-3 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i b (c+d x)}{d}\right)}{8 b}","-\frac{3 e^{i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i b (c+d x)}{d}\right)}{8 b}+\frac{3^{-m-1} e^{3 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i b (c+d x)}{d}\right)}{8 b}-\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i b (c+d x)}{d}\right)}{8 b}+\frac{3^{-m-1} e^{-3 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i b (c+d x)}{d}\right)}{8 b}",1,"(-3*E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(8*b*(((-I)*b*(c + d*x))/d)^m) - (3*(c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(8*b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + (3^(-1 - m)*E^((3*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-3*I)*b*(c + d*x))/d])/(8*b*(((-I)*b*(c + d*x))/d)^m) + (3^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((3*I)*b*(c + d*x))/d])/(8*b*E^((3*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",8,3,16,0.1875,1,"{3312, 3308, 2181}"
73,1,162,0,0.2172653,"\int (c+d x)^m \sin ^2(a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x]^2,x]","\frac{i 2^{-m-3} e^{2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i b (c+d x)}{d}\right)}{b}-\frac{i 2^{-m-3} e^{-2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{2 d (m+1)}","\frac{i 2^{-m-3} e^{2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i b (c+d x)}{d}\right)}{b}-\frac{i 2^{-m-3} e^{-2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{2 d (m+1)}",1,"(c + d*x)^(1 + m)/(2*d*(1 + m)) + (I*2^(-3 - m)*E^((2*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - (I*2^(-3 - m)*(c + d*x)^m*Gamma[1 + m, ((2*I)*b*(c + d*x))/d])/(b*E^((2*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",5,3,16,0.1875,1,"{3312, 3307, 2181}"
74,1,127,0,0.0884659,"\int (c+d x)^m \sin (a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x],x]","-\frac{e^{i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i b (c+d x)}{d}\right)}{2 b}-\frac{e^{-i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i b (c+d x)}{d}\right)}{2 b}","-\frac{e^{i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i b (c+d x)}{d}\right)}{2 b}-\frac{e^{-i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i b (c+d x)}{d}\right)}{2 b}",1,"-(E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(2*b*(((-I)*b*(c + d*x))/d)^m) - ((c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(2*b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",3,2,14,0.1429,1,"{3308, 2181}"
75,0,0,0,0.0186464,"\int (c+d x)^m \csc (a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x],x]","\int (c+d x)^m \csc (a+b x) \, dx","\text{Int}\left(\csc (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x], x]","A",0,0,0,0,-1,"{}"
76,0,0,0,0.0365495,"\int (c+d x)^m \csc ^2(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^2,x]","\int (c+d x)^m \csc ^2(a+b x) \, dx","\text{Int}\left(\csc ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
77,1,79,0,0.0774144,"\int x^{3+m} \sin (a+b x) \, dx","Int[x^(3 + m)*Sin[a + b*x],x]","\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+4,-i b x)}{2 b^4}-\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+4,i b x)}{2 b^4}","\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+4,-i b x)}{2 b^4}-\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+4,i b x)}{2 b^4}",1,"((I/2)*E^(I*a)*x^m*Gamma[4 + m, (-I)*b*x])/(b^4*((-I)*b*x)^m) - ((I/2)*x^m*Gamma[4 + m, I*b*x])/(b^4*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
78,1,75,0,0.0727324,"\int x^{2+m} \sin (a+b x) \, dx","Int[x^(2 + m)*Sin[a + b*x],x]","\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+3,-i b x)}{2 b^3}+\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+3,i b x)}{2 b^3}","\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+3,-i b x)}{2 b^3}+\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+3,i b x)}{2 b^3}",1,"(E^(I*a)*x^m*Gamma[3 + m, (-I)*b*x])/(2*b^3*((-I)*b*x)^m) + (x^m*Gamma[3 + m, I*b*x])/(2*b^3*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
79,1,79,0,0.0708763,"\int x^{1+m} \sin (a+b x) \, dx","Int[x^(1 + m)*Sin[a + b*x],x]","\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+2,i b x)}{2 b^2}-\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+2,-i b x)}{2 b^2}","\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+2,i b x)}{2 b^2}-\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+2,-i b x)}{2 b^2}",1,"((-I/2)*E^(I*a)*x^m*Gamma[2 + m, (-I)*b*x])/(b^2*((-I)*b*x)^m) + ((I/2)*x^m*Gamma[2 + m, I*b*x])/(b^2*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
80,1,75,0,0.0657262,"\int x^m \sin (a+b x) \, dx","Int[x^m*Sin[a + b*x],x]","-\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+1,-i b x)}{2 b}-\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+1,i b x)}{2 b}","-\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+1,-i b x)}{2 b}-\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+1,i b x)}{2 b}",1,"-(E^(I*a)*x^m*Gamma[1 + m, (-I)*b*x])/(2*b*((-I)*b*x)^m) - (x^m*Gamma[1 + m, I*b*x])/(2*b*E^(I*a)*(I*b*x)^m)","A",3,2,10,0.2000,1,"{3308, 2181}"
81,1,69,0,0.0679546,"\int x^{-1+m} \sin (a+b x) \, dx","Int[x^(-1 + m)*Sin[a + b*x],x]","\frac{1}{2} i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m,-i b x)-\frac{1}{2} i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m,i b x)","\frac{1}{2} i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m,-i b x)-\frac{1}{2} i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m,i b x)",1,"((I/2)*E^(I*a)*x^m*Gamma[m, (-I)*b*x])/((-I)*b*x)^m - ((I/2)*x^m*Gamma[m, I*b*x])/(E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
82,1,71,0,0.0706639,"\int x^{-2+m} \sin (a+b x) \, dx","Int[x^(-2 + m)*Sin[a + b*x],x]","\frac{1}{2} e^{i a} b x^m (-i b x)^{-m} \text{Gamma}(m-1,-i b x)+\frac{1}{2} e^{-i a} b x^m (i b x)^{-m} \text{Gamma}(m-1,i b x)","\frac{1}{2} e^{i a} b x^m (-i b x)^{-m} \text{Gamma}(m-1,-i b x)+\frac{1}{2} e^{-i a} b x^m (i b x)^{-m} \text{Gamma}(m-1,i b x)",1,"(b*E^(I*a)*x^m*Gamma[-1 + m, (-I)*b*x])/(2*((-I)*b*x)^m) + (b*x^m*Gamma[-1 + m, I*b*x])/(2*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
83,1,79,0,0.0717161,"\int x^{-3+m} \sin (a+b x) \, dx","Int[x^(-3 + m)*Sin[a + b*x],x]","\frac{1}{2} i e^{-i a} b^2 x^m (i b x)^{-m} \text{Gamma}(m-2,i b x)-\frac{1}{2} i e^{i a} b^2 x^m (-i b x)^{-m} \text{Gamma}(m-2,-i b x)","\frac{1}{2} i e^{-i a} b^2 x^m (i b x)^{-m} \text{Gamma}(m-2,i b x)-\frac{1}{2} i e^{i a} b^2 x^m (-i b x)^{-m} \text{Gamma}(m-2,-i b x)",1,"((-I/2)*b^2*E^(I*a)*x^m*Gamma[-2 + m, (-I)*b*x])/((-I)*b*x)^m + ((I/2)*b^2*x^m*Gamma[-2 + m, I*b*x])/(E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
84,1,97,0,0.1616785,"\int x^{3+m} \sin ^2(a+b x) \, dx","Int[x^(3 + m)*Sin[a + b*x]^2,x]","\frac{e^{2 i a} 2^{-m-6} x^m (-i b x)^{-m} \text{Gamma}(m+4,-2 i b x)}{b^4}+\frac{e^{-2 i a} 2^{-m-6} x^m (i b x)^{-m} \text{Gamma}(m+4,2 i b x)}{b^4}+\frac{x^{m+4}}{2 (m+4)}","\frac{e^{2 i a} 2^{-m-6} x^m (-i b x)^{-m} \text{Gamma}(m+4,-2 i b x)}{b^4}+\frac{e^{-2 i a} 2^{-m-6} x^m (i b x)^{-m} \text{Gamma}(m+4,2 i b x)}{b^4}+\frac{x^{m+4}}{2 (m+4)}",1,"x^(4 + m)/(2*(4 + m)) + (2^(-6 - m)*E^((2*I)*a)*x^m*Gamma[4 + m, (-2*I)*b*x])/(b^4*((-I)*b*x)^m) + (2^(-6 - m)*x^m*Gamma[4 + m, (2*I)*b*x])/(b^4*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
85,1,103,0,0.1428072,"\int x^{2+m} \sin ^2(a+b x) \, dx","Int[x^(2 + m)*Sin[a + b*x]^2,x]","-\frac{i e^{2 i a} 2^{-m-5} x^m (-i b x)^{-m} \text{Gamma}(m+3,-2 i b x)}{b^3}+\frac{i e^{-2 i a} 2^{-m-5} x^m (i b x)^{-m} \text{Gamma}(m+3,2 i b x)}{b^3}+\frac{x^{m+3}}{2 (m+3)}","-\frac{i e^{2 i a} 2^{-m-5} x^m (-i b x)^{-m} \text{Gamma}(m+3,-2 i b x)}{b^3}+\frac{i e^{-2 i a} 2^{-m-5} x^m (i b x)^{-m} \text{Gamma}(m+3,2 i b x)}{b^3}+\frac{x^{m+3}}{2 (m+3)}",1,"x^(3 + m)/(2*(3 + m)) - (I*2^(-5 - m)*E^((2*I)*a)*x^m*Gamma[3 + m, (-2*I)*b*x])/(b^3*((-I)*b*x)^m) + (I*2^(-5 - m)*x^m*Gamma[3 + m, (2*I)*b*x])/(b^3*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
86,1,99,0,0.1428536,"\int x^{1+m} \sin ^2(a+b x) \, dx","Int[x^(1 + m)*Sin[a + b*x]^2,x]","-\frac{e^{2 i a} 2^{-m-4} x^m (-i b x)^{-m} \text{Gamma}(m+2,-2 i b x)}{b^2}-\frac{e^{-2 i a} 2^{-m-4} x^m (i b x)^{-m} \text{Gamma}(m+2,2 i b x)}{b^2}+\frac{x^{m+2}}{2 (m+2)}","-\frac{e^{2 i a} 2^{-m-4} x^m (-i b x)^{-m} \text{Gamma}(m+2,-2 i b x)}{b^2}-\frac{e^{-2 i a} 2^{-m-4} x^m (i b x)^{-m} \text{Gamma}(m+2,2 i b x)}{b^2}+\frac{x^{m+2}}{2 (m+2)}",1,"x^(2 + m)/(2*(2 + m)) - (2^(-4 - m)*E^((2*I)*a)*x^m*Gamma[2 + m, (-2*I)*b*x])/(b^2*((-I)*b*x)^m) - (2^(-4 - m)*x^m*Gamma[2 + m, (2*I)*b*x])/(b^2*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
87,1,103,0,0.1340331,"\int x^m \sin ^2(a+b x) \, dx","Int[x^m*Sin[a + b*x]^2,x]","\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \text{Gamma}(m+1,-2 i b x)}{b}-\frac{i e^{-2 i a} 2^{-m-3} x^m (i b x)^{-m} \text{Gamma}(m+1,2 i b x)}{b}+\frac{x^{m+1}}{2 (m+1)}","\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \text{Gamma}(m+1,-2 i b x)}{b}-\frac{i e^{-2 i a} 2^{-m-3} x^m (i b x)^{-m} \text{Gamma}(m+1,2 i b x)}{b}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) + (I*2^(-3 - m)*E^((2*I)*a)*x^m*Gamma[1 + m, (-2*I)*b*x])/(b*((-I)*b*x)^m) - (I*2^(-3 - m)*x^m*Gamma[1 + m, (2*I)*b*x])/(b*E^((2*I)*a)*(I*b*x)^m)","A",5,3,12,0.2500,1,"{3312, 3307, 2181}"
88,1,83,0,0.1303486,"\int x^{-1+m} \sin ^2(a+b x) \, dx","Int[x^(-1 + m)*Sin[a + b*x]^2,x]","e^{2 i a} 2^{-m-2} x^m (-i b x)^{-m} \text{Gamma}(m,-2 i b x)+e^{-2 i a} 2^{-m-2} x^m (i b x)^{-m} \text{Gamma}(m,2 i b x)+\frac{x^m}{2 m}","e^{2 i a} 2^{-m-2} x^m (-i b x)^{-m} \text{Gamma}(m,-2 i b x)+e^{-2 i a} 2^{-m-2} x^m (i b x)^{-m} \text{Gamma}(m,2 i b x)+\frac{x^m}{2 m}",1,"x^m/(2*m) + (2^(-2 - m)*E^((2*I)*a)*x^m*Gamma[m, (-2*I)*b*x])/((-I)*b*x)^m + (2^(-2 - m)*x^m*Gamma[m, (2*I)*b*x])/(E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
89,1,101,0,0.1370954,"\int x^{-2+m} \sin ^2(a+b x) \, dx","Int[x^(-2 + m)*Sin[a + b*x]^2,x]","-i e^{2 i a} b 2^{-m-1} x^m (-i b x)^{-m} \text{Gamma}(m-1,-2 i b x)+i e^{-2 i a} b 2^{-m-1} x^m (i b x)^{-m} \text{Gamma}(m-1,2 i b x)-\frac{x^{m-1}}{2 (1-m)}","-i e^{2 i a} b 2^{-m-1} x^m (-i b x)^{-m} \text{Gamma}(m-1,-2 i b x)+i e^{-2 i a} b 2^{-m-1} x^m (i b x)^{-m} \text{Gamma}(m-1,2 i b x)-\frac{x^{m-1}}{2 (1-m)}",1,"-x^(-1 + m)/(2*(1 - m)) - (I*2^(-1 - m)*b*E^((2*I)*a)*x^m*Gamma[-1 + m, (-2*I)*b*x])/((-I)*b*x)^m + (I*2^(-1 - m)*b*x^m*Gamma[-1 + m, (2*I)*b*x])/(E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
90,1,97,0,0.1731182,"\int x^{-3+m} \sin ^2(a+b x) \, dx","Int[x^(-3 + m)*Sin[a + b*x]^2,x]","-e^{2 i a} b^2 2^{-m} x^m (-i b x)^{-m} \text{Gamma}(m-2,-2 i b x)-e^{-2 i a} b^2 2^{-m} x^m (i b x)^{-m} \text{Gamma}(m-2,2 i b x)-\frac{x^{m-2}}{2 (2-m)}","-e^{2 i a} b^2 2^{-m} x^m (-i b x)^{-m} \text{Gamma}(m-2,-2 i b x)-e^{-2 i a} b^2 2^{-m} x^m (i b x)^{-m} \text{Gamma}(m-2,2 i b x)-\frac{x^{m-2}}{2 (2-m)}",1,"-x^(-2 + m)/(2*(2 - m)) - (b^2*E^((2*I)*a)*x^m*Gamma[-2 + m, (-2*I)*b*x])/(2^m*((-I)*b*x)^m) - (b^2*x^m*Gamma[-2 + m, (2*I)*b*x])/(2^m*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
91,1,42,0,0.1232705,"\int \left(\frac{x}{\csc ^{\frac{3}{2}}(e+f x)}-\frac{1}{3} x \sqrt{\csc (e+f x)}\right) \, dx","Int[x/Csc[e + f*x]^(3/2) - (x*Sqrt[Csc[e + f*x]])/3,x]","\frac{4}{9 f^2 \csc ^{\frac{3}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{3 f \sqrt{\csc (e+f x)}}","\frac{4}{9 f^2 \csc ^{\frac{3}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{3 f \sqrt{\csc (e+f x)}}",1,"4/(9*f^2*Csc[e + f*x]^(3/2)) - (2*x*Cos[e + f*x])/(3*f*Sqrt[Csc[e + f*x]])","A",4,2,28,0.07143,1,"{4187, 4189}"
92,1,111,0,0.2093954,"\int \left(\frac{x^2}{\csc ^{\frac{3}{2}}(e+f x)}-\frac{1}{3} x^2 \sqrt{\csc (e+f x)}\right) \, dx","Int[x^2/Csc[e + f*x]^(3/2) - (x^2*Sqrt[Csc[e + f*x]])/3,x]","\frac{8 x}{9 f^2 \csc ^{\frac{3}{2}}(e+f x)}+\frac{16 \cos (e+f x)}{27 f^3 \sqrt{\csc (e+f x)}}-\frac{16 \sqrt{\sin (e+f x)} \sqrt{\csc (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{27 f^3}-\frac{2 x^2 \cos (e+f x)}{3 f \sqrt{\csc (e+f x)}}","\frac{8 x}{9 f^2 \csc ^{\frac{3}{2}}(e+f x)}+\frac{16 \cos (e+f x)}{27 f^3 \sqrt{\csc (e+f x)}}-\frac{16 \sqrt{\sin (e+f x)} \sqrt{\csc (e+f x)} F\left(\left.\frac{1}{2} \left(e+f x-\frac{\pi }{2}\right)\right|2\right)}{27 f^3}-\frac{2 x^2 \cos (e+f x)}{3 f \sqrt{\csc (e+f x)}}",1,"(8*x)/(9*f^2*Csc[e + f*x]^(3/2)) + (16*Cos[e + f*x])/(27*f^3*Sqrt[Csc[e + f*x]]) - (2*x^2*Cos[e + f*x])/(3*f*Sqrt[Csc[e + f*x]]) - (16*Sqrt[Csc[e + f*x]]*EllipticF[(e - Pi/2 + f*x)/2, 2]*Sqrt[Sin[e + f*x]])/(27*f^3)","A",7,5,32,0.1562,1,"{4188, 4189, 3769, 3771, 2641}"
93,1,42,0,0.1061794,"\int \left(\frac{x}{\csc ^{\frac{5}{2}}(e+f x)}-\frac{3 x}{5 \sqrt{\csc (e+f x)}}\right) \, dx","Int[x/Csc[e + f*x]^(5/2) - (3*x)/(5*Sqrt[Csc[e + f*x]]),x]","\frac{4}{25 f^2 \csc ^{\frac{5}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{5 f \csc ^{\frac{3}{2}}(e+f x)}","\frac{4}{25 f^2 \csc ^{\frac{5}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{5 f \csc ^{\frac{3}{2}}(e+f x)}",1,"4/(25*f^2*Csc[e + f*x]^(5/2)) - (2*x*Cos[e + f*x])/(5*f*Csc[e + f*x]^(3/2))","A",4,2,28,0.07143,1,"{4187, 4189}"
94,1,83,0,0.1333727,"\int \left(\frac{x}{\csc ^{\frac{7}{2}}(e+f x)}-\frac{5}{21} x \sqrt{\csc (e+f x)}\right) \, dx","Int[x/Csc[e + f*x]^(7/2) - (5*x*Sqrt[Csc[e + f*x]])/21,x]","\frac{20}{63 f^2 \csc ^{\frac{3}{2}}(e+f x)}+\frac{4}{49 f^2 \csc ^{\frac{7}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{7 f \csc ^{\frac{5}{2}}(e+f x)}-\frac{10 x \cos (e+f x)}{21 f \sqrt{\csc (e+f x)}}","\frac{20}{63 f^2 \csc ^{\frac{3}{2}}(e+f x)}+\frac{4}{49 f^2 \csc ^{\frac{7}{2}}(e+f x)}-\frac{2 x \cos (e+f x)}{7 f \csc ^{\frac{5}{2}}(e+f x)}-\frac{10 x \cos (e+f x)}{21 f \sqrt{\csc (e+f x)}}",1,"4/(49*f^2*Csc[e + f*x]^(7/2)) - (2*x*Cos[e + f*x])/(7*f*Csc[e + f*x]^(5/2)) + 20/(63*f^2*Csc[e + f*x]^(3/2)) - (10*x*Cos[e + f*x])/(21*f*Sqrt[Csc[e + f*x]])","A",5,2,28,0.07143,1,"{4187, 4189}"
95,1,90,0,0.1182217,"\int (c+d x)^3 (a+a \sin (e+f x)) \, dx","Int[(c + d*x)^3*(a + a*Sin[e + f*x]),x]","\frac{6 a d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 a d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{a (c+d x)^3 \cos (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \sin (e+f x)}{f^4}","\frac{6 a d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 a d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{a (c+d x)^3 \cos (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \sin (e+f x)}{f^4}",1,"(a*(c + d*x)^4)/(4*d) + (6*a*d^2*(c + d*x)*Cos[e + f*x])/f^3 - (a*(c + d*x)^3*Cos[e + f*x])/f - (6*a*d^3*Sin[e + f*x])/f^4 + (3*a*d*(c + d*x)^2*Sin[e + f*x])/f^2","A",6,3,18,0.1667,1,"{3317, 3296, 2637}"
96,1,68,0,0.0883813,"\int (c+d x)^2 (a+a \sin (e+f x)) \, dx","Int[(c + d*x)^2*(a + a*Sin[e + f*x]),x]","\frac{2 a d (c+d x) \sin (e+f x)}{f^2}-\frac{a (c+d x)^2 \cos (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}+\frac{2 a d^2 \cos (e+f x)}{f^3}","\frac{2 a d (c+d x) \sin (e+f x)}{f^2}-\frac{a (c+d x)^2 \cos (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}+\frac{2 a d^2 \cos (e+f x)}{f^3}",1,"(a*(c + d*x)^3)/(3*d) + (2*a*d^2*Cos[e + f*x])/f^3 - (a*(c + d*x)^2*Cos[e + f*x])/f + (2*a*d*(c + d*x)*Sin[e + f*x])/f^2","A",5,3,18,0.1667,1,"{3317, 3296, 2638}"
97,1,45,0,0.0422202,"\int (c+d x) (a+a \sin (e+f x)) \, dx","Int[(c + d*x)*(a + a*Sin[e + f*x]),x]","-\frac{a (c+d x) \cos (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}+\frac{a d \sin (e+f x)}{f^2}","-\frac{a (c+d x) \cos (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}+\frac{a d \sin (e+f x)}{f^2}",1,"(a*(c + d*x)^2)/(2*d) - (a*(c + d*x)*Cos[e + f*x])/f + (a*d*Sin[e + f*x])/f^2","A",4,3,16,0.1875,1,"{3317, 3296, 2637}"
98,1,64,0,0.1500894,"\int \frac{a+a \sin (e+f x)}{c+d x} \, dx","Int[(a + a*Sin[e + f*x])/(c + d*x),x]","\frac{a \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{a \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{a \log (c+d x)}{d}","\frac{a \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{a \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{a \log (c+d x)}{d}",1,"(a*Log[c + d*x])/d + (a*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d + (a*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3299, 3302}"
99,1,88,0,0.2137198,"\int \frac{a+a \sin (e+f x)}{(c+d x)^2} \, dx","Int[(a + a*Sin[e + f*x])/(c + d*x)^2,x]","\frac{a f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{a f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \sin (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}","\frac{a f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{a f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \sin (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}",1,"-(a/(d*(c + d*x))) + (a*f*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d^2 - (a*Sin[e + f*x])/(d*(c + d*x)) - (a*f*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3299, 3302}"
100,1,123,0,0.2565654,"\int \frac{a+a \sin (e+f x)}{(c+d x)^3} \, dx","Int[(a + a*Sin[e + f*x])/(c + d*x)^3,x]","-\frac{a f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{2 d^3}-\frac{a f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{a f \cos (e+f x)}{2 d^2 (c+d x)}-\frac{a \sin (e+f x)}{2 d (c+d x)^2}-\frac{a}{2 d (c+d x)^2}","-\frac{a f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{2 d^3}-\frac{a f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{a f \cos (e+f x)}{2 d^2 (c+d x)}-\frac{a \sin (e+f x)}{2 d (c+d x)^2}-\frac{a}{2 d (c+d x)^2}",1,"-a/(2*d*(c + d*x)^2) - (a*f*Cos[e + f*x])/(2*d^2*(c + d*x)) - (a*f^2*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/(2*d^3) - (a*Sin[e + f*x])/(2*d*(c + d*x)^2) - (a*f^2*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/(2*d^3)","A",7,5,18,0.2778,1,"{3317, 3297, 3303, 3299, 3302}"
101,1,237,0,0.2954007,"\int (c+d x)^3 (a+a \sin (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + a*Sin[e + f*x])^2,x]","\frac{12 a^2 d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 a^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 a^2 c d^2 x}{4 f^2}+\frac{3 a^2 d (c+d x)^2 \sin ^2(e+f x)}{4 f^2}+\frac{6 a^2 d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{2 a^2 (c+d x)^3 \cos (e+f x)}{f}-\frac{a^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{3 a^2 (c+d x)^4}{8 d}-\frac{3 a^2 d^3 \sin ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \sin (e+f x)}{f^4}-\frac{3 a^2 d^3 x^2}{8 f^2}","\frac{12 a^2 d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 a^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 a^2 c d^2 x}{4 f^2}+\frac{3 a^2 d (c+d x)^2 \sin ^2(e+f x)}{4 f^2}+\frac{6 a^2 d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{2 a^2 (c+d x)^3 \cos (e+f x)}{f}-\frac{a^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{3 a^2 (c+d x)^4}{8 d}-\frac{3 a^2 d^3 \sin ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \sin (e+f x)}{f^4}-\frac{3 a^2 d^3 x^2}{8 f^2}",1,"(-3*a^2*c*d^2*x)/(4*f^2) - (3*a^2*d^3*x^2)/(8*f^2) + (3*a^2*(c + d*x)^4)/(8*d) + (12*a^2*d^2*(c + d*x)*Cos[e + f*x])/f^3 - (2*a^2*(c + d*x)^3*Cos[e + f*x])/f - (12*a^2*d^3*Sin[e + f*x])/f^4 + (6*a^2*d*(c + d*x)^2*Sin[e + f*x])/f^2 + (3*a^2*d^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) - (a^2*(c + d*x)^3*Cos[e + f*x]*Sin[e + f*x])/(2*f) - (3*a^2*d^3*Sin[e + f*x]^2)/(8*f^4) + (3*a^2*d*(c + d*x)^2*Sin[e + f*x]^2)/(4*f^2)","A",10,6,20,0.3000,1,"{3317, 3296, 2637, 3311, 32, 3310}"
102,1,168,0,0.1920804,"\int (c+d x)^2 (a+a \sin (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + a*Sin[e + f*x])^2,x]","\frac{a^2 d (c+d x) \sin ^2(e+f x)}{2 f^2}+\frac{4 a^2 d (c+d x) \sin (e+f x)}{f^2}-\frac{2 a^2 (c+d x)^2 \cos (e+f x)}{f}-\frac{a^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^3}{2 d}+\frac{4 a^2 d^2 \cos (e+f x)}{f^3}+\frac{a^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{a^2 d^2 x}{4 f^2}","\frac{a^2 d (c+d x) \sin ^2(e+f x)}{2 f^2}+\frac{4 a^2 d (c+d x) \sin (e+f x)}{f^2}-\frac{2 a^2 (c+d x)^2 \cos (e+f x)}{f}-\frac{a^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^3}{2 d}+\frac{4 a^2 d^2 \cos (e+f x)}{f^3}+\frac{a^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{a^2 d^2 x}{4 f^2}",1,"-(a^2*d^2*x)/(4*f^2) + (a^2*(c + d*x)^3)/(2*d) + (4*a^2*d^2*Cos[e + f*x])/f^3 - (2*a^2*(c + d*x)^2*Cos[e + f*x])/f + (4*a^2*d*(c + d*x)*Sin[e + f*x])/f^2 + (a^2*d^2*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) - (a^2*(c + d*x)^2*Cos[e + f*x]*Sin[e + f*x])/(2*f) + (a^2*d*(c + d*x)*Sin[e + f*x]^2)/(2*f^2)","A",9,7,20,0.3500,1,"{3317, 3296, 2638, 3311, 32, 2635, 8}"
103,1,118,0,0.1037401,"\int (c+d x) (a+a \sin (e+f x))^2 \, dx","Int[(c + d*x)*(a + a*Sin[e + f*x])^2,x]","-\frac{2 a^2 (c+d x) \cos (e+f x)}{f}-\frac{a^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{1}{2} a^2 c x+\frac{a^2 d \sin ^2(e+f x)}{4 f^2}+\frac{2 a^2 d \sin (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2","-\frac{2 a^2 (c+d x) \cos (e+f x)}{f}-\frac{a^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{1}{2} a^2 c x+\frac{a^2 d \sin ^2(e+f x)}{4 f^2}+\frac{2 a^2 d \sin (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2",1,"(a^2*c*x)/2 + (a^2*d*x^2)/4 + (a^2*(c + d*x)^2)/(2*d) - (2*a^2*(c + d*x)*Cos[e + f*x])/f + (2*a^2*d*Sin[e + f*x])/f^2 - (a^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(2*f) + (a^2*d*Sin[e + f*x]^2)/(4*f^2)","A",6,4,18,0.2222,1,"{3317, 3296, 2637, 3310}"
104,1,145,0,0.3706852,"\int \frac{(a+a \sin (e+f x))^2}{c+d x} \, dx","Int[(a + a*Sin[e + f*x])^2/(c + d*x),x]","\frac{2 a^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}-\frac{a^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}+\frac{a^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{2 a^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{3 a^2 \log (c+d x)}{2 d}","\frac{2 a^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}-\frac{a^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}+\frac{a^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{2 a^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{3 a^2 \log (c+d x)}{2 d}",1,"-(a^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(2*d) + (3*a^2*Log[c + d*x])/(2*d) + (2*a^2*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d + (2*a^2*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d + (a^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(2*d)","A",9,5,20,0.2500,1,"{3318, 3312, 3303, 3299, 3302}"
105,1,162,0,0.3325805,"\int \frac{(a+a \sin (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + a*Sin[e + f*x])^2/(c + d*x)^2,x]","\frac{a^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{2 a^2 f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a^2 f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}+\frac{a^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{4 a^2 \sin ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d (c+d x)}","\frac{a^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{2 a^2 f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a^2 f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}+\frac{a^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{4 a^2 \sin ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d (c+d x)}",1,"(2*a^2*f*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d^2 + (a^2*f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/d^2 - (4*a^2*Sin[e/2 + Pi/4 + (f*x)/2]^4)/(d*(c + d*x)) - (2*a^2*f*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2 + (a^2*f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/d^2","A",9,5,20,0.2500,1,"{3318, 3313, 3303, 3299, 3302}"
106,1,225,0,0.5061815,"\int \frac{(a+a \sin (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + a*Sin[e + f*x])^2/(c + d*x)^3,x]","-\frac{a^2 f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^3}+\frac{a^2 f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{d^3}-\frac{a^2 f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}-\frac{a^2 f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{4 a^2 f \sin ^3\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d^2 (c+d x)}-\frac{2 a^2 \sin ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d (c+d x)^2}","-\frac{a^2 f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^3}+\frac{a^2 f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{d^3}-\frac{a^2 f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}-\frac{a^2 f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{4 a^2 f \sin ^3\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d^2 (c+d x)}-\frac{2 a^2 \sin ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{d (c+d x)^2}",1,"(a^2*f^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/d^3 - (a^2*f^2*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d^3 - (4*a^2*f*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]^3)/(d^2*(c + d*x)) - (2*a^2*Sin[e/2 + Pi/4 + (f*x)/2]^4)/(d*(c + d*x)^2) - (a^2*f^2*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^3 - (a^2*f^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/d^3","A",15,8,20,0.4000,1,"{3318, 3314, 3309, 31, 3303, 3299, 3302, 3312}"
107,1,148,0,0.3061607,"\int \frac{(c+d x)^3}{a+a \sin (e+f x)} \, dx","Int[(c + d*x)^3/(a + a*Sin[e + f*x]),x]","-\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{a f^4}+\frac{6 d (c+d x)^2 \log \left(1-i e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^3}{a f}","-\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{a f^4}+\frac{6 d (c+d x)^2 \log \left(1-i e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^3}{a f}",1,"((-I)*(c + d*x)^3)/(a*f) - ((c + d*x)^3*Cot[e/2 + Pi/4 + (f*x)/2])/(a*f) + (6*d*(c + d*x)^2*Log[1 - I*E^(I*(e + f*x))])/(a*f^2) - ((12*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/(a*f^3) + (12*d^3*PolyLog[3, I*E^(I*(e + f*x))])/(a*f^4)","A",7,7,20,0.3500,1,"{3318, 4184, 3717, 2190, 2531, 2282, 6589}"
108,1,113,0,0.2183302,"\int \frac{(c+d x)^2}{a+a \sin (e+f x)} \, dx","Int[(c + d*x)^2/(a + a*Sin[e + f*x]),x]","-\frac{4 i d^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a f^3}+\frac{4 d (c+d x) \log \left(1-i e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^2}{a f}","-\frac{4 i d^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a f^3}+\frac{4 d (c+d x) \log \left(1-i e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^2}{a f}",1,"((-I)*(c + d*x)^2)/(a*f) - ((c + d*x)^2*Cot[e/2 + Pi/4 + (f*x)/2])/(a*f) + (4*d*(c + d*x)*Log[1 - I*E^(I*(e + f*x))])/(a*f^2) - ((4*I)*d^2*PolyLog[2, I*E^(I*(e + f*x))])/(a*f^3)","A",6,6,20,0.3000,1,"{3318, 4184, 3717, 2190, 2279, 2391}"
109,1,60,0,0.0636577,"\int \frac{c+d x}{a+a \sin (e+f x)} \, dx","Int[(c + d*x)/(a + a*Sin[e + f*x]),x]","\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^2}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}","\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^2}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}",1,"-(((c + d*x)*Cot[e/2 + Pi/4 + (f*x)/2])/(a*f)) + (2*d*Log[Sin[e/2 + Pi/4 + (f*x)/2]])/(a*f^2)","A",3,3,18,0.1667,1,"{3318, 4184, 3475}"
110,0,0,0,0.0606529,"\int \frac{1}{(c+d x) (a+a \sin (e+f x))} \, dx","Int[1/((c + d*x)*(a + a*Sin[e + f*x])),x]","\int \frac{1}{(c+d x) (a+a \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \sin (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
111,0,0,0,0.0651236,"\int \frac{1}{(c+d x)^2 (a+a \sin (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + a*Sin[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+a \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \sin (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
112,1,309,0,0.3767332,"\int \frac{(c+d x)^3}{(a+a \sin (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + a*Sin[e + f*x])^2,x]","-\frac{4 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{a^2 f^4}-\frac{2 d^2 (c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a^2 f^3}+\frac{2 d (c+d x)^2 \log \left(1-i e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a^2 f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{i (c+d x)^3}{3 a^2 f}+\frac{4 d^3 \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a^2 f^4}","-\frac{4 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,i e^{i (e+f x)}\right)}{a^2 f^4}-\frac{2 d^2 (c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a^2 f^3}+\frac{2 d (c+d x)^2 \log \left(1-i e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a^2 f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{i (c+d x)^3}{3 a^2 f}+\frac{4 d^3 \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a^2 f^4}",1,"((-I/3)*(c + d*x)^3)/(a^2*f) - (2*d^2*(c + d*x)*Cot[e/2 + Pi/4 + (f*x)/2])/(a^2*f^3) - ((c + d*x)^3*Cot[e/2 + Pi/4 + (f*x)/2])/(3*a^2*f) - (d*(c + d*x)^2*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(2*a^2*f^2) - ((c + d*x)^3*Cot[e/2 + Pi/4 + (f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(6*a^2*f) + (2*d*(c + d*x)^2*Log[1 - I*E^(I*(e + f*x))])/(a^2*f^2) + (4*d^3*Log[Sin[e/2 + Pi/4 + (f*x)/2]])/(a^2*f^4) - ((4*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(e + f*x))])/(a^2*f^3) + (4*d^3*PolyLog[3, I*E^(I*(e + f*x))])/(a^2*f^4)","A",10,9,20,0.4500,1,"{3318, 4186, 4184, 3475, 3717, 2190, 2531, 2282, 6589}"
113,1,243,0,0.2872148,"\int \frac{(c+d x)^2}{(a+a \sin (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + a*Sin[e + f*x])^2,x]","-\frac{4 i d^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{3 a^2 f^3}+\frac{4 d (c+d x) \log \left(1-i e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{i (c+d x)^2}{3 a^2 f}-\frac{2 d^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f^3}","-\frac{4 i d^2 \text{PolyLog}\left(2,i e^{i (e+f x)}\right)}{3 a^2 f^3}+\frac{4 d (c+d x) \log \left(1-i e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{i (c+d x)^2}{3 a^2 f}-\frac{2 d^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f^3}",1,"((-I/3)*(c + d*x)^2)/(a^2*f) - (2*d^2*Cot[e/2 + Pi/4 + (f*x)/2])/(3*a^2*f^3) - ((c + d*x)^2*Cot[e/2 + Pi/4 + (f*x)/2])/(3*a^2*f) - (d*(c + d*x)*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(3*a^2*f^2) - ((c + d*x)^2*Cot[e/2 + Pi/4 + (f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(6*a^2*f) + (4*d*(c + d*x)*Log[1 - I*E^(I*(e + f*x))])/(3*a^2*f^2) - (((4*I)/3)*d^2*PolyLog[2, I*E^(I*(e + f*x))])/(a^2*f^3)","A",9,9,20,0.4500,1,"{3318, 4186, 3767, 8, 4184, 3717, 2190, 2279, 2391}"
114,1,148,0,0.0891686,"\int \frac{c+d x}{(a+a \sin (e+f x))^2} \, dx","Int[(c + d*x)/(a + a*Sin[e + f*x])^2,x]","-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{d \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f^2}+\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{3 a^2 f^2}","-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{3 a^2 f}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f}-\frac{d \csc ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{6 a^2 f^2}+\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{3 a^2 f^2}",1,"-((c + d*x)*Cot[e/2 + Pi/4 + (f*x)/2])/(3*a^2*f) - (d*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(6*a^2*f^2) - ((c + d*x)*Cot[e/2 + Pi/4 + (f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]^2)/(6*a^2*f) + (2*d*Log[Sin[e/2 + Pi/4 + (f*x)/2]])/(3*a^2*f^2)","A",4,4,18,0.2222,1,"{3318, 4185, 4184, 3475}"
115,0,0,0,0.0557266,"\int \frac{1}{(c+d x) (a+a \sin (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + a*Sin[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+a \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \sin (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Sin[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
116,0,0,0,0.0518527,"\int \frac{1}{(c+d x)^2 (a+a \sin (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + a*Sin[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+a \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \sin (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Sin[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
117,1,147,0,0.2951397,"\int \frac{(c+d x)^3}{a-a \sin (e+f x)} \, dx","Int[(c + d*x)^3/(a - a*Sin[e + f*x]),x]","-\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{a f^4}+\frac{6 d (c+d x)^2 \log \left(1+i e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^3}{a f}","-\frac{12 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-i e^{i (e+f x)}\right)}{a f^4}+\frac{6 d (c+d x)^2 \log \left(1+i e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^3}{a f}",1,"((-I)*(c + d*x)^3)/(a*f) + (6*d*(c + d*x)^2*Log[1 + I*E^(I*(e + f*x))])/(a*f^2) - ((12*I)*d^2*(c + d*x)*PolyLog[2, (-I)*E^(I*(e + f*x))])/(a*f^3) + (12*d^3*PolyLog[3, (-I)*E^(I*(e + f*x))])/(a*f^4) + ((c + d*x)^3*Tan[e/2 + Pi/4 + (f*x)/2])/(a*f)","A",7,7,21,0.3333,1,"{3318, 4184, 3717, 2190, 2531, 2282, 6589}"
118,1,112,0,0.2121828,"\int \frac{(c+d x)^2}{a-a \sin (e+f x)} \, dx","Int[(c + d*x)^2/(a - a*Sin[e + f*x]),x]","-\frac{4 i d^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{a f^3}+\frac{4 d (c+d x) \log \left(1+i e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^2}{a f}","-\frac{4 i d^2 \text{PolyLog}\left(2,-i e^{i (e+f x)}\right)}{a f^3}+\frac{4 d (c+d x) \log \left(1+i e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}-\frac{i (c+d x)^2}{a f}",1,"((-I)*(c + d*x)^2)/(a*f) + (4*d*(c + d*x)*Log[1 + I*E^(I*(e + f*x))])/(a*f^2) - ((4*I)*d^2*PolyLog[2, (-I)*E^(I*(e + f*x))])/(a*f^3) + ((c + d*x)^2*Tan[e/2 + Pi/4 + (f*x)/2])/(a*f)","A",6,6,21,0.2857,1,"{3318, 4184, 3717, 2190, 2279, 2391}"
119,1,59,0,0.06638,"\int \frac{c+d x}{a-a \sin (e+f x)} \, dx","Int[(c + d*x)/(a - a*Sin[e + f*x]),x]","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^2}","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{a f}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^2}",1,"(2*d*Log[Cos[e/2 + Pi/4 + (f*x)/2]])/(a*f^2) + ((c + d*x)*Tan[e/2 + Pi/4 + (f*x)/2])/(a*f)","A",3,3,19,0.1579,1,"{3318, 4184, 3475}"
120,0,0,0,0.0748442,"\int \frac{1}{(c+d x) (a-a \sin (e+f x))} \, dx","Int[1/((c + d*x)*(a - a*Sin[e + f*x])),x]","\int \frac{1}{(c+d x) (a-a \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a-a \sin (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a - a*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
121,0,0,0,0.0642,"\int \frac{1}{(c+d x)^2 (a-a \sin (e+f x))} \, dx","Int[1/((c + d*x)^2*(a - a*Sin[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a-a \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a-a \sin (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a - a*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
122,1,120,0,0.1405269,"\int x^3 \sqrt{a+a \sin (c+d x)} \, dx","Int[x^3*Sqrt[a + a*Sin[c + d*x]],x]","\frac{12 x^2 \sqrt{a \sin (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \sin (c+d x)+a}}{d^4}+\frac{48 x \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d^3}-\frac{2 x^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}","\frac{12 x^2 \sqrt{a \sin (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \sin (c+d x)+a}}{d^4}+\frac{48 x \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d^3}-\frac{2 x^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}",1,"(-96*Sqrt[a + a*Sin[c + d*x]])/d^4 + (12*x^2*Sqrt[a + a*Sin[c + d*x]])/d^2 + (48*x*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/d^3 - (2*x^3*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/d","A",5,3,18,0.1667,1,"{3319, 3296, 2638}"
123,1,98,0,0.1030699,"\int x^2 \sqrt{a+a \sin (c+d x)} \, dx","Int[x^2*Sqrt[a + a*Sin[c + d*x]],x]","\frac{8 x \sqrt{a \sin (c+d x)+a}}{d^2}+\frac{16 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d^3}-\frac{2 x^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}","\frac{8 x \sqrt{a \sin (c+d x)+a}}{d^2}+\frac{16 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d^3}-\frac{2 x^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}",1,"(8*x*Sqrt[a + a*Sin[c + d*x]])/d^2 + (16*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/d^3 - (2*x^2*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/d","A",4,3,18,0.1667,1,"{3319, 3296, 2638}"
124,1,58,0,0.0681968,"\int x \sqrt{a+a \sin (c+d x)} \, dx","Int[x*Sqrt[a + a*Sin[c + d*x]],x]","\frac{4 \sqrt{a \sin (c+d x)+a}}{d^2}-\frac{2 x \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}","\frac{4 \sqrt{a \sin (c+d x)+a}}{d^2}-\frac{2 x \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{d}",1,"(4*Sqrt[a + a*Sin[c + d*x]])/d^2 - (2*x*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/d","A",3,3,16,0.1875,1,"{3319, 3296, 2638}"
125,1,101,0,0.1390425,"\int \frac{\sqrt{a+a \sin (c+d x)}}{x} \, dx","Int[Sqrt[a + a*Sin[c + d*x]]/x,x]","\sin \left(\frac{1}{4} (2 c+\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}+\cos \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}","\sin \left(\frac{1}{4} (2 c+\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}+\cos \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}",1,"CosIntegral[(d*x)/2]*Csc[c/2 + Pi/4 + (d*x)/2]*Sin[(2*c + Pi)/4]*Sqrt[a + a*Sin[c + d*x]] + Cos[(2*c + Pi)/4]*Csc[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]]*SinIntegral[(d*x)/2]","A",4,4,18,0.2222,1,"{3319, 3303, 3299, 3302}"
126,1,130,0,0.1531899,"\int \frac{\sqrt{a+a \sin (c+d x)}}{x^2} \, dx","Int[Sqrt[a + a*Sin[c + d*x]]/x^2,x]","-\frac{1}{2} d \sin \left(\frac{1}{4} (2 c-\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{1}{2} d \sin \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{\sqrt{a \sin (c+d x)+a}}{x}","-\frac{1}{2} d \sin \left(\frac{1}{4} (2 c-\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{1}{2} d \sin \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{\sqrt{a \sin (c+d x)+a}}{x}",1,"-(Sqrt[a + a*Sin[c + d*x]]/x) - (d*CosIntegral[(d*x)/2]*Csc[c/2 + Pi/4 + (d*x)/2]*Sin[(2*c - Pi)/4]*Sqrt[a + a*Sin[c + d*x]])/2 - (d*Csc[c/2 + Pi/4 + (d*x)/2]*Sin[(2*c + Pi)/4]*Sqrt[a + a*Sin[c + d*x]]*SinIntegral[(d*x)/2])/2","A",5,5,18,0.2778,1,"{3319, 3297, 3303, 3299, 3302}"
127,1,174,0,0.1930826,"\int \frac{\sqrt{a+a \sin (c+d x)}}{x^3} \, dx","Int[Sqrt[a + a*Sin[c + d*x]]/x^3,x]","-\frac{1}{8} d^2 \sin \left(\frac{1}{4} (2 c+\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{1}{8} d^2 \cos \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{\sqrt{a \sin (c+d x)+a}}{2 x^2}-\frac{d \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{4 x}","-\frac{1}{8} d^2 \sin \left(\frac{1}{4} (2 c+\pi )\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{1}{8} d^2 \cos \left(\frac{1}{4} (2 c+\pi )\right) \text{Si}\left(\frac{d x}{2}\right) \csc \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}-\frac{\sqrt{a \sin (c+d x)+a}}{2 x^2}-\frac{d \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (c+d x)+a}}{4 x}",1,"-Sqrt[a + a*Sin[c + d*x]]/(2*x^2) - (d*Cot[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]])/(4*x) - (d^2*CosIntegral[(d*x)/2]*Csc[c/2 + Pi/4 + (d*x)/2]*Sin[(2*c + Pi)/4]*Sqrt[a + a*Sin[c + d*x]])/8 - (d^2*Cos[(2*c + Pi)/4]*Csc[c/2 + Pi/4 + (d*x)/2]*Sqrt[a + a*Sin[c + d*x]]*SinIntegral[(d*x)/2])/8","A",6,5,18,0.2778,1,"{3319, 3297, 3303, 3299, 3302}"
128,1,337,0,0.2300832,"\int x^3 (a+a \sin (e+f x))^{3/2} \, dx","Int[x^3*(a + a*Sin[e + f*x])^(3/2),x]","\frac{8 a x^2 \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f^2}+\frac{16 a x^2 \sqrt{a \sin (e+f x)+a}}{f^2}-\frac{64 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{27 f^4}-\frac{1280 a \sqrt{a \sin (e+f x)+a}}{9 f^4}+\frac{32 a x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}+\frac{640 a x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}-\frac{4 a x^3 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}","\frac{8 a x^2 \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f^2}+\frac{16 a x^2 \sqrt{a \sin (e+f x)+a}}{f^2}-\frac{64 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{27 f^4}-\frac{1280 a \sqrt{a \sin (e+f x)+a}}{9 f^4}+\frac{32 a x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}+\frac{640 a x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}-\frac{4 a x^3 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}",1,"(-1280*a*Sqrt[a + a*Sin[e + f*x]])/(9*f^4) + (16*a*x^2*Sqrt[a + a*Sin[e + f*x]])/f^2 + (640*a*x*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(9*f^3) - (8*a*x^3*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) + (32*a*x*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(9*f^3) - (4*a*x^3*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) - (64*a*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/(27*f^4) + (8*a*x^2*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/(3*f^2)","A",9,5,18,0.2778,1,"{3319, 3311, 3296, 2638, 3310}"
129,1,271,0,0.1793066,"\int x^2 (a+a \sin (e+f x))^{3/2} \, dx","Int[x^2*(a + a*Sin[e + f*x])^(3/2),x]","\frac{16 a x \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^2}+\frac{32 a x \sqrt{a \sin (e+f x)+a}}{3 f^2}+\frac{224 a \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}-\frac{32 a \cos ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{27 f^3}-\frac{4 a x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}","\frac{16 a x \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^2}+\frac{32 a x \sqrt{a \sin (e+f x)+a}}{3 f^2}+\frac{224 a \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^3}-\frac{32 a \cos ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{27 f^3}-\frac{4 a x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}",1,"(32*a*x*Sqrt[a + a*Sin[e + f*x]])/(3*f^2) + (224*a*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(9*f^3) - (8*a*x^2*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) - (32*a*Cos[e/2 + Pi/4 + (f*x)/2]^2*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(27*f^3) - (4*a*x^2*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) + (16*a*x*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/(9*f^2)","A",7,5,18,0.2778,1,"{3319, 3311, 3296, 2638, 2633}"
130,1,165,0,0.0911621,"\int x (a+a \sin (e+f x))^{3/2} \, dx","Int[x*(a + a*Sin[e + f*x])^(3/2),x]","\frac{8 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^2}+\frac{16 a \sqrt{a \sin (e+f x)+a}}{3 f^2}-\frac{4 a x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}","\frac{8 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{9 f^2}+\frac{16 a \sqrt{a \sin (e+f x)+a}}{3 f^2}-\frac{4 a x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}-\frac{8 a x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{3 f}",1,"(16*a*Sqrt[a + a*Sin[e + f*x]])/(3*f^2) - (8*a*x*Cot[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) - (4*a*x*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(3*f) + (8*a*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/(9*f^2)","A",4,4,16,0.2500,1,"{3319, 3310, 3296, 2638}"
131,1,221,0,0.2759931,"\int \frac{(a+a \sin (e+f x))^{3/2}}{x} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)/x,x]","\frac{3}{2} a \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{1}{2} a \cos \left(\frac{3}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{1}{2} a \sin \left(\frac{3}{4} (2 e-\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{2} a \cos \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}","\frac{3}{2} a \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{1}{2} a \cos \left(\frac{3}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{1}{2} a \sin \left(\frac{3}{4} (2 e-\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{2} a \cos \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}",1,"(a*Cos[(3*(2*e - Pi))/4]*CosIntegral[(3*f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/2 + (3*a*CosIntegral[(f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(2*e + Pi)/4]*Sqrt[a + a*Sin[e + f*x]])/2 + (3*a*Cos[(2*e + Pi)/4]*Csc[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(f*x)/2])/2 - (a*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(3*(2*e - Pi))/4]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(3*f*x)/2])/2","A",9,5,18,0.2778,1,"{3319, 3312, 3303, 3299, 3302}"
132,1,263,0,0.3004117,"\int \frac{(a+a \sin (e+f x))^{3/2}}{x^2} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)/x^2,x]","-\frac{3}{4} a f \sin \left(\frac{1}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{4} a f \sin \left(\frac{1}{4} (6 e+\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{3}{4} a f \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{4} a f \cos \left(\frac{1}{4} (6 e+\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{2 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{x}","-\frac{3}{4} a f \sin \left(\frac{1}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{4} a f \sin \left(\frac{1}{4} (6 e+\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{3}{4} a f \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{3}{4} a f \cos \left(\frac{1}{4} (6 e+\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{2 a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{x}",1,"(-3*a*f*CosIntegral[(f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(2*e - Pi)/4]*Sqrt[a + a*Sin[e + f*x]])/4 + (3*a*f*CosIntegral[(3*f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(6*e + Pi)/4]*Sqrt[a + a*Sin[e + f*x]])/4 - (2*a*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/x - (3*a*f*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(2*e + Pi)/4]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(f*x)/2])/4 + (3*a*f*Cos[(6*e + Pi)/4]*Csc[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(3*f*x)/2])/4","A",9,5,18,0.2778,1,"{3319, 3313, 3303, 3299, 3302}"
133,1,332,0,0.3755859,"\int \frac{(a+a \sin (e+f x))^{3/2}}{x^3} \, dx","Int[(a + a*Sin[e + f*x])^(3/2)/x^3,x]","-\frac{3}{16} a f^2 \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{9}{16} a f^2 \cos \left(\frac{3}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{9}{16} a f^2 \sin \left(\frac{3}{4} (2 e-\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{3}{16} a f^2 \cos \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{x^2}-\frac{3 a f \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{2 x}","-\frac{3}{16} a f^2 \sin \left(\frac{1}{4} (2 e+\pi )\right) \text{CosIntegral}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{9}{16} a f^2 \cos \left(\frac{3}{4} (2 e-\pi )\right) \text{CosIntegral}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}+\frac{9}{16} a f^2 \sin \left(\frac{3}{4} (2 e-\pi )\right) \text{Si}\left(\frac{3 f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{3}{16} a f^2 \cos \left(\frac{1}{4} (2 e+\pi )\right) \text{Si}\left(\frac{f x}{2}\right) \csc \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}-\frac{a \sin ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{x^2}-\frac{3 a f \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \sqrt{a \sin (e+f x)+a}}{2 x}",1,"(-9*a*f^2*Cos[(3*(2*e - Pi))/4]*CosIntegral[(3*f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/16 - (3*a*f^2*CosIntegral[(f*x)/2]*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(2*e + Pi)/4]*Sqrt[a + a*Sin[e + f*x]])/16 - (3*a*f*Cos[e/2 + Pi/4 + (f*x)/2]*Sin[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]])/(2*x) - (a*Sin[e/2 + Pi/4 + (f*x)/2]^2*Sqrt[a + a*Sin[e + f*x]])/x^2 - (3*a*f^2*Cos[(2*e + Pi)/4]*Csc[e/2 + Pi/4 + (f*x)/2]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(f*x)/2])/16 + (9*a*f^2*Csc[e/2 + Pi/4 + (f*x)/2]*Sin[(3*(2*e - Pi))/4]*Sqrt[a + a*Sin[e + f*x]]*SinIntegral[(3*f*x)/2])/16","A",13,6,18,0.3333,1,"{3319, 3314, 3303, 3299, 3302, 3312}"
134,1,417,0,0.2492563,"\int \frac{x^3}{\sqrt{a+a \sin (c+d x)}} \, dx","Int[x^3/Sqrt[a + a*Sin[c + d*x]],x]","\frac{12 i x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{12 i x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{48 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}+\frac{48 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}-\frac{96 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^4 \sqrt{a \sin (c+d x)+a}}+\frac{96 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^4 \sqrt{a \sin (c+d x)+a}}-\frac{4 x^3 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}","\frac{12 i x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{12 i x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{48 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}+\frac{48 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}-\frac{96 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^4 \sqrt{a \sin (c+d x)+a}}+\frac{96 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^4 \sqrt{a \sin (c+d x)+a}}-\frac{4 x^3 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}",1,"(-4*x^3*ArcTanh[E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d*Sqrt[a + a*Sin[c + d*x]]) + ((12*I)*x^2*PolyLog[2, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]]) - ((12*I)*x^2*PolyLog[2, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]]) - (48*x*PolyLog[3, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^3*Sqrt[a + a*Sin[c + d*x]]) + (48*x*PolyLog[3, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^3*Sqrt[a + a*Sin[c + d*x]]) - ((96*I)*PolyLog[4, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^4*Sqrt[a + a*Sin[c + d*x]]) + ((96*I)*PolyLog[4, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^4*Sqrt[a + a*Sin[c + d*x]])","A",10,6,18,0.3333,1,"{3319, 4183, 2531, 6609, 2282, 6589}"
135,1,293,0,0.1833182,"\int \frac{x^2}{\sqrt{a+a \sin (c+d x)}} \, dx","Int[x^2/Sqrt[a + a*Sin[c + d*x]],x]","\frac{8 i x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{8 i x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{16 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}+\frac{16 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}-\frac{4 x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}","\frac{8 i x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{8 i x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{16 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}+\frac{16 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^3 \sqrt{a \sin (c+d x)+a}}-\frac{4 x^2 \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}",1,"(-4*x^2*ArcTanh[E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d*Sqrt[a + a*Sin[c + d*x]]) + ((8*I)*x*PolyLog[2, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]]) - ((8*I)*x*PolyLog[2, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]]) - (16*PolyLog[3, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^3*Sqrt[a + a*Sin[c + d*x]]) + (16*PolyLog[3, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^3*Sqrt[a + a*Sin[c + d*x]])","A",8,5,18,0.2778,1,"{3319, 4183, 2531, 2282, 6589}"
136,1,175,0,0.092206,"\int \frac{x}{\sqrt{a+a \sin (c+d x)}} \, dx","Int[x/Sqrt[a + a*Sin[c + d*x]],x]","\frac{4 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{4 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{4 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}","\frac{4 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{4 i \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d^2 \sqrt{a \sin (c+d x)+a}}-\frac{4 x \sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 c+2 d x+\pi )}\right)}{d \sqrt{a \sin (c+d x)+a}}",1,"(-4*x*ArcTanh[E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d*Sqrt[a + a*Sin[c + d*x]]) + ((4*I)*PolyLog[2, -E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]]) - ((4*I)*PolyLog[2, E^((I/4)*(2*c + Pi + 2*d*x))]*Sin[c/2 + Pi/4 + (d*x)/2])/(d^2*Sqrt[a + a*Sin[c + d*x]])","A",6,4,16,0.2500,1,"{3319, 4183, 2279, 2391}"
137,0,0,0,0.0736267,"\int \frac{1}{x \sqrt{a+a \sin (c+d x)}} \, dx","Int[1/(x*Sqrt[a + a*Sin[c + d*x]]),x]","\int \frac{1}{x \sqrt{a+a \sin (c+d x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a \sin (c+d x)+a}},x\right)",0,"Defer[Int][1/(x*Sqrt[a + a*Sin[c + d*x]]), x]","A",0,0,0,0,-1,"{}"
138,0,0,0,0.0735011,"\int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx","Int[1/(x^2*Sqrt[a + a*Sin[c + d*x]]),x]","\int \frac{1}{x^2 \sqrt{a+a \sin (c+d x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a \sin (c+d x)+a}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[a + a*Sin[c + d*x]]), x]","A",0,0,0,0,-1,"{}"
139,1,691,0,0.3536777,"\int \frac{x^3}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[x^3/(a + a*Sin[e + f*x])^(3/2),x]","\frac{3 i x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{3 i x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{12 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{12 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}+\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{3 x^2}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{24 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{x^3 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}","\frac{3 i x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{3 i x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{12 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{12 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}+\frac{24 i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^4 \sqrt{a \sin (e+f x)+a}}-\frac{3 x^2}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{24 x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{x^3 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x^3 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}",1,"(-3*x^2)/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - (x^3*Cot[e/2 + Pi/4 + (f*x)/2])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - (24*x*ArcTanh[E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]]) - (x^3*ArcTanh[E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f*Sqrt[a + a*Sin[e + f*x]]) + ((24*I)*PolyLog[2, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^4*Sqrt[a + a*Sin[e + f*x]]) + ((3*I)*x^2*PolyLog[2, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - ((24*I)*PolyLog[2, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^4*Sqrt[a + a*Sin[e + f*x]]) - ((3*I)*x^2*PolyLog[2, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - (12*x*PolyLog[3, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]]) + (12*x*PolyLog[3, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]]) - ((24*I)*PolyLog[4, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^4*Sqrt[a + a*Sin[e + f*x]]) + ((24*I)*PolyLog[4, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^4*Sqrt[a + a*Sin[e + f*x]])","A",16,9,18,0.5000,1,"{3319, 4186, 4183, 2279, 2391, 2531, 6609, 2282, 6589}"
140,1,435,0,0.2351908,"\int \frac{x^2}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[x^2/(a + a*Sin[e + f*x])^(3/2),x]","\frac{2 i x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{2 i x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{2 x}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(\cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}","\frac{2 i x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{2 i x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}+\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{2 x}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{4 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(\cos \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)\right)}{a f^3 \sqrt{a \sin (e+f x)+a}}-\frac{x^2 \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x^2 \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}",1,"(-2*x)/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - (x^2*Cot[e/2 + Pi/4 + (f*x)/2])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - (x^2*ArcTanh[E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f*Sqrt[a + a*Sin[e + f*x]]) - (4*ArcTanh[Cos[e/2 + Pi/4 + (f*x)/2]]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]]) + ((2*I)*x*PolyLog[2, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - ((2*I)*x*PolyLog[2, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - (4*PolyLog[3, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]]) + (4*PolyLog[3, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^3*Sqrt[a + a*Sin[e + f*x]])","A",10,7,18,0.3889,1,"{3319, 4186, 3770, 4183, 2531, 2282, 6589}"
141,1,249,0,0.1277788,"\int \frac{x}{(a+a \sin (e+f x))^{3/2}} \, dx","Int[x/(a + a*Sin[e + f*x])^(3/2),x]","\frac{i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{1}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}","\frac{i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{i \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{1}{a f^2 \sqrt{a \sin (e+f x)+a}}-\frac{x \sin \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right) \tanh ^{-1}\left(e^{\frac{1}{4} i (2 e+2 f x+\pi )}\right)}{a f \sqrt{a \sin (e+f x)+a}}-\frac{x \cot \left(\frac{e}{2}+\frac{f x}{2}+\frac{\pi }{4}\right)}{2 a f \sqrt{a \sin (e+f x)+a}}",1,"-(1/(a*f^2*Sqrt[a + a*Sin[e + f*x]])) - (x*Cot[e/2 + Pi/4 + (f*x)/2])/(2*a*f*Sqrt[a + a*Sin[e + f*x]]) - (x*ArcTanh[E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f*Sqrt[a + a*Sin[e + f*x]]) + (I*PolyLog[2, -E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]]) - (I*PolyLog[2, E^((I/4)*(2*e + Pi + 2*f*x))]*Sin[e/2 + Pi/4 + (f*x)/2])/(a*f^2*Sqrt[a + a*Sin[e + f*x]])","A",7,5,16,0.3125,1,"{3319, 4185, 4183, 2279, 2391}"
142,0,0,0,0.0833333,"\int \frac{1}{x (a+a \sin (e+f x))^{3/2}} \, dx","Int[1/(x*(a + a*Sin[e + f*x])^(3/2)),x]","\int \frac{1}{x (a+a \sin (e+f x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x (a \sin (e+f x)+a)^{3/2}},x\right)",0,"Defer[Int][1/(x*(a + a*Sin[e + f*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.08029,"\int \frac{1}{x^2 (a+a \sin (e+f x))^{3/2}} \, dx","Int[1/(x^2*(a + a*Sin[e + f*x])^(3/2)),x]","\int \frac{1}{x^2 (a+a \sin (e+f x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x^2 (a \sin (e+f x)+a)^{3/2}},x\right)",0,"Defer[Int][1/(x^2*(a + a*Sin[e + f*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0689206,"\int \frac{\sqrt[3]{a+a \sin (c+d x)}}{x} \, dx","Int[(a + a*Sin[c + d*x])^(1/3)/x,x]","\int \frac{\sqrt[3]{a+a \sin (c+d x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt[3]{a \sin (c+d x)+a}}{x},x\right)",0,"Defer[Int][(a + a*Sin[c + d*x])^(1/3)/x, x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0477629,"\int (c+d x)^m (a+a \sin (e+f x))^n \, dx","Int[(c + d*x)^m*(a + a*Sin[e + f*x])^n,x]","\int (c+d x)^m (a+a \sin (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a \sin (e+f x)+a)^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + a*Sin[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
146,1,449,0,0.6050776,"\int (c+d x)^m (a+a \sin (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + a*Sin[e + f*x])^3,x]","-\frac{15 a^3 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{3 i a^3 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^3 3^{-m-1} e^{3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i f (c+d x)}{d}\right)}{8 f}-\frac{15 a^3 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{8 f}-\frac{3 i a^3 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^3 3^{-m-1} e^{-3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i f (c+d x)}{d}\right)}{8 f}+\frac{5 a^3 (c+d x)^{m+1}}{2 d (m+1)}","-\frac{15 a^3 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{3 i a^3 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^3 3^{-m-1} e^{3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i f (c+d x)}{d}\right)}{8 f}-\frac{15 a^3 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{8 f}-\frac{3 i a^3 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^3 3^{-m-1} e^{-3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i f (c+d x)}{d}\right)}{8 f}+\frac{5 a^3 (c+d x)^{m+1}}{2 d (m+1)}",1,"(5*a^3*(c + d*x)^(1 + m))/(2*d*(1 + m)) - (15*a^3*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(8*f*(((-I)*f*(c + d*x))/d)^m) - (15*a^3*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(8*E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + ((3*I)*2^(-3 - m)*a^3*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - ((3*I)*2^(-3 - m)*a^3*(c + d*x)^m*Gamma[1 + m, ((2*I)*f*(c + d*x))/d])/(E^((2*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + (3^(-1 - m)*a^3*E^((3*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-3*I)*f*(c + d*x))/d])/(8*f*(((-I)*f*(c + d*x))/d)^m) + (3^(-1 - m)*a^3*(c + d*x)^m*Gamma[1 + m, ((3*I)*f*(c + d*x))/d])/(8*E^((3*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",12,5,20,0.2500,1,"{3318, 3312, 3307, 2181, 3308}"
147,1,299,0,0.3692388,"\int (c+d x)^m (a+a \sin (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + a*Sin[e + f*x])^2,x]","-\frac{a^2 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{f}+\frac{i a^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{a^2 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{f}-\frac{i a^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{3 a^2 (c+d x)^{m+1}}{2 d (m+1)}","-\frac{a^2 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{f}+\frac{i a^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{a^2 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{f}-\frac{i a^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{3 a^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(3*a^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) - (a^2*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - (a^2*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + (I*2^(-3 - m)*a^2*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - (I*2^(-3 - m)*a^2*(c + d*x)^m*Gamma[1 + m, ((2*I)*f*(c + d*x))/d])/(E^((2*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",9,5,20,0.2500,1,"{3318, 3312, 3307, 2181, 3308}"
148,1,148,0,0.1442179,"\int (c+d x)^m (a+a \sin (e+f x)) \, dx","Int[(c + d*x)^m*(a + a*Sin[e + f*x]),x]","-\frac{a e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{a e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}","-\frac{a e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{a e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"(a*(c + d*x)^(1 + m))/(d*(1 + m)) - (a*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(2*f*(((-I)*f*(c + d*x))/d)^m) - (a*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(2*E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",5,3,18,0.1667,1,"{3317, 3308, 2181}"
149,0,0,0,0.0550764,"\int \frac{(c+d x)^m}{a+a \sin (e+f x)} \, dx","Int[(c + d*x)^m/(a + a*Sin[e + f*x]),x]","\int \frac{(c+d x)^m}{a+a \sin (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a \sin (e+f x)+a},x\right)",0,"Defer[Int][(c + d*x)^m/(a + a*Sin[e + f*x]), x]","A",0,0,0,0,-1,"{}"
150,0,0,0,0.0530645,"\int \frac{(c+d x)^m}{(a+a \sin (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + a*Sin[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+a \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a \sin (e+f x)+a)^2},x\right)",0,"Defer[Int][(c + d*x)^m/(a + a*Sin[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
151,1,90,0,0.1225386,"\int (c+d x)^3 (a+b \sin (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Sin[e + f*x]),x]","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 b d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{b (c+d x)^3 \cos (e+f x)}{f}-\frac{6 b d^3 \sin (e+f x)}{f^4}","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{3 b d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{b (c+d x)^3 \cos (e+f x)}{f}-\frac{6 b d^3 \sin (e+f x)}{f^4}",1,"(a*(c + d*x)^4)/(4*d) + (6*b*d^2*(c + d*x)*Cos[e + f*x])/f^3 - (b*(c + d*x)^3*Cos[e + f*x])/f - (6*b*d^3*Sin[e + f*x])/f^4 + (3*b*d*(c + d*x)^2*Sin[e + f*x])/f^2","A",6,3,18,0.1667,1,"{3317, 3296, 2637}"
152,1,68,0,0.0856717,"\int (c+d x)^2 (a+b \sin (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Sin[e + f*x]),x]","\frac{a (c+d x)^3}{3 d}+\frac{2 b d (c+d x) \sin (e+f x)}{f^2}-\frac{b (c+d x)^2 \cos (e+f x)}{f}+\frac{2 b d^2 \cos (e+f x)}{f^3}","\frac{a (c+d x)^3}{3 d}+\frac{2 b d (c+d x) \sin (e+f x)}{f^2}-\frac{b (c+d x)^2 \cos (e+f x)}{f}+\frac{2 b d^2 \cos (e+f x)}{f^3}",1,"(a*(c + d*x)^3)/(3*d) + (2*b*d^2*Cos[e + f*x])/f^3 - (b*(c + d*x)^2*Cos[e + f*x])/f + (2*b*d*(c + d*x)*Sin[e + f*x])/f^2","A",5,3,18,0.1667,1,"{3317, 3296, 2638}"
153,1,45,0,0.0423611,"\int (c+d x) (a+b \sin (e+f x)) \, dx","Int[(c + d*x)*(a + b*Sin[e + f*x]),x]","\frac{a (c+d x)^2}{2 d}-\frac{b (c+d x) \cos (e+f x)}{f}+\frac{b d \sin (e+f x)}{f^2}","\frac{a (c+d x)^2}{2 d}-\frac{b (c+d x) \cos (e+f x)}{f}+\frac{b d \sin (e+f x)}{f^2}",1,"(a*(c + d*x)^2)/(2*d) - (b*(c + d*x)*Cos[e + f*x])/f + (b*d*Sin[e + f*x])/f^2","A",4,3,16,0.1875,1,"{3317, 3296, 2637}"
154,1,64,0,0.1235176,"\int \frac{a+b \sin (e+f x)}{c+d x} \, dx","Int[(a + b*Sin[e + f*x])/(c + d*x),x]","\frac{a \log (c+d x)}{d}+\frac{b \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{b \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}","\frac{a \log (c+d x)}{d}+\frac{b \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{b \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}",1,"(a*Log[c + d*x])/d + (b*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d + (b*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3299, 3302}"
155,1,88,0,0.155229,"\int \frac{a+b \sin (e+f x)}{(c+d x)^2} \, dx","Int[(a + b*Sin[e + f*x])/(c + d*x)^2,x]","-\frac{a}{d (c+d x)}+\frac{b f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{b f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{b \sin (e+f x)}{d (c+d x)}","-\frac{a}{d (c+d x)}+\frac{b f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{b f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{b \sin (e+f x)}{d (c+d x)}",1,"-(a/(d*(c + d*x))) + (b*f*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d^2 - (b*Sin[e + f*x])/(d*(c + d*x)) - (b*f*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3299, 3302}"
156,1,123,0,0.1899286,"\int \frac{a+b \sin (e+f x)}{(c+d x)^3} \, dx","Int[(a + b*Sin[e + f*x])/(c + d*x)^3,x]","-\frac{a}{2 d (c+d x)^2}-\frac{b f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{2 d^3}-\frac{b f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{b f \cos (e+f x)}{2 d^2 (c+d x)}-\frac{b \sin (e+f x)}{2 d (c+d x)^2}","-\frac{a}{2 d (c+d x)^2}-\frac{b f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{2 d^3}-\frac{b f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{b f \cos (e+f x)}{2 d^2 (c+d x)}-\frac{b \sin (e+f x)}{2 d (c+d x)^2}",1,"-a/(2*d*(c + d*x)^2) - (b*f*Cos[e + f*x])/(2*d^2*(c + d*x)) - (b*f^2*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/(2*d^3) - (b*Sin[e + f*x])/(2*d*(c + d*x)^2) - (b*f^2*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/(2*d^3)","A",7,5,18,0.2778,1,"{3317, 3297, 3303, 3299, 3302}"
157,1,250,0,0.2671179,"\int (c+d x)^3 (a+b \sin (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Sin[e + f*x])^2,x]","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{6 a b d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{2 a b (c+d x)^3 \cos (e+f x)}{f}-\frac{12 a b d^3 \sin (e+f x)}{f^4}+\frac{3 b^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 b^2 c d^2 x}{4 f^2}+\frac{3 b^2 d (c+d x)^2 \sin ^2(e+f x)}{4 f^2}-\frac{b^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{b^2 (c+d x)^4}{8 d}-\frac{3 b^2 d^3 \sin ^2(e+f x)}{8 f^4}-\frac{3 b^2 d^3 x^2}{8 f^2}","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \cos (e+f x)}{f^3}+\frac{6 a b d (c+d x)^2 \sin (e+f x)}{f^2}-\frac{2 a b (c+d x)^3 \cos (e+f x)}{f}-\frac{12 a b d^3 \sin (e+f x)}{f^4}+\frac{3 b^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 b^2 c d^2 x}{4 f^2}+\frac{3 b^2 d (c+d x)^2 \sin ^2(e+f x)}{4 f^2}-\frac{b^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{b^2 (c+d x)^4}{8 d}-\frac{3 b^2 d^3 \sin ^2(e+f x)}{8 f^4}-\frac{3 b^2 d^3 x^2}{8 f^2}",1,"(-3*b^2*c*d^2*x)/(4*f^2) - (3*b^2*d^3*x^2)/(8*f^2) + (a^2*(c + d*x)^4)/(4*d) + (b^2*(c + d*x)^4)/(8*d) + (12*a*b*d^2*(c + d*x)*Cos[e + f*x])/f^3 - (2*a*b*(c + d*x)^3*Cos[e + f*x])/f - (12*a*b*d^3*Sin[e + f*x])/f^4 + (6*a*b*d*(c + d*x)^2*Sin[e + f*x])/f^2 + (3*b^2*d^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) - (b^2*(c + d*x)^3*Cos[e + f*x]*Sin[e + f*x])/(2*f) - (3*b^2*d^3*Sin[e + f*x]^2)/(8*f^4) + (3*b^2*d*(c + d*x)^2*Sin[e + f*x]^2)/(4*f^2)","A",10,6,20,0.3000,1,"{3317, 3296, 2637, 3311, 32, 3310}"
158,1,182,0,0.1919876,"\int (c+d x)^2 (a+b \sin (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Sin[e + f*x])^2,x]","\frac{a^2 (c+d x)^3}{3 d}+\frac{4 a b d (c+d x) \sin (e+f x)}{f^2}-\frac{2 a b (c+d x)^2 \cos (e+f x)}{f}+\frac{4 a b d^2 \cos (e+f x)}{f^3}+\frac{b^2 d (c+d x) \sin ^2(e+f x)}{2 f^2}-\frac{b^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{b^2 (c+d x)^3}{6 d}+\frac{b^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{b^2 d^2 x}{4 f^2}","\frac{a^2 (c+d x)^3}{3 d}+\frac{4 a b d (c+d x) \sin (e+f x)}{f^2}-\frac{2 a b (c+d x)^2 \cos (e+f x)}{f}+\frac{4 a b d^2 \cos (e+f x)}{f^3}+\frac{b^2 d (c+d x) \sin ^2(e+f x)}{2 f^2}-\frac{b^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{b^2 (c+d x)^3}{6 d}+\frac{b^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{b^2 d^2 x}{4 f^2}",1,"-(b^2*d^2*x)/(4*f^2) + (a^2*(c + d*x)^3)/(3*d) + (b^2*(c + d*x)^3)/(6*d) + (4*a*b*d^2*Cos[e + f*x])/f^3 - (2*a*b*(c + d*x)^2*Cos[e + f*x])/f + (4*a*b*d*(c + d*x)*Sin[e + f*x])/f^2 + (b^2*d^2*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) - (b^2*(c + d*x)^2*Cos[e + f*x]*Sin[e + f*x])/(2*f) + (b^2*d*(c + d*x)*Sin[e + f*x]^2)/(2*f^2)","A",9,7,20,0.3500,1,"{3317, 3296, 2638, 3311, 32, 2635, 8}"
159,1,116,0,0.0975296,"\int (c+d x) (a+b \sin (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Sin[e + f*x])^2,x]","\frac{a^2 (c+d x)^2}{2 d}-\frac{2 a b (c+d x) \cos (e+f x)}{f}+\frac{2 a b d \sin (e+f x)}{f^2}-\frac{b^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{1}{2} b^2 c x+\frac{b^2 d \sin ^2(e+f x)}{4 f^2}+\frac{1}{4} b^2 d x^2","\frac{a^2 (c+d x)^2}{2 d}-\frac{2 a b (c+d x) \cos (e+f x)}{f}+\frac{2 a b d \sin (e+f x)}{f^2}-\frac{b^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{1}{2} b^2 c x+\frac{b^2 d \sin ^2(e+f x)}{4 f^2}+\frac{1}{4} b^2 d x^2",1,"(b^2*c*x)/2 + (b^2*d*x^2)/4 + (a^2*(c + d*x)^2)/(2*d) - (2*a*b*(c + d*x)*Cos[e + f*x])/f + (2*a*b*d*Sin[e + f*x])/f^2 - (b^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(2*f) + (b^2*d*Sin[e + f*x]^2)/(4*f^2)","A",6,4,18,0.2222,1,"{3317, 3296, 2637, 3310}"
160,1,156,0,0.3243636,"\int \frac{(a+b \sin (e+f x))^2}{c+d x} \, dx","Int[(a + b*Sin[e + f*x])^2/(c + d*x),x]","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{2 a b \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}-\frac{b^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}+\frac{b^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{b^2 \log (c+d x)}{2 d}","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d}+\frac{2 a b \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}-\frac{b^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}+\frac{b^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{b^2 \log (c+d x)}{2 d}",1,"-(b^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(2*d) + (a^2*Log[c + d*x])/d + (b^2*Log[c + d*x])/(2*d) + (2*a*b*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d + (2*a*b*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d + (b^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(2*d)","A",10,5,20,0.2500,1,"{3317, 3303, 3299, 3302, 3312}"
161,1,183,0,0.3340108,"\int \frac{(a+b \sin (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + b*Sin[e + f*x])^2/(c + d*x)^2,x]","-\frac{a^2}{d (c+d x)}+\frac{2 a b f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a b f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{2 a b \sin (e+f x)}{d (c+d x)}+\frac{b^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{b^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{b^2 \sin ^2(e+f x)}{d (c+d x)}","-\frac{a^2}{d (c+d x)}+\frac{2 a b f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a b f \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{2 a b \sin (e+f x)}{d (c+d x)}+\frac{b^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{b^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{b^2 \sin ^2(e+f x)}{d (c+d x)}",1,"-(a^2/(d*(c + d*x))) + (2*a*b*f*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d^2 + (b^2*f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/d^2 - (2*a*b*Sin[e + f*x])/(d*(c + d*x)) - (b^2*Sin[e + f*x]^2)/(d*(c + d*x)) - (2*a*b*f*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2 + (b^2*f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/d^2","A",11,7,20,0.3500,1,"{3317, 3297, 3303, 3299, 3302, 3313, 12}"
162,1,245,0,0.4242022,"\int \frac{(a+b \sin (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + b*Sin[e + f*x])^2/(c + d*x)^3,x]","-\frac{a^2}{2 d (c+d x)^2}-\frac{a b f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^3}-\frac{a b f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{a b f \cos (e+f x)}{d^2 (c+d x)}-\frac{a b \sin (e+f x)}{d (c+d x)^2}+\frac{b^2 f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{d^3}-\frac{b^2 f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}-\frac{b^2 f \sin (e+f x) \cos (e+f x)}{d^2 (c+d x)}-\frac{b^2 \sin ^2(e+f x)}{2 d (c+d x)^2}","-\frac{a^2}{2 d (c+d x)^2}-\frac{a b f^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^3}-\frac{a b f^2 \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{a b f \cos (e+f x)}{d^2 (c+d x)}-\frac{a b \sin (e+f x)}{d (c+d x)^2}+\frac{b^2 f^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{d^3}-\frac{b^2 f^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}-\frac{b^2 f \sin (e+f x) \cos (e+f x)}{d^2 (c+d x)}-\frac{b^2 \sin ^2(e+f x)}{2 d (c+d x)^2}",1,"-a^2/(2*d*(c + d*x)^2) - (a*b*f*Cos[e + f*x])/(d^2*(c + d*x)) + (b^2*f^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/d^3 - (a*b*f^2*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d^3 - (a*b*Sin[e + f*x])/(d*(c + d*x)^2) - (b^2*f*Cos[e + f*x]*Sin[e + f*x])/(d^2*(c + d*x)) - (b^2*Sin[e + f*x]^2)/(2*d*(c + d*x)^2) - (a*b*f^2*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^3 - (b^2*f^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/d^3","A",14,8,20,0.4000,1,"{3317, 3297, 3303, 3299, 3302, 3314, 31, 3312}"
163,1,495,0,0.9691978,"\int \frac{(c+d x)^3}{a+b \sin (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Sin[e + f*x]),x]","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \sqrt{a^2-b^2}}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{6 d^3 \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^4 \sqrt{a^2-b^2}}-\frac{6 d^3 \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^4 \sqrt{a^2-b^2}}-\frac{i (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \sqrt{a^2-b^2}}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{6 d^3 \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^4 \sqrt{a^2-b^2}}-\frac{6 d^3 \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^4 \sqrt{a^2-b^2}}-\frac{i (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}",1,"((-I)*(c + d*x)^3*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) + (I*(c + d*x)^3*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) - (3*d*(c + d*x)^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2) + (3*d*(c + d*x)^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2) - ((6*I)*d^2*(c + d*x)*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^3) + ((6*I)*d^2*(c + d*x)*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^3) + (6*d^3*PolyLog[4, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^4) - (6*d^3*PolyLog[4, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^4)","A",12,7,20,0.3500,1,"{3323, 2264, 2190, 2531, 6609, 2282, 6589}"
164,1,367,0,0.8215615,"\int \frac{(c+d x)^2}{a+b \sin (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Sin[e + f*x]),x]","-\frac{2 d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{2 d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{2 i d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{2 i d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \sqrt{a^2-b^2}}-\frac{i (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}","-\frac{2 d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{2 d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{2 i d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{2 i d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \sqrt{a^2-b^2}}-\frac{i (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}",1,"((-I)*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) + (I*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) - (2*d*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2) + (2*d*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2) - ((2*I)*d^2*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^3) + ((2*I)*d^2*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^3)","A",10,6,20,0.3000,1,"{3323, 2264, 2190, 2531, 2282, 6589}"
165,1,234,0,0.4528967,"\int \frac{c+d x}{a+b \sin (e+f x)} \, dx","Int[(c + d*x)/(a + b*Sin[e + f*x]),x]","-\frac{d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{i (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}","-\frac{d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{i (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \sqrt{a^2-b^2}}+\frac{i (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \sqrt{a^2-b^2}}",1,"((-I)*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) + (I*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f) - (d*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2) + (d*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*f^2)","A",8,5,18,0.2778,1,"{3323, 2264, 2190, 2279, 2391}"
166,0,0,0,0.0642031,"\int \frac{1}{(c+d x) (a+b \sin (e+f x))} \, dx","Int[1/((c + d*x)*(a + b*Sin[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sin (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
167,0,0,0,0.0610818,"\int \frac{1}{(c+d x)^2 (a+b \sin (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + b*Sin[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \sin (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sin (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Sin[e + f*x])), x]","A",0,0,0,0,-1,"{}"
168,1,925,0,1.6548722,"\int \frac{(c+d x)^3}{(a+b \sin (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + b*Sin[e + f*x])^2,x]","-\frac{6 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}-\frac{6 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}+\frac{6 a \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}-\frac{6 a \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}+\frac{6 i (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}+\frac{6 i (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}-\frac{6 i a (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{6 i a (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}-\frac{3 (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right) f^2}-\frac{3 (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right) f^2}-\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}+\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}+\frac{i (c+d x)^3}{\left(a^2-b^2\right) f}-\frac{i a (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} f}+\frac{i a (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} f}+\frac{b (c+d x)^3 \cos (e+f x)}{\left(a^2-b^2\right) f (a+b \sin (e+f x))}","-\frac{6 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}-\frac{6 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}+\frac{6 a \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}-\frac{6 a \text{PolyLog}\left(4,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}+\frac{6 i (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}+\frac{6 i (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}-\frac{6 i a (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{6 i a (c+d x) \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}-\frac{3 (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right) f^2}-\frac{3 (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right) f^2}-\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}+\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}+\frac{i (c+d x)^3}{\left(a^2-b^2\right) f}-\frac{i a (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} f}+\frac{i a (c+d x)^3 \log \left(1-\frac{i b e^{i (e+f x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} f}+\frac{b (c+d x)^3 \cos (e+f x)}{\left(a^2-b^2\right) f (a+b \sin (e+f x))}",1,"(I*(c + d*x)^3)/((a^2 - b^2)*f) - (3*d*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) - (I*a*(c + d*x)^3*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) - (3*d*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) + (I*a*(c + d*x)^3*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) + ((6*I)*d^2*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^3) - (3*a*d*(c + d*x)^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) + ((6*I)*d^2*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^3) + (3*a*d*(c + d*x)^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) - (6*d^3*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^4) - ((6*I)*a*d^2*(c + d*x)*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^3) - (6*d^3*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^4) + ((6*I)*a*d^2*(c + d*x)*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^3) + (6*a*d^3*PolyLog[4, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^4) - (6*a*d^3*PolyLog[4, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^4) + (b*(c + d*x)^3*Cos[e + f*x])/((a^2 - b^2)*f*(a + b*Sin[e + f*x]))","A",22,9,20,0.4500,1,"{3324, 3323, 2264, 2190, 2531, 6609, 2282, 6589, 4519}"
169,1,671,0,1.2051432,"\int \frac{(c+d x)^2}{(a+b \sin (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Sin[e + f*x])^2,x]","-\frac{2 a d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 a d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 i d^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)}+\frac{2 i d^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \left(a^2-b^2\right)}-\frac{2 i a d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}+\frac{2 i a d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}-\frac{2 d (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)}-\frac{2 d (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)}-\frac{i a (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{i a (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{b (c+d x)^2 \cos (e+f x)}{f \left(a^2-b^2\right) (a+b \sin (e+f x))}+\frac{i (c+d x)^2}{f \left(a^2-b^2\right)}","-\frac{2 a d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 a d (c+d x) \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 i d^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)}+\frac{2 i d^2 \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \left(a^2-b^2\right)}-\frac{2 i a d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}+\frac{2 i a d^2 \text{PolyLog}\left(3,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}-\frac{2 d (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)}-\frac{2 d (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)}-\frac{i a (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{i a (c+d x)^2 \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{b (c+d x)^2 \cos (e+f x)}{f \left(a^2-b^2\right) (a+b \sin (e+f x))}+\frac{i (c+d x)^2}{f \left(a^2-b^2\right)}",1,"(I*(c + d*x)^2)/((a^2 - b^2)*f) - (2*d*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) - (I*a*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) - (2*d*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) + (I*a*(c + d*x)^2*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) + ((2*I)*d^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^3) - (2*a*d*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) + ((2*I)*d^2*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^3) + (2*a*d*(c + d*x)*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) - ((2*I)*a*d^2*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^3) + ((2*I)*a*d^2*PolyLog[3, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^3) + (b*(c + d*x)^2*Cos[e + f*x])/((a^2 - b^2)*f*(a + b*Sin[e + f*x]))","A",18,10,20,0.5000,1,"{3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391}"
170,1,305,0,0.5503628,"\int \frac{c+d x}{(a+b \sin (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Sin[e + f*x])^2,x]","-\frac{a d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{a d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}-\frac{i a (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{i a (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{b (c+d x) \cos (e+f x)}{f \left(a^2-b^2\right) (a+b \sin (e+f x))}-\frac{d \log (a+b \sin (e+f x))}{f^2 \left(a^2-b^2\right)}","-\frac{a d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{a d \text{PolyLog}\left(2,\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}-\frac{i a (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{a-\sqrt{a^2-b^2}}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{i a (c+d x) \log \left(1-\frac{i b e^{i (e+f x)}}{\sqrt{a^2-b^2}+a}\right)}{f \left(a^2-b^2\right)^{3/2}}+\frac{b (c+d x) \cos (e+f x)}{f \left(a^2-b^2\right) (a+b \sin (e+f x))}-\frac{d \log (a+b \sin (e+f x))}{f^2 \left(a^2-b^2\right)}",1,"((-I)*a*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) + (I*a*(c + d*x)*Log[1 - (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) - (d*Log[a + b*Sin[e + f*x]])/((a^2 - b^2)*f^2) - (a*d*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) + (a*d*PolyLog[2, (I*b*E^(I*(e + f*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f^2) + (b*(c + d*x)*Cos[e + f*x])/((a^2 - b^2)*f*(a + b*Sin[e + f*x]))","A",11,8,18,0.4444,1,"{3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
171,0,0,0,0.0592222,"\int \frac{1}{(c+d x) (a+b \sin (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + b*Sin[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sin (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Sin[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.0568414,"\int \frac{1}{(c+d x)^2 (a+b \sin (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + b*Sin[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sin (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Sin[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
173,0,0,0,0.0510695,"\int (c+d x)^m (a+b \sin (e+f x))^n \, dx","Int[(c + d*x)^m*(a + b*Sin[e + f*x])^n,x]","\int (c+d x)^m (a+b \sin (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a+b \sin (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + b*Sin[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
174,1,607,0,0.7642038,"\int (c+d x)^m (a+b \sin (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + b*Sin[e + f*x])^3,x]","-\frac{3 a^2 b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{3 a^2 b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{3 i a b^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{3 i a b^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{3 b^3 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{b^3 3^{-m-1} e^{3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i f (c+d x)}{d}\right)}{8 f}-\frac{3 b^3 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{b^3 3^{-m-1} e^{-3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i f (c+d x)}{d}\right)}{8 f}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}+\frac{3 a b^2 (c+d x)^{m+1}}{2 d (m+1)}","-\frac{3 a^2 b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{3 a^2 b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{3 i a b^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{3 i a b^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{3 b^3 e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{b^3 3^{-m-1} e^{3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i f (c+d x)}{d}\right)}{8 f}-\frac{3 b^3 e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{8 f}+\frac{b^3 3^{-m-1} e^{-3 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i f (c+d x)}{d}\right)}{8 f}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}+\frac{3 a b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^3*(c + d*x)^(1 + m))/(d*(1 + m)) + (3*a*b^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) - (3*a^2*b*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(2*f*(((-I)*f*(c + d*x))/d)^m) - (3*b^3*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(8*f*(((-I)*f*(c + d*x))/d)^m) - (3*a^2*b*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(2*E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) - (3*b^3*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(8*E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + ((3*I)*2^(-3 - m)*a*b^2*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - ((3*I)*2^(-3 - m)*a*b^2*(c + d*x)^m*Gamma[1 + m, ((2*I)*f*(c + d*x))/d])/(E^((2*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + (3^(-1 - m)*b^3*E^((3*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-3*I)*f*(c + d*x))/d])/(8*f*(((-I)*f*(c + d*x))/d)^m) + (3^(-1 - m)*b^3*(c + d*x)^m*Gamma[1 + m, ((3*I)*f*(c + d*x))/d])/(8*E^((3*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",18,5,20,0.2500,1,"{3317, 3308, 2181, 3312, 3307}"
175,1,318,0,0.3920428,"\int (c+d x)^m (a+b \sin (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + b*Sin[e + f*x])^2,x]","-\frac{a b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{f}-\frac{a b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{f}+\frac{i b^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{i b^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}+\frac{b^2 (c+d x)^{m+1}}{2 d (m+1)}","-\frac{a b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{f}-\frac{a b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{f}+\frac{i b^2 2^{-m-3} e^{2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i f (c+d x)}{d}\right)}{f}-\frac{i b^2 2^{-m-3} e^{-2 i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i f (c+d x)}{d}\right)}{f}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}+\frac{b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^2*(c + d*x)^(1 + m))/(d*(1 + m)) + (b^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) - (a*b*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - (a*b*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m) + (I*2^(-3 - m)*b^2*E^((2*I)*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*f*(c + d*x))/d])/(f*(((-I)*f*(c + d*x))/d)^m) - (I*2^(-3 - m)*b^2*(c + d*x)^m*Gamma[1 + m, ((2*I)*f*(c + d*x))/d])/(E^((2*I)*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",10,5,20,0.2500,1,"{3317, 3308, 2181, 3312, 3307}"
176,1,148,0,0.1489975,"\int (c+d x)^m (a+b \sin (e+f x)) \, dx","Int[(c + d*x)^m*(a + b*Sin[e + f*x]),x]","-\frac{b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}","-\frac{b e^{i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(-\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i f (c+d x)}{d}\right)}{2 f}-\frac{b e^{-i \left(e-\frac{c f}{d}\right)} (c+d x)^m \left(\frac{i f (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{i f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"(a*(c + d*x)^(1 + m))/(d*(1 + m)) - (b*E^(I*(e - (c*f)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*f*(c + d*x))/d])/(2*f*(((-I)*f*(c + d*x))/d)^m) - (b*(c + d*x)^m*Gamma[1 + m, (I*f*(c + d*x))/d])/(2*E^(I*(e - (c*f)/d))*f*((I*f*(c + d*x))/d)^m)","A",5,3,18,0.1667,1,"{3317, 3308, 2181}"
177,0,0,0,0.0573369,"\int \frac{(c+d x)^m}{a+b \sin (e+f x)} \, dx","Int[(c + d*x)^m/(a + b*Sin[e + f*x]),x]","\int \frac{(c+d x)^m}{a+b \sin (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+b \sin (e+f x)},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*Sin[e + f*x]), x]","A",0,0,0,0,-1,"{}"
178,0,0,0,0.0551485,"\int \frac{(c+d x)^m}{(a+b \sin (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + b*Sin[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+b \sin (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a+b \sin (e+f x))^2},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*Sin[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
179,1,164,0,0.3401987,"\int \frac{(e+f x)^3 \sin (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{i (e+f x)^3}{a d}+\frac{(e+f x)^4}{4 a f}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{i (e+f x)^3}{a d}+\frac{(e+f x)^4}{4 a f}",1,"(I*(e + f*x)^3)/(a*d) + (e + f*x)^4/(4*a*f) + ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4)","A",9,9,26,0.3462,1,"{4515, 32, 3318, 4184, 3717, 2190, 2531, 2282, 6589}"
180,1,129,0,0.2573871,"\int \frac{(e+f x)^2 \sin (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{i (e+f x)^2}{a d}+\frac{(e+f x)^3}{3 a f}","\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{i (e+f x)^2}{a d}+\frac{(e+f x)^3}{3 a f}",1,"(I*(e + f*x)^2)/(a*d) + (e + f*x)^3/(3*a*f) + ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3)","A",8,8,26,0.3077,1,"{4515, 32, 3318, 4184, 3717, 2190, 2279, 2391}"
181,1,76,0,0.095287,"\int \frac{(e+f x) \sin (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x])/(a + a*Sin[c + d*x]),x]","-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}","-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}",1,"(e*x)/a + (f*x^2)/(2*a) + ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2)","A",5,4,24,0.1667,1,"{4515, 3318, 4184, 3475}"
182,1,28,0,0.0380084,"\int \frac{\sin (c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sin[c + d*x]/(a + a*Sin[c + d*x]),x]","\frac{\cos (c+d x)}{d (a \sin (c+d x)+a)}+\frac{x}{a}","\frac{\cos (c+d x)}{d (a \sin (c+d x)+a)}+\frac{x}{a}",1,"x/a + Cos[c + d*x]/(d*(a + a*Sin[c + d*x]))","A",2,2,19,0.1053,1,"{2735, 2648}"
183,0,0,0,0.0480519,"\int \frac{\sin (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sin (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin (c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
184,0,0,0,0.0466772,"\int \frac{\sin (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sin (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin (c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
185,1,247,0,0.4719177,"\int \frac{(e+f x)^3 \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}+\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}-\frac{6 f^3 \sin (c+d x)}{a d^4}-\frac{(e+f x)^3 \cos (c+d x)}{a d}-\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{i (e+f x)^3}{a d}-\frac{(e+f x)^4}{4 a f}","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}+\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}-\frac{6 f^3 \sin (c+d x)}{a d^4}-\frac{(e+f x)^3 \cos (c+d x)}{a d}-\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{i (e+f x)^3}{a d}-\frac{(e+f x)^4}{4 a f}",1,"((-I)*(e + f*x)^3)/(a*d) - (e + f*x)^4/(4*a*f) + (6*f^2*(e + f*x)*Cos[c + d*x])/(a*d^3) - ((e + f*x)^3*Cos[c + d*x])/(a*d) - ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) - ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) + (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) - (6*f^3*Sin[c + d*x])/(a*d^4) + (3*f*(e + f*x)^2*Sin[c + d*x])/(a*d^2)","A",14,11,28,0.3929,1,"{4515, 3296, 2637, 32, 3318, 4184, 3717, 2190, 2531, 2282, 6589}"
186,1,188,0,0.3478194,"\int \frac{(e+f x)^2 \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{2 f (e+f x) \sin (c+d x)}{a d^2}+\frac{2 f^2 \cos (c+d x)}{a d^3}-\frac{(e+f x)^2 \cos (c+d x)}{a d}-\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{i (e+f x)^2}{a d}-\frac{(e+f x)^3}{3 a f}","-\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{2 f (e+f x) \sin (c+d x)}{a d^2}+\frac{2 f^2 \cos (c+d x)}{a d^3}-\frac{(e+f x)^2 \cos (c+d x)}{a d}-\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{i (e+f x)^2}{a d}-\frac{(e+f x)^3}{3 a f}",1,"((-I)*(e + f*x)^2)/(a*d) - (e + f*x)^3/(3*a*f) + (2*f^2*Cos[c + d*x])/(a*d^3) - ((e + f*x)^2*Cos[c + d*x])/(a*d) - ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) - ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) + (2*f*(e + f*x)*Sin[c + d*x])/(a*d^2)","A",12,10,28,0.3571,1,"{4515, 3296, 2638, 32, 3318, 4184, 3717, 2190, 2279, 2391}"
187,1,111,0,0.1596961,"\int \frac{(e+f x) \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\frac{f \sin (c+d x)}{a d^2}+\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}-\frac{(e+f x) \cos (c+d x)}{a d}-\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{e x}{a}-\frac{f x^2}{2 a}","\frac{f \sin (c+d x)}{a d^2}+\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}-\frac{(e+f x) \cos (c+d x)}{a d}-\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{e x}{a}-\frac{f x^2}{2 a}",1,"-((e*x)/a) - (f*x^2)/(2*a) - ((e + f*x)*Cos[c + d*x])/(a*d) - ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2) + (f*Sin[c + d*x])/(a*d^2)","A",8,6,26,0.2308,1,"{4515, 3296, 2637, 3318, 4184, 3475}"
188,1,45,0,0.0815769,"\int \frac{\sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sin[c + d*x]^2/(a + a*Sin[c + d*x]),x]","-\frac{\cos (c+d x)}{a d}-\frac{\cos (c+d x)}{a d (\sin (c+d x)+1)}-\frac{x}{a}","-\frac{\cos (c+d x)}{a d}-\frac{\cos (c+d x)}{a d (\sin (c+d x)+1)}-\frac{x}{a}",1,"-(x/a) - Cos[c + d*x]/(a*d) - Cos[c + d*x]/(a*d*(1 + Sin[c + d*x]))","A",4,4,21,0.1905,1,"{2746, 12, 2735, 2648}"
189,0,0,0,0.071648,"\int \frac{\sin ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sin ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin ^2(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
190,0,0,0,0.0690869,"\int \frac{\sin ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sin ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin ^2(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
191,1,382,0,0.6212564,"\int \frac{(e+f x)^3 \sin ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}+\frac{3 f^2 (e+f x) \sin (c+d x) \cos (c+d x)}{4 a d^3}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \sin ^2(c+d x)}{4 a d^2}-\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}-\frac{3 f^3 \sin ^2(c+d x)}{8 a d^4}+\frac{6 f^3 \sin (c+d x)}{a d^4}+\frac{(e+f x)^3 \cos (c+d x)}{a d}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^3 \sin (c+d x) \cos (c+d x)}{2 a d}-\frac{3 e f^2 x}{4 a d^2}-\frac{3 f^3 x^2}{8 a d^2}+\frac{i (e+f x)^3}{a d}+\frac{3 (e+f x)^4}{8 a f}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}+\frac{3 f^2 (e+f x) \sin (c+d x) \cos (c+d x)}{4 a d^3}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \sin ^2(c+d x)}{4 a d^2}-\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}-\frac{3 f^3 \sin ^2(c+d x)}{8 a d^4}+\frac{6 f^3 \sin (c+d x)}{a d^4}+\frac{(e+f x)^3 \cos (c+d x)}{a d}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^3 \sin (c+d x) \cos (c+d x)}{2 a d}-\frac{3 e f^2 x}{4 a d^2}-\frac{3 f^3 x^2}{8 a d^2}+\frac{i (e+f x)^3}{a d}+\frac{3 (e+f x)^4}{8 a f}",1,"(-3*e*f^2*x)/(4*a*d^2) - (3*f^3*x^2)/(8*a*d^2) + (I*(e + f*x)^3)/(a*d) + (3*(e + f*x)^4)/(8*a*f) - (6*f^2*(e + f*x)*Cos[c + d*x])/(a*d^3) + ((e + f*x)^3*Cos[c + d*x])/(a*d) + ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) + (6*f^3*Sin[c + d*x])/(a*d^4) - (3*f*(e + f*x)^2*Sin[c + d*x])/(a*d^2) + (3*f^2*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(4*a*d^3) - ((e + f*x)^3*Cos[c + d*x]*Sin[c + d*x])/(2*a*d) - (3*f^3*Sin[c + d*x]^2)/(8*a*d^4) + (3*f*(e + f*x)^2*Sin[c + d*x]^2)/(4*a*d^2)","A",19,13,28,0.4643,1,"{4515, 3311, 32, 3310, 3296, 2637, 3318, 4184, 3717, 2190, 2531, 2282, 6589}"
192,1,278,0,0.492938,"\int \frac{(e+f x)^2 \sin ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{f (e+f x) \sin ^2(c+d x)}{2 a d^2}-\frac{2 f (e+f x) \sin (c+d x)}{a d^2}-\frac{2 f^2 \cos (c+d x)}{a d^3}+\frac{f^2 \sin (c+d x) \cos (c+d x)}{4 a d^3}+\frac{(e+f x)^2 \cos (c+d x)}{a d}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^2 \sin (c+d x) \cos (c+d x)}{2 a d}-\frac{f^2 x}{4 a d^2}+\frac{i (e+f x)^2}{a d}+\frac{(e+f x)^3}{2 a f}","\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{f (e+f x) \sin ^2(c+d x)}{2 a d^2}-\frac{2 f (e+f x) \sin (c+d x)}{a d^2}-\frac{2 f^2 \cos (c+d x)}{a d^3}+\frac{f^2 \sin (c+d x) \cos (c+d x)}{4 a d^3}+\frac{(e+f x)^2 \cos (c+d x)}{a d}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^2 \sin (c+d x) \cos (c+d x)}{2 a d}-\frac{f^2 x}{4 a d^2}+\frac{i (e+f x)^2}{a d}+\frac{(e+f x)^3}{2 a f}",1,"-(f^2*x)/(4*a*d^2) + (I*(e + f*x)^2)/(a*d) + (e + f*x)^3/(2*a*f) - (2*f^2*Cos[c + d*x])/(a*d^3) + ((e + f*x)^2*Cos[c + d*x])/(a*d) + ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - (2*f*(e + f*x)*Sin[c + d*x])/(a*d^2) + (f^2*Cos[c + d*x]*Sin[c + d*x])/(4*a*d^3) - ((e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(2*a*d) + (f*(e + f*x)*Sin[c + d*x]^2)/(2*a*d^2)","A",17,13,28,0.4643,1,"{4515, 3311, 32, 2635, 8, 3296, 2638, 3318, 4184, 3717, 2190, 2279, 2391}"
193,1,158,0,0.2197056,"\int \frac{(e+f x) \sin ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{f \sin ^2(c+d x)}{4 a d^2}-\frac{f \sin (c+d x)}{a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 a d}+\frac{3 e x}{2 a}+\frac{3 f x^2}{4 a}","\frac{f \sin ^2(c+d x)}{4 a d^2}-\frac{f \sin (c+d x)}{a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 a d}+\frac{3 e x}{2 a}+\frac{3 f x^2}{4 a}",1,"(3*e*x)/(2*a) + (3*f*x^2)/(4*a) + ((e + f*x)*Cos[c + d*x])/(a*d) + ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2) - (f*Sin[c + d*x])/(a*d^2) - ((e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*a*d) + (f*Sin[c + d*x]^2)/(4*a*d^2)","A",11,7,26,0.2692,1,"{4515, 3310, 3296, 2637, 3318, 4184, 3475}"
194,1,75,0,0.0619893,"\int \frac{\sin ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sin[c + d*x]^3/(a + a*Sin[c + d*x]),x]","\frac{2 \cos (c+d x)}{a d}+\frac{\sin ^2(c+d x) \cos (c+d x)}{d (a \sin (c+d x)+a)}-\frac{3 \sin (c+d x) \cos (c+d x)}{2 a d}+\frac{3 x}{2 a}","\frac{2 \cos (c+d x)}{a d}+\frac{\sin ^2(c+d x) \cos (c+d x)}{d (a \sin (c+d x)+a)}-\frac{3 \sin (c+d x) \cos (c+d x)}{2 a d}+\frac{3 x}{2 a}",1,"(3*x)/(2*a) + (2*Cos[c + d*x])/(a*d) - (3*Cos[c + d*x]*Sin[c + d*x])/(2*a*d) + (Cos[c + d*x]*Sin[c + d*x]^2)/(d*(a + a*Sin[c + d*x]))","A",2,2,21,0.09524,1,"{2767, 2734}"
195,0,0,0,0.0685952,"\int \frac{\sin ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sin ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin ^3(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
196,0,0,0,0.0691858,"\int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sin[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sin ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sin ^3(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sin[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
197,1,352,0,0.4689499,"\int \frac{(e+f x)^3 \csc (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Csc[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}+\frac{i (e+f x)^3}{a d}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}+\frac{i (e+f x)^3}{a d}",1,"(I*(e + f*x)^3)/(a*d) - (2*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (6*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) - (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) + (6*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) - ((6*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) + ((6*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4)","A",17,10,26,0.3846,1,"{4535, 4183, 2531, 6609, 2282, 6589, 3318, 4184, 3717, 2190}"
198,1,249,0,0.3295951,"\int \frac{(e+f x)^2 \csc (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Csc[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}+\frac{i (e+f x)^2}{a d}","\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}+\frac{i (e+f x)^2}{a d}",1,"(I*(e + f*x)^2)/(a*d) - (2*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + ((2*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) + ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - ((2*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (2*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (2*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3)","A",14,11,26,0.4231,1,"{4535, 4183, 2531, 2282, 6589, 3318, 4184, 3717, 2190, 2279, 2391}"
199,1,134,0,0.1565365,"\int \frac{(e+f x) \csc (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Csc[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}","\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}",1,"(-2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2) + (I*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - (I*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2)","A",9,7,24,0.2917,1,"{4535, 4183, 2279, 2391, 3318, 4184, 3475}"
200,1,38,0,0.0537851,"\int \frac{\csc (c+d x)}{a+a \sin (c+d x)} \, dx","Int[Csc[c + d*x]/(a + a*Sin[c + d*x]),x]","\frac{\cos (c+d x)}{d (a \sin (c+d x)+a)}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}","\frac{\cos (c+d x)}{d (a \sin (c+d x)+a)}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}",1,"-(ArcTanh[Cos[c + d*x]]/(a*d)) + Cos[c + d*x]/(d*(a + a*Sin[c + d*x]))","A",3,3,19,0.1579,1,"{2747, 3770, 2648}"
201,0,0,0,0.05991,"\int \frac{\csc (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\csc (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc (c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
202,0,0,0,0.0552685,"\int \frac{\csc (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\csc (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc (c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
203,1,463,0,0.7758453,"\int \frac{(e+f x)^3 \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Csc[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}+\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^3 \cot (c+d x)}{a d}+\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{2 i (e+f x)^3}{a d}","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}+\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{3 f (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^3 \cot (c+d x)}{a d}+\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{2 i (e+f x)^3}{a d}",1,"((-2*I)*(e + f*x)^3)/(a*d) + (2*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) - ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - ((e + f*x)^3*Cot[c + d*x])/(a*d) + (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + (3*f*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) + ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - ((3*I)*f^2*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) - (6*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) + (3*f^3*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^4) + ((6*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) - ((6*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4)","A",24,10,28,0.3571,1,"{4535, 4184, 3717, 2190, 2531, 2282, 6589, 4183, 6609, 3318}"
204,1,327,0,0.5088245,"\int \frac{(e+f x)^2 \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Csc[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^2 \cot (c+d x)}{a d}+\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{2 i (e+f x)^2}{a d}","-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}+\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x)^2 \cot (c+d x)}{a d}+\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{2 i (e+f x)^2}{a d}",1,"((-2*I)*(e + f*x)^2)/(a*d) + (2*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) - ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - ((e + f*x)^2*Cot[c + d*x])/(a*d) + (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) + (2*f*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) + ((2*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (I*f^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (2*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) - (2*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3)","A",20,11,28,0.3929,1,"{4535, 4184, 3717, 2190, 2279, 2391, 4183, 2531, 2282, 6589, 3318}"
205,1,169,0,0.1893514,"\int \frac{(e+f x) \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Csc[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x) \cot (c+d x)}{a d}+\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}","-\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}+\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}-\frac{(e+f x) \cot (c+d x)}{a d}+\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}",1,"(2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) - ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) - ((e + f*x)*Cot[c + d*x])/(a*d) + (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2) + (f*Log[Sin[c + d*x]])/(a*d^2) - (I*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) + (I*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2)","A",12,7,26,0.2692,1,"{4535, 4184, 3475, 4183, 2279, 2391, 3318}"
206,1,51,0,0.0766124,"\int \frac{\csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Csc[c + d*x]^2/(a + a*Sin[c + d*x]),x]","-\frac{2 \cot (c+d x)}{a d}+\frac{\tanh ^{-1}(\cos (c+d x))}{a d}+\frac{\cot (c+d x)}{d (a \sin (c+d x)+a)}","-\frac{2 \cot (c+d x)}{a d}+\frac{\tanh ^{-1}(\cos (c+d x))}{a d}+\frac{\cot (c+d x)}{d (a \sin (c+d x)+a)}",1,"ArcTanh[Cos[c + d*x]]/(a*d) - (2*Cot[c + d*x])/(a*d) + Cot[c + d*x]/(d*(a + a*Sin[c + d*x]))","A",5,5,21,0.2381,1,"{2768, 2748, 3767, 8, 3770}"
207,0,0,0,0.0692805,"\int \frac{\csc ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\csc ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc ^2(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
208,0,0,0,0.0681111,"\int \frac{\csc ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\csc ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc ^2(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
209,1,600,0,1.1082365,"\int \frac{(e+f x)^3 \csc ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Csc[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{2 a d^2}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^4}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}-\frac{3 f (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{3 f (e+f x)^2 \csc (c+d x)}{2 a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x)^3 \cot (c+d x)}{a d}-\frac{3 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{2 i (e+f x)^3}{a d}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{2 a d^2}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^4}-\frac{12 f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}-\frac{6 f (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d^2}-\frac{3 f (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{3 f (e+f x)^2 \csc (c+d x)}{2 a d^2}+\frac{(e+f x)^3 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x)^3 \cot (c+d x)}{a d}-\frac{3 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{2 i (e+f x)^3}{a d}",1,"((2*I)*(e + f*x)^3)/(a*d) - (6*f^2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d^3) - (3*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)^3*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + ((e + f*x)^3*Cot[c + d*x])/(a*d) - (3*f*(e + f*x)^2*Csc[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Cot[c + d*x]*Csc[c + d*x])/(2*a*d) - (6*f*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) - (3*f*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) + ((3*I)*f^3*PolyLog[2, -E^(I*(c + d*x))])/(a*d^4) + (((9*I)/2)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - ((3*I)*f^3*PolyLog[2, E^(I*(c + d*x))])/(a*d^4) - (((9*I)/2)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + ((3*I)*f^2*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) - (9*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) - (12*f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) + (9*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) - (3*f^3*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^4) - ((9*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) + ((9*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4)","A",40,13,28,0.4643,1,"{4535, 4186, 4183, 2279, 2391, 2531, 6609, 2282, 6589, 4184, 3717, 2190, 3318}"
210,1,392,0,0.7221681,"\int \frac{(e+f x)^2 \csc ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Csc[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{3 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}-\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{f (e+f x) \csc (c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cos (c+d x))}{a d^3}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x)^2 \cot (c+d x)}{a d}-\frac{3 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^2 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{2 i (e+f x)^2}{a d}","\frac{3 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}+\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{4 f (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d^2}-\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{f (e+f x) \csc (c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cos (c+d x))}{a d^3}+\frac{(e+f x)^2 \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x)^2 \cot (c+d x)}{a d}-\frac{3 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^2 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{2 i (e+f x)^2}{a d}",1,"((2*I)*(e + f*x)^2)/(a*d) - (3*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) - (f^2*ArcTanh[Cos[c + d*x]])/(a*d^3) + ((e + f*x)^2*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + ((e + f*x)^2*Cot[c + d*x])/(a*d) - (f*(e + f*x)*Csc[c + d*x])/(a*d^2) - ((e + f*x)^2*Cot[c + d*x]*Csc[c + d*x])/(2*a*d) - (4*f*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d^2) - (2*f*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) + ((3*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) + ((4*I)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - ((3*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (I*f^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) - (3*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (3*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3)","A",30,13,28,0.4643,1,"{4535, 4186, 3770, 4183, 2531, 2282, 6589, 4184, 3717, 2190, 2279, 2391, 3318}"
211,1,216,0,0.2831363,"\int \frac{(e+f x) \csc ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Csc[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{3 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{2 a d^2}-\frac{3 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{2 a d^2}-\frac{f \csc (c+d x)}{2 a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}-\frac{f \log (\sin (c+d x))}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x) \cot (c+d x)}{a d}-\frac{3 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x) \cot (c+d x) \csc (c+d x)}{2 a d}","\frac{3 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{2 a d^2}-\frac{3 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{2 a d^2}-\frac{f \csc (c+d x)}{2 a d^2}-\frac{2 f \log \left(\sin \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)\right)}{a d^2}-\frac{f \log (\sin (c+d x))}{a d^2}+\frac{(e+f x) \cot \left(\frac{c}{2}+\frac{d x}{2}+\frac{\pi }{4}\right)}{a d}+\frac{(e+f x) \cot (c+d x)}{a d}-\frac{3 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x) \cot (c+d x) \csc (c+d x)}{2 a d}",1,"(-3*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)*Cot[c/2 + Pi/4 + (d*x)/2])/(a*d) + ((e + f*x)*Cot[c + d*x])/(a*d) - (f*Csc[c + d*x])/(2*a*d^2) - ((e + f*x)*Cot[c + d*x]*Csc[c + d*x])/(2*a*d) - (2*f*Log[Sin[c/2 + Pi/4 + (d*x)/2]])/(a*d^2) - (f*Log[Sin[c + d*x]])/(a*d^2) + (((3*I)/2)*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - (((3*I)/2)*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2)","A",19,8,26,0.3077,1,"{4535, 4185, 4183, 2279, 2391, 4184, 3475, 3318}"
212,1,82,0,0.0895943,"\int \frac{\csc ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Csc[c + d*x]^3/(a + a*Sin[c + d*x]),x]","\frac{2 \cot (c+d x)}{a d}-\frac{3 \tanh ^{-1}(\cos (c+d x))}{2 a d}-\frac{3 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{\cot (c+d x) \csc (c+d x)}{d (a \sin (c+d x)+a)}","\frac{2 \cot (c+d x)}{a d}-\frac{3 \tanh ^{-1}(\cos (c+d x))}{2 a d}-\frac{3 \cot (c+d x) \csc (c+d x)}{2 a d}+\frac{\cot (c+d x) \csc (c+d x)}{d (a \sin (c+d x)+a)}",1,"(-3*ArcTanh[Cos[c + d*x]])/(2*a*d) + (2*Cot[c + d*x])/(a*d) - (3*Cot[c + d*x]*Csc[c + d*x])/(2*a*d) + (Cot[c + d*x]*Csc[c + d*x])/(d*(a + a*Sin[c + d*x]))","A",6,6,21,0.2857,1,"{2768, 2748, 3768, 3770, 3767, 8}"
213,0,0,0,0.0669059,"\int \frac{\csc ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\csc ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc ^3(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
214,0,0,0,0.0664905,"\int \frac{\csc ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Csc[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\csc ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\csc ^3(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Csc[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
215,0,0,0,0.0623214,"\int \frac{(e+f x)^m \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sin[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sin ^2(c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sin ^2(c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Sin[c + d*x]^2)/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
216,0,0,0,0.0391888,"\int \frac{(e+f x)^m \sin (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sin[c + d*x])/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sin (c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sin (c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Sin[c + d*x])/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
217,0,0,0,0.0508557,"\int \frac{(e+f x)^m}{a+a \sin (c+d x)} \, dx","Int[(e + f*x)^m/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{(e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][(e + f*x)^m/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
218,0,0,0,0.0413263,"\int \frac{(e+f x)^m \csc (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Csc[c + d*x])/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \csc (c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\csc (c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Csc[c + d*x])/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
219,0,0,0,0.0646949,"\int \frac{(e+f x)^m \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Csc[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \csc ^2(c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\csc ^2(c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Csc[c + d*x]^2)/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
220,1,544,0,0.9676035,"\int \frac{(e+f x)^3 \sin (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{6 a f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{6 a f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{i a (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{(e+f x)^4}{4 b f}","\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{6 a f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{6 a f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{i a (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{(e+f x)^4}{4 b f}",1,"(e + f*x)^4/(4*b*f) + (I*a*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - (I*a*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (3*a*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (3*a*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + ((6*I)*a*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - ((6*I)*a*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - (6*a*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4) + (6*a*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4)","A",14,9,26,0.3462,1,"{4515, 32, 3323, 2264, 2190, 2531, 6609, 2282, 6589}"
221,1,408,0,0.8586071,"\int \frac{(e+f x)^2 \sin (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{2 a f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{2 a f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{2 i a f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{2 i a f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{i a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{(e+f x)^3}{3 b f}","\frac{2 a f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{2 a f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{2 i a f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{2 i a f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{i a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{(e+f x)^3}{3 b f}",1,"(e + f*x)^3/(3*b*f) + (I*a*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - (I*a*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (2*a*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (2*a*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + ((2*I)*a*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - ((2*I)*a*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3)","A",12,8,26,0.3077,1,"{4515, 32, 3323, 2264, 2190, 2531, 2282, 6589}"
222,1,267,0,0.5845553,"\int \frac{(e+f x) \sin (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{e x}{b}+\frac{f x^2}{2 b}","\frac{a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}-\frac{i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}+\frac{e x}{b}+\frac{f x^2}{2 b}",1,"(e*x)/b + (f*x^2)/(2*b) + (I*a*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - (I*a*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (a*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (a*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2)","A",10,6,24,0.2500,1,"{4515, 3323, 2264, 2190, 2279, 2391}"
223,1,57,0,0.0676604,"\int \frac{\sin (c+d x)}{a+b \sin (c+d x)} \, dx","Int[Sin[c + d*x]/(a + b*Sin[c + d*x]),x]","\frac{x}{b}-\frac{2 a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}","\frac{x}{b}-\frac{2 a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}",1,"x/b - (2*a*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b*Sqrt[a^2 - b^2]*d)","A",4,4,19,0.2105,1,"{2735, 2660, 618, 204}"
224,1,643,0,1.1759244,"\int \frac{(e+f x)^3 \sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{6 i a^2 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3 \sqrt{a^2-b^2}}+\frac{6 i a^2 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3 \sqrt{a^2-b^2}}-\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4 \sqrt{a^2-b^2}}-\frac{6 a^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a (e+f x)^4}{4 b^2 f}+\frac{6 f^2 (e+f x) \cos (c+d x)}{b d^3}+\frac{3 f (e+f x)^2 \sin (c+d x)}{b d^2}-\frac{6 f^3 \sin (c+d x)}{b d^4}-\frac{(e+f x)^3 \cos (c+d x)}{b d}","-\frac{6 i a^2 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3 \sqrt{a^2-b^2}}+\frac{6 i a^2 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3 \sqrt{a^2-b^2}}-\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4 \sqrt{a^2-b^2}}-\frac{6 a^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a (e+f x)^4}{4 b^2 f}+\frac{6 f^2 (e+f x) \cos (c+d x)}{b d^3}+\frac{3 f (e+f x)^2 \sin (c+d x)}{b d^2}-\frac{6 f^3 \sin (c+d x)}{b d^4}-\frac{(e+f x)^3 \cos (c+d x)}{b d}",1,"-(a*(e + f*x)^4)/(4*b^2*f) + (6*f^2*(e + f*x)*Cos[c + d*x])/(b*d^3) - ((e + f*x)^3*Cos[c + d*x])/(b*d) - (I*a^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) + (I*a^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) - (3*a^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) + (3*a^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) - ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^3) + ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^3) + (6*a^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^4) - (6*a^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^4) - (6*f^3*Sin[c + d*x])/(b*d^4) + (3*f*(e + f*x)^2*Sin[c + d*x])/(b*d^2)","A",19,11,28,0.3929,1,"{4515, 3296, 2637, 32, 3323, 2264, 2190, 2531, 6609, 2282, 6589}"
225,1,479,0,1.0380801,"\int \frac{(e+f x)^2 \sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}-\frac{2 i a^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3 \sqrt{a^2-b^2}}+\frac{2 i a^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a (e+f x)^3}{3 b^2 f}+\frac{2 f (e+f x) \sin (c+d x)}{b d^2}+\frac{2 f^2 \cos (c+d x)}{b d^3}-\frac{(e+f x)^2 \cos (c+d x)}{b d}","-\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}-\frac{2 i a^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3 \sqrt{a^2-b^2}}+\frac{2 i a^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a (e+f x)^3}{3 b^2 f}+\frac{2 f (e+f x) \sin (c+d x)}{b d^2}+\frac{2 f^2 \cos (c+d x)}{b d^3}-\frac{(e+f x)^2 \cos (c+d x)}{b d}",1,"-(a*(e + f*x)^3)/(3*b^2*f) + (2*f^2*Cos[c + d*x])/(b*d^3) - ((e + f*x)^2*Cos[c + d*x])/(b*d) - (I*a^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) + (I*a^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) - (2*a^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) + (2*a^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) - ((2*I)*a^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^3) + ((2*I)*a^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^3) + (2*f*(e + f*x)*Sin[c + d*x])/(b*d^2)","A",16,10,28,0.3571,1,"{4515, 3296, 2638, 32, 3323, 2264, 2190, 2531, 2282, 6589}"
226,1,311,0,0.5508268,"\int \frac{(e+f x) \sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a e x}{b^2}-\frac{a f x^2}{2 b^2}+\frac{f \sin (c+d x)}{b d^2}-\frac{(e+f x) \cos (c+d x)}{b d}","-\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2 \sqrt{a^2-b^2}}+\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2 \sqrt{a^2-b^2}}-\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}+\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a e x}{b^2}-\frac{a f x^2}{2 b^2}+\frac{f \sin (c+d x)}{b d^2}-\frac{(e+f x) \cos (c+d x)}{b d}",1,"-((a*e*x)/b^2) - (a*f*x^2)/(2*b^2) - ((e + f*x)*Cos[c + d*x])/(b*d) - (I*a^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) + (I*a^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d) - (a^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) + (a^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*Sqrt[a^2 - b^2]*d^2) + (f*Sin[c + d*x])/(b*d^2)","A",13,8,26,0.3077,1,"{4515, 3296, 2637, 3323, 2264, 2190, 2279, 2391}"
227,1,75,0,0.106451,"\int \frac{\sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Sin[c + d*x]^2/(a + b*Sin[c + d*x]),x]","\frac{2 a^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a x}{b^2}-\frac{\cos (c+d x)}{b d}","\frac{2 a^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^2 d \sqrt{a^2-b^2}}-\frac{a x}{b^2}-\frac{\cos (c+d x)}{b d}",1,"-((a*x)/b^2) + (2*a^2*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b^2*Sqrt[a^2 - b^2]*d) - Cos[c + d*x]/(b*d)","A",6,6,21,0.2857,1,"{2746, 12, 2735, 2660, 618, 204}"
228,1,802,0,1.3411999,"\int \frac{(e+f x)^3 \sin ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sin[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","\frac{(e+f x)^4}{8 b f}+\frac{a^2 (e+f x)^4}{4 b^3 f}+\frac{a \cos (c+d x) (e+f x)^3}{b^2 d}+\frac{i a^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{b^3 \sqrt{a^2-b^2} d}-\frac{i a^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{b^3 \sqrt{a^2-b^2} d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^3}{2 b d}+\frac{3 f \sin ^2(c+d x) (e+f x)^2}{4 b d^2}+\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{b^3 \sqrt{a^2-b^2} d^2}-\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{b^3 \sqrt{a^2-b^2} d^2}-\frac{3 a f \sin (c+d x) (e+f x)^2}{b^2 d^2}-\frac{6 a f^2 \cos (c+d x) (e+f x)}{b^2 d^3}+\frac{6 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{b^3 \sqrt{a^2-b^2} d^3}-\frac{6 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{b^3 \sqrt{a^2-b^2} d^3}+\frac{3 f^2 \cos (c+d x) \sin (c+d x) (e+f x)}{4 b d^3}-\frac{3 f^3 x^2}{8 b d^2}-\frac{3 f^3 \sin ^2(c+d x)}{8 b d^4}-\frac{3 e f^2 x}{4 b d^2}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 \sqrt{a^2-b^2} d^4}+\frac{6 a^3 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b^3 \sqrt{a^2-b^2} d^4}+\frac{6 a f^3 \sin (c+d x)}{b^2 d^4}","\frac{(e+f x)^4}{8 b f}+\frac{a^2 (e+f x)^4}{4 b^3 f}+\frac{a \cos (c+d x) (e+f x)^3}{b^2 d}+\frac{i a^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{b^3 \sqrt{a^2-b^2} d}-\frac{i a^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{b^3 \sqrt{a^2-b^2} d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^3}{2 b d}+\frac{3 f \sin ^2(c+d x) (e+f x)^2}{4 b d^2}+\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{b^3 \sqrt{a^2-b^2} d^2}-\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{b^3 \sqrt{a^2-b^2} d^2}-\frac{3 a f \sin (c+d x) (e+f x)^2}{b^2 d^2}-\frac{6 a f^2 \cos (c+d x) (e+f x)}{b^2 d^3}+\frac{6 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{b^3 \sqrt{a^2-b^2} d^3}-\frac{6 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{b^3 \sqrt{a^2-b^2} d^3}+\frac{3 f^2 \cos (c+d x) \sin (c+d x) (e+f x)}{4 b d^3}-\frac{3 f^3 x^2}{8 b d^2}-\frac{3 f^3 \sin ^2(c+d x)}{8 b d^4}-\frac{3 e f^2 x}{4 b d^2}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 \sqrt{a^2-b^2} d^4}+\frac{6 a^3 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b^3 \sqrt{a^2-b^2} d^4}+\frac{6 a f^3 \sin (c+d x)}{b^2 d^4}",1,"(-3*e*f^2*x)/(4*b*d^2) - (3*f^3*x^2)/(8*b*d^2) + (a^2*(e + f*x)^4)/(4*b^3*f) + (e + f*x)^4/(8*b*f) - (6*a*f^2*(e + f*x)*Cos[c + d*x])/(b^2*d^3) + (a*(e + f*x)^3*Cos[c + d*x])/(b^2*d) + (I*a^3*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) - (I*a^3*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) + (3*a^3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) - (3*a^3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) + ((6*I)*a^3*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^3) - ((6*I)*a^3*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^3) - (6*a^3*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^4) + (6*a^3*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^4) + (6*a*f^3*Sin[c + d*x])/(b^2*d^4) - (3*a*f*(e + f*x)^2*Sin[c + d*x])/(b^2*d^2) + (3*f^2*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^3) - ((e + f*x)^3*Cos[c + d*x]*Sin[c + d*x])/(2*b*d) - (3*f^3*Sin[c + d*x]^2)/(8*b*d^4) + (3*f*(e + f*x)^2*Sin[c + d*x]^2)/(4*b*d^2)","A",24,13,28,0.4643,1,"{4515, 3311, 32, 3310, 3296, 2637, 3323, 2264, 2190, 2531, 6609, 2282, 6589}"
229,1,592,0,1.1802811,"\int \frac{(e+f x)^2 \sin ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sin[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2 \sqrt{a^2-b^2}}-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2 \sqrt{a^2-b^2}}+\frac{2 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3 \sqrt{a^2-b^2}}-\frac{2 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3 \sqrt{a^2-b^2}}+\frac{i a^3 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}-\frac{i a^3 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{a^2 (e+f x)^3}{3 b^3 f}-\frac{2 a f (e+f x) \sin (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cos (c+d x)}{b^2 d^3}+\frac{a (e+f x)^2 \cos (c+d x)}{b^2 d}+\frac{f (e+f x) \sin ^2(c+d x)}{2 b d^2}+\frac{f^2 \sin (c+d x) \cos (c+d x)}{4 b d^3}-\frac{(e+f x)^2 \sin (c+d x) \cos (c+d x)}{2 b d}-\frac{f^2 x}{4 b d^2}+\frac{(e+f x)^3}{6 b f}","\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2 \sqrt{a^2-b^2}}-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2 \sqrt{a^2-b^2}}+\frac{2 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3 \sqrt{a^2-b^2}}-\frac{2 i a^3 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3 \sqrt{a^2-b^2}}+\frac{i a^3 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}-\frac{i a^3 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{a^2 (e+f x)^3}{3 b^3 f}-\frac{2 a f (e+f x) \sin (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cos (c+d x)}{b^2 d^3}+\frac{a (e+f x)^2 \cos (c+d x)}{b^2 d}+\frac{f (e+f x) \sin ^2(c+d x)}{2 b d^2}+\frac{f^2 \sin (c+d x) \cos (c+d x)}{4 b d^3}-\frac{(e+f x)^2 \sin (c+d x) \cos (c+d x)}{2 b d}-\frac{f^2 x}{4 b d^2}+\frac{(e+f x)^3}{6 b f}",1,"-(f^2*x)/(4*b*d^2) + (a^2*(e + f*x)^3)/(3*b^3*f) + (e + f*x)^3/(6*b*f) - (2*a*f^2*Cos[c + d*x])/(b^2*d^3) + (a*(e + f*x)^2*Cos[c + d*x])/(b^2*d) + (I*a^3*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) - (I*a^3*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) + (2*a^3*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) + ((2*I)*a^3*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^3) - ((2*I)*a^3*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^3) - (2*a*f*(e + f*x)*Sin[c + d*x])/(b^2*d^2) + (f^2*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^3) - ((e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(2*b*d) + (f*(e + f*x)*Sin[c + d*x]^2)/(2*b*d^2)","A",21,13,28,0.4643,1,"{4515, 3311, 32, 2635, 8, 3296, 2638, 3323, 2264, 2190, 2531, 2282, 6589}"
230,1,382,0,0.6657393,"\int \frac{(e+f x) \sin ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Sin[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","\frac{a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2 \sqrt{a^2-b^2}}-\frac{a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2 \sqrt{a^2-b^2}}+\frac{i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}-\frac{i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{a^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}-\frac{a f \sin (c+d x)}{b^2 d^2}+\frac{a (e+f x) \cos (c+d x)}{b^2 d}+\frac{f \sin ^2(c+d x)}{4 b d^2}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 b d}+\frac{e x}{2 b}+\frac{f x^2}{4 b}","\frac{a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2 \sqrt{a^2-b^2}}-\frac{a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2 \sqrt{a^2-b^2}}+\frac{i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}-\frac{i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{a^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}-\frac{a f \sin (c+d x)}{b^2 d^2}+\frac{a (e+f x) \cos (c+d x)}{b^2 d}+\frac{f \sin ^2(c+d x)}{4 b d^2}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 b d}+\frac{e x}{2 b}+\frac{f x^2}{4 b}",1,"(a^2*e*x)/b^3 + (e*x)/(2*b) + (a^2*f*x^2)/(2*b^3) + (f*x^2)/(4*b) + (a*(e + f*x)*Cos[c + d*x])/(b^2*d) + (I*a^3*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) - (I*a^3*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d) + (a^3*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) - (a^3*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*Sqrt[a^2 - b^2]*d^2) - (a*f*Sin[c + d*x])/(b^2*d^2) - ((e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*b*d) + (f*Sin[c + d*x]^2)/(4*b*d^2)","A",16,9,26,0.3462,1,"{4515, 3310, 3296, 2637, 3323, 2264, 2190, 2279, 2391}"
231,1,107,0,0.1855401,"\int \frac{\sin ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Sin[c + d*x]^3/(a + b*Sin[c + d*x]),x]","-\frac{2 a^3 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{x \left(2 a^2+b^2\right)}{2 b^3}+\frac{a \cos (c+d x)}{b^2 d}-\frac{\sin (c+d x) \cos (c+d x)}{2 b d}","-\frac{2 a^3 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^3 d \sqrt{a^2-b^2}}+\frac{x \left(2 a^2+b^2\right)}{2 b^3}+\frac{a \cos (c+d x)}{b^2 d}-\frac{\sin (c+d x) \cos (c+d x)}{2 b d}",1,"((2*a^2 + b^2)*x)/(2*b^3) - (2*a^3*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b^3*Sqrt[a^2 - b^2]*d) + (a*Cos[c + d*x])/(b^2*d) - (Cos[c + d*x]*Sin[c + d*x])/(2*b*d)","A",6,6,21,0.2857,1,"{2793, 3023, 2735, 2660, 618, 204}"
232,1,732,0,1.1172115,"\int \frac{(e+f x)^3 \csc (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Csc[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^3 \sqrt{a^2-b^2}}-\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^3 \sqrt{a^2-b^2}}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{6 b f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^4 \sqrt{a^2-b^2}}+\frac{6 b f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^4 \sqrt{a^2-b^2}}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}+\frac{i b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}","\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^3 \sqrt{a^2-b^2}}-\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^3 \sqrt{a^2-b^2}}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{6 b f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^4 \sqrt{a^2-b^2}}+\frac{6 b f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^4 \sqrt{a^2-b^2}}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}+\frac{i b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}",1,"(-2*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) + (I*b*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) - (I*b*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) + ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2) - (6*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) + ((6*I)*b*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^3) - ((6*I)*b*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^3) - ((6*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) + ((6*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4) - (6*b*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^4) + (6*b*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^4)","A",22,9,26,0.3462,1,"{4535, 4183, 2531, 6609, 2282, 6589, 3323, 2264, 2190}"
233,1,528,0,0.9463775,"\int \frac{(e+f x)^2 \csc (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Csc[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{2 b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}+\frac{2 i b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^3 \sqrt{a^2-b^2}}-\frac{2 i b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^3 \sqrt{a^2-b^2}}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{i b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}","\frac{2 b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}+\frac{2 i b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^3 \sqrt{a^2-b^2}}-\frac{2 i b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^3 \sqrt{a^2-b^2}}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{i b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}",1,"(-2*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) + (I*b*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) - (I*b*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) + ((2*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (2*b*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2) - (2*b*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2) - (2*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (2*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) + ((2*I)*b*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^3) - ((2*I)*b*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^3)","A",18,8,26,0.3077,1,"{4535, 4183, 2531, 2282, 6589, 3323, 2264, 2190}"
234,1,325,0,0.6150574,"\int \frac{(e+f x) \csc (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Csc[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{i b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}","\frac{b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d^2 \sqrt{a^2-b^2}}-\frac{b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d^2 \sqrt{a^2-b^2}}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}+\frac{i b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{i b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a d \sqrt{a^2-b^2}}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}",1,"(-2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) + (I*b*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) - (I*b*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d) + (I*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - (I*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (b*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2) - (b*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*Sqrt[a^2 - b^2]*d^2)","A",14,7,24,0.2917,1,"{4535, 4183, 2279, 2391, 3323, 2264, 2190}"
235,1,67,0,0.0829515,"\int \frac{\csc (c+d x)}{a+b \sin (c+d x)} \, dx","Int[Csc[c + d*x]/(a + b*Sin[c + d*x]),x]","-\frac{2 b \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}","-\frac{2 b \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a d \sqrt{a^2-b^2}}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}",1,"(-2*b*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(a*Sqrt[a^2 - b^2]*d) - ArcTanh[Cos[c + d*x]]/(a*d)","A",5,5,19,0.2632,1,"{2747, 3770, 2660, 618, 204}"
236,1,882,0,1.5512265,"\int \frac{(e+f x)^3 \csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Csc[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) f^3}{2 a d^4}+\frac{6 i b \text{PolyLog}\left(4,-e^{i (c+d x)}\right) f^3}{a^2 d^4}-\frac{6 i b \text{PolyLog}\left(4,e^{i (c+d x)}\right) f^3}{a^2 d^4}+\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{a^2 \sqrt{a^2-b^2} d^4}-\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{a^2 \sqrt{a^2-b^2} d^4}-\frac{3 i (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) f^2}{a d^3}+\frac{6 b (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right) f^2}{a^2 d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right) f^2}{a^2 d^3}-\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{a^2 \sqrt{a^2-b^2} d^3}+\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{a^2 \sqrt{a^2-b^2} d^3}+\frac{3 (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right) f}{a d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) f}{a^2 d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) f}{a^2 d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{a^2 \sqrt{a^2-b^2} d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{a^2 \sqrt{a^2-b^2} d^2}-\frac{i (e+f x)^3}{a d}+\frac{2 b (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}-\frac{(e+f x)^3 \cot (c+d x)}{a d}-\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 \sqrt{a^2-b^2} d}+\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 \sqrt{a^2-b^2} d}","\frac{3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) f^3}{2 a d^4}+\frac{6 i b \text{PolyLog}\left(4,-e^{i (c+d x)}\right) f^3}{a^2 d^4}-\frac{6 i b \text{PolyLog}\left(4,e^{i (c+d x)}\right) f^3}{a^2 d^4}+\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{a^2 \sqrt{a^2-b^2} d^4}-\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{a^2 \sqrt{a^2-b^2} d^4}-\frac{3 i (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) f^2}{a d^3}+\frac{6 b (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right) f^2}{a^2 d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right) f^2}{a^2 d^3}-\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{a^2 \sqrt{a^2-b^2} d^3}+\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{a^2 \sqrt{a^2-b^2} d^3}+\frac{3 (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right) f}{a d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) f}{a^2 d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) f}{a^2 d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{a^2 \sqrt{a^2-b^2} d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{a^2 \sqrt{a^2-b^2} d^2}-\frac{i (e+f x)^3}{a d}+\frac{2 b (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}-\frac{(e+f x)^3 \cot (c+d x)}{a d}-\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 \sqrt{a^2-b^2} d}+\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 \sqrt{a^2-b^2} d}",1,"((-I)*(e + f*x)^3)/(a*d) + (2*b*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a^2*d) - ((e + f*x)^3*Cot[c + d*x])/(a*d) - (I*b^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (I*b^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (3*f*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((3*I)*b*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2) - ((3*I)*f^2*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (6*b*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a^2*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a^2*d^3) - ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^3) + ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^3) + (3*f^3*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^4) + ((6*I)*b*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a^2*d^4) - ((6*I)*b*f^3*PolyLog[4, E^(I*(c + d*x))])/(a^2*d^4) + (6*b^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^4) - (6*b^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^4)","A",29,11,28,0.3929,1,"{4535, 4184, 3717, 2190, 2531, 2282, 6589, 4183, 6609, 3323, 2264}"
237,1,639,0,1.2055928,"\int \frac{(e+f x)^2 \csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Csc[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^2 \sqrt{a^2-b^2}}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^2 \sqrt{a^2-b^2}}-\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^3 \sqrt{a^2-b^2}}+\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^3 \sqrt{a^2-b^2}}-\frac{2 i b f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}+\frac{2 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a^2 d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{2 b (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \cot (c+d x)}{a d}-\frac{i (e+f x)^2}{a d}","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^2 \sqrt{a^2-b^2}}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^2 \sqrt{a^2-b^2}}-\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^3 \sqrt{a^2-b^2}}+\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^3 \sqrt{a^2-b^2}}-\frac{2 i b f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}+\frac{2 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a^2 d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}-\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{2 b (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{2 f (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \cot (c+d x)}{a d}-\frac{i (e+f x)^2}{a d}",1,"((-I)*(e + f*x)^2)/(a*d) + (2*b*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a^2*d) - ((e + f*x)^2*Cot[c + d*x])/(a*d) - (I*b^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (I*b^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (2*f*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((2*I)*b*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + ((2*I)*b*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2) + (2*b^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2) - (I*f^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (2*b*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a^2*d^3) - (2*b*f^2*PolyLog[3, E^(I*(c + d*x))])/(a^2*d^3) - ((2*I)*b^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^3) + ((2*I)*b^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^3)","A",24,12,28,0.4286,1,"{4535, 4184, 3717, 2190, 2279, 2391, 4183, 2531, 2282, 6589, 3323, 2264}"
238,1,370,0,0.6164112,"\int \frac{(e+f x) \csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Csc[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^2 \sqrt{a^2-b^2}}+\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^2 \sqrt{a^2-b^2}}-\frac{i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}-\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot (c+d x)}{a d}","-\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d^2 \sqrt{a^2-b^2}}+\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d^2 \sqrt{a^2-b^2}}-\frac{i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}-\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot (c+d x)}{a d}",1,"(2*b*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a^2*d) - ((e + f*x)*Cot[c + d*x])/(a*d) - (I*b^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (I*b^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d) + (f*Log[Sin[c + d*x]])/(a*d^2) - (I*b*f*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + (I*b*f*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - (b^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2) + (b^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*Sqrt[a^2 - b^2]*d^2)","A",17,9,26,0.3462,1,"{4535, 4184, 3475, 4183, 2279, 2391, 3323, 2264, 2190}"
239,1,83,0,0.1281759,"\int \frac{\csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Csc[c + d*x]^2/(a + b*Sin[c + d*x]),x]","\frac{2 b^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{b \tanh ^{-1}(\cos (c+d x))}{a^2 d}-\frac{\cot (c+d x)}{a d}","\frac{2 b^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a^2 d \sqrt{a^2-b^2}}+\frac{b \tanh ^{-1}(\cos (c+d x))}{a^2 d}-\frac{\cot (c+d x)}{a d}",1,"(2*b^2*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(a^2*Sqrt[a^2 - b^2]*d) + (b*ArcTanh[Cos[c + d*x]])/(a^2*d) - Cot[c + d*x]/(a*d)","A",7,7,21,0.3333,1,"{2802, 12, 2747, 3770, 2660, 618, 204}"
240,0,0,0,0.0683369,"\int \frac{(e+f x)^m \sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sin[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sin ^2(c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sin ^2(c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Sin[c + d*x]^2)/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
241,0,0,0,0.0415453,"\int \frac{(e+f x)^m \sin (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sin[c + d*x])/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sin (c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sin (c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Sin[c + d*x])/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
242,0,0,0,0.0536151,"\int \frac{(e+f x)^m}{a+b \sin (c+d x)} \, dx","Int[(e + f*x)^m/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{(e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][(e + f*x)^m/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
243,0,0,0,0.0416573,"\int \frac{(e+f x)^m \csc (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Csc[c + d*x])/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \csc (c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\csc (c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Csc[c + d*x])/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
244,0,0,0,0.0678792,"\int \frac{(e+f x)^m \csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Csc[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \csc ^2(c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\csc ^2(c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Csc[c + d*x]^2)/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
245,1,574,0,1.6167535,"\int \frac{(e+f x) \sin (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)*Sin[c + d*x])/(a + b*Sin[c + d*x])^2,x]","\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{a f \log (a+b \sin (c+d x))}{b d^2 \left(a^2-b^2\right)}+\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \left(a^2-b^2\right)^{3/2}}-\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \left(a^2-b^2\right)^{3/2}}-\frac{i (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}+\frac{i (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}-\frac{a (e+f x) \cos (c+d x)}{d \left(a^2-b^2\right) (a+b \sin (c+d x))}","\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{a^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{a f \log (a+b \sin (c+d x))}{b d^2 \left(a^2-b^2\right)}+\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \left(a^2-b^2\right)^{3/2}}-\frac{i a^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \left(a^2-b^2\right)^{3/2}}-\frac{i (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d \sqrt{a^2-b^2}}+\frac{i (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d \sqrt{a^2-b^2}}-\frac{a (e+f x) \cos (c+d x)}{d \left(a^2-b^2\right) (a+b \sin (c+d x))}",1,"(I*a^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - (I*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - (I*a^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + (I*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (a*f*Log[a + b*Sin[c + d*x]])/(b*(a^2 - b^2)*d^2) + (a^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - (f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (a^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + (f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (a*(e + f*x)*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",21,9,24,0.3750,1,"{6742, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
246,1,1106,0,2.5566328,"\int \frac{(e+f x)^2 \sin (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)^2*Sin[c + d*x])/(a + b*Sin[c + d*x])^2,x]","\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d}-\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d}+\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{i (e+f x)^2 a}{b \left(a^2-b^2\right) d}+\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^2}+\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^3}-\frac{(e+f x)^2 \cos (c+d x) a}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}-\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}+\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}-\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^3}","\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d}-\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d}+\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{i (e+f x)^2 a}{b \left(a^2-b^2\right) d}+\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^2}+\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right) d^3}-\frac{(e+f x)^2 \cos (c+d x) a}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}-\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}+\frac{i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}-\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d^3}",1,"((-I)*a*(e + f*x)^2)/(b*(a^2 - b^2)*d) + (2*a*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) + (I*a^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - (I*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (2*a*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) - (I*a^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + (I*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - ((2*I)*a*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) + (2*a^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - (2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - ((2*I)*a*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) - (2*a^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + (2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + ((2*I)*a^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - ((2*I)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - ((2*I)*a^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + ((2*I)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - (a*(e + f*x)^2*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",30,11,26,0.4231,1,"{6742, 3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391}"
247,1,1512,0,3.0664444,"\int \frac{(e+f x)^3 \sin (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)^3*Sin[c + d*x])/(a + b*Sin[c + d*x])^2,x]","\frac{6 a \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right) d^4}+\frac{6 a \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right) d^4}+\frac{6 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \sqrt{a^2-b^2} d^4}-\frac{6 a^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{6 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \sqrt{a^2-b^2} d^4}+\frac{6 a^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{6 i a (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right) d^3}-\frac{6 i a (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right) d^3}-\frac{6 i (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \sqrt{a^2-b^2} d^3}+\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{6 i (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \sqrt{a^2-b^2} d^3}-\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right) d^2}+\frac{3 a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right) d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \sqrt{a^2-b^2} d^2}+\frac{3 a^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \sqrt{a^2-b^2} d^2}-\frac{3 a^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{i a (e+f x)^3}{b \left(a^2-b^2\right) d}-\frac{i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}+\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right)^{3/2} d}+\frac{i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}-\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right)^{3/2} d}-\frac{a (e+f x)^3 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}","\frac{6 a \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right) d^4}+\frac{6 a \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right) d^4}+\frac{6 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \sqrt{a^2-b^2} d^4}-\frac{6 a^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{6 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \sqrt{a^2-b^2} d^4}+\frac{6 a^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{6 i a (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right) d^3}-\frac{6 i a (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right) d^3}-\frac{6 i (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \sqrt{a^2-b^2} d^3}+\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{6 i (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \sqrt{a^2-b^2} d^3}-\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right) d^2}+\frac{3 a (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right) d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \sqrt{a^2-b^2} d^2}+\frac{3 a^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \sqrt{a^2-b^2} d^2}-\frac{3 a^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{i a (e+f x)^3}{b \left(a^2-b^2\right) d}-\frac{i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}+\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right)^{3/2} d}+\frac{i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \sqrt{a^2-b^2} d}-\frac{i a^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right)^{3/2} d}-\frac{a (e+f x)^3 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}",1,"((-I)*a*(e + f*x)^3)/(b*(a^2 - b^2)*d) + (3*a*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) + (I*a^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - (I*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) + (3*a*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) - (I*a^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + (I*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d) - ((6*I)*a*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) + (3*a^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - (3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - ((6*I)*a*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) - (3*a^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + (3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + (6*a*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) + ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) + (6*a*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) - ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - (6*a^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) + (6*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4) + (6*a^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) - (6*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4) - (a*(e + f*x)^3*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",36,10,26,0.3846,1,"{6742, 3324, 3323, 2264, 2190, 2531, 6609, 2282, 6589, 4519}"
248,1,751,0,2.955134,"\int \frac{(e+f x) \sin (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)*Sin[c + d*x])/(a + b*Sin[c + d*x])^3,x]","\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{5/2}}-\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{5/2}}-\frac{3 a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{a f}{2 b d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}+\frac{3 a^2 f \log (a+b \sin (c+d x))}{2 b d^2 \left(a^2-b^2\right)^2}-\frac{f \log (a+b \sin (c+d x))}{b d^2 \left(a^2-b^2\right)}+\frac{3 i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d \left(a^2-b^2\right)^{5/2}}-\frac{3 i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d \left(a^2-b^2\right)^{5/2}}-\frac{3 i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d \left(a^2-b^2\right)^{3/2}}+\frac{3 i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d \left(a^2-b^2\right)^{3/2}}-\frac{3 a^2 (e+f x) \cos (c+d x)}{2 d \left(a^2-b^2\right)^2 (a+b \sin (c+d x))}-\frac{a (e+f x) \cos (c+d x)}{2 d \left(a^2-b^2\right) (a+b \sin (c+d x))^2}+\frac{(e+f x) \cos (c+d x)}{d \left(a^2-b^2\right) (a+b \sin (c+d x))}","\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{5/2}}-\frac{3 a^3 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{5/2}}-\frac{3 a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 a f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}-\frac{a f}{2 b d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}+\frac{3 a^2 f \log (a+b \sin (c+d x))}{2 b d^2 \left(a^2-b^2\right)^2}-\frac{f \log (a+b \sin (c+d x))}{b d^2 \left(a^2-b^2\right)}+\frac{3 i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d \left(a^2-b^2\right)^{5/2}}-\frac{3 i a^3 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d \left(a^2-b^2\right)^{5/2}}-\frac{3 i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d \left(a^2-b^2\right)^{3/2}}+\frac{3 i a (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d \left(a^2-b^2\right)^{3/2}}-\frac{3 a^2 (e+f x) \cos (c+d x)}{2 d \left(a^2-b^2\right)^2 (a+b \sin (c+d x))}-\frac{a (e+f x) \cos (c+d x)}{2 d \left(a^2-b^2\right) (a+b \sin (c+d x))^2}+\frac{(e+f x) \cos (c+d x)}{d \left(a^2-b^2\right) (a+b \sin (c+d x))}",1,"(((3*I)/2)*a^3*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) - (((3*I)/2)*a*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - (((3*I)/2)*a^3*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) + (((3*I)/2)*a*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + (3*a^2*f*Log[a + b*Sin[c + d*x]])/(2*b*(a^2 - b^2)^2*d^2) - (f*Log[a + b*Sin[c + d*x]])/(b*(a^2 - b^2)*d^2) + (3*a^3*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(5/2)*d^2) - (3*a*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(3/2)*d^2) - (3*a^3*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(5/2)*d^2) + (3*a*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(3/2)*d^2) - (a*(e + f*x)*Cos[c + d*x])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x])^2) - (a*f)/(2*b*(a^2 - b^2)*d^2*(a + b*Sin[c + d*x])) - (3*a^2*(e + f*x)*Cos[c + d*x])/(2*(a^2 - b^2)^2*d*(a + b*Sin[c + d*x])) + ((e + f*x)*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",48,11,24,0.4583,1,"{6742, 3325, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31, 32}"
249,1,1584,0,5.9431659,"\int \frac{(e+f x)^2 \sin (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)^2*Sin[c + d*x])/(a + b*Sin[c + d*x])^3,x]","\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}-\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}+\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^2}-\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^2}+\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{3 i (e+f x)^2 a^2}{2 b \left(a^2-b^2\right)^2 d}+\frac{3 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^2}+\frac{3 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^2}-\frac{3 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{3 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{3 (e+f x)^2 \cos (c+d x) a^2}{2 \left(a^2-b^2\right)^2 d (a+b \sin (c+d x))}+\frac{2 f^2 \tan ^{-1}\left(\frac{b+a \tan \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}+\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}-\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{f (e+f x) a}{b \left(a^2-b^2\right) d^2 (a+b \sin (c+d x))}-\frac{(e+f x)^2 \cos (c+d x) a}{2 \left(a^2-b^2\right) d (a+b \sin (c+d x))^2}+\frac{i (e+f x)^2}{b \left(a^2-b^2\right) d}-\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}-\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{(e+f x)^2 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}","\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}-\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}+\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^2}-\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^2}+\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{3 i (e+f x)^2 a^2}{2 b \left(a^2-b^2\right)^2 d}+\frac{3 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^2}+\frac{3 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^2}-\frac{3 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{3 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{3 (e+f x)^2 \cos (c+d x) a^2}{2 \left(a^2-b^2\right)^2 d (a+b \sin (c+d x))}+\frac{2 f^2 \tan ^{-1}\left(\frac{b+a \tan \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}+\frac{3 i (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}-\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^2}-\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 i f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{f (e+f x) a}{b \left(a^2-b^2\right) d^2 (a+b \sin (c+d x))}-\frac{(e+f x)^2 \cos (c+d x) a}{2 \left(a^2-b^2\right) d (a+b \sin (c+d x))^2}+\frac{i (e+f x)^2}{b \left(a^2-b^2\right) d}-\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}-\frac{2 f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{(e+f x)^2 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}",1,"(((-3*I)/2)*a^2*(e + f*x)^2)/(b*(a^2 - b^2)^2*d) + (I*(e + f*x)^2)/(b*(a^2 - b^2)*d) + (2*a*f^2*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b*(a^2 - b^2)^(3/2)*d^3) + (3*a^2*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^2) - (2*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) + (((3*I)/2)*a^3*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) - (((3*I)/2)*a*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + (3*a^2*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^2) - (2*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) - (((3*I)/2)*a^3*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) + (((3*I)/2)*a*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - ((3*I)*a^2*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^3) + ((2*I)*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) + (3*a^3*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^2) - (3*a*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - ((3*I)*a^2*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^3) + ((2*I)*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) - (3*a^3*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^2) + (3*a*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + ((3*I)*a^3*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^3) - ((3*I)*a*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - ((3*I)*a^3*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^3) + ((3*I)*a*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - (a*(e + f*x)^2*Cos[c + d*x])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x])^2) - (a*f*(e + f*x))/(b*(a^2 - b^2)*d^2*(a + b*Sin[c + d*x])) - (3*a^2*(e + f*x)^2*Cos[c + d*x])/(2*(a^2 - b^2)^2*d*(a + b*Sin[c + d*x])) + ((e + f*x)^2*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",73,16,26,0.6154,1,"{6742, 3325, 3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391, 4422, 2660, 618, 204}"
250,1,2348,0,8.3740391,"\int \frac{(e+f x)^3 \sin (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)^3*Sin[c + d*x])/(a + b*Sin[c + d*x])^3,x]","\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}-\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d^2}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d^2}+\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^4}+\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^4}-\frac{3 i (e+f x)^3 a^2}{2 b \left(a^2-b^2\right)^2 d}+\frac{9 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{2 b \left(a^2-b^2\right)^2 d^2}+\frac{9 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{2 b \left(a^2-b^2\right)^2 d^2}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}+\frac{9 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^4}+\frac{9 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^4}-\frac{3 (e+f x)^3 \cos (c+d x) a^2}{2 \left(a^2-b^2\right)^2 d (a+b \sin (c+d x))}-\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}-\frac{3 i f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}+\frac{3 i f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{3 f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d^2}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{3 f (e+f x)^2 a}{2 b \left(a^2-b^2\right) d^2 (a+b \sin (c+d x))}-\frac{(e+f x)^3 \cos (c+d x) a}{2 \left(a^2-b^2\right) d (a+b \sin (c+d x))^2}+\frac{i (e+f x)^3}{b \left(a^2-b^2\right) d}-\frac{3 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}-\frac{3 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^4}-\frac{6 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^4}+\frac{(e+f x)^3 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}","\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}-\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d^2}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{2 b \left(a^2-b^2\right)^{5/2} d^2}+\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^3}-\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^4}+\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^3}{b \left(a^2-b^2\right)^{5/2} d^4}-\frac{3 i (e+f x)^3 a^2}{2 b \left(a^2-b^2\right)^2 d}+\frac{9 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{2 b \left(a^2-b^2\right)^2 d^2}+\frac{9 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{2 b \left(a^2-b^2\right)^2 d^2}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^3}+\frac{9 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^4}+\frac{9 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a^2}{b \left(a^2-b^2\right)^2 d^4}-\frac{3 (e+f x)^3 \cos (c+d x) a^2}{2 \left(a^2-b^2\right)^2 d (a+b \sin (c+d x))}-\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}-\frac{3 i f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{3 i (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d}+\frac{3 i f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}-\frac{3 f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d^2}+\frac{3 f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{2 b \left(a^2-b^2\right)^{3/2} d^2}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^3}+\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{9 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) a}{b \left(a^2-b^2\right)^{3/2} d^4}-\frac{3 f (e+f x)^2 a}{2 b \left(a^2-b^2\right) d^2 (a+b \sin (c+d x))}-\frac{(e+f x)^3 \cos (c+d x) a}{2 \left(a^2-b^2\right) d (a+b \sin (c+d x))^2}+\frac{i (e+f x)^3}{b \left(a^2-b^2\right) d}-\frac{3 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}-\frac{3 f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^4}-\frac{6 f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{b \left(a^2-b^2\right) d^4}+\frac{(e+f x)^3 \cos (c+d x)}{\left(a^2-b^2\right) d (a+b \sin (c+d x))}",1,"(((-3*I)/2)*a^2*(e + f*x)^3)/(b*(a^2 - b^2)^2*d) + (I*(e + f*x)^3)/(b*(a^2 - b^2)*d) - ((3*I)*a*f^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + (9*a^2*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^2*d^2) - (3*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) + (((3*I)/2)*a^3*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) - (((3*I)/2)*a*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) + ((3*I)*a*f^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + (9*a^2*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^2*d^2) - (3*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^2) - (((3*I)/2)*a^3*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d) + (((3*I)/2)*a*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d) - (3*a*f^3*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) - ((9*I)*a^2*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) + (9*a^3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(5/2)*d^2) - (9*a*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(3/2)*d^2) + (3*a*f^3*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) - ((9*I)*a^2*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) - (9*a^3*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(5/2)*d^2) + (9*a*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(2*b*(a^2 - b^2)^(3/2)*d^2) + (9*a^2*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^4) - (6*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) + ((9*I)*a^3*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^3) - ((9*I)*a*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + (9*a^2*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^2*d^4) - (6*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) - ((9*I)*a^3*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^3) + ((9*I)*a*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - (9*a^3*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^4) + (9*a*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) + (9*a^3*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(5/2)*d^4) - (9*a*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) - (a*(e + f*x)^3*Cos[c + d*x])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x])^2) - (3*a*f*(e + f*x)^2)/(2*b*(a^2 - b^2)*d^2*(a + b*Sin[c + d*x])) - (3*a^2*(e + f*x)^3*Cos[c + d*x])/(2*(a^2 - b^2)^2*d*(a + b*Sin[c + d*x])) + ((e + f*x)^3*Cos[c + d*x])/((a^2 - b^2)*d*(a + b*Sin[c + d*x]))","A",92,14,26,0.5385,1,"{6742, 3325, 3324, 3323, 2264, 2190, 2531, 6609, 2282, 6589, 4519, 4422, 2279, 2391}"
251,1,151,0,0.2339643,"\int \frac{(e+f x)^3 \cos (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{12 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{12 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{a d^4}+\frac{2 (e+f x)^3 \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^4}{4 a f}","\frac{12 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{12 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{a d^4}+\frac{2 (e+f x)^3 \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^4}{4 a f}",1,"((-I/4)*(e + f*x)^4)/(a*f) + (2*(e + f*x)^3*Log[1 - I*E^(I*(c + d*x))])/(a*d) - ((6*I)*f*(e + f*x)^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) + (12*f^2*(e + f*x)*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^3) + ((12*I)*f^3*PolyLog[4, I*E^(I*(c + d*x))])/(a*d^4)","A",6,6,26,0.2308,1,"{4517, 2190, 2531, 6609, 2282, 6589}"
252,1,114,0,0.2113581,"\int \frac{(e+f x)^2 \cos (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x])/(a + a*Sin[c + d*x]),x]","-\frac{4 i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{4 f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{2 (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^3}{3 a f}","-\frac{4 i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{4 f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{2 (e+f x)^2 \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^3}{3 a f}",1,"((-I/3)*(e + f*x)^3)/(a*f) + (2*(e + f*x)^2*Log[1 - I*E^(I*(c + d*x))])/(a*d) - ((4*I)*f*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) + (4*f^2*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^3)","A",5,5,26,0.1923,1,"{4517, 2190, 2531, 2282, 6589}"
253,1,79,0,0.1250632,"\int \frac{(e+f x) \cos (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x])/(a + a*Sin[c + d*x]),x]","-\frac{2 i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{2 (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^2}{2 a f}","-\frac{2 i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}+\frac{2 (e+f x) \log \left(1-i e^{i (c+d x)}\right)}{a d}-\frac{i (e+f x)^2}{2 a f}",1,"((-I/2)*(e + f*x)^2)/(a*f) + (2*(e + f*x)*Log[1 - I*E^(I*(c + d*x))])/(a*d) - ((2*I)*f*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2)","A",4,4,24,0.1667,1,"{4517, 2190, 2279, 2391}"
254,1,16,0,0.0253777,"\int \frac{\cos (c+d x)}{a+a \sin (c+d x)} \, dx","Int[Cos[c + d*x]/(a + a*Sin[c + d*x]),x]","\frac{\log (\sin (c+d x)+1)}{a d}","\frac{\log (\sin (c+d x)+1)}{a d}",1,"Log[1 + Sin[c + d*x]]/(a*d)","A",2,2,19,0.1053,1,"{2667, 31}"
255,0,0,0,0.0468099,"\int \frac{\cos (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\cos (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\cos (c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Cos[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
256,0,0,0,0.047282,"\int \frac{\cos (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\cos (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\cos (c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Cos[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
257,1,99,0,0.1441758,"\int \frac{(e+f x)^3 \cos ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}-\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}+\frac{6 f^3 \sin (c+d x)}{a d^4}+\frac{(e+f x)^3 \cos (c+d x)}{a d}+\frac{(e+f x)^4}{4 a f}","-\frac{6 f^2 (e+f x) \cos (c+d x)}{a d^3}-\frac{3 f (e+f x)^2 \sin (c+d x)}{a d^2}+\frac{6 f^3 \sin (c+d x)}{a d^4}+\frac{(e+f x)^3 \cos (c+d x)}{a d}+\frac{(e+f x)^4}{4 a f}",1,"(e + f*x)^4/(4*a*f) - (6*f^2*(e + f*x)*Cos[c + d*x])/(a*d^3) + ((e + f*x)^3*Cos[c + d*x])/(a*d) + (6*f^3*Sin[c + d*x])/(a*d^4) - (3*f*(e + f*x)^2*Sin[c + d*x])/(a*d^2)","A",6,4,28,0.1429,1,"{4523, 32, 3296, 2637}"
258,1,75,0,0.1148281,"\int \frac{(e+f x)^2 \cos ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{2 f (e+f x) \sin (c+d x)}{a d^2}-\frac{2 f^2 \cos (c+d x)}{a d^3}+\frac{(e+f x)^2 \cos (c+d x)}{a d}+\frac{(e+f x)^3}{3 a f}","-\frac{2 f (e+f x) \sin (c+d x)}{a d^2}-\frac{2 f^2 \cos (c+d x)}{a d^3}+\frac{(e+f x)^2 \cos (c+d x)}{a d}+\frac{(e+f x)^3}{3 a f}",1,"(e + f*x)^3/(3*a*f) - (2*f^2*Cos[c + d*x])/(a*d^3) + ((e + f*x)^2*Cos[c + d*x])/(a*d) - (2*f*(e + f*x)*Sin[c + d*x])/(a*d^2)","A",5,4,28,0.1429,1,"{4523, 32, 3296, 2638}"
259,1,51,0,0.0641802,"\int \frac{(e+f x) \cos ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{f \sin (c+d x)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}","-\frac{f \sin (c+d x)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}",1,"(e*x)/a + (f*x^2)/(2*a) + ((e + f*x)*Cos[c + d*x])/(a*d) - (f*Sin[c + d*x])/(a*d^2)","A",4,3,26,0.1154,1,"{4523, 3296, 2637}"
260,1,19,0,0.0421265,"\int \frac{\cos ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Cos[c + d*x]^2/(a + a*Sin[c + d*x]),x]","\frac{\cos (c+d x)}{a d}+\frac{x}{a}","\frac{\cos (c+d x)}{a d}+\frac{x}{a}",1,"x/a + Cos[c + d*x]/(a*d)","A",2,2,21,0.09524,1,"{2682, 8}"
261,1,72,0,0.2014799,"\int \frac{\cos ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])),x]","-\frac{\sin \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\cos \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f}+\frac{\log (e+f x)}{a f}","-\frac{\sin \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\cos \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f}+\frac{\log (e+f x)}{a f}",1,"Log[e + f*x]/(a*f) - (CosIntegral[(d*e)/f + d*x]*Sin[c - (d*e)/f])/(a*f) - (Cos[c - (d*e)/f]*SinIntegral[(d*e)/f + d*x])/(a*f)","A",5,5,28,0.1786,1,"{4523, 31, 3303, 3299, 3302}"
262,1,95,0,0.2001078,"\int \frac{\cos ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","-\frac{d \cos \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{d \sin \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{\sin (c+d x)}{a f (e+f x)}-\frac{1}{a f (e+f x)}","-\frac{d \cos \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{d \sin \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{\sin (c+d x)}{a f (e+f x)}-\frac{1}{a f (e+f x)}",1,"-(1/(a*f*(e + f*x))) - (d*Cos[c - (d*e)/f]*CosIntegral[(d*e)/f + d*x])/(a*f^2) + Sin[c + d*x]/(a*f*(e + f*x)) + (d*Sin[c - (d*e)/f]*SinIntegral[(d*e)/f + d*x])/(a*f^2)","A",6,6,28,0.2143,1,"{4523, 32, 3297, 3303, 3299, 3302}"
263,1,219,0,0.242949,"\int \frac{(e+f x)^3 \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{3 f^2 (e+f x) \sin ^2(c+d x)}{4 a d^3}-\frac{6 f^2 (e+f x) \sin (c+d x)}{a d^3}+\frac{3 f (e+f x)^2 \cos (c+d x)}{a d^2}-\frac{3 f (e+f x)^2 \sin (c+d x) \cos (c+d x)}{4 a d^2}-\frac{6 f^3 \cos (c+d x)}{a d^4}+\frac{3 f^3 \sin (c+d x) \cos (c+d x)}{8 a d^4}-\frac{(e+f x)^3 \sin ^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \sin (c+d x)}{a d}-\frac{3 f^3 x}{8 a d^3}+\frac{(e+f x)^3}{4 a d}","\frac{3 f^2 (e+f x) \sin ^2(c+d x)}{4 a d^3}-\frac{6 f^2 (e+f x) \sin (c+d x)}{a d^3}+\frac{3 f (e+f x)^2 \cos (c+d x)}{a d^2}-\frac{3 f (e+f x)^2 \sin (c+d x) \cos (c+d x)}{4 a d^2}-\frac{6 f^3 \cos (c+d x)}{a d^4}+\frac{3 f^3 \sin (c+d x) \cos (c+d x)}{8 a d^4}-\frac{(e+f x)^3 \sin ^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \sin (c+d x)}{a d}-\frac{3 f^3 x}{8 a d^3}+\frac{(e+f x)^3}{4 a d}",1,"(-3*f^3*x)/(8*a*d^3) + (e + f*x)^3/(4*a*d) - (6*f^3*Cos[c + d*x])/(a*d^4) + (3*f*(e + f*x)^2*Cos[c + d*x])/(a*d^2) - (6*f^2*(e + f*x)*Sin[c + d*x])/(a*d^3) + ((e + f*x)^3*Sin[c + d*x])/(a*d) + (3*f^3*Cos[c + d*x]*Sin[c + d*x])/(8*a*d^4) - (3*f*(e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(4*a*d^2) + (3*f^2*(e + f*x)*Sin[c + d*x]^2)/(4*a*d^3) - ((e + f*x)^3*Sin[c + d*x]^2)/(2*a*d)","A",10,8,28,0.2857,1,"{4523, 3296, 2638, 4404, 3311, 32, 2635, 8}"
264,1,161,0,0.1727807,"\int \frac{(e+f x)^2 \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{2 f (e+f x) \cos (c+d x)}{a d^2}-\frac{f (e+f x) \sin (c+d x) \cos (c+d x)}{2 a d^2}+\frac{f^2 \sin ^2(c+d x)}{4 a d^3}-\frac{2 f^2 \sin (c+d x)}{a d^3}-\frac{(e+f x)^2 \sin ^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \sin (c+d x)}{a d}+\frac{e f x}{2 a d}+\frac{f^2 x^2}{4 a d}","\frac{2 f (e+f x) \cos (c+d x)}{a d^2}-\frac{f (e+f x) \sin (c+d x) \cos (c+d x)}{2 a d^2}+\frac{f^2 \sin ^2(c+d x)}{4 a d^3}-\frac{2 f^2 \sin (c+d x)}{a d^3}-\frac{(e+f x)^2 \sin ^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \sin (c+d x)}{a d}+\frac{e f x}{2 a d}+\frac{f^2 x^2}{4 a d}",1,"(e*f*x)/(2*a*d) + (f^2*x^2)/(4*a*d) + (2*f*(e + f*x)*Cos[c + d*x])/(a*d^2) - (2*f^2*Sin[c + d*x])/(a*d^3) + ((e + f*x)^2*Sin[c + d*x])/(a*d) - (f*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*a*d^2) + (f^2*Sin[c + d*x]^2)/(4*a*d^3) - ((e + f*x)^2*Sin[c + d*x]^2)/(2*a*d)","A",7,5,28,0.1786,1,"{4523, 3296, 2637, 4404, 3310}"
265,1,91,0,0.0910735,"\int \frac{(e+f x) \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{f \cos (c+d x)}{a d^2}-\frac{f \sin (c+d x) \cos (c+d x)}{4 a d^2}-\frac{(e+f x) \sin ^2(c+d x)}{2 a d}+\frac{(e+f x) \sin (c+d x)}{a d}+\frac{f x}{4 a d}","\frac{f \cos (c+d x)}{a d^2}-\frac{f \sin (c+d x) \cos (c+d x)}{4 a d^2}-\frac{(e+f x) \sin ^2(c+d x)}{2 a d}+\frac{(e+f x) \sin (c+d x)}{a d}+\frac{f x}{4 a d}",1,"(f*x)/(4*a*d) + (f*Cos[c + d*x])/(a*d^2) + ((e + f*x)*Sin[c + d*x])/(a*d) - (f*Cos[c + d*x]*Sin[c + d*x])/(4*a*d^2) - ((e + f*x)*Sin[c + d*x]^2)/(2*a*d)","A",6,6,26,0.2308,1,"{4523, 3296, 2638, 4404, 2635, 8}"
266,1,32,0,0.045625,"\int \frac{\cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Cos[c + d*x]^3/(a + a*Sin[c + d*x]),x]","\frac{\sin (c+d x)}{a d}-\frac{\sin ^2(c+d x)}{2 a d}","\frac{\sin (c+d x)}{a d}-\frac{\sin ^2(c+d x)}{2 a d}",1,"Sin[c + d*x]/(a*d) - Sin[c + d*x]^2/(2*a*d)","A",2,1,21,0.04762,1,"{2667}"
267,1,128,0,0.2962188,"\int \frac{\cos ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])),x]","-\frac{\sin \left(2 c-\frac{2 d e}{f}\right) \text{CosIntegral}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}+\frac{\cos \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\sin \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\cos \left(2 c-\frac{2 d e}{f}\right) \text{Si}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}","-\frac{\sin \left(2 c-\frac{2 d e}{f}\right) \text{CosIntegral}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}+\frac{\cos \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\sin \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{\cos \left(2 c-\frac{2 d e}{f}\right) \text{Si}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}",1,"(Cos[c - (d*e)/f]*CosIntegral[(d*e)/f + d*x])/(a*f) - (CosIntegral[(2*d*e)/f + 2*d*x]*Sin[2*c - (2*d*e)/f])/(2*a*f) - (Sin[c - (d*e)/f]*SinIntegral[(d*e)/f + d*x])/(a*f) - (Cos[2*c - (2*d*e)/f]*SinIntegral[(2*d*e)/f + 2*d*x])/(2*a*f)","A",9,6,28,0.2143,1,"{4523, 3303, 3299, 3302, 4406, 12}"
268,1,175,0,0.3341094,"\int \frac{\cos ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Cos[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","-\frac{d \sin \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f^2}-\frac{d \cos \left(2 c-\frac{2 d e}{f}\right) \text{CosIntegral}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}+\frac{d \sin \left(2 c-\frac{2 d e}{f}\right) \text{Si}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}-\frac{d \cos \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{\sin (2 c+2 d x)}{2 a f (e+f x)}-\frac{\cos (c+d x)}{a f (e+f x)}","-\frac{d \sin \left(c-\frac{d e}{f}\right) \text{CosIntegral}\left(\frac{d e}{f}+d x\right)}{a f^2}-\frac{d \cos \left(2 c-\frac{2 d e}{f}\right) \text{CosIntegral}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}+\frac{d \sin \left(2 c-\frac{2 d e}{f}\right) \text{Si}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}-\frac{d \cos \left(c-\frac{d e}{f}\right) \text{Si}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{\sin (2 c+2 d x)}{2 a f (e+f x)}-\frac{\cos (c+d x)}{a f (e+f x)}",1,"-(Cos[c + d*x]/(a*f*(e + f*x))) - (d*Cos[2*c - (2*d*e)/f]*CosIntegral[(2*d*e)/f + 2*d*x])/(a*f^2) - (d*CosIntegral[(d*e)/f + d*x]*Sin[c - (d*e)/f])/(a*f^2) + Sin[2*c + 2*d*x]/(2*a*f*(e + f*x)) - (d*Cos[c - (d*e)/f]*SinIntegral[(d*e)/f + d*x])/(a*f^2) + (d*Sin[2*c - (2*d*e)/f]*SinIntegral[(2*d*e)/f + 2*d*x])/(a*f^2)","A",11,7,28,0.2500,1,"{4523, 3297, 3303, 3299, 3302, 4406, 12}"
269,1,502,0,0.4883112,"\int \frac{(e+f x)^3 \sec (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sec[c + d*x])/(a + a*Sin[c + d*x]),x]","-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{3 i f^3 \text{PolyLog}\left(4,-i e^{i (c+d x)}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{a d^4}+\frac{3 f^2 (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}+\frac{3 f (e+f x)^2 \tan (c+d x)}{2 a d^2}-\frac{3 f (e+f x)^2 \sec (c+d x)}{2 a d^2}-\frac{i (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3 \sec ^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec (c+d x)}{2 a d}-\frac{3 i f (e+f x)^2}{2 a d^2}","-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{3 i f^3 \text{PolyLog}\left(4,-i e^{i (c+d x)}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{a d^4}+\frac{3 f^2 (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}+\frac{3 f (e+f x)^2 \tan (c+d x)}{2 a d^2}-\frac{3 f (e+f x)^2 \sec (c+d x)}{2 a d^2}-\frac{i (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3 \sec ^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec (c+d x)}{2 a d}-\frac{3 i f (e+f x)^2}{2 a d^2}",1,"(((-3*I)/2)*f*(e + f*x)^2)/(a*d^2) - ((6*I)*f^2*(e + f*x)*ArcTan[E^(I*(c + d*x))])/(a*d^3) - (I*(e + f*x)^3*ArcTan[E^(I*(c + d*x))])/(a*d) + (3*f^2*(e + f*x)*Log[1 + E^((2*I)*(c + d*x))])/(a*d^3) + ((3*I)*f^3*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^4) + (((3*I)/2)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - ((3*I)*f^3*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^4) - (((3*I)/2)*f*(e + f*x)^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - (((3*I)/2)*f^3*PolyLog[2, -E^((2*I)*(c + d*x))])/(a*d^4) - (3*f^2*(e + f*x)*PolyLog[3, (-I)*E^(I*(c + d*x))])/(a*d^3) + (3*f^2*(e + f*x)*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^3) - ((3*I)*f^3*PolyLog[4, (-I)*E^(I*(c + d*x))])/(a*d^4) + ((3*I)*f^3*PolyLog[4, I*E^(I*(c + d*x))])/(a*d^4) - (3*f*(e + f*x)^2*Sec[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Sec[c + d*x]^2)/(2*a*d) + (3*f*(e + f*x)^2*Tan[c + d*x])/(2*a*d^2) + ((e + f*x)^3*Sec[c + d*x]*Tan[c + d*x])/(2*a*d)","A",22,13,26,0.5000,1,"{4531, 4186, 4181, 2279, 2391, 2531, 6609, 2282, 6589, 4409, 4184, 3719, 2190}"
270,1,278,0,0.2666787,"\int \frac{(e+f x)^2 \sec (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sec[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{i f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{f (e+f x) \tan (c+d x)}{a d^2}-\frac{f (e+f x) \sec (c+d x)}{a d^2}+\frac{f^2 \tanh ^{-1}(\sin (c+d x))}{a d^3}+\frac{f^2 \log (\cos (c+d x))}{a d^3}-\frac{i (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^2 \sec ^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec (c+d x)}{2 a d}","\frac{i f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^3}+\frac{f (e+f x) \tan (c+d x)}{a d^2}-\frac{f (e+f x) \sec (c+d x)}{a d^2}+\frac{f^2 \tanh ^{-1}(\sin (c+d x))}{a d^3}+\frac{f^2 \log (\cos (c+d x))}{a d^3}-\frac{i (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^2 \sec ^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec (c+d x)}{2 a d}",1,"((-I)*(e + f*x)^2*ArcTan[E^(I*(c + d*x))])/(a*d) + (f^2*ArcTanh[Sin[c + d*x]])/(a*d^3) + (f^2*Log[Cos[c + d*x]])/(a*d^3) + (I*f*(e + f*x)*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - (I*f*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - (f^2*PolyLog[3, (-I)*E^(I*(c + d*x))])/(a*d^3) + (f^2*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^3) - (f*(e + f*x)*Sec[c + d*x])/(a*d^2) - ((e + f*x)^2*Sec[c + d*x]^2)/(2*a*d) + (f*(e + f*x)*Tan[c + d*x])/(a*d^2) + ((e + f*x)^2*Sec[c + d*x]*Tan[c + d*x])/(2*a*d)","A",13,10,26,0.3846,1,"{4531, 4186, 3770, 4181, 2531, 2282, 6589, 4409, 4184, 3475}"
271,1,172,0,0.1388394,"\int \frac{(e+f x) \sec (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sec[c + d*x])/(a + a*Sin[c + d*x]),x]","\frac{i f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^2}-\frac{i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^2}+\frac{f \tan (c+d x)}{2 a d^2}-\frac{f \sec (c+d x)}{2 a d^2}-\frac{i (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x) \sec ^2(c+d x)}{2 a d}+\frac{(e+f x) \tan (c+d x) \sec (c+d x)}{2 a d}","\frac{i f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^2}-\frac{i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^2}+\frac{f \tan (c+d x)}{2 a d^2}-\frac{f \sec (c+d x)}{2 a d^2}-\frac{i (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x) \sec ^2(c+d x)}{2 a d}+\frac{(e+f x) \tan (c+d x) \sec (c+d x)}{2 a d}",1,"((-I)*(e + f*x)*ArcTan[E^(I*(c + d*x))])/(a*d) + ((I/2)*f*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - ((I/2)*f*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - (f*Sec[c + d*x])/(2*a*d^2) - ((e + f*x)*Sec[c + d*x]^2)/(2*a*d) + (f*Tan[c + d*x])/(2*a*d^2) + ((e + f*x)*Sec[c + d*x]*Tan[c + d*x])/(2*a*d)","A",10,8,24,0.3333,1,"{4531, 4185, 4181, 2279, 2391, 4409, 3767, 8}"
272,1,37,0,0.051378,"\int \frac{\sec (c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sec[c + d*x]/(a + a*Sin[c + d*x]),x]","\frac{\tanh ^{-1}(\sin (c+d x))}{2 a d}-\frac{1}{2 d (a \sin (c+d x)+a)}","\frac{\tanh ^{-1}(\sin (c+d x))}{2 a d}-\frac{1}{2 d (a \sin (c+d x)+a)}",1,"ArcTanh[Sin[c + d*x]]/(2*a*d) - 1/(2*d*(a + a*Sin[c + d*x]))","A",4,3,19,0.1579,1,"{2667, 44, 206}"
273,0,0,0,0.0453772,"\int \frac{\sec (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sec (c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec (c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
274,0,0,0,0.0456112,"\int \frac{\sec (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sec (c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec (c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
275,1,475,0,0.5939109,"\int \frac{(e+f x)^3 \sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sec[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\frac{i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^3}-\frac{i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{a d^3}-\frac{f^3 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right)}{a d^4}+\frac{f^2 (e+f x) \tan (c+d x)}{a d^3}-\frac{f^2 (e+f x) \sec (c+d x)}{a d^3}+\frac{2 f (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right)}{a d^2}-\frac{i f (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^2}-\frac{f (e+f x)^2 \sec ^2(c+d x)}{2 a d^2}+\frac{f (e+f x)^2 \tan (c+d x) \sec (c+d x)}{2 a d^2}+\frac{f^3 \tanh ^{-1}(\sin (c+d x))}{a d^4}+\frac{f^3 \log (\cos (c+d x))}{a d^4}+\frac{2 (e+f x)^3 \tan (c+d x)}{3 a d}-\frac{(e+f x)^3 \sec ^3(c+d x)}{3 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec ^2(c+d x)}{3 a d}-\frac{2 i (e+f x)^3}{3 a d}","\frac{i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{a d^3}-\frac{i f^2 (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{a d^3}-\frac{f^3 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right)}{a d^4}+\frac{f^2 (e+f x) \tan (c+d x)}{a d^3}-\frac{f^2 (e+f x) \sec (c+d x)}{a d^3}+\frac{2 f (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right)}{a d^2}-\frac{i f (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^2}-\frac{f (e+f x)^2 \sec ^2(c+d x)}{2 a d^2}+\frac{f (e+f x)^2 \tan (c+d x) \sec (c+d x)}{2 a d^2}+\frac{f^3 \tanh ^{-1}(\sin (c+d x))}{a d^4}+\frac{f^3 \log (\cos (c+d x))}{a d^4}+\frac{2 (e+f x)^3 \tan (c+d x)}{3 a d}-\frac{(e+f x)^3 \sec ^3(c+d x)}{3 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec ^2(c+d x)}{3 a d}-\frac{2 i (e+f x)^3}{3 a d}",1,"(((-2*I)/3)*(e + f*x)^3)/(a*d) - (I*f*(e + f*x)^2*ArcTan[E^(I*(c + d*x))])/(a*d^2) + (f^3*ArcTanh[Sin[c + d*x]])/(a*d^4) + (2*f*(e + f*x)^2*Log[1 + E^((2*I)*(c + d*x))])/(a*d^2) + (f^3*Log[Cos[c + d*x]])/(a*d^4) + (I*f^2*(e + f*x)*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^3) - (I*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - ((2*I)*f^2*(e + f*x)*PolyLog[2, -E^((2*I)*(c + d*x))])/(a*d^3) - (f^3*PolyLog[3, (-I)*E^(I*(c + d*x))])/(a*d^4) + (f^3*PolyLog[3, I*E^(I*(c + d*x))])/(a*d^4) + (f^3*PolyLog[3, -E^((2*I)*(c + d*x))])/(a*d^4) - (f^2*(e + f*x)*Sec[c + d*x])/(a*d^3) - (f*(e + f*x)^2*Sec[c + d*x]^2)/(2*a*d^2) - ((e + f*x)^3*Sec[c + d*x]^3)/(3*a*d) + (f^2*(e + f*x)*Tan[c + d*x])/(a*d^3) + (2*(e + f*x)^3*Tan[c + d*x])/(3*a*d) + (f*(e + f*x)^2*Sec[c + d*x]*Tan[c + d*x])/(2*a*d^2) + ((e + f*x)^3*Sec[c + d*x]^2*Tan[c + d*x])/(3*a*d)","A",20,12,28,0.4286,1,"{4531, 4186, 4184, 3475, 3719, 2190, 2531, 2282, 6589, 4409, 3770, 4181}"
276,1,343,0,0.3776502,"\int \frac{(e+f x)^2 \sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sec[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\frac{i f^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{3 a d^3}-\frac{i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{3 a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{3 a d^3}+\frac{4 f (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{3 a d^2}-\frac{2 i f (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{3 a d^2}-\frac{f (e+f x) \sec ^2(c+d x)}{3 a d^2}+\frac{f (e+f x) \tan (c+d x) \sec (c+d x)}{3 a d^2}+\frac{f^2 \tan (c+d x)}{3 a d^3}-\frac{f^2 \sec (c+d x)}{3 a d^3}+\frac{2 (e+f x)^2 \tan (c+d x)}{3 a d}-\frac{(e+f x)^2 \sec ^3(c+d x)}{3 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec ^2(c+d x)}{3 a d}-\frac{2 i (e+f x)^2}{3 a d}","\frac{i f^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{3 a d^3}-\frac{i f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{3 a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{3 a d^3}+\frac{4 f (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{3 a d^2}-\frac{2 i f (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{3 a d^2}-\frac{f (e+f x) \sec ^2(c+d x)}{3 a d^2}+\frac{f (e+f x) \tan (c+d x) \sec (c+d x)}{3 a d^2}+\frac{f^2 \tan (c+d x)}{3 a d^3}-\frac{f^2 \sec (c+d x)}{3 a d^3}+\frac{2 (e+f x)^2 \tan (c+d x)}{3 a d}-\frac{(e+f x)^2 \sec ^3(c+d x)}{3 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec ^2(c+d x)}{3 a d}-\frac{2 i (e+f x)^2}{3 a d}",1,"(((-2*I)/3)*(e + f*x)^2)/(a*d) - (((2*I)/3)*f*(e + f*x)*ArcTan[E^(I*(c + d*x))])/(a*d^2) + (4*f*(e + f*x)*Log[1 + E^((2*I)*(c + d*x))])/(3*a*d^2) + ((I/3)*f^2*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^3) - ((I/3)*f^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^3) - (((2*I)/3)*f^2*PolyLog[2, -E^((2*I)*(c + d*x))])/(a*d^3) - (f^2*Sec[c + d*x])/(3*a*d^3) - (f*(e + f*x)*Sec[c + d*x]^2)/(3*a*d^2) - ((e + f*x)^2*Sec[c + d*x]^3)/(3*a*d) + (f^2*Tan[c + d*x])/(3*a*d^3) + (2*(e + f*x)^2*Tan[c + d*x])/(3*a*d) + (f*(e + f*x)*Sec[c + d*x]*Tan[c + d*x])/(3*a*d^2) + ((e + f*x)^2*Sec[c + d*x]^2*Tan[c + d*x])/(3*a*d)","A",16,12,28,0.4286,1,"{4531, 4186, 3767, 8, 4184, 3719, 2190, 2279, 2391, 4409, 4185, 4181}"
277,1,152,0,0.1450673,"\int \frac{(e+f x) \sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sec[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","-\frac{f \sec ^2(c+d x)}{6 a d^2}+\frac{f \tanh ^{-1}(\sin (c+d x))}{6 a d^2}+\frac{2 f \log (\cos (c+d x))}{3 a d^2}+\frac{f \tan (c+d x) \sec (c+d x)}{6 a d^2}+\frac{2 (e+f x) \tan (c+d x)}{3 a d}-\frac{(e+f x) \sec ^3(c+d x)}{3 a d}+\frac{(e+f x) \tan (c+d x) \sec ^2(c+d x)}{3 a d}","-\frac{f \sec ^2(c+d x)}{6 a d^2}+\frac{f \tanh ^{-1}(\sin (c+d x))}{6 a d^2}+\frac{2 f \log (\cos (c+d x))}{3 a d^2}+\frac{f \tan (c+d x) \sec (c+d x)}{6 a d^2}+\frac{2 (e+f x) \tan (c+d x)}{3 a d}-\frac{(e+f x) \sec ^3(c+d x)}{3 a d}+\frac{(e+f x) \tan (c+d x) \sec ^2(c+d x)}{3 a d}",1,"(f*ArcTanh[Sin[c + d*x]])/(6*a*d^2) + (2*f*Log[Cos[c + d*x]])/(3*a*d^2) - (f*Sec[c + d*x]^2)/(6*a*d^2) - ((e + f*x)*Sec[c + d*x]^3)/(3*a*d) + (2*(e + f*x)*Tan[c + d*x])/(3*a*d) + (f*Sec[c + d*x]*Tan[c + d*x])/(6*a*d^2) + ((e + f*x)*Sec[c + d*x]^2*Tan[c + d*x])/(3*a*d)","A",7,7,26,0.2692,1,"{4531, 4185, 4184, 3475, 4409, 3768, 3770}"
278,1,42,0,0.0514837,"\int \frac{\sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sec[c + d*x]^2/(a + a*Sin[c + d*x]),x]","\frac{2 \tan (c+d x)}{3 a d}-\frac{\sec (c+d x)}{3 d (a \sin (c+d x)+a)}","\frac{2 \tan (c+d x)}{3 a d}-\frac{\sec (c+d x)}{3 d (a \sin (c+d x)+a)}",1,"-Sec[c + d*x]/(3*d*(a + a*Sin[c + d*x])) + (2*Tan[c + d*x])/(3*a*d)","A",3,3,21,0.1429,1,"{2672, 3767, 8}"
279,0,0,0,0.0662987,"\int \frac{\sec ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sec ^2(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec ^2(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]^2/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
280,0,0,0,0.0670309,"\int \frac{\sec ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sec ^2(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec ^2(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]^2/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
281,1,698,0,0.7353701,"\int \frac{(e+f x)^3 \sec ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sec[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{4 a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{4 a d^3}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{8 a d^2}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{8 a d^2}+\frac{5 i f^3 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^4}-\frac{5 i f^3 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^4}-\frac{i f^3 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-i e^{i (c+d x)}\right)}{4 a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{4 a d^4}+\frac{f^2 (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{a d^3}-\frac{5 i f^2 (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}-\frac{f^2 (e+f x) \sec ^2(c+d x)}{4 a d^3}+\frac{f^2 (e+f x) \tan (c+d x) \sec (c+d x)}{4 a d^3}+\frac{f (e+f x)^2 \tan (c+d x)}{2 a d^2}-\frac{f (e+f x)^2 \sec ^3(c+d x)}{4 a d^2}-\frac{9 f (e+f x)^2 \sec (c+d x)}{8 a d^2}+\frac{f (e+f x)^2 \tan (c+d x) \sec ^2(c+d x)}{4 a d^2}+\frac{f^3 \tan (c+d x)}{4 a d^4}-\frac{f^3 \sec (c+d x)}{4 a d^4}-\frac{3 i (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x)^3 \sec ^4(c+d x)}{4 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x)^3 \tan (c+d x) \sec (c+d x)}{8 a d}-\frac{i f (e+f x)^2}{2 a d^2}","-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{4 a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{4 a d^3}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{8 a d^2}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{8 a d^2}+\frac{5 i f^3 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{2 a d^4}-\frac{5 i f^3 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{2 a d^4}-\frac{i f^3 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-i e^{i (c+d x)}\right)}{4 a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,i e^{i (c+d x)}\right)}{4 a d^4}+\frac{f^2 (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{a d^3}-\frac{5 i f^2 (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{a d^3}-\frac{f^2 (e+f x) \sec ^2(c+d x)}{4 a d^3}+\frac{f^2 (e+f x) \tan (c+d x) \sec (c+d x)}{4 a d^3}+\frac{f (e+f x)^2 \tan (c+d x)}{2 a d^2}-\frac{f (e+f x)^2 \sec ^3(c+d x)}{4 a d^2}-\frac{9 f (e+f x)^2 \sec (c+d x)}{8 a d^2}+\frac{f (e+f x)^2 \tan (c+d x) \sec ^2(c+d x)}{4 a d^2}+\frac{f^3 \tan (c+d x)}{4 a d^4}-\frac{f^3 \sec (c+d x)}{4 a d^4}-\frac{3 i (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x)^3 \sec ^4(c+d x)}{4 a d}+\frac{(e+f x)^3 \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x)^3 \tan (c+d x) \sec (c+d x)}{8 a d}-\frac{i f (e+f x)^2}{2 a d^2}",1,"((-I/2)*f*(e + f*x)^2)/(a*d^2) - ((5*I)*f^2*(e + f*x)*ArcTan[E^(I*(c + d*x))])/(a*d^3) - (((3*I)/4)*(e + f*x)^3*ArcTan[E^(I*(c + d*x))])/(a*d) + (f^2*(e + f*x)*Log[1 + E^((2*I)*(c + d*x))])/(a*d^3) + (((5*I)/2)*f^3*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^4) + (((9*I)/8)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - (((5*I)/2)*f^3*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^4) - (((9*I)/8)*f*(e + f*x)^2*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - ((I/2)*f^3*PolyLog[2, -E^((2*I)*(c + d*x))])/(a*d^4) - (9*f^2*(e + f*x)*PolyLog[3, (-I)*E^(I*(c + d*x))])/(4*a*d^3) + (9*f^2*(e + f*x)*PolyLog[3, I*E^(I*(c + d*x))])/(4*a*d^3) - (((9*I)/4)*f^3*PolyLog[4, (-I)*E^(I*(c + d*x))])/(a*d^4) + (((9*I)/4)*f^3*PolyLog[4, I*E^(I*(c + d*x))])/(a*d^4) - (f^3*Sec[c + d*x])/(4*a*d^4) - (9*f*(e + f*x)^2*Sec[c + d*x])/(8*a*d^2) - (f^2*(e + f*x)*Sec[c + d*x]^2)/(4*a*d^3) - (f*(e + f*x)^2*Sec[c + d*x]^3)/(4*a*d^2) - ((e + f*x)^3*Sec[c + d*x]^4)/(4*a*d) + (f^3*Tan[c + d*x])/(4*a*d^4) + (f*(e + f*x)^2*Tan[c + d*x])/(2*a*d^2) + (f^2*(e + f*x)*Sec[c + d*x]*Tan[c + d*x])/(4*a*d^3) + (3*(e + f*x)^3*Sec[c + d*x]*Tan[c + d*x])/(8*a*d) + (f*(e + f*x)^2*Sec[c + d*x]^2*Tan[c + d*x])/(4*a*d^2) + ((e + f*x)^3*Sec[c + d*x]^3*Tan[c + d*x])/(4*a*d)","A",32,16,28,0.5714,1,"{4531, 4186, 4185, 4181, 2279, 2391, 2531, 6609, 2282, 6589, 4409, 3767, 8, 4184, 3719, 2190}"
282,1,431,0,0.3979815,"\int \frac{(e+f x)^2 \sec ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sec[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{3 i f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{4 a d^2}-\frac{3 i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{4 a d^2}-\frac{3 f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{4 a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{4 a d^3}+\frac{f (e+f x) \tan (c+d x)}{3 a d^2}-\frac{f (e+f x) \sec ^3(c+d x)}{6 a d^2}-\frac{3 f (e+f x) \sec (c+d x)}{4 a d^2}+\frac{f (e+f x) \tan (c+d x) \sec ^2(c+d x)}{6 a d^2}-\frac{f^2 \sec ^2(c+d x)}{12 a d^3}+\frac{5 f^2 \tanh ^{-1}(\sin (c+d x))}{6 a d^3}+\frac{f^2 \log (\cos (c+d x))}{3 a d^3}+\frac{f^2 \tan (c+d x) \sec (c+d x)}{12 a d^3}-\frac{3 i (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x)^2 \sec ^4(c+d x)}{4 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x)^2 \tan (c+d x) \sec (c+d x)}{8 a d}","\frac{3 i f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{4 a d^2}-\frac{3 i f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{4 a d^2}-\frac{3 f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{4 a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{4 a d^3}+\frac{f (e+f x) \tan (c+d x)}{3 a d^2}-\frac{f (e+f x) \sec ^3(c+d x)}{6 a d^2}-\frac{3 f (e+f x) \sec (c+d x)}{4 a d^2}+\frac{f (e+f x) \tan (c+d x) \sec ^2(c+d x)}{6 a d^2}-\frac{f^2 \sec ^2(c+d x)}{12 a d^3}+\frac{5 f^2 \tanh ^{-1}(\sin (c+d x))}{6 a d^3}+\frac{f^2 \log (\cos (c+d x))}{3 a d^3}+\frac{f^2 \tan (c+d x) \sec (c+d x)}{12 a d^3}-\frac{3 i (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x)^2 \sec ^4(c+d x)}{4 a d}+\frac{(e+f x)^2 \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x)^2 \tan (c+d x) \sec (c+d x)}{8 a d}",1,"(((-3*I)/4)*(e + f*x)^2*ArcTan[E^(I*(c + d*x))])/(a*d) + (5*f^2*ArcTanh[Sin[c + d*x]])/(6*a*d^3) + (f^2*Log[Cos[c + d*x]])/(3*a*d^3) + (((3*I)/4)*f*(e + f*x)*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - (((3*I)/4)*f*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - (3*f^2*PolyLog[3, (-I)*E^(I*(c + d*x))])/(4*a*d^3) + (3*f^2*PolyLog[3, I*E^(I*(c + d*x))])/(4*a*d^3) - (3*f*(e + f*x)*Sec[c + d*x])/(4*a*d^2) - (f^2*Sec[c + d*x]^2)/(12*a*d^3) - (f*(e + f*x)*Sec[c + d*x]^3)/(6*a*d^2) - ((e + f*x)^2*Sec[c + d*x]^4)/(4*a*d) + (f*(e + f*x)*Tan[c + d*x])/(3*a*d^2) + (f^2*Sec[c + d*x]*Tan[c + d*x])/(12*a*d^3) + (3*(e + f*x)^2*Sec[c + d*x]*Tan[c + d*x])/(8*a*d) + (f*(e + f*x)*Sec[c + d*x]^2*Tan[c + d*x])/(6*a*d^2) + ((e + f*x)^2*Sec[c + d*x]^3*Tan[c + d*x])/(4*a*d)","A",17,12,28,0.4286,1,"{4531, 4186, 3768, 3770, 4181, 2531, 2282, 6589, 4409, 4185, 4184, 3475}"
283,1,241,0,0.1914729,"\int \frac{(e+f x) \sec ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)*Sec[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","\frac{3 i f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{8 a d^2}-\frac{3 i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{8 a d^2}+\frac{f \tan ^3(c+d x)}{12 a d^2}+\frac{f \tan (c+d x)}{4 a d^2}-\frac{f \sec ^3(c+d x)}{12 a d^2}-\frac{3 f \sec (c+d x)}{8 a d^2}-\frac{3 i (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x) \sec ^4(c+d x)}{4 a d}+\frac{(e+f x) \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x) \tan (c+d x) \sec (c+d x)}{8 a d}","\frac{3 i f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{8 a d^2}-\frac{3 i f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{8 a d^2}+\frac{f \tan ^3(c+d x)}{12 a d^2}+\frac{f \tan (c+d x)}{4 a d^2}-\frac{f \sec ^3(c+d x)}{12 a d^2}-\frac{3 f \sec (c+d x)}{8 a d^2}-\frac{3 i (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{4 a d}-\frac{(e+f x) \sec ^4(c+d x)}{4 a d}+\frac{(e+f x) \tan (c+d x) \sec ^3(c+d x)}{4 a d}+\frac{3 (e+f x) \tan (c+d x) \sec (c+d x)}{8 a d}",1,"(((-3*I)/4)*(e + f*x)*ArcTan[E^(I*(c + d*x))])/(a*d) + (((3*I)/8)*f*PolyLog[2, (-I)*E^(I*(c + d*x))])/(a*d^2) - (((3*I)/8)*f*PolyLog[2, I*E^(I*(c + d*x))])/(a*d^2) - (3*f*Sec[c + d*x])/(8*a*d^2) - (f*Sec[c + d*x]^3)/(12*a*d^2) - ((e + f*x)*Sec[c + d*x]^4)/(4*a*d) + (f*Tan[c + d*x])/(4*a*d^2) + (3*(e + f*x)*Sec[c + d*x]*Tan[c + d*x])/(8*a*d) + ((e + f*x)*Sec[c + d*x]^3*Tan[c + d*x])/(4*a*d) + (f*Tan[c + d*x]^3)/(12*a*d^2)","A",11,7,26,0.2692,1,"{4531, 4185, 4181, 2279, 2391, 4409, 3767}"
284,1,77,0,0.0798467,"\int \frac{\sec ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[Sec[c + d*x]^3/(a + a*Sin[c + d*x]),x]","-\frac{a}{8 d (a \sin (c+d x)+a)^2}+\frac{1}{8 d (a-a \sin (c+d x))}-\frac{1}{4 d (a \sin (c+d x)+a)}+\frac{3 \tanh ^{-1}(\sin (c+d x))}{8 a d}","-\frac{a}{8 d (a \sin (c+d x)+a)^2}+\frac{1}{8 d (a-a \sin (c+d x))}-\frac{1}{4 d (a \sin (c+d x)+a)}+\frac{3 \tanh ^{-1}(\sin (c+d x))}{8 a d}",1,"(3*ArcTanh[Sin[c + d*x]])/(8*a*d) + 1/(8*d*(a - a*Sin[c + d*x])) - a/(8*d*(a + a*Sin[c + d*x])^2) - 1/(4*d*(a + a*Sin[c + d*x]))","A",4,3,21,0.1429,1,"{2667, 44, 206}"
285,0,0,0,0.0721693,"\int \frac{\sec ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])),x]","\int \frac{\sec ^3(c+d x)}{(e+f x) (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec ^3(c+d x)}{(e+f x) (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]^3/((e + f*x)*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
286,0,0,0,0.0721515,"\int \frac{\sec ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","Int[Sec[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])),x]","\int \frac{\sec ^3(c+d x)}{(e+f x)^2 (a+a \sin (c+d x))} \, dx","\text{Int}\left(\frac{\sec ^3(c+d x)}{(e+f x)^2 (a \sin (c+d x)+a)},x\right)",0,"Defer[Int][Sec[c + d*x]^3/((e + f*x)^2*(a + a*Sin[c + d*x])), x]","A",0,0,0,0,-1,"{}"
287,1,449,0,0.6425428,"\int \frac{(e+f x)^m \cos ^4(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x]^4)/(a + a*Sin[c + d*x]),x]","\frac{e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{8 a d}-\frac{i 2^{-m-3} e^{2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{3^{-m-1} e^{3 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i d (e+f x)}{f}\right)}{8 a d}+\frac{e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{8 a d}+\frac{i 2^{-m-3} e^{-2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{3^{-m-1} e^{-3 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i d (e+f x)}{f}\right)}{8 a d}+\frac{(e+f x)^{m+1}}{2 a f (m+1)}","\frac{e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{8 a d}-\frac{i 2^{-m-3} e^{2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{3^{-m-1} e^{3 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 i d (e+f x)}{f}\right)}{8 a d}+\frac{e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{8 a d}+\frac{i 2^{-m-3} e^{-2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{3^{-m-1} e^{-3 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{3 i d (e+f x)}{f}\right)}{8 a d}+\frac{(e+f x)^{m+1}}{2 a f (m+1)}",1,"(e + f*x)^(1 + m)/(2*a*f*(1 + m)) + (E^(I*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-I)*d*(e + f*x))/f])/(8*a*d*(((-I)*d*(e + f*x))/f)^m) + ((e + f*x)^m*Gamma[1 + m, (I*d*(e + f*x))/f])/(8*a*d*E^(I*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m) - (I*2^(-3 - m)*E^((2*I)*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-2*I)*d*(e + f*x))/f])/(a*d*(((-I)*d*(e + f*x))/f)^m) + (I*2^(-3 - m)*(e + f*x)^m*Gamma[1 + m, ((2*I)*d*(e + f*x))/f])/(a*d*E^((2*I)*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m) + (3^(-1 - m)*E^((3*I)*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-3*I)*d*(e + f*x))/f])/(8*a*d*(((-I)*d*(e + f*x))/f)^m) + (3^(-1 - m)*(e + f*x)^m*Gamma[1 + m, ((3*I)*d*(e + f*x))/f])/(8*a*d*E^((3*I)*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m)","A",14,6,28,0.2143,1,"{4523, 3312, 3307, 2181, 4406, 3308}"
288,1,277,0,0.3190529,"\int \frac{(e+f x)^m \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x]^3)/(a + a*Sin[c + d*x]),x]","-\frac{i e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{2^{-m-3} e^{2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{i e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{2^{-m-3} e^{-2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i d (e+f x)}{f}\right)}{a d}","-\frac{i e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{2^{-m-3} e^{2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i d (e+f x)}{f}\right)}{a d}+\frac{i e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{2^{-m-3} e^{-2 i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i d (e+f x)}{f}\right)}{a d}",1,"((-I/2)*E^(I*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-I)*d*(e + f*x))/f])/(a*d*(((-I)*d*(e + f*x))/f)^m) + ((I/2)*(e + f*x)^m*Gamma[1 + m, (I*d*(e + f*x))/f])/(a*d*E^(I*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m) + (2^(-3 - m)*E^((2*I)*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-2*I)*d*(e + f*x))/f])/(a*d*(((-I)*d*(e + f*x))/f)^m) + (2^(-3 - m)*(e + f*x)^m*Gamma[1 + m, ((2*I)*d*(e + f*x))/f])/(a*d*E^((2*I)*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m)","A",9,6,28,0.2143,1,"{4523, 3307, 2181, 4406, 12, 3308}"
289,1,154,0,0.1765913,"\int \frac{(e+f x)^m \cos ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\frac{e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{(e+f x)^{m+1}}{a f (m+1)}","\frac{e^{i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(-\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,-\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{e^{-i \left(c-\frac{d e}{f}\right)} (e+f x)^m \left(\frac{i d (e+f x)}{f}\right)^{-m} \text{Gamma}\left(m+1,\frac{i d (e+f x)}{f}\right)}{2 a d}+\frac{(e+f x)^{m+1}}{a f (m+1)}",1,"(e + f*x)^(1 + m)/(a*f*(1 + m)) + (E^(I*(c - (d*e)/f))*(e + f*x)^m*Gamma[1 + m, ((-I)*d*(e + f*x))/f])/(2*a*d*(((-I)*d*(e + f*x))/f)^m) + ((e + f*x)^m*Gamma[1 + m, (I*d*(e + f*x))/f])/(2*a*d*E^(I*(c - (d*e)/f))*((I*d*(e + f*x))/f)^m)","A",5,4,28,0.1429,1,"{4523, 32, 3308, 2181}"
290,0,0,0,0.0437905,"\int \frac{(e+f x)^m \cos (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x])/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \cos (c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\cos (c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Cos[c + d*x])/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
291,0,0,0,0.0636119,"\int \frac{(e+f x)^m}{a+a \sin (c+d x)} \, dx","Int[(e + f*x)^m/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{(e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][(e + f*x)^m/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
292,0,0,0,0.044138,"\int \frac{(e+f x)^m \sec (c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sec[c + d*x])/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sec (c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sec (c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Sec[c + d*x])/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
293,0,0,0,0.0735751,"\int \frac{(e+f x)^m \sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sec[c + d*x]^2)/(a + a*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sec ^2(c+d x)}{a+a \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sec ^2(c+d x) (e+f x)^m}{a \sin (c+d x)+a},x\right)",0,"Defer[Int][((e + f*x)^m*Sec[c + d*x]^2)/(a + a*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
294,1,432,0,0.6077506,"\int \frac{(e+f x)^3 \cos (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{6 i f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4}+\frac{(e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^4}{4 b f}","\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{6 i f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4}+\frac{(e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^4}{4 b f}",1,"((-I/4)*(e + f*x)^4)/(b*f) + ((e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d) + ((e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d) - ((3*I)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^2) + (6*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^3) + (6*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^3) + ((6*I)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^4) + ((6*I)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^4)","A",11,6,26,0.2308,1,"{4519, 2190, 2531, 6609, 2282, 6589}"
295,1,320,0,0.5125692,"\int \frac{(e+f x)^2 \cos (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{2 i f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{(e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^3}{3 b f}","-\frac{2 i f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3}+\frac{2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3}+\frac{(e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^3}{3 b f}",1,"((-I/3)*(e + f*x)^3)/(b*f) + ((e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d) + ((e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d) - ((2*I)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^2) + (2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^3) + (2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^3)","A",9,5,26,0.1923,1,"{4519, 2190, 2531, 2282, 6589}"
296,1,212,0,0.2847077,"\int \frac{(e+f x) \cos (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{i f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{i f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{(e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^2}{2 b f}","-\frac{i f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2}-\frac{i f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2}+\frac{(e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d}+\frac{(e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d}-\frac{i (e+f x)^2}{2 b f}",1,"((-I/2)*(e + f*x)^2)/(b*f) + ((e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d) + ((e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d) - (I*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*d^2) - (I*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*d^2)","A",7,4,24,0.1667,1,"{4519, 2190, 2279, 2391}"
297,1,18,0,0.0263503,"\int \frac{\cos (c+d x)}{a+b \sin (c+d x)} \, dx","Int[Cos[c + d*x]/(a + b*Sin[c + d*x]),x]","\frac{\log (a+b \sin (c+d x))}{b d}","\frac{\log (a+b \sin (c+d x))}{b d}",1,"Log[a + b*Sin[c + d*x]]/(b*d)","A",2,2,19,0.1053,1,"{2668, 31}"
298,1,618,0,1.0676356,"\int \frac{(e+f x)^3 \cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}-\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4}+\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4}+\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a (e+f x)^4}{4 b^2 f}-\frac{6 f^2 (e+f x) \cos (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \sin (c+d x)}{b d^2}+\frac{6 f^3 \sin (c+d x)}{b d^4}+\frac{(e+f x)^3 \cos (c+d x)}{b d}","\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}-\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}-\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^4}+\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^4}+\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a (e+f x)^4}{4 b^2 f}-\frac{6 f^2 (e+f x) \cos (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \sin (c+d x)}{b d^2}+\frac{6 f^3 \sin (c+d x)}{b d^4}+\frac{(e+f x)^3 \cos (c+d x)}{b d}",1,"(a*(e + f*x)^4)/(4*b^2*f) - (6*f^2*(e + f*x)*Cos[c + d*x])/(b*d^3) + ((e + f*x)^3*Cos[c + d*x])/(b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (3*Sqrt[a^2 - b^2]*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^2) - (3*Sqrt[a^2 - b^2]*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^2) + ((6*I)*Sqrt[a^2 - b^2]*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^3) - ((6*I)*Sqrt[a^2 - b^2]*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^3) - (6*Sqrt[a^2 - b^2]*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^4) + (6*Sqrt[a^2 - b^2]*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^4) + (6*f^3*Sin[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Sin[c + d*x])/(b*d^2)","A",18,11,28,0.3929,1,"{4525, 32, 3296, 2637, 3323, 2264, 2190, 2531, 6609, 2282, 6589}"
299,1,460,0,0.9287335,"\int \frac{(e+f x)^2 \cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}-\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a (e+f x)^3}{3 b^2 f}-\frac{2 f (e+f x) \sin (c+d x)}{b d^2}-\frac{2 f^2 \cos (c+d x)}{b d^3}+\frac{(e+f x)^2 \cos (c+d x)}{b d}","\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^3}-\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^3}+\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a (e+f x)^3}{3 b^2 f}-\frac{2 f (e+f x) \sin (c+d x)}{b d^2}-\frac{2 f^2 \cos (c+d x)}{b d^3}+\frac{(e+f x)^2 \cos (c+d x)}{b d}",1,"(a*(e + f*x)^3)/(3*b^2*f) - (2*f^2*Cos[c + d*x])/(b*d^3) + ((e + f*x)^2*Cos[c + d*x])/(b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (2*Sqrt[a^2 - b^2]*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^2) - (2*Sqrt[a^2 - b^2]*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^2) + ((2*I)*Sqrt[a^2 - b^2]*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^3) - ((2*I)*Sqrt[a^2 - b^2]*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^3) - (2*f*(e + f*x)*Sin[c + d*x])/(b*d^2)","A",15,10,28,0.3571,1,"{4525, 32, 3296, 2638, 3323, 2264, 2190, 2531, 2282, 6589}"
300,1,298,0,0.5350246,"\int \frac{(e+f x) \cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a e x}{b^2}+\frac{a f x^2}{2 b^2}-\frac{f \sin (c+d x)}{b d^2}+\frac{(e+f x) \cos (c+d x)}{b d}","\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d^2}-\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d^2}+\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^2 d}-\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^2 d}+\frac{a e x}{b^2}+\frac{a f x^2}{2 b^2}-\frac{f \sin (c+d x)}{b d^2}+\frac{(e+f x) \cos (c+d x)}{b d}",1,"(a*e*x)/b^2 + (a*f*x^2)/(2*b^2) + ((e + f*x)*Cos[c + d*x])/(b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d) + (Sqrt[a^2 - b^2]*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^2*d^2) - (Sqrt[a^2 - b^2]*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^2*d^2) - (f*Sin[c + d*x])/(b*d^2)","A",12,8,26,0.3077,1,"{4525, 3296, 2637, 3323, 2264, 2190, 2279, 2391}"
301,1,70,0,0.1158431,"\int \frac{\cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Cos[c + d*x]^2/(a + b*Sin[c + d*x]),x]","-\frac{2 \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^2 d}+\frac{a x}{b^2}+\frac{\cos (c+d x)}{b d}","-\frac{2 \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b^2 d}+\frac{a x}{b^2}+\frac{\cos (c+d x)}{b d}",1,"(a*x)/b^2 - (2*Sqrt[a^2 - b^2]*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b^2*d) + Cos[c + d*x]/(b*d)","A",5,5,21,0.2381,1,"{2695, 2735, 2660, 618, 204}"
302,1,737,0,0.8809091,"\int \frac{(e+f x)^3 \cos ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","-\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^4}-\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^4}-\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 b^3 f}-\frac{6 a f^2 (e+f x) \sin (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \cos (c+d x)}{b^2 d^2}-\frac{6 a f^3 \cos (c+d x)}{b^2 d^4}+\frac{a (e+f x)^3 \sin (c+d x)}{b^2 d}+\frac{3 f^2 (e+f x) \sin ^2(c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \sin (c+d x) \cos (c+d x)}{4 b d^2}+\frac{3 f^3 \sin (c+d x) \cos (c+d x)}{8 b d^4}-\frac{(e+f x)^3 \sin ^2(c+d x)}{2 b d}-\frac{3 f^3 x}{8 b d^3}+\frac{(e+f x)^3}{4 b d}","-\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}+\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^4}-\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^4}-\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 b^3 f}-\frac{6 a f^2 (e+f x) \sin (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \cos (c+d x)}{b^2 d^2}-\frac{6 a f^3 \cos (c+d x)}{b^2 d^4}+\frac{a (e+f x)^3 \sin (c+d x)}{b^2 d}+\frac{3 f^2 (e+f x) \sin ^2(c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \sin (c+d x) \cos (c+d x)}{4 b d^2}+\frac{3 f^3 \sin (c+d x) \cos (c+d x)}{8 b d^4}-\frac{(e+f x)^3 \sin ^2(c+d x)}{2 b d}-\frac{3 f^3 x}{8 b d^3}+\frac{(e+f x)^3}{4 b d}",1,"(-3*f^3*x)/(8*b*d^3) + (e + f*x)^3/(4*b*d) + ((I/4)*(a^2 - b^2)*(e + f*x)^4)/(b^3*f) - (6*a*f^3*Cos[c + d*x])/(b^2*d^4) + (3*a*f*(e + f*x)^2*Cos[c + d*x])/(b^2*d^2) - ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d) - ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^2) + ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^2) - (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^3) - (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^3) - ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^4) - ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^4) - (6*a*f^2*(e + f*x)*Sin[c + d*x])/(b^2*d^3) + (a*(e + f*x)^3*Sin[c + d*x])/(b^2*d) + (3*f^3*Cos[c + d*x]*Sin[c + d*x])/(8*b*d^4) - (3*f*(e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^2) + (3*f^2*(e + f*x)*Sin[c + d*x]^2)/(4*b*d^3) - ((e + f*x)^3*Sin[c + d*x]^2)/(2*b*d)","A",21,14,28,0.5000,1,"{4525, 3296, 2638, 4404, 3311, 32, 2635, 8, 4519, 2190, 2531, 6609, 2282, 6589}"
303,1,548,0,0.7333071,"\int \frac{(e+f x)^2 \cos ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \cos (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sin (c+d x)}{b^2 d^3}+\frac{a (e+f x)^2 \sin (c+d x)}{b^2 d}-\frac{f (e+f x) \sin (c+d x) \cos (c+d x)}{2 b d^2}+\frac{f^2 \sin ^2(c+d x)}{4 b d^3}-\frac{(e+f x)^2 \sin ^2(c+d x)}{2 b d}+\frac{e f x}{2 b d}+\frac{f^2 x^2}{4 b d}","\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^3}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^3}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \cos (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sin (c+d x)}{b^2 d^3}+\frac{a (e+f x)^2 \sin (c+d x)}{b^2 d}-\frac{f (e+f x) \sin (c+d x) \cos (c+d x)}{2 b d^2}+\frac{f^2 \sin ^2(c+d x)}{4 b d^3}-\frac{(e+f x)^2 \sin ^2(c+d x)}{2 b d}+\frac{e f x}{2 b d}+\frac{f^2 x^2}{4 b d}",1,"(e*f*x)/(2*b*d) + (f^2*x^2)/(4*b*d) + ((I/3)*(a^2 - b^2)*(e + f*x)^3)/(b^3*f) + (2*a*f*(e + f*x)*Cos[c + d*x])/(b^2*d^2) - ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d) - ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^2) + ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^2) - (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^3) - (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^3) - (2*a*f^2*Sin[c + d*x])/(b^2*d^3) + (a*(e + f*x)^2*Sin[c + d*x])/(b^2*d) - (f*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*b*d^2) + (f^2*Sin[c + d*x]^2)/(4*b*d^3) - ((e + f*x)^2*Sin[c + d*x]^2)/(2*b*d)","A",16,10,28,0.3571,1,"{4525, 3296, 2637, 4404, 3310, 4519, 2190, 2531, 2282, 6589}"
304,1,351,0,0.4092492,"\int \frac{(e+f x) \cos ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^3)/(a + b*Sin[c + d*x]),x]","\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 b^3 f}+\frac{a f \cos (c+d x)}{b^2 d^2}+\frac{a (e+f x) \sin (c+d x)}{b^2 d}-\frac{f \sin (c+d x) \cos (c+d x)}{4 b d^2}-\frac{(e+f x) \sin ^2(c+d x)}{2 b d}+\frac{f x}{4 b d}","\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d^2}+\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d^2}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b^3 d}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b^3 d}+\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 b^3 f}+\frac{a f \cos (c+d x)}{b^2 d^2}+\frac{a (e+f x) \sin (c+d x)}{b^2 d}-\frac{f \sin (c+d x) \cos (c+d x)}{4 b d^2}-\frac{(e+f x) \sin ^2(c+d x)}{2 b d}+\frac{f x}{4 b d}",1,"(f*x)/(4*b*d) + ((I/2)*(a^2 - b^2)*(e + f*x)^2)/(b^3*f) + (a*f*Cos[c + d*x])/(b^2*d^2) - ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d) - ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d) + (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b^3*d^2) + (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b^3*d^2) + (a*(e + f*x)*Sin[c + d*x])/(b^2*d) - (f*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^2) - ((e + f*x)*Sin[c + d*x]^2)/(2*b*d)","A",13,10,26,0.3846,1,"{4525, 3296, 2638, 4404, 2635, 8, 4519, 2190, 2279, 2391}"
305,1,61,0,0.0677086,"\int \frac{\cos ^3(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Cos[c + d*x]^3/(a + b*Sin[c + d*x]),x]","-\frac{\left(a^2-b^2\right) \log (a+b \sin (c+d x))}{b^3 d}+\frac{a \sin (c+d x)}{b^2 d}-\frac{\sin ^2(c+d x)}{2 b d}","-\frac{\left(a^2-b^2\right) \log (a+b \sin (c+d x))}{b^3 d}+\frac{a \sin (c+d x)}{b^2 d}-\frac{\sin ^2(c+d x)}{2 b d}",1,"-(((a^2 - b^2)*Log[a + b*Sin[c + d*x]])/(b^3*d)) + (a*Sin[c + d*x])/(b^2*d) - Sin[c + d*x]^2/(2*b*d)","A",3,2,21,0.09524,1,"{2668, 697}"
306,1,937,0,1.6175905,"\int \frac{(e+f x)^3 \sec (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sec[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{6 i a \text{PolyLog}\left(4,-i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{6 i a \text{PolyLog}\left(4,i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{3 i b \text{PolyLog}\left(4,-e^{2 i (c+d x)}\right) f^3}{4 \left(a^2-b^2\right) d^4}-\frac{6 a (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{6 a (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{3 b (e+f x) \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right) f^2}{2 \left(a^2-b^2\right) d^3}+\frac{3 i a (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}-\frac{3 i a (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right) d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right) f}{2 \left(a^2-b^2\right) d^2}-\frac{2 i a (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{\left(a^2-b^2\right) d}-\frac{b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right) d}-\frac{b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right) d}+\frac{b (e+f x)^3 \log \left(1+e^{2 i (c+d x)}\right)}{\left(a^2-b^2\right) d}","-\frac{6 i a \text{PolyLog}\left(4,-i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{6 i a \text{PolyLog}\left(4,i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{3 i b \text{PolyLog}\left(4,-e^{2 i (c+d x)}\right) f^3}{4 \left(a^2-b^2\right) d^4}-\frac{6 a (e+f x) \text{PolyLog}\left(3,-i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{6 a (e+f x) \text{PolyLog}\left(3,i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 b (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{3 b (e+f x) \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right) f^2}{2 \left(a^2-b^2\right) d^3}+\frac{3 i a (e+f x)^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}-\frac{3 i a (e+f x)^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right) d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right) f}{2 \left(a^2-b^2\right) d^2}-\frac{2 i a (e+f x)^3 \tan ^{-1}\left(e^{i (c+d x)}\right)}{\left(a^2-b^2\right) d}-\frac{b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right) d}-\frac{b (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right) d}+\frac{b (e+f x)^3 \log \left(1+e^{2 i (c+d x)}\right)}{\left(a^2-b^2\right) d}",1,"((-2*I)*a*(e + f*x)^3*ArcTan[E^(I*(c + d*x))])/((a^2 - b^2)*d) - (b*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) - (b*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) + (b*(e + f*x)^3*Log[1 + E^((2*I)*(c + d*x))])/((a^2 - b^2)*d) + ((3*I)*a*f*(e + f*x)^2*PolyLog[2, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) - ((3*I)*a*f*(e + f*x)^2*PolyLog[2, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) - (((3*I)/2)*b*f*(e + f*x)^2*PolyLog[2, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^2) - (6*a*f^2*(e + f*x)*PolyLog[3, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) + (6*a*f^2*(e + f*x)*PolyLog[3, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) + (3*b*f^2*(e + f*x)*PolyLog[3, -E^((2*I)*(c + d*x))])/(2*(a^2 - b^2)*d^3) - ((6*I)*a*f^3*PolyLog[4, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^4) + ((6*I)*a*f^3*PolyLog[4, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^4) - ((6*I)*b*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^4) - ((6*I)*b*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^4) + (((3*I)/4)*b*f^3*PolyLog[4, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^4)","A",29,10,26,0.3846,1,"{4533, 4519, 2190, 2531, 6609, 2282, 6589, 6742, 4181, 3719}"
307,1,667,0,1.1429922,"\int \frac{(e+f x)^2 \sec (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sec[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{2 i a f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{2 i a f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i b f (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{2 a f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}+\frac{2 a f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)}+\frac{b f^2 \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right)}{2 d^3 \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)}+\frac{b (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right)}{d \left(a^2-b^2\right)}-\frac{2 i a (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{d \left(a^2-b^2\right)}","\frac{2 i a f (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{2 i a f (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i b f (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{2 a f^2 \text{PolyLog}\left(3,-i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}+\frac{2 a f^2 \text{PolyLog}\left(3,i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)}+\frac{b f^2 \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right)}{2 d^3 \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)}+\frac{b (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right)}{d \left(a^2-b^2\right)}-\frac{2 i a (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right)}{d \left(a^2-b^2\right)}",1,"((-2*I)*a*(e + f*x)^2*ArcTan[E^(I*(c + d*x))])/((a^2 - b^2)*d) - (b*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) - (b*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) + (b*(e + f*x)^2*Log[1 + E^((2*I)*(c + d*x))])/((a^2 - b^2)*d) + ((2*I)*a*f*(e + f*x)*PolyLog[2, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) - ((2*I)*a*f*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) + ((2*I)*b*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) + ((2*I)*b*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) - (I*b*f*(e + f*x)*PolyLog[2, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^2) - (2*a*f^2*PolyLog[3, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) + (2*a*f^2*PolyLog[3, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) - (2*b*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) - (2*b*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) + (b*f^2*PolyLog[3, -E^((2*I)*(c + d*x))])/(2*(a^2 - b^2)*d^3)","A",24,9,26,0.3462,1,"{4533, 4519, 2190, 2531, 2282, 6589, 6742, 4181, 3719}"
308,1,413,0,0.6353187,"\int \frac{(e+f x) \sec (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Sec[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{i a f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i a f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i b f \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 d^2 \left(a^2-b^2\right)}-\frac{b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)}-\frac{b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)}+\frac{b (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{d \left(a^2-b^2\right)}-\frac{2 i a (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{d \left(a^2-b^2\right)}","\frac{i a f \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i a f \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i b f \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{2 d^2 \left(a^2-b^2\right)}-\frac{b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)}-\frac{b (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)}+\frac{b (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{d \left(a^2-b^2\right)}-\frac{2 i a (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{d \left(a^2-b^2\right)}",1,"((-2*I)*a*(e + f*x)*ArcTan[E^(I*(c + d*x))])/((a^2 - b^2)*d) - (b*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) - (b*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d) + (b*(e + f*x)*Log[1 + E^((2*I)*(c + d*x))])/((a^2 - b^2)*d) + (I*a*f*PolyLog[2, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) - (I*a*f*PolyLog[2, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^2) + (I*b*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) + (I*b*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) - ((I/2)*b*f*PolyLog[2, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^2)","A",19,8,24,0.3333,1,"{4533, 4519, 2190, 2279, 2391, 6742, 4181, 3719}"
309,1,75,0,0.080833,"\int \frac{\sec (c+d x)}{a+b \sin (c+d x)} \, dx","Int[Sec[c + d*x]/(a + b*Sin[c + d*x]),x]","-\frac{b \log (a+b \sin (c+d x))}{d \left(a^2-b^2\right)}-\frac{\log (1-\sin (c+d x))}{2 d (a+b)}+\frac{\log (\sin (c+d x)+1)}{2 d (a-b)}","-\frac{b \log (a+b \sin (c+d x))}{d \left(a^2-b^2\right)}-\frac{\log (1-\sin (c+d x))}{2 d (a+b)}+\frac{\log (\sin (c+d x)+1)}{2 d (a-b)}",1,"-Log[1 - Sin[c + d*x]]/(2*(a + b)*d) + Log[1 + Sin[c + d*x]]/(2*(a - b)*d) - (b*Log[a + b*Sin[c + d*x]])/((a^2 - b^2)*d)","A",6,4,19,0.2105,1,"{2668, 706, 31, 633}"
310,1,923,0,1.9366878,"\int \frac{(e+f x)^3 \sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Sec[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{6 b \text{PolyLog}\left(3,-i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{6 b \text{PolyLog}\left(3,i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{3 a \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right) f^3}{2 \left(a^2-b^2\right) d^4}-\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right)^{3/2} d^4}+\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right)^{3/2} d^4}+\frac{6 i b (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 i b (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{3 i a (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right)^{3/2} d^3}-\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right)^{3/2} d^3}-\frac{6 i b (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 a (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right)^{3/2} d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right)^{3/2} d^2}-\frac{i a (e+f x)^3}{\left(a^2-b^2\right) d}+\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} d}-\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} d}-\frac{b (e+f x)^3 \sec (c+d x)}{\left(a^2-b^2\right) d}+\frac{a (e+f x)^3 \tan (c+d x)}{\left(a^2-b^2\right) d}","-\frac{6 b \text{PolyLog}\left(3,-i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{6 b \text{PolyLog}\left(3,i e^{i (c+d x)}\right) f^3}{\left(a^2-b^2\right) d^4}+\frac{3 a \text{PolyLog}\left(3,-e^{2 i (c+d x)}\right) f^3}{2 \left(a^2-b^2\right) d^4}-\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right)^{3/2} d^4}+\frac{6 b^2 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^3}{\left(a^2-b^2\right)^{3/2} d^4}+\frac{6 i b (e+f x) \text{PolyLog}\left(2,-i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{6 i b (e+f x) \text{PolyLog}\left(2,i e^{i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}-\frac{3 i a (e+f x) \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right) f^2}{\left(a^2-b^2\right) d^3}+\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right)^{3/2} d^3}-\frac{6 i b^2 (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f^2}{\left(a^2-b^2\right)^{3/2} d^3}-\frac{6 i b (e+f x)^2 \tan ^{-1}\left(e^{i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 a (e+f x)^2 \log \left(1+e^{2 i (c+d x)}\right) f}{\left(a^2-b^2\right) d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right)^{3/2} d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) f}{\left(a^2-b^2\right)^{3/2} d^2}-\frac{i a (e+f x)^3}{\left(a^2-b^2\right) d}+\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} d}-\frac{i b^2 (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2} d}-\frac{b (e+f x)^3 \sec (c+d x)}{\left(a^2-b^2\right) d}+\frac{a (e+f x)^3 \tan (c+d x)}{\left(a^2-b^2\right) d}",1,"((-I)*a*(e + f*x)^3)/((a^2 - b^2)*d) - ((6*I)*b*f*(e + f*x)^2*ArcTan[E^(I*(c + d*x))])/((a^2 - b^2)*d^2) + (I*b^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - (I*b^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + (3*a*f*(e + f*x)^2*Log[1 + E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^2) + ((6*I)*b*f^2*(e + f*x)*PolyLog[2, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) - ((6*I)*b*f^2*(e + f*x)*PolyLog[2, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) + (3*b^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - ((3*I)*a*f^2*(e + f*x)*PolyLog[2, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^3) - (6*b*f^3*PolyLog[3, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^4) + (6*b*f^3*PolyLog[3, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^4) + ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) - ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) + (3*a*f^3*PolyLog[3, -E^((2*I)*(c + d*x))])/(2*(a^2 - b^2)*d^4) - (6*b^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^4) + (6*b^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^4) - (b*(e + f*x)^3*Sec[c + d*x])/((a^2 - b^2)*d) + (a*(e + f*x)^3*Tan[c + d*x])/((a^2 - b^2)*d)","A",29,13,28,0.4643,1,"{4533, 3323, 2264, 2190, 2531, 6609, 2282, 6589, 6742, 4184, 3719, 4409, 4181}"
311,1,659,0,1.4335536,"\int \frac{(e+f x)^2 \sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Sec[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}-\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}+\frac{2 i b f^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{i a f^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}+\frac{2 a f (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{4 i b f (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{a (e+f x)^2 \tan (c+d x)}{d \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \sec (c+d x)}{d \left(a^2-b^2\right)}-\frac{i a (e+f x)^2}{d \left(a^2-b^2\right)}","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}-\frac{2 i b^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}+\frac{2 i b f^2 \text{PolyLog}\left(2,-i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(2,i e^{i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}-\frac{i a f^2 \text{PolyLog}\left(2,-e^{2 i (c+d x)}\right)}{d^3 \left(a^2-b^2\right)}+\frac{2 a f (e+f x) \log \left(1+e^{2 i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}-\frac{4 i b f (e+f x) \tan ^{-1}\left(e^{i (c+d x)}\right)}{d^2 \left(a^2-b^2\right)}+\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{i b^2 (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{a (e+f x)^2 \tan (c+d x)}{d \left(a^2-b^2\right)}-\frac{b (e+f x)^2 \sec (c+d x)}{d \left(a^2-b^2\right)}-\frac{i a (e+f x)^2}{d \left(a^2-b^2\right)}",1,"((-I)*a*(e + f*x)^2)/((a^2 - b^2)*d) - ((4*I)*b*f*(e + f*x)*ArcTan[E^(I*(c + d*x))])/((a^2 - b^2)*d^2) + (I*b^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - (I*b^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + (2*a*f*(e + f*x)*Log[1 + E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^2) + ((2*I)*b*f^2*PolyLog[2, (-I)*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) - ((2*I)*b*f^2*PolyLog[2, I*E^(I*(c + d*x))])/((a^2 - b^2)*d^3) + (2*b^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (I*a*f^2*PolyLog[2, -E^((2*I)*(c + d*x))])/((a^2 - b^2)*d^3) + ((2*I)*b^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) - ((2*I)*b^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) - (b*(e + f*x)^2*Sec[c + d*x])/((a^2 - b^2)*d) + (a*(e + f*x)^2*Tan[c + d*x])/((a^2 - b^2)*d)","A",24,14,28,0.5000,1,"{4533, 3323, 2264, 2190, 2531, 2282, 6589, 6742, 4184, 3719, 2279, 2391, 4409, 4181}"
312,1,349,0,0.7947908,"\int \frac{(e+f x) \sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Sec[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{b f \tanh ^{-1}(\sin (c+d x))}{d^2 \left(a^2-b^2\right)}+\frac{a f \log (\cos (c+d x))}{d^2 \left(a^2-b^2\right)}+\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{a (e+f x) \tan (c+d x)}{d \left(a^2-b^2\right)}-\frac{b (e+f x) \sec (c+d x)}{d \left(a^2-b^2\right)}","\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{b^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{b f \tanh ^{-1}(\sin (c+d x))}{d^2 \left(a^2-b^2\right)}+\frac{a f \log (\cos (c+d x))}{d^2 \left(a^2-b^2\right)}+\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{i b^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{a (e+f x) \tan (c+d x)}{d \left(a^2-b^2\right)}-\frac{b (e+f x) \sec (c+d x)}{d \left(a^2-b^2\right)}",1,"(b*f*ArcTanh[Sin[c + d*x]])/((a^2 - b^2)*d^2) + (I*b^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - (I*b^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + (a*f*Log[Cos[c + d*x]])/((a^2 - b^2)*d^2) + (b^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (b^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (b*(e + f*x)*Sec[c + d*x])/((a^2 - b^2)*d) + (a*(e + f*x)*Tan[c + d*x])/((a^2 - b^2)*d)","A",15,11,26,0.4231,1,"{4533, 3323, 2264, 2190, 2279, 2391, 6742, 4184, 3475, 4409, 3770}"
313,1,84,0,0.1006077,"\int \frac{\sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[Sec[c + d*x]^2/(a + b*Sin[c + d*x]),x]","-\frac{2 b^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{\sec (c+d x) (b-a \sin (c+d x))}{d \left(a^2-b^2\right)}","-\frac{2 b^2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{\sec (c+d x) (b-a \sin (c+d x))}{d \left(a^2-b^2\right)}",1,"(-2*b^2*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/((a^2 - b^2)^(3/2)*d) - (Sec[c + d*x]*(b - a*Sin[c + d*x]))/((a^2 - b^2)*d)","A",5,5,21,0.2381,1,"{2696, 12, 2660, 618, 204}"
314,0,0,0,0.0713742,"\int \frac{(e+f x)^m \cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \cos ^2(c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\cos ^2(c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Cos[c + d*x]^2)/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
315,0,0,0,0.0457507,"\int \frac{(e+f x)^m \cos (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Cos[c + d*x])/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \cos (c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\cos (c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Cos[c + d*x])/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
316,0,0,0,0.0582688,"\int \frac{(e+f x)^m}{a+b \sin (c+d x)} \, dx","Int[(e + f*x)^m/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{(e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][(e + f*x)^m/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
317,0,0,0,0.044306,"\int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sec[c + d*x])/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sec (c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sec (c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Sec[c + d*x])/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
318,0,0,0,0.0672621,"\int \frac{(e+f x)^m \sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^m*Sec[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\int \frac{(e+f x)^m \sec ^2(c+d x)}{a+b \sin (c+d x)} \, dx","\text{Int}\left(\frac{\sec ^2(c+d x) (e+f x)^m}{a+b \sin (c+d x)},x\right)",0,"Defer[Int][((e + f*x)^m*Sec[c + d*x]^2)/(a + b*Sin[c + d*x]), x]","A",0,0,0,0,-1,"{}"
319,1,77,0,0.0717487,"\int \frac{(e+f x) \cos (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)*Cos[c + d*x])/(a + b*Sin[c + d*x])^2,x]","\frac{2 f \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{e+f x}{b d (a+b \sin (c+d x))}","\frac{2 f \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{e+f x}{b d (a+b \sin (c+d x))}",1,"(2*f*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b*Sqrt[a^2 - b^2]*d^2) - (e + f*x)/(b*d*(a + b*Sin[c + d*x]))","A",4,4,24,0.1667,1,"{4422, 2660, 618, 204}"
320,1,280,0,0.5276712,"\int \frac{(e+f x)^2 \cos (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)^2*Cos[c + d*x])/(a + b*Sin[c + d*x])^2,x]","-\frac{2 f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{2 f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{2 i f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{2 i f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{(e+f x)^2}{b d (a+b \sin (c+d x))}","-\frac{2 f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{2 f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{2 i f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{2 i f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{(e+f x)^2}{b d (a+b \sin (c+d x))}",1,"((-2*I)*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + ((2*I)*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (2*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) + (2*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - (e + f*x)^2/(b*d*(a + b*Sin[c + d*x]))","A",9,6,26,0.2308,1,"{4422, 3323, 2264, 2190, 2279, 2391}"
321,1,418,0,0.8852681,"\int \frac{(e+f x)^3 \cos (c+d x)}{(a+b \sin (c+d x))^2} \, dx","Int[((e + f*x)^3*Cos[c + d*x])/(a + b*Sin[c + d*x])^2,x]","-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{6 i f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{6 i f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \sqrt{a^2-b^2}}-\frac{3 i f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{3 i f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{(e+f x)^3}{b d (a+b \sin (c+d x))}","-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \sqrt{a^2-b^2}}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \sqrt{a^2-b^2}}-\frac{6 i f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \sqrt{a^2-b^2}}+\frac{6 i f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \sqrt{a^2-b^2}}-\frac{3 i f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \sqrt{a^2-b^2}}+\frac{3 i f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \sqrt{a^2-b^2}}-\frac{(e+f x)^3}{b d (a+b \sin (c+d x))}",1,"((-3*I)*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) + ((3*I)*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^2) - (6*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) + (6*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^3) - ((6*I)*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4) + ((6*I)*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*Sqrt[a^2 - b^2]*d^4) - (e + f*x)^3/(b*d*(a + b*Sin[c + d*x]))","A",11,7,26,0.2692,1,"{4422, 3323, 2264, 2190, 2531, 2282, 6589}"
322,1,116,0,0.0967485,"\int \frac{(e+f x) \cos (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)*Cos[c + d*x])/(a + b*Sin[c + d*x])^3,x]","\frac{a f \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{f \cos (c+d x)}{2 d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}-\frac{e+f x}{2 b d (a+b \sin (c+d x))^2}","\frac{a f \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{f \cos (c+d x)}{2 d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}-\frac{e+f x}{2 b d (a+b \sin (c+d x))^2}",1,"(a*f*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(b*(a^2 - b^2)^(3/2)*d^2) - (e + f*x)/(2*b*d*(a + b*Sin[c + d*x])^2) + (f*Cos[c + d*x])/(2*(a^2 - b^2)*d^2*(a + b*Sin[c + d*x]))","A",6,6,24,0.2500,1,"{4422, 2664, 12, 2660, 618, 204}"
323,1,357,0,0.6111931,"\int \frac{(e+f x)^2 \cos (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)^2*Cos[c + d*x])/(a + b*Sin[c + d*x])^3,x]","-\frac{a f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{a f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}-\frac{i a f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{i a f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{f (e+f x) \cos (c+d x)}{d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}-\frac{f^2 \log (a+b \sin (c+d x))}{b d^3 \left(a^2-b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sin (c+d x))^2}","-\frac{a f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{a f^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}-\frac{i a f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{i a f (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{f (e+f x) \cos (c+d x)}{d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}-\frac{f^2 \log (a+b \sin (c+d x))}{b d^3 \left(a^2-b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sin (c+d x))^2}",1,"((-I)*a*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + (I*a*f*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - (f^2*Log[a + b*Sin[c + d*x]])/(b*(a^2 - b^2)*d^3) - (a*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + (a*f^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - (e + f*x)^2/(2*b*d*(a + b*Sin[c + d*x])^2) + (f*(e + f*x)*Cos[c + d*x])/((a^2 - b^2)*d^2*(a + b*Sin[c + d*x]))","A",12,9,26,0.3462,1,"{4422, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
324,1,753,0,1.2742044,"\int \frac{(e+f x)^3 \cos (c+d x)}{(a+b \sin (c+d x))^3} \, dx","Int[((e + f*x)^3*Cos[c + d*x])/(a + b*Sin[c + d*x])^3,x]","-\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{3 i f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \left(a^2-b^2\right)}+\frac{3 i f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \left(a^2-b^2\right)}-\frac{3 i a f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \left(a^2-b^2\right)^{3/2}}+\frac{3 i a f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \left(a^2-b^2\right)^{3/2}}-\frac{3 f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)}-\frac{3 f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)}-\frac{3 i a f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 i a f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 f (e+f x)^2 \cos (c+d x)}{2 d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}+\frac{3 i f (e+f x)^2}{2 b d^2 \left(a^2-b^2\right)}-\frac{(e+f x)^3}{2 b d (a+b \sin (c+d x))^2}","-\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)^{3/2}}+\frac{3 i f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \left(a^2-b^2\right)}+\frac{3 i f^3 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \left(a^2-b^2\right)}-\frac{3 i a f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^4 \left(a^2-b^2\right)^{3/2}}+\frac{3 i a f^3 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^4 \left(a^2-b^2\right)^{3/2}}-\frac{3 f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{b d^3 \left(a^2-b^2\right)}-\frac{3 f^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{b d^3 \left(a^2-b^2\right)}-\frac{3 i a f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 i a f (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{2 b d^2 \left(a^2-b^2\right)^{3/2}}+\frac{3 f (e+f x)^2 \cos (c+d x)}{2 d^2 \left(a^2-b^2\right) (a+b \sin (c+d x))}+\frac{3 i f (e+f x)^2}{2 b d^2 \left(a^2-b^2\right)}-\frac{(e+f x)^3}{2 b d (a+b \sin (c+d x))^2}",1,"(((3*I)/2)*f*(e + f*x)^2)/(b*(a^2 - b^2)*d^2) - (3*f^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) - (((3*I)/2)*a*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) - (3*f^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^3) + (((3*I)/2)*a*f*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^2) + ((3*I)*f^3*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) - (3*a*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) + ((3*I)*f^3*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)*d^4) + (3*a*f^2*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^3) - ((3*I)*a*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) + ((3*I)*a*f^3*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(b*(a^2 - b^2)^(3/2)*d^4) - (e + f*x)^3/(2*b*d*(a + b*Sin[c + d*x])^2) + (3*f*(e + f*x)^2*Cos[c + d*x])/(2*(a^2 - b^2)*d^2*(a + b*Sin[c + d*x]))","A",19,11,26,0.4231,1,"{4422, 3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391}"
325,1,765,0,1.425676,"\int \frac{(e+f x)^3 \cos (c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^3}+\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^3}-\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}+\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^4}-\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^4}{4 b f}","-\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^3}+\frac{6 i f^2 \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^3}-\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{3 f \sqrt{a^2-b^2} (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}+\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^4}-\frac{6 f^3 \sqrt{a^2-b^2} \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^4}{4 b f}",1,"-(e + f*x)^4/(4*b*f) - (2*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d) + ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (3*Sqrt[a^2 - b^2]*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^2) + (3*Sqrt[a^2 - b^2]*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^2) - (6*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) - ((6*I)*Sqrt[a^2 - b^2]*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^3) + ((6*I)*Sqrt[a^2 - b^2]*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^3) - ((6*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) + ((6*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4) + (6*Sqrt[a^2 - b^2]*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^4) - (6*Sqrt[a^2 - b^2]*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^4)","A",33,14,32,0.4375,1,"{4543, 4408, 3296, 2637, 4183, 2531, 6609, 2282, 6589, 4525, 32, 3323, 2264, 2190}"
326,1,557,0,1.1903021,"\int \frac{(e+f x)^2 \cos (c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}-\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^3}+\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^3}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3}{3 b f}","-\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{2 f \sqrt{a^2-b^2} (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}-\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^3}+\frac{2 i f^2 \sqrt{a^2-b^2} \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^3}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}-\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{(e+f x)^3}{3 b f}",1,"-(e + f*x)^3/(3*b*f) - (2*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d) + ((2*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (2*Sqrt[a^2 - b^2]*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^2) + (2*Sqrt[a^2 - b^2]*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^2) - (2*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (2*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) - ((2*I)*Sqrt[a^2 - b^2]*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^3) + ((2*I)*Sqrt[a^2 - b^2]*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^3)","A",27,13,32,0.4062,1,"{4543, 4408, 3296, 2638, 4183, 2531, 2282, 6589, 4525, 32, 3323, 2264, 2190}"
327,1,351,0,0.6604717,"\int \frac{(e+f x) \cos (c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{e x}{b}-\frac{f x^2}{2 b}","-\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d^2}+\frac{f \sqrt{a^2-b^2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d^2}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b d}+\frac{i \sqrt{a^2-b^2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{e x}{b}-\frac{f x^2}{2 b}",1,"-((e*x)/b) - (f*x^2)/(2*b) - (2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) - (I*Sqrt[a^2 - b^2]*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d) + (I*Sqrt[a^2 - b^2]*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d) + (I*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - (I*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) - (Sqrt[a^2 - b^2]*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b*d^2) + (Sqrt[a^2 - b^2]*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b*d^2)","A",21,11,30,0.3667,1,"{4543, 4408, 3296, 2637, 4183, 2279, 2391, 4525, 3323, 2264, 2190}"
328,1,75,0,0.1844071,"\int \frac{\cos (c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{2 \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a b d}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}-\frac{x}{b}","\frac{2 \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a b d}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}-\frac{x}{b}",1,"-(x/b) + (2*Sqrt[a^2 - b^2]*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(a*b*d) - ArcTanh[Cos[c + d*x]]/(a*d)","A",6,6,25,0.2400,1,"{2889, 3058, 2660, 618, 204, 3770}"
329,1,763,0,1.3590561,"\int \frac{(e+f x)^3 \cos ^2(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^2*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^3}+\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^3}-\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}+\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^4}+\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a d^4}+\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 a b^2 f}+\frac{(e+f x)^3 \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^4}{4 a f}+\frac{6 f^2 (e+f x) \sin (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \cos (c+d x)}{b d^2}+\frac{6 f^3 \cos (c+d x)}{b d^4}-\frac{(e+f x)^3 \sin (c+d x)}{b d}","\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^3}+\frac{6 f^2 \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^3}-\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{3 i f \left(a^2-b^2\right) (e+f x)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}+\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^4}+\frac{6 i f^3 \left(a^2-b^2\right) \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a d^4}+\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x)^3 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 a b^2 f}+\frac{(e+f x)^3 \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^4}{4 a f}+\frac{6 f^2 (e+f x) \sin (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \cos (c+d x)}{b d^2}+\frac{6 f^3 \cos (c+d x)}{b d^4}-\frac{(e+f x)^3 \sin (c+d x)}{b d}",1,"((-I/4)*(e + f*x)^4)/(a*f) - ((I/4)*(a^2 - b^2)*(e + f*x)^4)/(a*b^2*f) + (6*f^3*Cos[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Cos[c + d*x])/(b*d^2) + ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d) + ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d) + ((e + f*x)^3*Log[1 - E^((2*I)*(c + d*x))])/(a*d) - ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^2) - ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^2) - (((3*I)/2)*f*(e + f*x)^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^2) + (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^3) + (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^3) + (3*f^2*(e + f*x)*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^3) + ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^4) + ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^4) + (((3*I)/4)*f^3*PolyLog[4, E^((2*I)*(c + d*x))])/(a*d^4) + (6*f^2*(e + f*x)*Sin[c + d*x])/(b*d^3) - ((e + f*x)^3*Sin[c + d*x])/(b*d)","A",34,17,34,0.5000,1,"{4543, 4408, 4404, 3311, 32, 2635, 8, 3717, 2190, 2531, 6609, 2282, 6589, 4525, 3296, 2638, 4519}"
330,1,566,0,1.122317,"\int \frac{(e+f x)^2 \cos ^2(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^2*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}+\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^3}+\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^3}-\frac{i f (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^3}+\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 a b^2 f}+\frac{(e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^3}{3 a f}-\frac{2 f (e+f x) \cos (c+d x)}{b d^2}+\frac{2 f^2 \sin (c+d x)}{b d^3}-\frac{(e+f x)^2 \sin (c+d x)}{b d}","-\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}+\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^3}+\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^3}-\frac{i f (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^3}+\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 a b^2 f}+\frac{(e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^3}{3 a f}-\frac{2 f (e+f x) \cos (c+d x)}{b d^2}+\frac{2 f^2 \sin (c+d x)}{b d^3}-\frac{(e+f x)^2 \sin (c+d x)}{b d}",1,"((-I/3)*(e + f*x)^3)/(a*f) - ((I/3)*(a^2 - b^2)*(e + f*x)^3)/(a*b^2*f) - (2*f*(e + f*x)*Cos[c + d*x])/(b*d^2) + ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d) + ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d) + ((e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a*d) - ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^2) - ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^2) - (I*f*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^2) + (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^3) + (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^3) + (f^2*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^3) + (2*f^2*Sin[c + d*x])/(b*d^3) - ((e + f*x)^2*Sin[c + d*x])/(b*d)","A",26,13,34,0.3824,1,"{4543, 4408, 4404, 3310, 3717, 2190, 2531, 2282, 6589, 4525, 3296, 2637, 4519}"
331,1,379,0,0.6311953,"\int \frac{(e+f x) \cos ^2(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^2*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}-\frac{i f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a d^2}+\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 a b^2 f}+\frac{(e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^2}{2 a f}-\frac{f \cos (c+d x)}{b d^2}-\frac{(e+f x) \sin (c+d x)}{b d}","-\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d^2}-\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d^2}-\frac{i f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a d^2}+\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^2 d}+\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^2 d}-\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 a b^2 f}+\frac{(e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a d}-\frac{i (e+f x)^2}{2 a f}-\frac{f \cos (c+d x)}{b d^2}-\frac{(e+f x) \sin (c+d x)}{b d}",1,"((-I/2)*(e + f*x)^2)/(a*f) - ((I/2)*(a^2 - b^2)*(e + f*x)^2)/(a*b^2*f) - (f*Cos[c + d*x])/(b*d^2) + ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d) + ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d) + ((e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a*d) - (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^2*d^2) - (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^2*d^2) - ((I/2)*f*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^2) - ((e + f*x)*Sin[c + d*x])/(b*d)","A",22,13,32,0.4062,1,"{4543, 4408, 4404, 2635, 8, 3717, 2190, 2279, 2391, 4525, 3296, 2638, 4519}"
332,1,59,0,0.1078528,"\int \frac{\cos ^2(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]^2*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{\left(a^2-b^2\right) \log (a+b \sin (c+d x))}{a b^2 d}+\frac{\log (\sin (c+d x))}{a d}-\frac{\sin (c+d x)}{b d}","\frac{\left(a^2-b^2\right) \log (a+b \sin (c+d x))}{a b^2 d}+\frac{\log (\sin (c+d x))}{a d}-\frac{\sin (c+d x)}{b d}",1,"Log[Sin[c + d*x]]/(a*d) + ((a^2 - b^2)*Log[a + b*Sin[c + d*x]])/(a*b^2*d) - Sin[c + d*x]/(b*d)","A",4,3,27,0.1111,1,"{2837, 12, 894}"
333,1,1138,0,2.1074783,"\int \frac{(e+f x)^3 \cos ^3(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^3*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{\left(a^2-b^2\right) (e+f x)^4}{4 b^3 f}-\frac{(e+f x)^4}{8 b f}-\frac{2 \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^3}{a d}+\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^3}{a b^2 d}+\frac{\cos (c+d x) (e+f x)^3}{a d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a b^3 d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^3}{2 b d}-\frac{3 f \cos ^2(c+d x) (e+f x)^2}{4 b d^2}+\frac{3 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)^2}{a d^2}+\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d^2}-\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d^2}-\frac{3 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)^2}{a b^2 d^2}-\frac{3 f \sin (c+d x) (e+f x)^2}{a d^2}-\frac{6 \left(a^2-b^2\right) f^2 \cos (c+d x) (e+f x)}{a b^2 d^3}-\frac{6 f^2 \cos (c+d x) (e+f x)}{a d^3}-\frac{6 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^3}-\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^3}+\frac{3 f^2 \cos (c+d x) \sin (c+d x) (e+f x)}{4 b d^3}+\frac{3 f^3 x^2}{8 b d^2}+\frac{3 f^3 \cos ^2(c+d x)}{8 b d^4}+\frac{3 e f^2 x}{4 b d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^4}+\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a b^3 d^4}+\frac{6 \left(a^2-b^2\right) f^3 \sin (c+d x)}{a b^2 d^4}+\frac{6 f^3 \sin (c+d x)}{a d^4}","\frac{\left(a^2-b^2\right) (e+f x)^4}{4 b^3 f}-\frac{(e+f x)^4}{8 b f}-\frac{2 \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^3}{a d}+\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^3}{a b^2 d}+\frac{\cos (c+d x) (e+f x)^3}{a d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a b^3 d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^3}{2 b d}-\frac{3 f \cos ^2(c+d x) (e+f x)^2}{4 b d^2}+\frac{3 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)^2}{a d^2}+\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d^2}-\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d^2}-\frac{3 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)^2}{a b^2 d^2}-\frac{3 f \sin (c+d x) (e+f x)^2}{a d^2}-\frac{6 \left(a^2-b^2\right) f^2 \cos (c+d x) (e+f x)}{a b^2 d^3}-\frac{6 f^2 \cos (c+d x) (e+f x)}{a d^3}-\frac{6 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^3}-\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^3}+\frac{3 f^2 \cos (c+d x) \sin (c+d x) (e+f x)}{4 b d^3}+\frac{3 f^3 x^2}{8 b d^2}+\frac{3 f^3 \cos ^2(c+d x)}{8 b d^4}+\frac{3 e f^2 x}{4 b d^2}-\frac{6 i f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a d^4}-\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^4}+\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a b^3 d^4}+\frac{6 \left(a^2-b^2\right) f^3 \sin (c+d x)}{a b^2 d^4}+\frac{6 f^3 \sin (c+d x)}{a d^4}",1,"(3*e*f^2*x)/(4*b*d^2) + (3*f^3*x^2)/(8*b*d^2) - (e + f*x)^4/(8*b*f) + ((a^2 - b^2)*(e + f*x)^4)/(4*b^3*f) - (2*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a*d) - (6*f^2*(e + f*x)*Cos[c + d*x])/(a*d^3) - (6*(a^2 - b^2)*f^2*(e + f*x)*Cos[c + d*x])/(a*b^2*d^3) + ((e + f*x)^3*Cos[c + d*x])/(a*d) + ((a^2 - b^2)*(e + f*x)^3*Cos[c + d*x])/(a*b^2*d) + (3*f^3*Cos[c + d*x]^2)/(8*b*d^4) - (3*f*(e + f*x)^2*Cos[c + d*x]^2)/(4*b*d^2) + (I*(a^2 - b^2)^(3/2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d) + ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (3*(a^2 - b^2)^(3/2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^2) - (3*(a^2 - b^2)^(3/2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^2) - (6*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) + ((6*I)*(a^2 - b^2)^(3/2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^3) - ((6*I)*(a^2 - b^2)^(3/2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^3) - ((6*I)*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a*d^4) + ((6*I)*f^3*PolyLog[4, E^(I*(c + d*x))])/(a*d^4) - (6*(a^2 - b^2)^(3/2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^4) + (6*(a^2 - b^2)^(3/2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^4) + (6*f^3*Sin[c + d*x])/(a*d^4) + (6*(a^2 - b^2)*f^3*Sin[c + d*x])/(a*b^2*d^4) - (3*f*(e + f*x)^2*Sin[c + d*x])/(a*d^2) - (3*(a^2 - b^2)*f*(e + f*x)^2*Sin[c + d*x])/(a*b^2*d^2) + (3*f^2*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^3) - ((e + f*x)^3*Cos[c + d*x]*Sin[c + d*x])/(2*b*d)","A",53,18,34,0.5294,1,"{4543, 4408, 4405, 3311, 3296, 2637, 2633, 4183, 2531, 6609, 2282, 6589, 4525, 32, 3310, 3323, 2264, 2190}"
334,1,825,0,1.6327003,"\int \frac{(e+f x)^2 \cos ^3(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^3*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{\left(a^2-b^2\right) (e+f x)^3}{3 b^3 f}-\frac{(e+f x)^3}{6 b f}-\frac{2 \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d}+\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^2}{a b^2 d}+\frac{\cos (c+d x) (e+f x)^2}{a d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^2}{2 b d}-\frac{f \cos ^2(c+d x) (e+f x)}{2 b d^2}+\frac{2 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^2}+\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^2}-\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^2}-\frac{2 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)}{a b^2 d^2}-\frac{2 f \sin (c+d x) (e+f x)}{a d^2}+\frac{f^2 x}{4 b d^2}-\frac{2 \left(a^2-b^2\right) f^2 \cos (c+d x)}{a b^2 d^3}-\frac{2 f^2 \cos (c+d x)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^3}-\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a b^3 d^3}+\frac{f^2 \cos (c+d x) \sin (c+d x)}{4 b d^3}","\frac{\left(a^2-b^2\right) (e+f x)^3}{3 b^3 f}-\frac{(e+f x)^3}{6 b f}-\frac{2 \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d}+\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^2}{a b^2 d}+\frac{\cos (c+d x) (e+f x)^2}{a d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a b^3 d}-\frac{\cos (c+d x) \sin (c+d x) (e+f x)^2}{2 b d}-\frac{f \cos ^2(c+d x) (e+f x)}{2 b d^2}+\frac{2 i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 i f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^2}+\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^2}-\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a b^3 d^2}-\frac{2 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)}{a b^2 d^2}-\frac{2 f \sin (c+d x) (e+f x)}{a d^2}+\frac{f^2 x}{4 b d^2}-\frac{2 \left(a^2-b^2\right) f^2 \cos (c+d x)}{a b^2 d^3}-\frac{2 f^2 \cos (c+d x)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^3}+\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^3}-\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a b^3 d^3}+\frac{f^2 \cos (c+d x) \sin (c+d x)}{4 b d^3}",1,"(f^2*x)/(4*b*d^2) - (e + f*x)^3/(6*b*f) + ((a^2 - b^2)*(e + f*x)^3)/(3*b^3*f) - (2*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d) - (2*f^2*Cos[c + d*x])/(a*d^3) - (2*(a^2 - b^2)*f^2*Cos[c + d*x])/(a*b^2*d^3) + ((e + f*x)^2*Cos[c + d*x])/(a*d) + ((a^2 - b^2)*(e + f*x)^2*Cos[c + d*x])/(a*b^2*d) - (f*(e + f*x)*Cos[c + d*x]^2)/(2*b*d^2) + (I*(a^2 - b^2)^(3/2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d) + ((2*I)*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + (2*(a^2 - b^2)^(3/2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^2) - (2*(a^2 - b^2)^(3/2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^2) - (2*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a*d^3) + (2*f^2*PolyLog[3, E^(I*(c + d*x))])/(a*d^3) + ((2*I)*(a^2 - b^2)^(3/2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^3) - ((2*I)*(a^2 - b^2)^(3/2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^3) - (2*f*(e + f*x)*Sin[c + d*x])/(a*d^2) - (2*(a^2 - b^2)*f*(e + f*x)*Sin[c + d*x])/(a*b^2*d^2) + (f^2*Cos[c + d*x]*Sin[c + d*x])/(4*b*d^3) - ((e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(2*b*d)","A",41,18,34,0.5294,1,"{4543, 4408, 4405, 3310, 3296, 2638, 4183, 2531, 2282, 6589, 4525, 3311, 32, 2635, 8, 3323, 2264, 2190}"
335,1,524,0,0.8989531,"\int \frac{(e+f x) \cos ^3(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^3*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^2}-\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^3 d^2}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{f \left(a^2-b^2\right) \sin (c+d x)}{a b^2 d^2}+\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^3 d}+\frac{\left(a^2-b^2\right) (e+f x) \cos (c+d x)}{a b^2 d}+\frac{e x \left(a^2-b^2\right)}{b^3}+\frac{f x^2 \left(a^2-b^2\right)}{2 b^3}-\frac{f \sin (c+d x)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{f \cos ^2(c+d x)}{4 b d^2}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 b d}-\frac{e x}{2 b}-\frac{f x^2}{4 b}","\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d^2}-\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^3 d^2}+\frac{i f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^2}-\frac{f \left(a^2-b^2\right) \sin (c+d x)}{a b^2 d^2}+\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a b^3 d}-\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a b^3 d}+\frac{\left(a^2-b^2\right) (e+f x) \cos (c+d x)}{a b^2 d}+\frac{e x \left(a^2-b^2\right)}{b^3}+\frac{f x^2 \left(a^2-b^2\right)}{2 b^3}-\frac{f \sin (c+d x)}{a d^2}+\frac{(e+f x) \cos (c+d x)}{a d}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d}-\frac{f \cos ^2(c+d x)}{4 b d^2}-\frac{(e+f x) \sin (c+d x) \cos (c+d x)}{2 b d}-\frac{e x}{2 b}-\frac{f x^2}{4 b}",1,"-(e*x)/(2*b) + ((a^2 - b^2)*e*x)/b^3 - (f*x^2)/(4*b) + ((a^2 - b^2)*f*x^2)/(2*b^3) - (2*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d) + ((e + f*x)*Cos[c + d*x])/(a*d) + ((a^2 - b^2)*(e + f*x)*Cos[c + d*x])/(a*b^2*d) - (f*Cos[c + d*x]^2)/(4*b*d^2) + (I*(a^2 - b^2)^(3/2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d) + (I*f*PolyLog[2, -E^(I*(c + d*x))])/(a*d^2) - (I*f*PolyLog[2, E^(I*(c + d*x))])/(a*d^2) + ((a^2 - b^2)^(3/2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a*b^3*d^2) - ((a^2 - b^2)^(3/2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a*b^3*d^2) - (f*Sin[c + d*x])/(a*d^2) - ((a^2 - b^2)*f*Sin[c + d*x])/(a*b^2*d^2) - ((e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*b*d)","A",31,14,32,0.4375,1,"{4543, 4408, 4405, 2633, 3296, 2637, 4183, 2279, 2391, 4525, 3310, 3323, 2264, 2190}"
336,1,124,0,0.2797235,"\int \frac{\cos ^3(c+d x) \cot (c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]^3*Cot[c + d*x])/(a + b*Sin[c + d*x]),x]","-\frac{2 \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a b^3 d}+\frac{x \left(2 a^2-3 b^2\right)}{2 b^3}+\frac{a \cos (c+d x)}{b^2 d}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}-\frac{\sin (c+d x) \cos (c+d x)}{2 b d}","-\frac{2 \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a b^3 d}+\frac{x \left(2 a^2-3 b^2\right)}{2 b^3}+\frac{a \cos (c+d x)}{b^2 d}-\frac{\tanh ^{-1}(\cos (c+d x))}{a d}-\frac{\sin (c+d x) \cos (c+d x)}{2 b d}",1,"((2*a^2 - 3*b^2)*x)/(2*b^3) - (2*(a^2 - b^2)^(3/2)*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(a*b^3*d) - ArcTanh[Cos[c + d*x]]/(a*d) + (a*Cos[c + d*x])/(b^2*d) - (Cos[c + d*x]*Sin[c + d*x])/(2*b*d)","A",6,6,27,0.2222,1,"{2895, 3057, 2660, 618, 204, 3770}"
337,1,852,0,1.7821501,"\int \frac{(e+f x)^3 \cos (c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{i b (e+f x)^4}{4 a^2 f}+\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 a^2 b f}-\frac{\csc (c+d x) (e+f x)^3}{a d}-\frac{\left(a^2-b^2\right) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b d}-\frac{\left(a^2-b^2\right) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{6 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d^2}+\frac{3 i \left(a^2-b^2\right) f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b d^2}+\frac{3 i \left(a^2-b^2\right) f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)^2}{2 a^2 d^2}+\frac{6 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 \left(a^2-b^2\right) f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b d^3}-\frac{6 \left(a^2-b^2\right) f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b d^3}-\frac{3 b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) (e+f x)}{2 a^2 d^3}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^4}-\frac{6 i \left(a^2-b^2\right) f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^4}-\frac{6 i \left(a^2-b^2\right) f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b d^4}-\frac{3 i b f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a^2 d^4}","\frac{i b (e+f x)^4}{4 a^2 f}+\frac{i \left(a^2-b^2\right) (e+f x)^4}{4 a^2 b f}-\frac{\csc (c+d x) (e+f x)^3}{a d}-\frac{\left(a^2-b^2\right) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b d}-\frac{\left(a^2-b^2\right) \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{6 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d^2}+\frac{3 i \left(a^2-b^2\right) f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b d^2}+\frac{3 i \left(a^2-b^2\right) f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)^2}{2 a^2 d^2}+\frac{6 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 \left(a^2-b^2\right) f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b d^3}-\frac{6 \left(a^2-b^2\right) f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b d^3}-\frac{3 b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) (e+f x)}{2 a^2 d^3}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^4}-\frac{6 i \left(a^2-b^2\right) f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^4}-\frac{6 i \left(a^2-b^2\right) f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b d^4}-\frac{3 i b f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a^2 d^4}",1,"((I/4)*b*(e + f*x)^4)/(a^2*f) + ((I/4)*(a^2 - b^2)*(e + f*x)^4)/(a^2*b*f) - (6*f*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d^2) - ((e + f*x)^3*Csc[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d) - ((a^2 - b^2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d) - (b*(e + f*x)^3*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) + ((6*I)*f^2*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^3) + ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^2) + ((3*I)*(a^2 - b^2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^2) + (((3*I)/2)*b*f*(e + f*x)^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2) - (6*f^3*PolyLog[3, -E^(I*(c + d*x))])/(a*d^4) + (6*f^3*PolyLog[3, E^(I*(c + d*x))])/(a*d^4) - (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^3) - (6*(a^2 - b^2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^3) - (3*b*f^2*(e + f*x)*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a^2*d^3) - ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^4) - ((6*I)*(a^2 - b^2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^4) - (((3*I)/4)*b*f^3*PolyLog[4, E^((2*I)*(c + d*x))])/(a^2*d^4)","A",48,19,34,0.5588,1,"{4543, 4408, 3296, 2638, 4410, 4183, 2531, 2282, 6589, 4404, 3311, 32, 2635, 8, 3717, 2190, 6609, 4525, 4519}"
338,1,616,0,1.3871848,"\int \frac{(e+f x)^2 \cos (c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^2}+\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^2}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^3}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^3}+\frac{i b f (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a^2 d^2}-\frac{b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^3}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d}+\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 a^2 b f}-\frac{b (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{i b (e+f x)^3}{3 a^2 f}-\frac{4 f (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \csc (c+d x)}{a d}","\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^2}+\frac{2 i f \left(a^2-b^2\right) (e+f x) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^2}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^3}-\frac{2 f^2 \left(a^2-b^2\right) \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^3}+\frac{i b f (e+f x) \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a^2 d^2}-\frac{b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^3}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d}+\frac{i \left(a^2-b^2\right) (e+f x)^3}{3 a^2 b f}-\frac{b (e+f x)^2 \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{i b (e+f x)^3}{3 a^2 f}-\frac{4 f (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \csc (c+d x)}{a d}",1,"((I/3)*b*(e + f*x)^3)/(a^2*f) + ((I/3)*(a^2 - b^2)*(e + f*x)^3)/(a^2*b*f) - (4*f*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d^2) - ((e + f*x)^2*Csc[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d) - ((a^2 - b^2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d) - (b*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) + ((2*I)*f^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^3) - ((2*I)*f^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^3) + ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^2) + ((2*I)*(a^2 - b^2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^2) + (I*b*f*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2) - (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^3) - (2*(a^2 - b^2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^3) - (b*f^2*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a^2*d^3)","A",37,17,34,0.5000,1,"{4543, 4408, 3296, 2637, 4410, 4183, 2279, 2391, 4404, 3310, 3717, 2190, 2531, 2282, 6589, 4525, 4519}"
339,1,386,0,0.7842687,"\int \frac{(e+f x) \cos (c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^2}+\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a^2 d^2}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d}+\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 a^2 b f}-\frac{b (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{i b (e+f x)^2}{2 a^2 f}-\frac{f \tanh ^{-1}(\cos (c+d x))}{a d^2}-\frac{(e+f x) \csc (c+d x)}{a d}","\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d^2}+\frac{i f \left(a^2-b^2\right) \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a^2 d^2}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b d}+\frac{i \left(a^2-b^2\right) (e+f x)^2}{2 a^2 b f}-\frac{b (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{i b (e+f x)^2}{2 a^2 f}-\frac{f \tanh ^{-1}(\cos (c+d x))}{a d^2}-\frac{(e+f x) \csc (c+d x)}{a d}",1,"((I/2)*b*(e + f*x)^2)/(a^2*f) + ((I/2)*(a^2 - b^2)*(e + f*x)^2)/(a^2*b*f) - (f*ArcTanh[Cos[c + d*x]])/(a*d^2) - ((e + f*x)*Csc[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d) - ((a^2 - b^2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d) - (b*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) + (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b*d^2) + (I*(a^2 - b^2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b*d^2) + ((I/2)*b*f*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2)","A",28,15,32,0.4688,1,"{4543, 4408, 3296, 2638, 4410, 3770, 4404, 2635, 8, 3717, 2190, 2279, 2391, 4525, 4519}"
340,1,60,0,0.1234611,"\int \frac{\cos (c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{\left(1-\frac{b^2}{a^2}\right) \log (a+b \sin (c+d x))}{b d}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{\csc (c+d x)}{a d}","-\frac{\left(1-\frac{b^2}{a^2}\right) \log (a+b \sin (c+d x))}{b d}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{\csc (c+d x)}{a d}",1,"-(Csc[c + d*x]/(a*d)) - (b*Log[Sin[c + d*x]])/(a^2*d) - ((1 - b^2/a^2)*Log[a + b*Sin[c + d*x]])/(b*d)","A",4,3,27,0.1111,1,"{2837, 12, 894}"
341,1,1144,0,2.6563011,"\int \frac{(e+f x)^3 \cos ^2(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^2*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{\left(a^2-b^2\right) (e+f x)^4}{4 a b^2 f}-\frac{(e+f x)^4}{4 a f}+\frac{2 b \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{b \cos (c+d x) (e+f x)^3}{a^2 d}-\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^3}{a^2 b d}-\frac{\cot (c+d x) (e+f x)^3}{a d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^2 d}-\frac{i (e+f x)^3}{a d}+\frac{3 f \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)^2}{a^2 d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)^2}{a^2 d^2}-\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d^2}+\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d^2}+\frac{3 b f \sin (c+d x) (e+f x)^2}{a^2 d^2}+\frac{3 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)^2}{a^2 b d^2}+\frac{6 b f^2 \cos (c+d x) (e+f x)}{a^2 d^3}+\frac{6 \left(a^2-b^2\right) f^2 \cos (c+d x) (e+f x)}{a^2 b d^3}-\frac{3 i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right) (e+f x)}{a^2 d^3}-\frac{6 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right) (e+f x)}{a^2 d^3}-\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^3}+\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}+\frac{6 i b f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a^2 d^4}-\frac{6 i b f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a^2 d^4}+\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^4}-\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^4}-\frac{6 b f^3 \sin (c+d x)}{a^2 d^4}-\frac{6 \left(a^2-b^2\right) f^3 \sin (c+d x)}{a^2 b d^4}","-\frac{\left(a^2-b^2\right) (e+f x)^4}{4 a b^2 f}-\frac{(e+f x)^4}{4 a f}+\frac{2 b \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{b \cos (c+d x) (e+f x)^3}{a^2 d}-\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^3}{a^2 b d}-\frac{\cot (c+d x) (e+f x)^3}{a d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^2 d}-\frac{i (e+f x)^3}{a d}+\frac{3 f \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)^2}{a^2 d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)^2}{a^2 d^2}-\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d^2}+\frac{3 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d^2}+\frac{3 b f \sin (c+d x) (e+f x)^2}{a^2 d^2}+\frac{3 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)^2}{a^2 b d^2}+\frac{6 b f^2 \cos (c+d x) (e+f x)}{a^2 d^3}+\frac{6 \left(a^2-b^2\right) f^2 \cos (c+d x) (e+f x)}{a^2 b d^3}-\frac{3 i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right) (e+f x)}{a^2 d^3}-\frac{6 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right) (e+f x)}{a^2 d^3}-\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^3}+\frac{6 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a d^4}+\frac{6 i b f^3 \text{PolyLog}\left(4,-e^{i (c+d x)}\right)}{a^2 d^4}-\frac{6 i b f^3 \text{PolyLog}\left(4,e^{i (c+d x)}\right)}{a^2 d^4}+\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^4}-\frac{6 \left(a^2-b^2\right)^{3/2} f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^4}-\frac{6 b f^3 \sin (c+d x)}{a^2 d^4}-\frac{6 \left(a^2-b^2\right) f^3 \sin (c+d x)}{a^2 b d^4}",1,"((-I)*(e + f*x)^3)/(a*d) - (e + f*x)^4/(4*a*f) - ((a^2 - b^2)*(e + f*x)^4)/(4*a*b^2*f) + (2*b*(e + f*x)^3*ArcTanh[E^(I*(c + d*x))])/(a^2*d) + (6*b*f^2*(e + f*x)*Cos[c + d*x])/(a^2*d^3) + (6*(a^2 - b^2)*f^2*(e + f*x)*Cos[c + d*x])/(a^2*b*d^3) - (b*(e + f*x)^3*Cos[c + d*x])/(a^2*d) - ((a^2 - b^2)*(e + f*x)^3*Cos[c + d*x])/(a^2*b*d) - ((e + f*x)^3*Cot[c + d*x])/(a*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (I*(a^2 - b^2)^(3/2)*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (3*f*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((3*I)*b*f*(e + f*x)^2*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - (3*(a^2 - b^2)^(3/2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) + (3*(a^2 - b^2)^(3/2)*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) - ((3*I)*f^2*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (6*b*f^2*(e + f*x)*PolyLog[3, -E^(I*(c + d*x))])/(a^2*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, E^(I*(c + d*x))])/(a^2*d^3) - ((6*I)*(a^2 - b^2)^(3/2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^3) + ((6*I)*(a^2 - b^2)^(3/2)*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^3) + (3*f^3*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a*d^4) + ((6*I)*b*f^3*PolyLog[4, -E^(I*(c + d*x))])/(a^2*d^4) - ((6*I)*b*f^3*PolyLog[4, E^(I*(c + d*x))])/(a^2*d^4) + (6*(a^2 - b^2)^(3/2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^4) - (6*(a^2 - b^2)^(3/2)*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^4) - (6*b*f^3*Sin[c + d*x])/(a^2*d^4) - (6*(a^2 - b^2)*f^3*Sin[c + d*x])/(a^2*b*d^4) + (3*b*f*(e + f*x)^2*Sin[c + d*x])/(a^2*d^2) + (3*(a^2 - b^2)*f*(e + f*x)^2*Sin[c + d*x])/(a^2*b*d^2)","A",66,20,36,0.5556,1,"{4543, 4408, 3311, 32, 3310, 3720, 3717, 2190, 2531, 2282, 6589, 4405, 3296, 2637, 2633, 4183, 6609, 4525, 3323, 2264}"
342,1,840,0,2.1519413,"\int \frac{(e+f x)^2 \cos ^2(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^2*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{\left(a^2-b^2\right) (e+f x)^3}{3 a b^2 f}-\frac{(e+f x)^3}{3 a f}+\frac{2 b \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a^2 d}-\frac{b \cos (c+d x) (e+f x)^2}{a^2 d}-\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^2}{a^2 b d}-\frac{\cot (c+d x) (e+f x)^2}{a d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d}-\frac{i (e+f x)^2}{a d}+\frac{2 f \log \left(1-e^{2 i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a^2 d^2}+\frac{2 i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a^2 d^2}-\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^2}+\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^2}+\frac{2 b f \sin (c+d x) (e+f x)}{a^2 d^2}+\frac{2 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)}{a^2 b d^2}+\frac{2 b f^2 \cos (c+d x)}{a^2 d^3}+\frac{2 \left(a^2-b^2\right) f^2 \cos (c+d x)}{a^2 b d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^3}+\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^3}","-\frac{\left(a^2-b^2\right) (e+f x)^3}{3 a b^2 f}-\frac{(e+f x)^3}{3 a f}+\frac{2 b \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a^2 d}-\frac{b \cos (c+d x) (e+f x)^2}{a^2 d}-\frac{\left(a^2-b^2\right) \cos (c+d x) (e+f x)^2}{a^2 b d}-\frac{\cot (c+d x) (e+f x)^2}{a d}-\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^2 d}-\frac{i (e+f x)^2}{a d}+\frac{2 f \log \left(1-e^{2 i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a^2 d^2}+\frac{2 i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a^2 d^2}-\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^2}+\frac{2 \left(a^2-b^2\right)^{3/2} f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^2 d^2}+\frac{2 b f \sin (c+d x) (e+f x)}{a^2 d^2}+\frac{2 \left(a^2-b^2\right) f \sin (c+d x) (e+f x)}{a^2 b d^2}+\frac{2 b f^2 \cos (c+d x)}{a^2 d^3}+\frac{2 \left(a^2-b^2\right) f^2 \cos (c+d x)}{a^2 b d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{a d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a^2 d^3}-\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^3}+\frac{2 i \left(a^2-b^2\right)^{3/2} f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^3}",1,"((-I)*(e + f*x)^2)/(a*d) - (e + f*x)^3/(3*a*f) - ((a^2 - b^2)*(e + f*x)^3)/(3*a*b^2*f) + (2*b*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a^2*d) + (2*b*f^2*Cos[c + d*x])/(a^2*d^3) + (2*(a^2 - b^2)*f^2*Cos[c + d*x])/(a^2*b*d^3) - (b*(e + f*x)^2*Cos[c + d*x])/(a^2*d) - ((a^2 - b^2)*(e + f*x)^2*Cos[c + d*x])/(a^2*b*d) - ((e + f*x)^2*Cot[c + d*x])/(a*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (I*(a^2 - b^2)^(3/2)*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (2*f*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a*d^2) - ((2*I)*b*f*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + ((2*I)*b*f*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - (2*(a^2 - b^2)^(3/2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) + (2*(a^2 - b^2)^(3/2)*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) - (I*f^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a*d^3) + (2*b*f^2*PolyLog[3, -E^(I*(c + d*x))])/(a^2*d^3) - (2*b*f^2*PolyLog[3, E^(I*(c + d*x))])/(a^2*d^3) - ((2*I)*(a^2 - b^2)^(3/2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^3) + ((2*I)*(a^2 - b^2)^(3/2)*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^3) + (2*b*f*(e + f*x)*Sin[c + d*x])/(a^2*d^2) + (2*(a^2 - b^2)*f*(e + f*x)*Sin[c + d*x])/(a^2*b*d^2)","A",53,22,36,0.6111,1,"{4543, 4408, 3311, 32, 2635, 8, 3720, 3717, 2190, 2279, 2391, 4405, 3310, 3296, 2638, 4183, 2531, 2282, 6589, 4525, 3323, 2264}"
343,1,517,0,1.1424289,"\int \frac{(e+f x) \cos ^2(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^2*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^2}+\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^2 d^2}-\frac{i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}+\frac{f \left(a^2-b^2\right) \sin (c+d x)}{a^2 b d^2}-\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^2 d}-\frac{\left(a^2-b^2\right) (e+f x) \cos (c+d x)}{a^2 b d}+\frac{e x \left(1-\frac{a^2}{b^2}\right)}{a}+\frac{f x^2 \left(1-\frac{a^2}{b^2}\right)}{2 a}+\frac{b f \sin (c+d x)}{a^2 d^2}-\frac{b (e+f x) \cos (c+d x)}{a^2 d}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot (c+d x)}{a d}-\frac{e x}{a}-\frac{f x^2}{2 a}","-\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d^2}+\frac{f \left(a^2-b^2\right)^{3/2} \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^2 d^2}-\frac{i b f \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a^2 d^2}+\frac{f \left(a^2-b^2\right) \sin (c+d x)}{a^2 b d^2}-\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^2 d}+\frac{i \left(a^2-b^2\right)^{3/2} (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^2 d}-\frac{\left(a^2-b^2\right) (e+f x) \cos (c+d x)}{a^2 b d}+\frac{e x \left(1-\frac{a^2}{b^2}\right)}{a}+\frac{f x^2 \left(1-\frac{a^2}{b^2}\right)}{2 a}+\frac{b f \sin (c+d x)}{a^2 d^2}-\frac{b (e+f x) \cos (c+d x)}{a^2 d}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{i (c+d x)}\right)}{a^2 d}+\frac{f \log (\sin (c+d x))}{a d^2}-\frac{(e+f x) \cot (c+d x)}{a d}-\frac{e x}{a}-\frac{f x^2}{2 a}",1,"-((e*x)/a) + ((1 - a^2/b^2)*e*x)/a - (f*x^2)/(2*a) + ((1 - a^2/b^2)*f*x^2)/(2*a) + (2*b*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a^2*d) - (b*(e + f*x)*Cos[c + d*x])/(a^2*d) - ((a^2 - b^2)*(e + f*x)*Cos[c + d*x])/(a^2*b*d) - ((e + f*x)*Cot[c + d*x])/(a*d) - (I*(a^2 - b^2)^(3/2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (I*(a^2 - b^2)^(3/2)*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d) + (f*Log[Sin[c + d*x]])/(a*d^2) - (I*b*f*PolyLog[2, -E^(I*(c + d*x))])/(a^2*d^2) + (I*b*f*PolyLog[2, E^(I*(c + d*x))])/(a^2*d^2) - ((a^2 - b^2)^(3/2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) + ((a^2 - b^2)^(3/2)*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^2*d^2) + (b*f*Sin[c + d*x])/(a^2*d^2) + ((a^2 - b^2)*f*Sin[c + d*x])/(a^2*b*d^2)","A",38,16,34,0.4706,1,"{4543, 4408, 3310, 3720, 3475, 4405, 2633, 3296, 2637, 4183, 2279, 2391, 4525, 3323, 2264, 2190}"
344,1,104,0,0.2702879,"\int \frac{\cos ^2(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]^2*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{2 \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a^2 b^2 d}+\frac{b \tanh ^{-1}(\cos (c+d x))}{a^2 d}-\frac{a x}{b^2}-\frac{\cot (c+d x)}{a d}-\frac{\cos (c+d x)}{b d}","\frac{2 \left(a^2-b^2\right)^{3/2} \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} (c+d x)\right)+b}{\sqrt{a^2-b^2}}\right)}{a^2 b^2 d}+\frac{b \tanh ^{-1}(\cos (c+d x))}{a^2 d}-\frac{a x}{b^2}-\frac{\cot (c+d x)}{a d}-\frac{\cos (c+d x)}{b d}",1,"-((a*x)/b^2) + (2*(a^2 - b^2)^(3/2)*ArcTan[(b + a*Tan[(c + d*x)/2])/Sqrt[a^2 - b^2]])/(a^2*b^2*d) + (b*ArcTanh[Cos[c + d*x]])/(a^2*d) - Cos[c + d*x]/(b*d) - Cot[c + d*x]/(a*d)","A",6,6,29,0.2069,1,"{2894, 3057, 2660, 618, 204, 3770}"
345,1,1432,0,2.9467381,"\int \frac{(e+f x)^3 \cos ^3(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^3*Cos[c + d*x]^3*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{i \left(a^2-b^2\right)^2 (e+f x)^4}{4 a^2 b^3 f}+\frac{i b (e+f x)^4}{4 a^2 f}+\frac{b \sin ^2(c+d x) (e+f x)^3}{2 a^2 d}+\frac{\left(a^2-b^2\right) \sin ^2(c+d x) (e+f x)^3}{2 a^2 b d}-\frac{\csc (c+d x) (e+f x)^3}{a d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^3 d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{\left(a^2-b^2\right) \sin (c+d x) (e+f x)^3}{a b^2 d}-\frac{\sin (c+d x) (e+f x)^3}{a d}-\frac{b (e+f x)^3}{4 a^2 d}-\frac{\left(a^2-b^2\right) (e+f x)^3}{4 a^2 b d}-\frac{6 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 \left(a^2-b^2\right) f \cos (c+d x) (e+f x)^2}{a b^2 d^2}-\frac{3 f \cos (c+d x) (e+f x)^2}{a d^2}-\frac{3 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d^2}-\frac{3 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)^2}{2 a^2 d^2}+\frac{3 b f \cos (c+d x) \sin (c+d x) (e+f x)^2}{4 a^2 d^2}+\frac{3 \left(a^2-b^2\right) f \cos (c+d x) \sin (c+d x) (e+f x)^2}{4 a^2 b d^2}-\frac{3 b f^2 \sin ^2(c+d x) (e+f x)}{4 a^2 d^3}-\frac{3 \left(a^2-b^2\right) f^2 \sin ^2(c+d x) (e+f x)}{4 a^2 b d^3}+\frac{6 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^3}+\frac{6 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^3}-\frac{3 b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) (e+f x)}{2 a^2 d^3}+\frac{6 \left(a^2-b^2\right) f^2 \sin (c+d x) (e+f x)}{a b^2 d^3}+\frac{6 f^2 \sin (c+d x) (e+f x)}{a d^3}+\frac{3 b f^3 x}{8 a^2 d^3}+\frac{3 \left(a^2-b^2\right) f^3 x}{8 a^2 b d^3}+\frac{6 \left(a^2-b^2\right) f^3 \cos (c+d x)}{a b^2 d^4}+\frac{6 f^3 \cos (c+d x)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^4}+\frac{6 i \left(a^2-b^2\right)^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^4}+\frac{6 i \left(a^2-b^2\right)^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^4}-\frac{3 i b f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a^2 d^4}-\frac{3 b f^3 \cos (c+d x) \sin (c+d x)}{8 a^2 d^4}-\frac{3 \left(a^2-b^2\right) f^3 \cos (c+d x) \sin (c+d x)}{8 a^2 b d^4}","-\frac{i \left(a^2-b^2\right)^2 (e+f x)^4}{4 a^2 b^3 f}+\frac{i b (e+f x)^4}{4 a^2 f}+\frac{b \sin ^2(c+d x) (e+f x)^3}{2 a^2 d}+\frac{\left(a^2-b^2\right) \sin ^2(c+d x) (e+f x)^3}{2 a^2 b d}-\frac{\csc (c+d x) (e+f x)^3}{a d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^3}{a^2 b^3 d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^3}{a^2 d}-\frac{\left(a^2-b^2\right) \sin (c+d x) (e+f x)^3}{a b^2 d}-\frac{\sin (c+d x) (e+f x)^3}{a d}-\frac{b (e+f x)^3}{4 a^2 d}-\frac{\left(a^2-b^2\right) (e+f x)^3}{4 a^2 b d}-\frac{6 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)^2}{a d^2}-\frac{3 \left(a^2-b^2\right) f \cos (c+d x) (e+f x)^2}{a b^2 d^2}-\frac{3 f \cos (c+d x) (e+f x)^2}{a d^2}-\frac{3 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d^2}-\frac{3 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d^2}+\frac{3 i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)^2}{2 a^2 d^2}+\frac{3 b f \cos (c+d x) \sin (c+d x) (e+f x)^2}{4 a^2 d^2}+\frac{3 \left(a^2-b^2\right) f \cos (c+d x) \sin (c+d x) (e+f x)^2}{4 a^2 b d^2}-\frac{3 b f^2 \sin ^2(c+d x) (e+f x)}{4 a^2 d^3}-\frac{3 \left(a^2-b^2\right) f^2 \sin ^2(c+d x) (e+f x)}{4 a^2 b d^3}+\frac{6 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right) (e+f x)}{a d^3}-\frac{6 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^3}+\frac{6 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^3}-\frac{3 b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right) (e+f x)}{2 a^2 d^3}+\frac{6 \left(a^2-b^2\right) f^2 \sin (c+d x) (e+f x)}{a b^2 d^3}+\frac{6 f^2 \sin (c+d x) (e+f x)}{a d^3}+\frac{3 b f^3 x}{8 a^2 d^3}+\frac{3 \left(a^2-b^2\right) f^3 x}{8 a^2 b d^3}+\frac{6 \left(a^2-b^2\right) f^3 \cos (c+d x)}{a b^2 d^4}+\frac{6 f^3 \cos (c+d x)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{i (c+d x)}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(3,e^{i (c+d x)}\right)}{a d^4}+\frac{6 i \left(a^2-b^2\right)^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^4}+\frac{6 i \left(a^2-b^2\right)^2 f^3 \text{PolyLog}\left(4,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^4}-\frac{3 i b f^3 \text{PolyLog}\left(4,e^{2 i (c+d x)}\right)}{4 a^2 d^4}-\frac{3 b f^3 \cos (c+d x) \sin (c+d x)}{8 a^2 d^4}-\frac{3 \left(a^2-b^2\right) f^3 \cos (c+d x) \sin (c+d x)}{8 a^2 b d^4}",1,"(3*b*f^3*x)/(8*a^2*d^3) + (3*(a^2 - b^2)*f^3*x)/(8*a^2*b*d^3) - (b*(e + f*x)^3)/(4*a^2*d) - ((a^2 - b^2)*(e + f*x)^3)/(4*a^2*b*d) + ((I/4)*b*(e + f*x)^4)/(a^2*f) - ((I/4)*(a^2 - b^2)^2*(e + f*x)^4)/(a^2*b^3*f) - (6*f*(e + f*x)^2*ArcTanh[E^(I*(c + d*x))])/(a*d^2) + (6*f^3*Cos[c + d*x])/(a*d^4) + (6*(a^2 - b^2)*f^3*Cos[c + d*x])/(a*b^2*d^4) - (3*f*(e + f*x)^2*Cos[c + d*x])/(a*d^2) - (3*(a^2 - b^2)*f*(e + f*x)^2*Cos[c + d*x])/(a*b^2*d^2) - ((e + f*x)^3*Csc[c + d*x])/(a*d) + ((a^2 - b^2)^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d) + ((a^2 - b^2)^2*(e + f*x)^3*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d) - (b*(e + f*x)^3*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) + ((6*I)*f^2*(e + f*x)*PolyLog[2, -E^(I*(c + d*x))])/(a*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[2, E^(I*(c + d*x))])/(a*d^3) - ((3*I)*(a^2 - b^2)^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) - ((3*I)*(a^2 - b^2)^2*f*(e + f*x)^2*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) + (((3*I)/2)*b*f*(e + f*x)^2*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2) - (6*f^3*PolyLog[3, -E^(I*(c + d*x))])/(a*d^4) + (6*f^3*PolyLog[3, E^(I*(c + d*x))])/(a*d^4) + (6*(a^2 - b^2)^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^3) + (6*(a^2 - b^2)^2*f^2*(e + f*x)*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^3) - (3*b*f^2*(e + f*x)*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a^2*d^3) + ((6*I)*(a^2 - b^2)^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^4) + ((6*I)*(a^2 - b^2)^2*f^3*PolyLog[4, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^4) - (((3*I)/4)*b*f^3*PolyLog[4, E^((2*I)*(c + d*x))])/(a^2*d^4) + (6*f^2*(e + f*x)*Sin[c + d*x])/(a*d^3) + (6*(a^2 - b^2)*f^2*(e + f*x)*Sin[c + d*x])/(a*b^2*d^3) - ((e + f*x)^3*Sin[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)^3*Sin[c + d*x])/(a*b^2*d) - (3*b*f^3*Cos[c + d*x]*Sin[c + d*x])/(8*a^2*d^4) - (3*(a^2 - b^2)*f^3*Cos[c + d*x]*Sin[c + d*x])/(8*a^2*b*d^4) + (3*b*f*(e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(4*a^2*d^2) + (3*(a^2 - b^2)*f*(e + f*x)^2*Cos[c + d*x]*Sin[c + d*x])/(4*a^2*b*d^2) - (3*b*f^2*(e + f*x)*Sin[c + d*x]^2)/(4*a^2*d^3) - (3*(a^2 - b^2)*f^2*(e + f*x)*Sin[c + d*x]^2)/(4*a^2*b*d^3) + (b*(e + f*x)^3*Sin[c + d*x]^2)/(2*a^2*d) + ((a^2 - b^2)*(e + f*x)^3*Sin[c + d*x]^2)/(2*a^2*b*d)","A",85,21,36,0.5833,1,"{4543, 4408, 3311, 3296, 2638, 3310, 4410, 4183, 2531, 2282, 6589, 4405, 32, 2635, 8, 4404, 3717, 2190, 6609, 4525, 4519}"
346,1,1051,0,2.2409827,"\int \frac{(e+f x)^2 \cos ^3(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)^2*Cos[c + d*x]^3*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{i \left(a^2-b^2\right)^2 (e+f x)^3}{3 a^2 b^3 f}+\frac{i b (e+f x)^3}{3 a^2 f}+\frac{b \sin ^2(c+d x) (e+f x)^2}{2 a^2 d}+\frac{\left(a^2-b^2\right) \sin ^2(c+d x) (e+f x)^2}{2 a^2 b d}-\frac{\csc (c+d x) (e+f x)^2}{a d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^2}{a^2 d}-\frac{\left(a^2-b^2\right) \sin (c+d x) (e+f x)^2}{a b^2 d}-\frac{\sin (c+d x) (e+f x)^2}{a d}-\frac{4 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 \left(a^2-b^2\right) f \cos (c+d x) (e+f x)}{a b^2 d^2}-\frac{2 f \cos (c+d x) (e+f x)}{a d^2}-\frac{2 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^2}-\frac{2 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)}{a^2 d^2}+\frac{b f \cos (c+d x) \sin (c+d x) (e+f x)}{2 a^2 d^2}+\frac{\left(a^2-b^2\right) f \cos (c+d x) \sin (c+d x) (e+f x)}{2 a^2 b d^2}-\frac{b f^2 x^2}{4 a^2 d}-\frac{\left(a^2-b^2\right) f^2 x^2}{4 a^2 b d}-\frac{b f^2 \sin ^2(c+d x)}{4 a^2 d^3}-\frac{\left(a^2-b^2\right) f^2 \sin ^2(c+d x)}{4 a^2 b d^3}-\frac{b e f x}{2 a^2 d}-\frac{\left(a^2-b^2\right) e f x}{2 a^2 b d}+\frac{2 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^3}+\frac{2 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^3}+\frac{2 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^3}-\frac{b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a^2 d^3}+\frac{2 \left(a^2-b^2\right) f^2 \sin (c+d x)}{a b^2 d^3}+\frac{2 f^2 \sin (c+d x)}{a d^3}","-\frac{i \left(a^2-b^2\right)^2 (e+f x)^3}{3 a^2 b^3 f}+\frac{i b (e+f x)^3}{3 a^2 f}+\frac{b \sin ^2(c+d x) (e+f x)^2}{2 a^2 d}+\frac{\left(a^2-b^2\right) \sin ^2(c+d x) (e+f x)^2}{2 a^2 b d}-\frac{\csc (c+d x) (e+f x)^2}{a d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 \log \left(1-\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)^2}{a^2 b^3 d}-\frac{b \log \left(1-e^{2 i (c+d x)}\right) (e+f x)^2}{a^2 d}-\frac{\left(a^2-b^2\right) \sin (c+d x) (e+f x)^2}{a b^2 d}-\frac{\sin (c+d x) (e+f x)^2}{a d}-\frac{4 f \tanh ^{-1}\left(e^{i (c+d x)}\right) (e+f x)}{a d^2}-\frac{2 \left(a^2-b^2\right) f \cos (c+d x) (e+f x)}{a b^2 d^2}-\frac{2 f \cos (c+d x) (e+f x)}{a d^2}-\frac{2 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^2}-\frac{2 i \left(a^2-b^2\right)^2 f \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right) (e+f x)}{a^2 b^3 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right) (e+f x)}{a^2 d^2}+\frac{b f \cos (c+d x) \sin (c+d x) (e+f x)}{2 a^2 d^2}+\frac{\left(a^2-b^2\right) f \cos (c+d x) \sin (c+d x) (e+f x)}{2 a^2 b d^2}-\frac{b f^2 x^2}{4 a^2 d}-\frac{\left(a^2-b^2\right) f^2 x^2}{4 a^2 b d}-\frac{b f^2 \sin ^2(c+d x)}{4 a^2 d^3}-\frac{\left(a^2-b^2\right) f^2 \sin ^2(c+d x)}{4 a^2 b d^3}-\frac{b e f x}{2 a^2 d}-\frac{\left(a^2-b^2\right) e f x}{2 a^2 b d}+\frac{2 i f^2 \text{PolyLog}\left(2,-e^{i (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,e^{i (c+d x)}\right)}{a d^3}+\frac{2 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^3}+\frac{2 \left(a^2-b^2\right)^2 f^2 \text{PolyLog}\left(3,\frac{i b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^3}-\frac{b f^2 \text{PolyLog}\left(3,e^{2 i (c+d x)}\right)}{2 a^2 d^3}+\frac{2 \left(a^2-b^2\right) f^2 \sin (c+d x)}{a b^2 d^3}+\frac{2 f^2 \sin (c+d x)}{a d^3}",1,"-(b*e*f*x)/(2*a^2*d) - ((a^2 - b^2)*e*f*x)/(2*a^2*b*d) - (b*f^2*x^2)/(4*a^2*d) - ((a^2 - b^2)*f^2*x^2)/(4*a^2*b*d) + ((I/3)*b*(e + f*x)^3)/(a^2*f) - ((I/3)*(a^2 - b^2)^2*(e + f*x)^3)/(a^2*b^3*f) - (4*f*(e + f*x)*ArcTanh[E^(I*(c + d*x))])/(a*d^2) - (2*f*(e + f*x)*Cos[c + d*x])/(a*d^2) - (2*(a^2 - b^2)*f*(e + f*x)*Cos[c + d*x])/(a*b^2*d^2) - ((e + f*x)^2*Csc[c + d*x])/(a*d) + ((a^2 - b^2)^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d) + ((a^2 - b^2)^2*(e + f*x)^2*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d) - (b*(e + f*x)^2*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) + ((2*I)*f^2*PolyLog[2, -E^(I*(c + d*x))])/(a*d^3) - ((2*I)*f^2*PolyLog[2, E^(I*(c + d*x))])/(a*d^3) - ((2*I)*(a^2 - b^2)^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) - ((2*I)*(a^2 - b^2)^2*f*(e + f*x)*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) + (I*b*f*(e + f*x)*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2) + (2*(a^2 - b^2)^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^3) + (2*(a^2 - b^2)^2*f^2*PolyLog[3, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^3) - (b*f^2*PolyLog[3, E^((2*I)*(c + d*x))])/(2*a^2*d^3) + (2*f^2*Sin[c + d*x])/(a*d^3) + (2*(a^2 - b^2)*f^2*Sin[c + d*x])/(a*b^2*d^3) - ((e + f*x)^2*Sin[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)^2*Sin[c + d*x])/(a*b^2*d) + (b*f*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*a^2*d^2) + ((a^2 - b^2)*f*(e + f*x)*Cos[c + d*x]*Sin[c + d*x])/(2*a^2*b*d^2) - (b*f^2*Sin[c + d*x]^2)/(4*a^2*d^3) - ((a^2 - b^2)*f^2*Sin[c + d*x]^2)/(4*a^2*b*d^3) + (b*(e + f*x)^2*Sin[c + d*x]^2)/(2*a^2*d) + ((a^2 - b^2)*(e + f*x)^2*Sin[c + d*x]^2)/(2*a^2*b*d)","A",60,20,36,0.5556,1,"{4543, 4408, 3311, 3296, 2637, 2633, 4410, 4183, 2279, 2391, 4405, 3310, 4404, 3717, 2190, 2531, 2282, 6589, 4525, 4519}"
347,1,641,0,1.2252826,"\int \frac{(e+f x) \cos ^3(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[((e + f*x)*Cos[c + d*x]^3*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","-\frac{i f \left(a^2-b^2\right)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^2}-\frac{i f \left(a^2-b^2\right)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^3 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a^2 d^2}-\frac{f \left(a^2-b^2\right) \cos (c+d x)}{a b^2 d^2}+\frac{f \left(a^2-b^2\right) \sin (c+d x) \cos (c+d x)}{4 a^2 b d^2}+\frac{\left(a^2-b^2\right)^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^3 d}+\frac{\left(a^2-b^2\right) (e+f x) \sin ^2(c+d x)}{2 a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x) \sin (c+d x)}{a b^2 d}-\frac{f x \left(a^2-b^2\right)}{4 a^2 b d}-\frac{i \left(a^2-b^2\right)^2 (e+f x)^2}{2 a^2 b^3 f}+\frac{b f \sin (c+d x) \cos (c+d x)}{4 a^2 d^2}-\frac{b (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{b (e+f x) \sin ^2(c+d x)}{2 a^2 d}-\frac{b f x}{4 a^2 d}+\frac{i b (e+f x)^2}{2 a^2 f}-\frac{f \cos (c+d x)}{a d^2}-\frac{f \tanh ^{-1}(\cos (c+d x))}{a d^2}-\frac{(e+f x) \sin (c+d x)}{a d}-\frac{(e+f x) \csc (c+d x)}{a d}","-\frac{i f \left(a^2-b^2\right)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d^2}-\frac{i f \left(a^2-b^2\right)^2 \text{PolyLog}\left(2,\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^3 d^2}+\frac{i b f \text{PolyLog}\left(2,e^{2 i (c+d x)}\right)}{2 a^2 d^2}-\frac{f \left(a^2-b^2\right) \cos (c+d x)}{a b^2 d^2}+\frac{f \left(a^2-b^2\right) \sin (c+d x) \cos (c+d x)}{4 a^2 b d^2}+\frac{\left(a^2-b^2\right)^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{a^2 b^3 d}+\frac{\left(a^2-b^2\right)^2 (e+f x) \log \left(1-\frac{i b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{a^2 b^3 d}+\frac{\left(a^2-b^2\right) (e+f x) \sin ^2(c+d x)}{2 a^2 b d}-\frac{\left(a^2-b^2\right) (e+f x) \sin (c+d x)}{a b^2 d}-\frac{f x \left(a^2-b^2\right)}{4 a^2 b d}-\frac{i \left(a^2-b^2\right)^2 (e+f x)^2}{2 a^2 b^3 f}+\frac{b f \sin (c+d x) \cos (c+d x)}{4 a^2 d^2}-\frac{b (e+f x) \log \left(1-e^{2 i (c+d x)}\right)}{a^2 d}+\frac{b (e+f x) \sin ^2(c+d x)}{2 a^2 d}-\frac{b f x}{4 a^2 d}+\frac{i b (e+f x)^2}{2 a^2 f}-\frac{f \cos (c+d x)}{a d^2}-\frac{f \tanh ^{-1}(\cos (c+d x))}{a d^2}-\frac{(e+f x) \sin (c+d x)}{a d}-\frac{(e+f x) \csc (c+d x)}{a d}",1,"-(b*f*x)/(4*a^2*d) - ((a^2 - b^2)*f*x)/(4*a^2*b*d) + ((I/2)*b*(e + f*x)^2)/(a^2*f) - ((I/2)*(a^2 - b^2)^2*(e + f*x)^2)/(a^2*b^3*f) - (f*ArcTanh[Cos[c + d*x]])/(a*d^2) - (f*Cos[c + d*x])/(a*d^2) - ((a^2 - b^2)*f*Cos[c + d*x])/(a*b^2*d^2) - ((e + f*x)*Csc[c + d*x])/(a*d) + ((a^2 - b^2)^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d) + ((a^2 - b^2)^2*(e + f*x)*Log[1 - (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d) - (b*(e + f*x)*Log[1 - E^((2*I)*(c + d*x))])/(a^2*d) - (I*(a^2 - b^2)^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) - (I*(a^2 - b^2)^2*f*PolyLog[2, (I*b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(a^2*b^3*d^2) + ((I/2)*b*f*PolyLog[2, E^((2*I)*(c + d*x))])/(a^2*d^2) - ((e + f*x)*Sin[c + d*x])/(a*d) - ((a^2 - b^2)*(e + f*x)*Sin[c + d*x])/(a*b^2*d) + (b*f*Cos[c + d*x]*Sin[c + d*x])/(4*a^2*d^2) + ((a^2 - b^2)*f*Cos[c + d*x]*Sin[c + d*x])/(4*a^2*b*d^2) + (b*(e + f*x)*Sin[c + d*x]^2)/(2*a^2*d) + ((a^2 - b^2)*(e + f*x)*Sin[c + d*x]^2)/(2*a^2*b*d)","A",45,17,34,0.5000,1,"{4543, 4408, 3310, 3296, 2638, 4410, 3770, 4405, 2635, 8, 4404, 3717, 2190, 2279, 2391, 4525, 4519}"
348,1,96,0,0.1550758,"\int \frac{\cos ^3(c+d x) \cot ^2(c+d x)}{a+b \sin (c+d x)} \, dx","Int[(Cos[c + d*x]^3*Cot[c + d*x]^2)/(a + b*Sin[c + d*x]),x]","\frac{\left(a^2-b^2\right)^2 \log (a+b \sin (c+d x))}{a^2 b^3 d}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{a \sin (c+d x)}{b^2 d}-\frac{\csc (c+d x)}{a d}+\frac{\sin ^2(c+d x)}{2 b d}","\frac{\left(a^2-b^2\right)^2 \log (a+b \sin (c+d x))}{a^2 b^3 d}-\frac{b \log (\sin (c+d x))}{a^2 d}-\frac{a \sin (c+d x)}{b^2 d}-\frac{\csc (c+d x)}{a d}+\frac{\sin ^2(c+d x)}{2 b d}",1,"-(Csc[c + d*x]/(a*d)) - (b*Log[Sin[c + d*x]])/(a^2*d) + ((a^2 - b^2)^2*Log[a + b*Sin[c + d*x]])/(a^2*b^3*d) - (a*Sin[c + d*x])/(b^2*d) + Sin[c + d*x]^2/(2*b*d)","A",4,3,29,0.1034,1,"{2837, 12, 894}"