1,1,137,0,0.1555457,"\int (c+d x)^m \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{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{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{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{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}",1,"-((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)) - (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",5,4,20,0.2000,1,"{4406, 12, 3308, 2181}"
2,1,156,0,0.1069976,"\int (c+d x)^4 \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{3 d^2 (c+d x)^2 \sin ^2(a+b x)}{2 b^3}-\frac{3 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^4}+\frac{d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}+\frac{3 d^4 \sin ^2(a+b x)}{4 b^5}+\frac{(c+d x)^4 \sin ^2(a+b x)}{2 b}+\frac{3 c d^3 x}{2 b^3}+\frac{3 d^4 x^2}{4 b^3}-\frac{(c+d x)^4}{4 b}","-\frac{3 d^2 (c+d x)^2 \sin ^2(a+b x)}{2 b^3}-\frac{3 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^4}+\frac{d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}+\frac{3 d^4 \sin ^2(a+b x)}{4 b^5}+\frac{(c+d x)^4 \sin ^2(a+b x)}{2 b}+\frac{3 c d^3 x}{2 b^3}+\frac{3 d^4 x^2}{4 b^3}-\frac{(c+d x)^4}{4 b}",1,"(3*c*d^3*x)/(2*b^3) + (3*d^4*x^2)/(4*b^3) - (c + d*x)^4/(4*b) - (3*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b^4) + (d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/b^2 + (3*d^4*Sin[a + b*x]^2)/(4*b^5) - (3*d^2*(c + d*x)^2*Sin[a + b*x]^2)/(2*b^3) + ((c + d*x)^4*Sin[a + b*x]^2)/(2*b)","A",5,4,20,0.2000,1,"{4404, 3311, 32, 3310}"
3,1,120,0,0.0834477,"\int (c+d x)^3 \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}-\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}+\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}+\frac{3 d^3 x}{8 b^3}-\frac{(c+d x)^3}{4 b}","-\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}-\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}+\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}+\frac{3 d^3 x}{8 b^3}-\frac{(c+d x)^3}{4 b}",1,"(3*d^3*x)/(8*b^3) - (c + d*x)^3/(4*b) - (3*d^3*Cos[a + b*x]*Sin[a + b*x])/(8*b^4) + (3*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) - (3*d^2*(c + d*x)*Sin[a + b*x]^2)/(4*b^3) + ((c + d*x)^3*Sin[a + b*x]^2)/(2*b)","A",5,5,20,0.2500,1,"{4404, 3311, 32, 2635, 8}"
4,1,89,0,0.0541044,"\int (c+d x)^2 \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x],x]","\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}-\frac{d^2 \sin ^2(a+b x)}{4 b^3}+\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}-\frac{c d x}{2 b}-\frac{d^2 x^2}{4 b}","\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}-\frac{d^2 \sin ^2(a+b x)}{4 b^3}+\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}-\frac{c d x}{2 b}-\frac{d^2 x^2}{4 b}",1,"-(c*d*x)/(2*b) - (d^2*x^2)/(4*b) + (d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b^2) - (d^2*Sin[a + b*x]^2)/(4*b^3) + ((c + d*x)^2*Sin[a + b*x]^2)/(2*b)","A",3,2,20,0.1000,1,"{4404, 3310}"
5,1,50,0,0.0259538,"\int (c+d x) \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]*Sin[a + b*x],x]","\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{(c+d x) \sin ^2(a+b x)}{2 b}-\frac{d x}{4 b}","\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{(c+d x) \sin ^2(a+b x)}{2 b}-\frac{d x}{4 b}",1,"-(d*x)/(4*b) + (d*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) + ((c + d*x)*Sin[a + b*x]^2)/(2*b)","A",3,3,18,0.1667,1,"{4404, 2635, 8}"
6,1,65,0,0.139341,"\int \frac{\cos (a+b x) \sin (a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x])/(c + d*x),x]","\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}","\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}",1,"(CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(2*d) + (Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d)","A",5,5,20,0.2500,1,"{4406, 12, 3303, 3299, 3302}"
7,1,85,0,0.1488342,"\int \frac{\cos (a+b x) \sin (a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x])/(c + d*x)^2,x]","\frac{b \cos \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 \sin \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+2 b x)}{2 d (c+d x)}","\frac{b \cos \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 \sin \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+2 b x)}{2 d (c+d x)}",1,"(b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^2 - Sin[2*a + 2*b*x]/(2*d*(c + d*x)) - (b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2","A",6,6,20,0.3000,1,"{4406, 12, 3297, 3303, 3299, 3302}"
8,1,114,0,0.1745153,"\int \frac{\cos (a+b x) \sin (a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x])/(c + d*x)^3,x]","-\frac{b^2 \sin \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 \cos \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 \cos (2 a+2 b x)}{2 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)^2}","-\frac{b^2 \sin \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 \cos \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 \cos (2 a+2 b x)}{2 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)^2}",1,"-(b*Cos[2*a + 2*b*x])/(2*d^2*(c + d*x)) - (b^2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/d^3 - Sin[2*a + 2*b*x]/(4*d*(c + d*x)^2) - (b^2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^3","A",7,6,20,0.3000,1,"{4406, 12, 3297, 3303, 3299, 3302}"
9,1,144,0,0.1976549,"\int \frac{\cos (a+b x) \sin (a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x])/(c + d*x)^4,x]","-\frac{2 b^3 \cos \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 \sin \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{b^2 \sin (2 a+2 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{6 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{6 d (c+d x)^3}","-\frac{2 b^3 \cos \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 \sin \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{b^2 \sin (2 a+2 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{6 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{6 d (c+d x)^3}",1,"-(b*Cos[2*a + 2*b*x])/(6*d^2*(c + d*x)^2) - (2*b^3*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(3*d^4) - Sin[2*a + 2*b*x]/(6*d*(c + d*x)^3) + (b^2*Sin[2*a + 2*b*x])/(3*d^3*(c + d*x)) + (2*b^3*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(3*d^4)","A",8,6,20,0.3000,1,"{4406, 12, 3297, 3303, 3299, 3302}"
10,1,8,0,0.0285319,"\int \frac{\cos (x) \sin (x)}{x} \, dx","Int[(Cos[x]*Sin[x])/x,x]","\frac{\text{Si}(2 x)}{2}","\frac{\text{Si}(2 x)}{2}",1,"SinIntegral[2*x]/2","A",3,3,8,0.3750,1,"{4406, 12, 3299}"
11,1,16,0,0.0457541,"\int \frac{\cos (x) \sin (x)}{x^2} \, dx","Int[(Cos[x]*Sin[x])/x^2,x]","\text{CosIntegral}(2 x)-\frac{\sin (2 x)}{2 x}","\text{CosIntegral}(2 x)-\frac{\sin (2 x)}{2 x}",1,"CosIntegral[2*x] - Sin[2*x]/(2*x)","A",4,4,8,0.5000,1,"{4406, 12, 3297, 3302}"
12,1,29,0,0.0589954,"\int \frac{\cos (x) \sin (x)}{x^3} \, dx","Int[(Cos[x]*Sin[x])/x^3,x]","-\text{Si}(2 x)-\frac{\sin (2 x)}{4 x^2}-\frac{\cos (2 x)}{2 x}","-\text{Si}(2 x)-\frac{\sin (2 x)}{4 x^2}-\frac{\cos (2 x)}{2 x}",1,"-Cos[2*x]/(2*x) - Sin[2*x]/(4*x^2) - SinIntegral[2*x]","A",5,4,8,0.5000,1,"{4406, 12, 3297, 3299}"
13,1,275,0,0.3299399,"\int (c+d x)^m \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{i 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{i 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{i 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{i 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{i 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{i 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{i 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{i 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,"((-I/8)*E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) + ((I/8)*(c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + ((I/8)*3^(-1 - m)*E^((3*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-3*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - ((I/8)*3^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((3*I)*b*(c + d*x))/d])/(b*E^((3*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",8,3,22,0.1364,1,"{4406, 3307, 2181}"
14,1,205,0,0.1997159,"\int (c+d x)^4 \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{4 d^2 (c+d x)^2 \sin ^3(a+b x)}{9 b^3}-\frac{8 d^2 (c+d x)^2 \sin (a+b x)}{3 b^3}-\frac{160 d^3 (c+d x) \cos (a+b x)}{27 b^4}-\frac{8 d^3 (c+d x) \sin ^2(a+b x) \cos (a+b x)}{27 b^4}+\frac{8 d (c+d x)^3 \cos (a+b x)}{9 b^2}+\frac{4 d (c+d x)^3 \sin ^2(a+b x) \cos (a+b x)}{9 b^2}+\frac{8 d^4 \sin ^3(a+b x)}{81 b^5}+\frac{160 d^4 \sin (a+b x)}{27 b^5}+\frac{(c+d x)^4 \sin ^3(a+b x)}{3 b}","-\frac{4 d^2 (c+d x)^2 \sin ^3(a+b x)}{9 b^3}-\frac{8 d^2 (c+d x)^2 \sin (a+b x)}{3 b^3}-\frac{160 d^3 (c+d x) \cos (a+b x)}{27 b^4}-\frac{8 d^3 (c+d x) \sin ^2(a+b x) \cos (a+b x)}{27 b^4}+\frac{8 d (c+d x)^3 \cos (a+b x)}{9 b^2}+\frac{4 d (c+d x)^3 \sin ^2(a+b x) \cos (a+b x)}{9 b^2}+\frac{8 d^4 \sin ^3(a+b x)}{81 b^5}+\frac{160 d^4 \sin (a+b x)}{27 b^5}+\frac{(c+d x)^4 \sin ^3(a+b x)}{3 b}",1,"(-160*d^3*(c + d*x)*Cos[a + b*x])/(27*b^4) + (8*d*(c + d*x)^3*Cos[a + b*x])/(9*b^2) + (160*d^4*Sin[a + b*x])/(27*b^5) - (8*d^2*(c + d*x)^2*Sin[a + b*x])/(3*b^3) - (8*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^2)/(27*b^4) + (4*d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x]^2)/(9*b^2) + (8*d^4*Sin[a + b*x]^3)/(81*b^5) - (4*d^2*(c + d*x)^2*Sin[a + b*x]^3)/(9*b^3) + ((c + d*x)^4*Sin[a + b*x]^3)/(3*b)","A",9,5,22,0.2273,1,"{4404, 3311, 3296, 2637, 3310}"
15,1,151,0,0.1345775,"\int (c+d x)^3 \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{2 d^2 (c+d x) \sin ^3(a+b x)}{9 b^3}-\frac{4 d^2 (c+d x) \sin (a+b x)}{3 b^3}+\frac{2 d (c+d x)^2 \cos (a+b x)}{3 b^2}+\frac{d (c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{3 b^2}+\frac{2 d^3 \cos ^3(a+b x)}{27 b^4}-\frac{14 d^3 \cos (a+b x)}{9 b^4}+\frac{(c+d x)^3 \sin ^3(a+b x)}{3 b}","-\frac{2 d^2 (c+d x) \sin ^3(a+b x)}{9 b^3}-\frac{4 d^2 (c+d x) \sin (a+b x)}{3 b^3}+\frac{2 d (c+d x)^2 \cos (a+b x)}{3 b^2}+\frac{d (c+d x)^2 \sin ^2(a+b x) \cos (a+b x)}{3 b^2}+\frac{2 d^3 \cos ^3(a+b x)}{27 b^4}-\frac{14 d^3 \cos (a+b x)}{9 b^4}+\frac{(c+d x)^3 \sin ^3(a+b x)}{3 b}",1,"(-14*d^3*Cos[a + b*x])/(9*b^4) + (2*d*(c + d*x)^2*Cos[a + b*x])/(3*b^2) + (2*d^3*Cos[a + b*x]^3)/(27*b^4) - (4*d^2*(c + d*x)*Sin[a + b*x])/(3*b^3) + (d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^2)/(3*b^2) - (2*d^2*(c + d*x)*Sin[a + b*x]^3)/(9*b^3) + ((c + d*x)^3*Sin[a + b*x]^3)/(3*b)","A",7,5,22,0.2273,1,"{4404, 3311, 3296, 2638, 2633}"
16,1,103,0,0.0772006,"\int (c+d x)^2 \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^2,x]","\frac{4 d (c+d x) \cos (a+b x)}{9 b^2}+\frac{2 d (c+d x) \sin ^2(a+b x) \cos (a+b x)}{9 b^2}-\frac{2 d^2 \sin ^3(a+b x)}{27 b^3}-\frac{4 d^2 \sin (a+b x)}{9 b^3}+\frac{(c+d x)^2 \sin ^3(a+b x)}{3 b}","\frac{4 d (c+d x) \cos (a+b x)}{9 b^2}+\frac{2 d (c+d x) \sin ^2(a+b x) \cos (a+b x)}{9 b^2}-\frac{2 d^2 \sin ^3(a+b x)}{27 b^3}-\frac{4 d^2 \sin (a+b x)}{9 b^3}+\frac{(c+d x)^2 \sin ^3(a+b x)}{3 b}",1,"(4*d*(c + d*x)*Cos[a + b*x])/(9*b^2) - (4*d^2*Sin[a + b*x])/(9*b^3) + (2*d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^2)/(9*b^2) - (2*d^2*Sin[a + b*x]^3)/(27*b^3) + ((c + d*x)^2*Sin[a + b*x]^3)/(3*b)","A",4,4,22,0.1818,1,"{4404, 3310, 3296, 2637}"
17,1,51,0,0.0332234,"\int (c+d x) \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{d \cos ^3(a+b x)}{9 b^2}+\frac{d \cos (a+b x)}{3 b^2}+\frac{(c+d x) \sin ^3(a+b x)}{3 b}","-\frac{d \cos ^3(a+b x)}{9 b^2}+\frac{d \cos (a+b x)}{3 b^2}+\frac{(c+d x) \sin ^3(a+b x)}{3 b}",1,"(d*Cos[a + b*x])/(3*b^2) - (d*Cos[a + b*x]^3)/(9*b^2) + ((c + d*x)*Sin[a + b*x]^3)/(3*b)","A",3,2,20,0.1000,1,"{4404, 2633}"
18,1,121,0,0.2699302,"\int \frac{\cos (a+b x) \sin ^2(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^2)/(c + d*x),x]","\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}-\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}","\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}-\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}",1,"(Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(4*d) - (Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(4*d) - (Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(4*d) + (Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(4*d)","A",8,4,22,0.1818,1,"{4406, 3303, 3299, 3302}"
19,1,168,0,0.301291,"\int \frac{\cos (a+b x) \sin ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^2)/(c + d*x)^2,x]","\frac{3 b \sin \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{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d^2}-\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\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{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\cos (a+b x)}{4 d (c+d x)}+\frac{\cos (3 a+3 b x)}{4 d (c+d x)}","\frac{3 b \sin \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{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d^2}-\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\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{Si}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\cos (a+b x)}{4 d (c+d x)}+\frac{\cos (3 a+3 b x)}{4 d (c+d x)}",1,"-Cos[a + b*x]/(4*d*(c + d*x)) + Cos[3*a + 3*b*x]/(4*d*(c + d*x)) + (3*b*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(4*d^2) - (b*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(4*d^2) - (b*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(4*d^2) + (3*b*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(4*d^2)","A",10,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
20,1,221,0,0.3581559,"\int \frac{\cos (a+b x) \sin ^2(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^2)/(c + d*x)^3,x]","-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\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{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{9 b^2 \sin \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{b \sin (a+b x)}{8 d^2 (c+d x)}-\frac{3 b \sin (3 a+3 b x)}{8 d^2 (c+d x)}-\frac{\cos (a+b x)}{8 d (c+d x)^2}+\frac{\cos (3 a+3 b x)}{8 d (c+d x)^2}","-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\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{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{9 b^2 \sin \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{b \sin (a+b x)}{8 d^2 (c+d x)}-\frac{3 b \sin (3 a+3 b x)}{8 d^2 (c+d x)}-\frac{\cos (a+b x)}{8 d (c+d x)^2}+\frac{\cos (3 a+3 b x)}{8 d (c+d x)^2}",1,"-Cos[a + b*x]/(8*d*(c + d*x)^2) + Cos[3*a + 3*b*x]/(8*d*(c + d*x)^2) - (b^2*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(8*d^3) + (9*b^2*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(8*d^3) + (b*Sin[a + b*x])/(8*d^2*(c + d*x)) - (3*b*Sin[3*a + 3*b*x])/(8*d^2*(c + d*x)) + (b^2*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d^3) - (9*b^2*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(8*d^3)","A",12,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
21,1,270,0,0.4195715,"\int \frac{\cos (a+b x) \sin ^2(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^2)/(c + d*x)^4,x]","-\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{24 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{24 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^2 \cos (a+b x)}{24 d^3 (c+d x)}-\frac{3 b^2 \cos (3 a+3 b x)}{8 d^3 (c+d x)}+\frac{b \sin (a+b x)}{24 d^2 (c+d x)^2}-\frac{b \sin (3 a+3 b x)}{8 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{12 d (c+d x)^3}+\frac{\cos (3 a+3 b x)}{12 d (c+d x)^3}","-\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{24 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{24 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^2 \cos (a+b x)}{24 d^3 (c+d x)}-\frac{3 b^2 \cos (3 a+3 b x)}{8 d^3 (c+d x)}+\frac{b \sin (a+b x)}{24 d^2 (c+d x)^2}-\frac{b \sin (3 a+3 b x)}{8 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{12 d (c+d x)^3}+\frac{\cos (3 a+3 b x)}{12 d (c+d x)^3}",1,"-Cos[a + b*x]/(12*d*(c + d*x)^3) + (b^2*Cos[a + b*x])/(24*d^3*(c + d*x)) + Cos[3*a + 3*b*x]/(12*d*(c + d*x)^3) - (3*b^2*Cos[3*a + 3*b*x])/(8*d^3*(c + d*x)) - (9*b^3*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(8*d^4) + (b^3*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(24*d^4) + (b*Sin[a + b*x])/(24*d^2*(c + d*x)^2) - (b*Sin[3*a + 3*b*x])/(8*d^2*(c + d*x)^2) + (b^3*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(24*d^4) - (9*b^3*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(8*d^4)","A",14,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
22,1,271,0,0.3310495,"\int (c+d x)^m \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]*Sin[a + b*x]^3,x]","-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}","-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}",1,"-((2^(-4 - 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)) - (2^(-4 - 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) + (E^((4*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*(((-I)*b*(c + d*x))/d)^m) + ((c + d*x)^m*Gamma[1 + m, ((4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*E^((4*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",8,3,22,0.1364,1,"{4406, 3308, 2181}"
23,1,260,0,0.2411044,"\int (c+d x)^4 \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]*Sin[a + b*x]^3,x]","-\frac{3 d^2 (c+d x)^2 \sin ^4(a+b x)}{16 b^3}-\frac{9 d^2 (c+d x)^2 \sin ^2(a+b x)}{16 b^3}-\frac{3 d^3 (c+d x) \sin ^3(a+b x) \cos (a+b x)}{32 b^4}-\frac{45 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{64 b^4}+\frac{d (c+d x)^3 \sin ^3(a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{8 b^2}+\frac{3 d^4 \sin ^4(a+b x)}{128 b^5}+\frac{45 d^4 \sin ^2(a+b x)}{128 b^5}+\frac{(c+d x)^4 \sin ^4(a+b x)}{4 b}+\frac{45 c d^3 x}{64 b^3}+\frac{45 d^4 x^2}{128 b^3}-\frac{3 (c+d x)^4}{32 b}","-\frac{3 d^2 (c+d x)^2 \sin ^4(a+b x)}{16 b^3}-\frac{9 d^2 (c+d x)^2 \sin ^2(a+b x)}{16 b^3}-\frac{3 d^3 (c+d x) \sin ^3(a+b x) \cos (a+b x)}{32 b^4}-\frac{45 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{64 b^4}+\frac{d (c+d x)^3 \sin ^3(a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{8 b^2}+\frac{3 d^4 \sin ^4(a+b x)}{128 b^5}+\frac{45 d^4 \sin ^2(a+b x)}{128 b^5}+\frac{(c+d x)^4 \sin ^4(a+b x)}{4 b}+\frac{45 c d^3 x}{64 b^3}+\frac{45 d^4 x^2}{128 b^3}-\frac{3 (c+d x)^4}{32 b}",1,"(45*c*d^3*x)/(64*b^3) + (45*d^4*x^2)/(128*b^3) - (3*(c + d*x)^4)/(32*b) - (45*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(64*b^4) + (3*d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/(8*b^2) + (45*d^4*Sin[a + b*x]^2)/(128*b^5) - (9*d^2*(c + d*x)^2*Sin[a + b*x]^2)/(16*b^3) - (3*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^3)/(32*b^4) + (d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x]^3)/(4*b^2) + (3*d^4*Sin[a + b*x]^4)/(128*b^5) - (3*d^2*(c + d*x)^2*Sin[a + b*x]^4)/(16*b^3) + ((c + d*x)^4*Sin[a + b*x]^4)/(4*b)","A",9,4,22,0.1818,1,"{4404, 3311, 32, 3310}"
24,1,196,0,0.1654019,"\int (c+d x)^3 \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \sin ^4(a+b x)}{32 b^3}-\frac{9 d^2 (c+d x) \sin ^2(a+b x)}{32 b^3}+\frac{3 d (c+d x)^2 \sin ^3(a+b x) \cos (a+b x)}{16 b^2}+\frac{9 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{3 d^3 \sin ^3(a+b x) \cos (a+b x)}{128 b^4}-\frac{45 d^3 \sin (a+b x) \cos (a+b x)}{256 b^4}+\frac{(c+d x)^3 \sin ^4(a+b x)}{4 b}+\frac{45 d^3 x}{256 b^3}-\frac{3 (c+d x)^3}{32 b}","-\frac{3 d^2 (c+d x) \sin ^4(a+b x)}{32 b^3}-\frac{9 d^2 (c+d x) \sin ^2(a+b x)}{32 b^3}+\frac{3 d (c+d x)^2 \sin ^3(a+b x) \cos (a+b x)}{16 b^2}+\frac{9 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{3 d^3 \sin ^3(a+b x) \cos (a+b x)}{128 b^4}-\frac{45 d^3 \sin (a+b x) \cos (a+b x)}{256 b^4}+\frac{(c+d x)^3 \sin ^4(a+b x)}{4 b}+\frac{45 d^3 x}{256 b^3}-\frac{3 (c+d x)^3}{32 b}",1,"(45*d^3*x)/(256*b^3) - (3*(c + d*x)^3)/(32*b) - (45*d^3*Cos[a + b*x]*Sin[a + b*x])/(256*b^4) + (9*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(32*b^2) - (9*d^2*(c + d*x)*Sin[a + b*x]^2)/(32*b^3) - (3*d^3*Cos[a + b*x]*Sin[a + b*x]^3)/(128*b^4) + (3*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^3)/(16*b^2) - (3*d^2*(c + d*x)*Sin[a + b*x]^4)/(32*b^3) + ((c + d*x)^3*Sin[a + b*x]^4)/(4*b)","A",9,5,22,0.2273,1,"{4404, 3311, 32, 2635, 8}"
25,1,134,0,0.0924045,"\int (c+d x)^2 \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{d (c+d x) \sin ^3(a+b x) \cos (a+b x)}{8 b^2}+\frac{3 d (c+d x) \sin (a+b x) \cos (a+b x)}{16 b^2}-\frac{d^2 \sin ^4(a+b x)}{32 b^3}-\frac{3 d^2 \sin ^2(a+b x)}{32 b^3}+\frac{(c+d x)^2 \sin ^4(a+b x)}{4 b}-\frac{3 c d x}{16 b}-\frac{3 d^2 x^2}{32 b}","\frac{d (c+d x) \sin ^3(a+b x) \cos (a+b x)}{8 b^2}+\frac{3 d (c+d x) \sin (a+b x) \cos (a+b x)}{16 b^2}-\frac{d^2 \sin ^4(a+b x)}{32 b^3}-\frac{3 d^2 \sin ^2(a+b x)}{32 b^3}+\frac{(c+d x)^2 \sin ^4(a+b x)}{4 b}-\frac{3 c d x}{16 b}-\frac{3 d^2 x^2}{32 b}",1,"(-3*c*d*x)/(16*b) - (3*d^2*x^2)/(32*b) + (3*d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(16*b^2) - (3*d^2*Sin[a + b*x]^2)/(32*b^3) + (d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^3)/(8*b^2) - (d^2*Sin[a + b*x]^4)/(32*b^3) + ((c + d*x)^2*Sin[a + b*x]^4)/(4*b)","A",4,2,22,0.09091,1,"{4404, 3310}"
26,1,72,0,0.04547,"\int (c+d x) \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{d \sin ^3(a+b x) \cos (a+b x)}{16 b^2}+\frac{3 d \sin (a+b x) \cos (a+b x)}{32 b^2}+\frac{(c+d x) \sin ^4(a+b x)}{4 b}-\frac{3 d x}{32 b}","\frac{d \sin ^3(a+b x) \cos (a+b x)}{16 b^2}+\frac{3 d \sin (a+b x) \cos (a+b x)}{32 b^2}+\frac{(c+d x) \sin ^4(a+b x)}{4 b}-\frac{3 d x}{32 b}",1,"(-3*d*x)/(32*b) + (3*d*Cos[a + b*x]*Sin[a + b*x])/(32*b^2) + (d*Cos[a + b*x]*Sin[a + b*x]^3)/(16*b^2) + ((c + d*x)*Sin[a + b*x]^4)/(4*b)","A",4,3,20,0.1500,1,"{4404, 2635, 8}"
27,1,129,0,0.2324363,"\int \frac{\cos (a+b x) \sin ^3(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^3)/(c + d*x),x]","-\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}-\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}","-\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}-\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}",1,"-(CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/(8*d) + (CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(4*d) + (Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(4*d) - (Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(8*d)","A",8,4,22,0.1818,1,"{4406, 3303, 3299, 3302}"
28,1,179,0,0.2802559,"\int \frac{\cos (a+b x) \sin ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^3)/(c + d*x)^2,x]","\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}-\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}+\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)}+\frac{\sin (4 a+4 b x)}{8 d (c+d x)}","\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}-\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}+\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)}+\frac{\sin (4 a+4 b x)}{8 d (c+d x)}",1,"(b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(2*d^2) - (b*Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/(2*d^2) - Sin[2*a + 2*b*x]/(4*d*(c + d*x)) + Sin[4*a + 4*b*x]/(8*d*(c + d*x)) - (b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d^2) + (b*Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(2*d^2)","A",10,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
29,1,229,0,0.3438398,"\int \frac{\cos (a+b x) \sin ^3(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^3)/(c + d*x)^3,x]","\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}+\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \cos (2 a+2 b x)}{4 d^2 (c+d x)}+\frac{b \cos (4 a+4 b x)}{4 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{8 d (c+d x)^2}+\frac{\sin (4 a+4 b x)}{16 d (c+d x)^2}","\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}+\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \cos (2 a+2 b x)}{4 d^2 (c+d x)}+\frac{b \cos (4 a+4 b x)}{4 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{8 d (c+d x)^2}+\frac{\sin (4 a+4 b x)}{16 d (c+d x)^2}",1,"-(b*Cos[2*a + 2*b*x])/(4*d^2*(c + d*x)) + (b*Cos[4*a + 4*b*x])/(4*d^2*(c + d*x)) + (b^2*CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/d^3 - (b^2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(2*d^3) - Sin[2*a + 2*b*x]/(8*d*(c + d*x)^2) + Sin[4*a + 4*b*x]/(16*d*(c + d*x)^2) - (b^2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d^3) + (b^2*Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/d^3","A",12,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
30,1,287,0,0.3894429,"\int \frac{\cos (a+b x) \sin ^3(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]*Sin[a + b*x]^3)/(c + d*x)^4,x]","-\frac{b^3 \cos \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{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^3 \sin \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{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^2 \sin (2 a+2 b x)}{6 d^3 (c+d x)}-\frac{b^2 \sin (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{12 d^2 (c+d x)^2}+\frac{b \cos (4 a+4 b x)}{12 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{12 d (c+d x)^3}+\frac{\sin (4 a+4 b x)}{24 d (c+d x)^3}","-\frac{b^3 \cos \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{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^3 \sin \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{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^2 \sin (2 a+2 b x)}{6 d^3 (c+d x)}-\frac{b^2 \sin (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{12 d^2 (c+d x)^2}+\frac{b \cos (4 a+4 b x)}{12 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{12 d (c+d x)^3}+\frac{\sin (4 a+4 b x)}{24 d (c+d x)^3}",1,"-(b*Cos[2*a + 2*b*x])/(12*d^2*(c + d*x)^2) + (b*Cos[4*a + 4*b*x])/(12*d^2*(c + d*x)^2) - (b^3*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(3*d^4) + (4*b^3*Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/(3*d^4) - Sin[2*a + 2*b*x]/(12*d*(c + d*x)^3) + (b^2*Sin[2*a + 2*b*x])/(6*d^3*(c + d*x)) + Sin[4*a + 4*b*x]/(24*d*(c + d*x)^3) - (b^2*Sin[4*a + 4*b*x])/(3*d^3*(c + d*x)) + (b^3*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(3*d^4) - (4*b^3*Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(3*d^4)","A",14,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
31,0,0,0,0.0182283,"\int (c+d x)^m \cot (a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x],x]","\int (c+d x)^m \cot (a+b x) \, dx","\text{Int}\left(\cot (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Cot[a + b*x], x]","A",0,0,0,0,-1,"{}"
32,1,151,0,0.220252,"\int (c+d x)^4 \cot (a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x],x]","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^5}{5 d}","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^5}{5 d}",1,"((-I/5)*(c + d*x)^5)/d + ((c + d*x)^4*Log[1 - E^((2*I)*(a + b*x))])/b - ((2*I)*d*(c + d*x)^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 + ((3*I)*d^3*(c + d*x)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 - (3*d^4*PolyLog[5, E^((2*I)*(a + b*x))])/(2*b^5)","A",7,6,14,0.4286,1,"{3717, 2190, 2531, 6609, 2282, 6589}"
33,1,127,0,0.1924855,"\int (c+d x)^3 \cot (a+b x) \, dx","Int[(c + d*x)^3*Cot[a + b*x],x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^4}{4 d}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^4}{4 d}",1,"((-I/4)*(c + d*x)^4)/d + ((c + d*x)^3*Log[1 - E^((2*I)*(a + b*x))])/b - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) + (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",6,6,14,0.4286,1,"{3717, 2190, 2531, 6609, 2282, 6589}"
34,1,93,0,0.1664325,"\int (c+d x)^2 \cot (a+b x) \, dx","Int[(c + d*x)^2*Cot[a + b*x],x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^3}{3 d}","-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^3}{3 d}",1,"((-I/3)*(c + d*x)^3)/d + ((c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b - (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3)","A",5,5,14,0.3571,1,"{3717, 2190, 2531, 2282, 6589}"
35,1,65,0,0.0963027,"\int (c+d x) \cot (a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x],x]","-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^2}{2 d}","-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{i (c+d x)^2}{2 d}",1,"((-I/2)*(c + d*x)^2)/d + ((c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b - ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",4,4,12,0.3333,1,"{3717, 2190, 2279, 2391}"
36,0,0,0,0.0208909,"\int \frac{\cot (a+b x)}{c+d x} \, dx","Int[Cot[a + b*x]/(c + d*x),x]","\int \frac{\cot (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{c+d x},x\right)",0,"Defer[Int][Cot[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
37,0,0,0,0.0207621,"\int \frac{\cot (a+b x)}{(c+d x)^2} \, dx","Int[Cot[a + b*x]/(c + d*x)^2,x]","\int \frac{\cot (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Cot[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
38,0,0,0,0.2039238,"\int (c+d x)^m \cot (a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x]*Csc[a + b*x],x]","\int (c+d x)^m \cot (a+b x) \csc (a+b x) \, dx","\text{Int}\left(\cot (a+b x) \csc (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Cot[a + b*x]*Csc[a + b*x], x]","A",0,0,0,0,-1,"{}"
39,1,208,0,0.1717112,"\int (c+d x)^4 \cot (a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x]*Csc[a + b*x],x]","-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{24 i d^4 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^5}+\frac{24 i d^4 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^5}-\frac{8 d (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^4 \csc (a+b x)}{b}","-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{24 i d^4 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^5}+\frac{24 i d^4 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^5}-\frac{8 d (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^4 \csc (a+b x)}{b}",1,"(-8*d*(c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b^2 - ((c + d*x)^4*Csc[a + b*x])/b + ((12*I)*d^2*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((12*I)*d^2*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^3 - (24*d^3*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^4 + (24*d^3*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^4 - ((24*I)*d^4*PolyLog[4, -E^(I*(a + b*x))])/b^5 + ((24*I)*d^4*PolyLog[4, E^(I*(a + b*x))])/b^5","A",10,6,20,0.3000,1,"{4410, 4183, 2531, 6609, 2282, 6589}"
40,1,146,0,0.1159818,"\int (c+d x)^3 \cot (a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^3*Cot[a + b*x]*Csc[a + b*x],x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \csc (a+b x)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \csc (a+b x)}{b}",1,"(-6*d*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b^2 - ((c + d*x)^3*Csc[a + b*x])/b + ((6*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((6*I)*d^2*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^3 - (6*d^3*PolyLog[3, -E^(I*(a + b*x))])/b^4 + (6*d^3*PolyLog[3, E^(I*(a + b*x))])/b^4","A",8,5,20,0.2500,1,"{4410, 4183, 2531, 2282, 6589}"
41,1,90,0,0.0622306,"\int (c+d x)^2 \cot (a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^2*Cot[a + b*x]*Csc[a + b*x],x]","\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \csc (a+b x)}{b}","\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \csc (a+b x)}{b}",1,"(-4*d*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b^2 - ((c + d*x)^2*Csc[a + b*x])/b + ((2*I)*d^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((2*I)*d^2*PolyLog[2, E^(I*(a + b*x))])/b^3","A",6,4,20,0.2000,1,"{4410, 4183, 2279, 2391}"
42,1,30,0,0.0195758,"\int (c+d x) \cot (a+b x) \csc (a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x]*Csc[a + b*x],x]","-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \csc (a+b x)}{b}","-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \csc (a+b x)}{b}",1,"-((d*ArcTanh[Cos[a + b*x]])/b^2) - ((c + d*x)*Csc[a + b*x])/b","A",2,2,18,0.1111,1,"{4410, 3770}"
43,0,0,0,0.1145182,"\int \frac{\cot (a+b x) \csc (a+b x)}{c+d x} \, dx","Int[(Cot[a + b*x]*Csc[a + b*x])/(c + d*x),x]","\int \frac{\cot (a+b x) \csc (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc (a+b x)}{c+d x},x\right)",0,"Defer[Int][(Cot[a + b*x]*Csc[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
44,0,0,0,0.1522284,"\int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx","Int[(Cot[a + b*x]*Csc[a + b*x])/(c + d*x)^2,x]","\int \frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Cot[a + b*x]*Csc[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
45,0,0,0,0.2165795,"\int (c+d x)^m \cot (a+b x) \csc ^2(a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x]*Csc[a + b*x]^2,x]","\int (c+d x)^m \cot (a+b x) \csc ^2(a+b x) \, dx","\text{Int}\left(\cot (a+b x) \csc ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Cot[a + b*x]*Csc[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
46,1,137,0,0.2560672,"\int (c+d x)^4 \cot (a+b x) \csc ^2(a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x]*Csc[a + b*x]^2,x]","-\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^4}+\frac{3 d^4 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^5}+\frac{6 d^2 (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \cot (a+b x)}{b^2}-\frac{(c+d x)^4 \csc ^2(a+b x)}{2 b}-\frac{2 i d (c+d x)^3}{b^2}","-\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^4}+\frac{3 d^4 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^5}+\frac{6 d^2 (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \cot (a+b x)}{b^2}-\frac{(c+d x)^4 \csc ^2(a+b x)}{2 b}-\frac{2 i d (c+d x)^3}{b^2}",1,"((-2*I)*d*(c + d*x)^3)/b^2 - (2*d*(c + d*x)^3*Cot[a + b*x])/b^2 - ((c + d*x)^4*Csc[a + b*x]^2)/(2*b) + (6*d^2*(c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b^3 - ((6*I)*d^3*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 + (3*d^4*PolyLog[3, E^((2*I)*(a + b*x))])/b^5","A",7,7,22,0.3182,1,"{4410, 4184, 3717, 2190, 2531, 2282, 6589}"
47,1,115,0,0.1736088,"\int (c+d x)^3 \cot (a+b x) \csc ^2(a+b x) \, dx","Int[(c + d*x)^3*Cot[a + b*x]*Csc[a + b*x]^2,x]","-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \csc ^2(a+b x)}{2 b}-\frac{3 i d (c+d x)^2}{2 b^2}","-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \csc ^2(a+b x)}{2 b}-\frac{3 i d (c+d x)^2}{2 b^2}",1,"(((-3*I)/2)*d*(c + d*x)^2)/b^2 - (3*d*(c + d*x)^2*Cot[a + b*x])/(2*b^2) - ((c + d*x)^3*Csc[a + b*x]^2)/(2*b) + (3*d^2*(c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b^3 - (((3*I)/2)*d^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^4","A",6,6,22,0.2727,1,"{4410, 4184, 3717, 2190, 2279, 2391}"
48,1,54,0,0.0653742,"\int (c+d x)^2 \cot (a+b x) \csc ^2(a+b x) \, dx","Int[(c + d*x)^2*Cot[a + b*x]*Csc[a + b*x]^2,x]","-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \csc ^2(a+b x)}{2 b}","-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \csc ^2(a+b x)}{2 b}",1,"-((d*(c + d*x)*Cot[a + b*x])/b^2) - ((c + d*x)^2*Csc[a + b*x]^2)/(2*b) + (d^2*Log[Sin[a + b*x]])/b^3","A",3,3,22,0.1364,1,"{4410, 4184, 3475}"
49,1,35,0,0.0314137,"\int (c+d x) \cot (a+b x) \csc ^2(a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x]*Csc[a + b*x]^2,x]","-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \csc ^2(a+b x)}{2 b}","-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \csc ^2(a+b x)}{2 b}",1,"-(d*Cot[a + b*x])/(2*b^2) - ((c + d*x)*Csc[a + b*x]^2)/(2*b)","A",3,3,20,0.1500,1,"{4410, 3767, 8}"
50,0,0,0,0.1365791,"\int \frac{\cot (a+b x) \csc ^2(a+b x)}{c+d x} \, dx","Int[(Cot[a + b*x]*Csc[a + b*x]^2)/(c + d*x),x]","\int \frac{\cot (a+b x) \csc ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Cot[a + b*x]*Csc[a + b*x]^2)/(c + d*x), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.1664828,"\int \frac{\cot (a+b x) \csc ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Cot[a + b*x]*Csc[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\cot (a+b x) \csc ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Cot[a + b*x]*Csc[a + b*x]^2)/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
52,1,196,0,0.4475232,"\int (c+d x)^{5/2} \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{4 b}","-\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{4 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(64*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(4*b) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(16*b^2)","A",10,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
53,1,168,0,0.2945395,"\int (c+d x)^{3/2} \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{4 b}","-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{4 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(4*b) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(32*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(32*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(16*b^2)","A",9,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
54,1,142,0,0.2306947,"\int \sqrt{c+d x} \cos (a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x],x]","\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{4 b}","\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{4 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(4*b) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(8*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(8*b^(3/2))","A",8,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
55,1,142,0,0.2209598,"\int \sqrt{c+d x} \cos (a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x],x]","\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{4 b}","\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{4 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(4*b) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(8*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(8*b^(3/2))","A",8,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
56,1,168,0,0.2752874,"\int (c+d x)^{3/2} \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{4 b}","-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{4 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(4*b) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(32*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(32*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(16*b^2)","A",9,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
57,1,196,0,0.3341436,"\int (c+d x)^{5/2} \cos (a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x],x]","-\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{4 b}","-\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{128 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{16 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{4 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(64*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(4*b) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(16*b^2)","A",10,8,22,0.3636,1,"{4406, 12, 3296, 3306, 3305, 3351, 3304, 3352}"
58,1,406,0,1.136737,"\int (c+d x)^{5/2} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{16 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{8 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{72 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{12 b}","-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{16 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{8 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{72 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{12 b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(8*b^2) - (5*d*(c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(72*b^2) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(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]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(144*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(144*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(16*b^(7/2)) - (15*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(16*b^3) + ((c + d*x)^(5/2)*Sin[a + b*x])/(4*b) + (5*d^2*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(144*b^3) - ((c + d*x)^(5/2)*Sin[3*a + 3*b*x])/(12*b)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
59,1,353,0,0.6842371,"\int (c+d x)^{3/2} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{8 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{24 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{12 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{8 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{24 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{12 b}",1,"(3*d*Sqrt[c + d*x]*Cos[a + b*x])/(8*b^2) - (d*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(24*b^2) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(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]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(24*b^(5/2)) - (d^(3/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(24*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(8*b^(5/2)) + ((c + d*x)^(3/2)*Sin[a + b*x])/(4*b) - ((c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(12*b)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
60,1,304,0,0.4699947,"\int \sqrt{c+d x} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \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{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{4 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{12 b}","\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \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{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{4 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{12 b}",1,"-(Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(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]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(12*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(12*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(4*b^(3/2)) + (Sqrt[c + d*x]*Sin[a + b*x])/(4*b) - (Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(12*b)","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
61,1,304,0,0.4678903,"\int \sqrt{c+d x} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \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{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{4 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{12 b}","\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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)}{4 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \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{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{12 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{4 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{12 b}",1,"-(Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(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]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(12*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(12*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(4*b^(3/2)) + (Sqrt[c + d*x]*Sin[a + b*x])/(4*b) - (Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(12*b)","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
62,1,353,0,0.5713503,"\int (c+d x)^{3/2} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{8 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{24 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{12 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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)}{8 b^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{24 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{8 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{24 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{12 b}",1,"(3*d*Sqrt[c + d*x]*Cos[a + b*x])/(8*b^2) - (d*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(24*b^2) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(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]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(24*b^(5/2)) - (d^(3/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(24*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(8*b^(5/2)) + ((c + d*x)^(3/2)*Sin[a + b*x])/(4*b) - ((c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(12*b)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
63,1,406,0,0.6676815,"\int (c+d x)^{5/2} \cos (a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x]^2,x]","-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{16 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{8 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{72 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{12 b}","-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{16 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{144 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{144 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{8 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{72 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{12 b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(8*b^2) - (5*d*(c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(72*b^2) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(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]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(144*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(144*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(16*b^(7/2)) - (15*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(16*b^3) + ((c + d*x)^(5/2)*Sin[a + b*x])/(4*b) + (5*d^2*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(144*b^3) - ((c + d*x)^(5/2)*Sin[3*a + 3*b*x])/(12*b)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
64,1,407,0,1.0514183,"\int (c+d x)^{5/2} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}-\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}-\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}-\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}-\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(128*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(8*b) - (15*d^2*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(2048*b^3) + ((c + d*x)^(5/2)*Cos[4*a + 4*b*x])/(32*b) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(256*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(256*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(32*b^2) - (5*d*(c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(256*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
65,1,351,0,0.6735824,"\int (c+d x)^{3/2} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}-\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}-\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(8*b) + ((c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(32*b) + (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(64*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(64*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(32*b^2) - (3*d*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(256*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
66,1,299,0,0.4991538,"\int \sqrt{c+d x} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x]^3,x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}+\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}+\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(8*b) + (Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(32*b) - (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(16*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(16*b^(3/2))","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
67,1,299,0,0.459801,"\int \sqrt{c+d x} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]*Sin[a + b*x]^3,x]","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}+\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}+\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(8*b) + (Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(32*b) - (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(16*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(16*b^(3/2))","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
68,1,351,0,0.5662055,"\int (c+d x)^{3/2} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}-\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}-\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(8*b) + ((c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(32*b) + (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(64*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(64*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(32*b^2) - (3*d*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(256*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
69,1,407,0,0.6969984,"\int (c+d x)^{5/2} \cos (a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x]^3,x]","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}-\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}-\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}-\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}-\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}+\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(128*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(8*b) - (15*d^2*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(2048*b^3) + ((c + d*x)^(5/2)*Cos[4*a + 4*b*x])/(32*b) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(256*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(256*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(32*b^2) - (5*d*(c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(256*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
70,1,267,0,0.2826961,"\int (c+d x)^m \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^2*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)}{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{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{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{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,"-(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) - ((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",8,3,22,0.1364,1,"{4406, 3308, 2181}"
71,1,205,0,0.2025369,"\int (c+d x)^4 \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^2*Sin[a + b*x],x]","-\frac{160 d^3 (c+d x) \sin (a+b x)}{27 b^4}+\frac{4 d^2 (c+d x)^2 \cos ^3(a+b x)}{9 b^3}+\frac{8 d^2 (c+d x)^2 \cos (a+b x)}{3 b^3}-\frac{8 d^3 (c+d x) \sin (a+b x) \cos ^2(a+b x)}{27 b^4}+\frac{8 d (c+d x)^3 \sin (a+b x)}{9 b^2}+\frac{4 d (c+d x)^3 \sin (a+b x) \cos ^2(a+b x)}{9 b^2}-\frac{8 d^4 \cos ^3(a+b x)}{81 b^5}-\frac{160 d^4 \cos (a+b x)}{27 b^5}-\frac{(c+d x)^4 \cos ^3(a+b x)}{3 b}","-\frac{160 d^3 (c+d x) \sin (a+b x)}{27 b^4}+\frac{4 d^2 (c+d x)^2 \cos ^3(a+b x)}{9 b^3}+\frac{8 d^2 (c+d x)^2 \cos (a+b x)}{3 b^3}-\frac{8 d^3 (c+d x) \sin (a+b x) \cos ^2(a+b x)}{27 b^4}+\frac{8 d (c+d x)^3 \sin (a+b x)}{9 b^2}+\frac{4 d (c+d x)^3 \sin (a+b x) \cos ^2(a+b x)}{9 b^2}-\frac{8 d^4 \cos ^3(a+b x)}{81 b^5}-\frac{160 d^4 \cos (a+b x)}{27 b^5}-\frac{(c+d x)^4 \cos ^3(a+b x)}{3 b}",1,"(-160*d^4*Cos[a + b*x])/(27*b^5) + (8*d^2*(c + d*x)^2*Cos[a + b*x])/(3*b^3) - (8*d^4*Cos[a + b*x]^3)/(81*b^5) + (4*d^2*(c + d*x)^2*Cos[a + b*x]^3)/(9*b^3) - ((c + d*x)^4*Cos[a + b*x]^3)/(3*b) - (160*d^3*(c + d*x)*Sin[a + b*x])/(27*b^4) + (8*d*(c + d*x)^3*Sin[a + b*x])/(9*b^2) - (8*d^3*(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x])/(27*b^4) + (4*d*(c + d*x)^3*Cos[a + b*x]^2*Sin[a + b*x])/(9*b^2)","A",9,5,22,0.2273,1,"{4405, 3311, 3296, 2638, 3310}"
72,1,151,0,0.1330796,"\int (c+d x)^3 \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^2*Sin[a + b*x],x]","\frac{2 d^2 (c+d x) \cos ^3(a+b x)}{9 b^3}+\frac{4 d^2 (c+d x) \cos (a+b x)}{3 b^3}+\frac{2 d (c+d x)^2 \sin (a+b x)}{3 b^2}+\frac{d (c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{3 b^2}+\frac{2 d^3 \sin ^3(a+b x)}{27 b^4}-\frac{14 d^3 \sin (a+b x)}{9 b^4}-\frac{(c+d x)^3 \cos ^3(a+b x)}{3 b}","\frac{2 d^2 (c+d x) \cos ^3(a+b x)}{9 b^3}+\frac{4 d^2 (c+d x) \cos (a+b x)}{3 b^3}+\frac{2 d (c+d x)^2 \sin (a+b x)}{3 b^2}+\frac{d (c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{3 b^2}+\frac{2 d^3 \sin ^3(a+b x)}{27 b^4}-\frac{14 d^3 \sin (a+b x)}{9 b^4}-\frac{(c+d x)^3 \cos ^3(a+b x)}{3 b}",1,"(4*d^2*(c + d*x)*Cos[a + b*x])/(3*b^3) + (2*d^2*(c + d*x)*Cos[a + b*x]^3)/(9*b^3) - ((c + d*x)^3*Cos[a + b*x]^3)/(3*b) - (14*d^3*Sin[a + b*x])/(9*b^4) + (2*d*(c + d*x)^2*Sin[a + b*x])/(3*b^2) + (d*(c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x])/(3*b^2) + (2*d^3*Sin[a + b*x]^3)/(27*b^4)","A",7,5,22,0.2273,1,"{4405, 3311, 3296, 2637, 2633}"
73,1,103,0,0.0790108,"\int (c+d x)^2 \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x],x]","\frac{4 d (c+d x) \sin (a+b x)}{9 b^2}+\frac{2 d (c+d x) \sin (a+b x) \cos ^2(a+b x)}{9 b^2}+\frac{2 d^2 \cos ^3(a+b x)}{27 b^3}+\frac{4 d^2 \cos (a+b x)}{9 b^3}-\frac{(c+d x)^2 \cos ^3(a+b x)}{3 b}","\frac{4 d (c+d x) \sin (a+b x)}{9 b^2}+\frac{2 d (c+d x) \sin (a+b x) \cos ^2(a+b x)}{9 b^2}+\frac{2 d^2 \cos ^3(a+b x)}{27 b^3}+\frac{4 d^2 \cos (a+b x)}{9 b^3}-\frac{(c+d x)^2 \cos ^3(a+b x)}{3 b}",1,"(4*d^2*Cos[a + b*x])/(9*b^3) + (2*d^2*Cos[a + b*x]^3)/(27*b^3) - ((c + d*x)^2*Cos[a + b*x]^3)/(3*b) + (4*d*(c + d*x)*Sin[a + b*x])/(9*b^2) + (2*d*(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x])/(9*b^2)","A",4,4,22,0.1818,1,"{4405, 3310, 3296, 2638}"
74,1,51,0,0.0342699,"\int (c+d x) \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x],x]","-\frac{d \sin ^3(a+b x)}{9 b^2}+\frac{d \sin (a+b x)}{3 b^2}-\frac{(c+d x) \cos ^3(a+b x)}{3 b}","-\frac{d \sin ^3(a+b x)}{9 b^2}+\frac{d \sin (a+b x)}{3 b^2}-\frac{(c+d x) \cos ^3(a+b x)}{3 b}",1,"-((c + d*x)*Cos[a + b*x]^3)/(3*b) + (d*Sin[a + b*x])/(3*b^2) - (d*Sin[a + b*x]^3)/(9*b^2)","A",3,2,20,0.1000,1,"{4405, 2633}"
75,1,121,0,0.2244397,"\int \frac{\cos ^2(a+b x) \sin (a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x])/(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{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\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{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\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) + (CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(4*d) + (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",8,4,22,0.1818,1,"{4406, 3303, 3299, 3302}"
76,1,168,0,0.2663862,"\int \frac{\cos ^2(a+b x) \sin (a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^2*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)}{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{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 (a+b x)}{4 d (c+d x)}-\frac{\sin (3 a+3 b x)}{4 d (c+d x)}","\frac{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{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 (a+b x)}{4 d (c+d x)}-\frac{\sin (3 a+3 b x)}{4 d (c+d x)}",1,"(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]/(4*d*(c + d*x)) - Sin[3*a + 3*b*x]/(4*d*(c + d*x)) - (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",10,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
77,1,221,0,0.3244175,"\int \frac{\cos ^2(a+b x) \sin (a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x])/(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{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{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{b \cos (a+b x)}{8 d^2 (c+d x)}-\frac{3 b \cos (3 a+3 b x)}{8 d^2 (c+d x)}-\frac{\sin (a+b x)}{8 d (c+d x)^2}-\frac{\sin (3 a+3 b x)}{8 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{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{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{b \cos (a+b x)}{8 d^2 (c+d x)}-\frac{3 b \cos (3 a+3 b x)}{8 d^2 (c+d x)}-\frac{\sin (a+b x)}{8 d (c+d x)^2}-\frac{\sin (3 a+3 b x)}{8 d (c+d x)^2}",1,"-(b*Cos[a + b*x])/(8*d^2*(c + d*x)) - (3*b*Cos[3*a + 3*b*x])/(8*d^2*(c + d*x)) - (9*b^2*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(8*d^3) - (b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(8*d^3) - Sin[a + b*x]/(8*d*(c + d*x)^2) - Sin[3*a + 3*b*x]/(8*d*(c + d*x)^2) - (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",12,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
78,1,270,0,0.3774519,"\int \frac{\cos ^2(a+b x) \sin (a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x])/(c + d*x)^4,x]","-\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{24 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{24 d^4}+\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^2 \sin (a+b x)}{24 d^3 (c+d x)}+\frac{3 b^2 \sin (3 a+3 b x)}{8 d^3 (c+d x)}-\frac{b \cos (a+b x)}{24 d^2 (c+d x)^2}-\frac{b \cos (3 a+3 b x)}{8 d^2 (c+d x)^2}-\frac{\sin (a+b x)}{12 d (c+d x)^3}-\frac{\sin (3 a+3 b x)}{12 d (c+d x)^3}","-\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{24 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{24 d^4}+\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^4}+\frac{b^2 \sin (a+b x)}{24 d^3 (c+d x)}+\frac{3 b^2 \sin (3 a+3 b x)}{8 d^3 (c+d x)}-\frac{b \cos (a+b x)}{24 d^2 (c+d x)^2}-\frac{b \cos (3 a+3 b x)}{8 d^2 (c+d x)^2}-\frac{\sin (a+b x)}{12 d (c+d x)^3}-\frac{\sin (3 a+3 b x)}{12 d (c+d x)^3}",1,"-(b*Cos[a + b*x])/(24*d^2*(c + d*x)^2) - (b*Cos[3*a + 3*b*x])/(8*d^2*(c + d*x)^2) - (b^3*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(24*d^4) - (9*b^3*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(8*d^4) - Sin[a + b*x]/(12*d*(c + d*x)^3) + (b^2*Sin[a + b*x])/(24*d^3*(c + d*x)) - Sin[3*a + 3*b*x]/(12*d*(c + d*x)^3) + (3*b^2*Sin[3*a + 3*b*x])/(8*d^3*(c + d*x)) + (b^3*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(24*d^4) + (9*b^3*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(8*d^4)","A",14,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
79,1,162,0,0.2047996,"\int (c+d x)^m \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{i 2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{i 2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{8 d (m+1)}","\frac{i 2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{i 2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{8 d (m+1)}",1,"(c + d*x)^(1 + m)/(8*d*(1 + m)) + (I*E^((4*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*(((-I)*b*(c + d*x))/d)^m) - (I*(c + d*x)^m*Gamma[1 + m, ((4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*E^((4*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",5,3,24,0.1250,1,"{4406, 3307, 2181}"
80,1,131,0,0.1643995,"\int (c+d x)^4 \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{3 d^2 (c+d x)^2 \sin (4 a+4 b x)}{128 b^3}+\frac{3 d^3 (c+d x) \cos (4 a+4 b x)}{256 b^4}-\frac{d (c+d x)^3 \cos (4 a+4 b x)}{32 b^2}-\frac{3 d^4 \sin (4 a+4 b x)}{1024 b^5}-\frac{(c+d x)^4 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^5}{40 d}","\frac{3 d^2 (c+d x)^2 \sin (4 a+4 b x)}{128 b^3}+\frac{3 d^3 (c+d x) \cos (4 a+4 b x)}{256 b^4}-\frac{d (c+d x)^3 \cos (4 a+4 b x)}{32 b^2}-\frac{3 d^4 \sin (4 a+4 b x)}{1024 b^5}-\frac{(c+d x)^4 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^5}{40 d}",1,"(c + d*x)^5/(40*d) + (3*d^3*(c + d*x)*Cos[4*a + 4*b*x])/(256*b^4) - (d*(c + d*x)^3*Cos[4*a + 4*b*x])/(32*b^2) - (3*d^4*Sin[4*a + 4*b*x])/(1024*b^5) + (3*d^2*(c + d*x)^2*Sin[4*a + 4*b*x])/(128*b^3) - ((c + d*x)^4*Sin[4*a + 4*b*x])/(32*b)","A",7,3,24,0.1250,1,"{4406, 3296, 2637}"
81,1,105,0,0.1303227,"\int (c+d x)^3 \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{3 d^2 (c+d x) \sin (4 a+4 b x)}{256 b^3}-\frac{3 d (c+d x)^2 \cos (4 a+4 b x)}{128 b^2}+\frac{3 d^3 \cos (4 a+4 b x)}{1024 b^4}-\frac{(c+d x)^3 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^4}{32 d}","\frac{3 d^2 (c+d x) \sin (4 a+4 b x)}{256 b^3}-\frac{3 d (c+d x)^2 \cos (4 a+4 b x)}{128 b^2}+\frac{3 d^3 \cos (4 a+4 b x)}{1024 b^4}-\frac{(c+d x)^3 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^4}{32 d}",1,"(c + d*x)^4/(32*d) + (3*d^3*Cos[4*a + 4*b*x])/(1024*b^4) - (3*d*(c + d*x)^2*Cos[4*a + 4*b*x])/(128*b^2) + (3*d^2*(c + d*x)*Sin[4*a + 4*b*x])/(256*b^3) - ((c + d*x)^3*Sin[4*a + 4*b*x])/(32*b)","A",6,3,24,0.1250,1,"{4406, 3296, 2638}"
82,1,79,0,0.122533,"\int (c+d x)^2 \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","-\frac{d (c+d x) \cos (4 a+4 b x)}{64 b^2}+\frac{d^2 \sin (4 a+4 b x)}{256 b^3}-\frac{(c+d x)^2 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^3}{24 d}","-\frac{d (c+d x) \cos (4 a+4 b x)}{64 b^2}+\frac{d^2 \sin (4 a+4 b x)}{256 b^3}-\frac{(c+d x)^2 \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^3}{24 d}",1,"(c + d*x)^3/(24*d) - (d*(c + d*x)*Cos[4*a + 4*b*x])/(64*b^2) + (d^2*Sin[4*a + 4*b*x])/(256*b^3) - ((c + d*x)^2*Sin[4*a + 4*b*x])/(32*b)","A",5,3,24,0.1250,1,"{4406, 3296, 2637}"
83,1,53,0,0.0537823,"\int (c+d x) \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","-\frac{d \cos (4 a+4 b x)}{128 b^2}-\frac{(c+d x) \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^2}{16 d}","-\frac{d \cos (4 a+4 b x)}{128 b^2}-\frac{(c+d x) \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^2}{16 d}",1,"(c + d*x)^2/(16*d) - (d*Cos[4*a + 4*b*x])/(128*b^2) - ((c + d*x)*Sin[4*a + 4*b*x])/(32*b)","A",4,3,22,0.1364,1,"{4406, 3296, 2638}"
84,1,78,0,0.1397413,"\int \frac{\cos ^2(a+b x) \sin ^2(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^2)/(c + d*x),x]","-\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\log (c+d x)}{8 d}","-\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\log (c+d x)}{8 d}",1,"-(Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/(8*d) + Log[c + d*x]/(8*d) + (Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(8*d)","A",5,4,24,0.1667,1,"{4406, 3303, 3299, 3302}"
85,1,104,0,0.1689822,"\int \frac{\cos ^2(a+b x) \sin ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^2)/(c + d*x)^2,x]","\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}+\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}+\frac{\cos (4 a+4 b x)}{8 d (c+d x)}-\frac{1}{8 d (c+d x)}","\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}+\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}+\frac{\cos (4 a+4 b x)}{8 d (c+d x)}-\frac{1}{8 d (c+d x)}",1,"-1/(8*d*(c + d*x)) + Cos[4*a + 4*b*x]/(8*d*(c + d*x)) + (b*CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/(2*d^2) + (b*Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(2*d^2)","A",6,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
86,1,127,0,0.1982845,"\int \frac{\cos ^2(a+b x) \sin ^2(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^2)/(c + d*x)^3,x]","\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \sin (4 a+4 b x)}{4 d^2 (c+d x)}+\frac{\cos (4 a+4 b x)}{16 d (c+d x)^2}-\frac{1}{16 d (c+d x)^2}","\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \sin (4 a+4 b x)}{4 d^2 (c+d x)}+\frac{\cos (4 a+4 b x)}{16 d (c+d x)^2}-\frac{1}{16 d (c+d x)^2}",1,"-1/(16*d*(c + d*x)^2) + Cos[4*a + 4*b*x]/(16*d*(c + d*x)^2) + (b^2*Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/d^3 - (b*Sin[4*a + 4*b*x])/(4*d^2*(c + d*x)) - (b^2*Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/d^3","A",7,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
87,1,158,0,0.2277873,"\int \frac{\cos ^2(a+b x) \sin ^2(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^2)/(c + d*x)^4,x]","-\frac{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}-\frac{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}-\frac{b^2 \cos (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \sin (4 a+4 b x)}{12 d^2 (c+d x)^2}+\frac{\cos (4 a+4 b x)}{24 d (c+d x)^3}-\frac{1}{24 d (c+d x)^3}","-\frac{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}-\frac{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}-\frac{b^2 \cos (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \sin (4 a+4 b x)}{12 d^2 (c+d x)^2}+\frac{\cos (4 a+4 b x)}{24 d (c+d x)^3}-\frac{1}{24 d (c+d x)^3}",1,"-1/(24*d*(c + d*x)^3) + Cos[4*a + 4*b*x]/(24*d*(c + d*x)^3) - (b^2*Cos[4*a + 4*b*x])/(3*d^3*(c + d*x)) - (4*b^3*CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/(3*d^4) - (b*Sin[4*a + 4*b*x])/(12*d^2*(c + d*x)^2) - (4*b^3*Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(3*d^4)","A",8,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
88,1,407,0,0.4025618,"\int (c+d x)^m \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^2*Sin[a + b*x]^3,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)}{16 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)}{32 b}+\frac{5^{-m-1} e^{5 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{5 i b (c+d x)}{d}\right)}{32 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)}{16 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)}{32 b}+\frac{5^{-m-1} e^{-5 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{5 i b (c+d x)}{d}\right)}{32 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)}{16 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)}{32 b}+\frac{5^{-m-1} e^{5 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{5 i b (c+d x)}{d}\right)}{32 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)}{16 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)}{32 b}+\frac{5^{-m-1} e^{-5 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{5 i b (c+d x)}{d}\right)}{32 b}",1,"-(E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(16*b*(((-I)*b*(c + d*x))/d)^m) - ((c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(16*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])/(32*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])/(32*b*E^((3*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + (5^(-1 - m)*E^((5*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-5*I)*b*(c + d*x))/d])/(32*b*(((-I)*b*(c + d*x))/d)^m) + (5^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((5*I)*b*(c + d*x))/d])/(32*b*E^((5*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",11,3,24,0.1250,1,"{4406, 3308, 2181}"
89,1,330,0,0.3910631,"\int (c+d x)^4 \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","-\frac{3 d^3 (c+d x) \sin (a+b x)}{b^4}-\frac{d^3 (c+d x) \sin (3 a+3 b x)}{54 b^4}+\frac{3 d^3 (c+d x) \sin (5 a+5 b x)}{1250 b^4}+\frac{3 d^2 (c+d x)^2 \cos (a+b x)}{2 b^3}+\frac{d^2 (c+d x)^2 \cos (3 a+3 b x)}{36 b^3}-\frac{3 d^2 (c+d x)^2 \cos (5 a+5 b x)}{500 b^3}+\frac{d (c+d x)^3 \sin (a+b x)}{2 b^2}+\frac{d (c+d x)^3 \sin (3 a+3 b x)}{36 b^2}-\frac{d (c+d x)^3 \sin (5 a+5 b x)}{100 b^2}-\frac{3 d^4 \cos (a+b x)}{b^5}-\frac{d^4 \cos (3 a+3 b x)}{162 b^5}+\frac{3 d^4 \cos (5 a+5 b x)}{6250 b^5}-\frac{(c+d x)^4 \cos (a+b x)}{8 b}-\frac{(c+d x)^4 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^4 \cos (5 a+5 b x)}{80 b}","-\frac{3 d^3 (c+d x) \sin (a+b x)}{b^4}-\frac{d^3 (c+d x) \sin (3 a+3 b x)}{54 b^4}+\frac{3 d^3 (c+d x) \sin (5 a+5 b x)}{1250 b^4}+\frac{3 d^2 (c+d x)^2 \cos (a+b x)}{2 b^3}+\frac{d^2 (c+d x)^2 \cos (3 a+3 b x)}{36 b^3}-\frac{3 d^2 (c+d x)^2 \cos (5 a+5 b x)}{500 b^3}+\frac{d (c+d x)^3 \sin (a+b x)}{2 b^2}+\frac{d (c+d x)^3 \sin (3 a+3 b x)}{36 b^2}-\frac{d (c+d x)^3 \sin (5 a+5 b x)}{100 b^2}-\frac{3 d^4 \cos (a+b x)}{b^5}-\frac{d^4 \cos (3 a+3 b x)}{162 b^5}+\frac{3 d^4 \cos (5 a+5 b x)}{6250 b^5}-\frac{(c+d x)^4 \cos (a+b x)}{8 b}-\frac{(c+d x)^4 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^4 \cos (5 a+5 b x)}{80 b}",1,"(-3*d^4*Cos[a + b*x])/b^5 + (3*d^2*(c + d*x)^2*Cos[a + b*x])/(2*b^3) - ((c + d*x)^4*Cos[a + b*x])/(8*b) - (d^4*Cos[3*a + 3*b*x])/(162*b^5) + (d^2*(c + d*x)^2*Cos[3*a + 3*b*x])/(36*b^3) - ((c + d*x)^4*Cos[3*a + 3*b*x])/(48*b) + (3*d^4*Cos[5*a + 5*b*x])/(6250*b^5) - (3*d^2*(c + d*x)^2*Cos[5*a + 5*b*x])/(500*b^3) + ((c + d*x)^4*Cos[5*a + 5*b*x])/(80*b) - (3*d^3*(c + d*x)*Sin[a + b*x])/b^4 + (d*(c + d*x)^3*Sin[a + b*x])/(2*b^2) - (d^3*(c + d*x)*Sin[3*a + 3*b*x])/(54*b^4) + (d*(c + d*x)^3*Sin[3*a + 3*b*x])/(36*b^2) + (3*d^3*(c + d*x)*Sin[5*a + 5*b*x])/(1250*b^4) - (d*(c + d*x)^3*Sin[5*a + 5*b*x])/(100*b^2)","A",17,3,24,0.1250,1,"{4406, 3296, 2638}"
90,1,259,0,0.2791568,"\int (c+d x)^3 \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{3 d^2 (c+d x) \cos (a+b x)}{4 b^3}+\frac{d^2 (c+d x) \cos (3 a+3 b x)}{72 b^3}-\frac{3 d^2 (c+d x) \cos (5 a+5 b x)}{1000 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x)}{8 b^2}+\frac{d (c+d x)^2 \sin (3 a+3 b x)}{48 b^2}-\frac{3 d (c+d x)^2 \sin (5 a+5 b x)}{400 b^2}-\frac{3 d^3 \sin (a+b x)}{4 b^4}-\frac{d^3 \sin (3 a+3 b x)}{216 b^4}+\frac{3 d^3 \sin (5 a+5 b x)}{5000 b^4}-\frac{(c+d x)^3 \cos (a+b x)}{8 b}-\frac{(c+d x)^3 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^3 \cos (5 a+5 b x)}{80 b}","\frac{3 d^2 (c+d x) \cos (a+b x)}{4 b^3}+\frac{d^2 (c+d x) \cos (3 a+3 b x)}{72 b^3}-\frac{3 d^2 (c+d x) \cos (5 a+5 b x)}{1000 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x)}{8 b^2}+\frac{d (c+d x)^2 \sin (3 a+3 b x)}{48 b^2}-\frac{3 d (c+d x)^2 \sin (5 a+5 b x)}{400 b^2}-\frac{3 d^3 \sin (a+b x)}{4 b^4}-\frac{d^3 \sin (3 a+3 b x)}{216 b^4}+\frac{3 d^3 \sin (5 a+5 b x)}{5000 b^4}-\frac{(c+d x)^3 \cos (a+b x)}{8 b}-\frac{(c+d x)^3 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^3 \cos (5 a+5 b x)}{80 b}",1,"(3*d^2*(c + d*x)*Cos[a + b*x])/(4*b^3) - ((c + d*x)^3*Cos[a + b*x])/(8*b) + (d^2*(c + d*x)*Cos[3*a + 3*b*x])/(72*b^3) - ((c + d*x)^3*Cos[3*a + 3*b*x])/(48*b) - (3*d^2*(c + d*x)*Cos[5*a + 5*b*x])/(1000*b^3) + ((c + d*x)^3*Cos[5*a + 5*b*x])/(80*b) - (3*d^3*Sin[a + b*x])/(4*b^4) + (3*d*(c + d*x)^2*Sin[a + b*x])/(8*b^2) - (d^3*Sin[3*a + 3*b*x])/(216*b^4) + (d*(c + d*x)^2*Sin[3*a + 3*b*x])/(48*b^2) + (3*d^3*Sin[5*a + 5*b*x])/(5000*b^4) - (3*d*(c + d*x)^2*Sin[5*a + 5*b*x])/(400*b^2)","A",14,3,24,0.1250,1,"{4406, 3296, 2637}"
91,1,184,0,0.1971794,"\int (c+d x)^2 \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{d (c+d x) \sin (a+b x)}{4 b^2}+\frac{d (c+d x) \sin (3 a+3 b x)}{72 b^2}-\frac{d (c+d x) \sin (5 a+5 b x)}{200 b^2}+\frac{d^2 \cos (a+b x)}{4 b^3}+\frac{d^2 \cos (3 a+3 b x)}{216 b^3}-\frac{d^2 \cos (5 a+5 b x)}{1000 b^3}-\frac{(c+d x)^2 \cos (a+b x)}{8 b}-\frac{(c+d x)^2 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^2 \cos (5 a+5 b x)}{80 b}","\frac{d (c+d x) \sin (a+b x)}{4 b^2}+\frac{d (c+d x) \sin (3 a+3 b x)}{72 b^2}-\frac{d (c+d x) \sin (5 a+5 b x)}{200 b^2}+\frac{d^2 \cos (a+b x)}{4 b^3}+\frac{d^2 \cos (3 a+3 b x)}{216 b^3}-\frac{d^2 \cos (5 a+5 b x)}{1000 b^3}-\frac{(c+d x)^2 \cos (a+b x)}{8 b}-\frac{(c+d x)^2 \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^2 \cos (5 a+5 b x)}{80 b}",1,"(d^2*Cos[a + b*x])/(4*b^3) - ((c + d*x)^2*Cos[a + b*x])/(8*b) + (d^2*Cos[3*a + 3*b*x])/(216*b^3) - ((c + d*x)^2*Cos[3*a + 3*b*x])/(48*b) - (d^2*Cos[5*a + 5*b*x])/(1000*b^3) + ((c + d*x)^2*Cos[5*a + 5*b*x])/(80*b) + (d*(c + d*x)*Sin[a + b*x])/(4*b^2) + (d*(c + d*x)*Sin[3*a + 3*b*x])/(72*b^2) - (d*(c + d*x)*Sin[5*a + 5*b*x])/(200*b^2)","A",11,3,24,0.1250,1,"{4406, 3296, 2638}"
92,1,109,0,0.0969841,"\int (c+d x) \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{d \sin (a+b x)}{8 b^2}+\frac{d \sin (3 a+3 b x)}{144 b^2}-\frac{d \sin (5 a+5 b x)}{400 b^2}-\frac{(c+d x) \cos (a+b x)}{8 b}-\frac{(c+d x) \cos (3 a+3 b x)}{48 b}+\frac{(c+d x) \cos (5 a+5 b x)}{80 b}","\frac{d \sin (a+b x)}{8 b^2}+\frac{d \sin (3 a+3 b x)}{144 b^2}-\frac{d \sin (5 a+5 b x)}{400 b^2}-\frac{(c+d x) \cos (a+b x)}{8 b}-\frac{(c+d x) \cos (3 a+3 b x)}{48 b}+\frac{(c+d x) \cos (5 a+5 b x)}{80 b}",1,"-((c + d*x)*Cos[a + b*x])/(8*b) - ((c + d*x)*Cos[3*a + 3*b*x])/(48*b) + ((c + d*x)*Cos[5*a + 5*b*x])/(80*b) + (d*Sin[a + b*x])/(8*b^2) + (d*Sin[3*a + 3*b*x])/(144*b^2) - (d*Sin[5*a + 5*b*x])/(400*b^2)","A",8,3,22,0.1364,1,"{4406, 3296, 2637}"
93,1,185,0,0.3386593,"\int \frac{\cos ^2(a+b x) \sin ^3(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^3)/(c + d*x),x]","-\frac{\sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}+\frac{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}-\frac{\cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}","-\frac{\sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}+\frac{\sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}-\frac{\cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}",1,"-(CosIntegral[(5*b*c)/d + 5*b*x]*Sin[5*a - (5*b*c)/d])/(16*d) + (CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(16*d) + (CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(8*d) + (Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d) + (Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(16*d) - (Cos[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(16*d)","A",11,4,24,0.1667,1,"{4406, 3303, 3299, 3302}"
94,1,257,0,0.4164784,"\int \frac{\cos ^2(a+b x) \sin ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^3)/(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)}{8 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)}{16 d^2}-\frac{5 b \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 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)}{16 d^2}+\frac{5 b \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{\sin (a+b x)}{8 d (c+d x)}-\frac{\sin (3 a+3 b x)}{16 d (c+d x)}+\frac{\sin (5 a+5 b x)}{16 d (c+d x)}","\frac{b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 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)}{16 d^2}-\frac{5 b \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 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)}{16 d^2}+\frac{5 b \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{\sin (a+b x)}{8 d (c+d x)}-\frac{\sin (3 a+3 b x)}{16 d (c+d x)}+\frac{\sin (5 a+5 b x)}{16 d (c+d x)}",1,"(b*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(8*d^2) + (3*b*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(16*d^2) - (5*b*Cos[5*a - (5*b*c)/d]*CosIntegral[(5*b*c)/d + 5*b*x])/(16*d^2) - Sin[a + b*x]/(8*d*(c + d*x)) - Sin[3*a + 3*b*x]/(16*d*(c + d*x)) + Sin[5*a + 5*b*x]/(16*d*(c + d*x)) - (b*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d^2) - (3*b*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(16*d^2) + (5*b*Sin[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(16*d^2)","A",14,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
95,1,338,0,0.5047498,"\int \frac{\cos ^2(a+b x) \sin ^3(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^3)/(c + d*x)^3,x]","\frac{25 b^2 \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}-\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)}{32 d^3}-\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{16 d^3}-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{16 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)}{32 d^3}+\frac{25 b^2 \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}-\frac{b \cos (a+b x)}{16 d^2 (c+d x)}-\frac{3 b \cos (3 a+3 b x)}{32 d^2 (c+d x)}+\frac{5 b \cos (5 a+5 b x)}{32 d^2 (c+d x)}-\frac{\sin (a+b x)}{16 d (c+d x)^2}-\frac{\sin (3 a+3 b x)}{32 d (c+d x)^2}+\frac{\sin (5 a+5 b x)}{32 d (c+d x)^2}","\frac{25 b^2 \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}-\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)}{32 d^3}-\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{16 d^3}-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{16 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)}{32 d^3}+\frac{25 b^2 \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}-\frac{b \cos (a+b x)}{16 d^2 (c+d x)}-\frac{3 b \cos (3 a+3 b x)}{32 d^2 (c+d x)}+\frac{5 b \cos (5 a+5 b x)}{32 d^2 (c+d x)}-\frac{\sin (a+b x)}{16 d (c+d x)^2}-\frac{\sin (3 a+3 b x)}{32 d (c+d x)^2}+\frac{\sin (5 a+5 b x)}{32 d (c+d x)^2}",1,"-(b*Cos[a + b*x])/(16*d^2*(c + d*x)) - (3*b*Cos[3*a + 3*b*x])/(32*d^2*(c + d*x)) + (5*b*Cos[5*a + 5*b*x])/(32*d^2*(c + d*x)) + (25*b^2*CosIntegral[(5*b*c)/d + 5*b*x]*Sin[5*a - (5*b*c)/d])/(32*d^3) - (9*b^2*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(32*d^3) - (b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(16*d^3) - Sin[a + b*x]/(16*d*(c + d*x)^2) - Sin[3*a + 3*b*x]/(32*d*(c + d*x)^2) + Sin[5*a + 5*b*x]/(32*d*(c + d*x)^2) - (b^2*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(16*d^3) - (9*b^2*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(32*d^3) + (25*b^2*Cos[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(32*d^3)","A",17,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
96,1,413,0,0.5904003,"\int \frac{\cos ^2(a+b x) \sin ^3(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^2*Sin[a + b*x]^3)/(c + d*x)^4,x]","-\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{48 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}+\frac{125 b^3 \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{48 d^4}+\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}-\frac{125 b^3 \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^2 \sin (a+b x)}{48 d^3 (c+d x)}+\frac{3 b^2 \sin (3 a+3 b x)}{32 d^3 (c+d x)}-\frac{25 b^2 \sin (5 a+5 b x)}{96 d^3 (c+d x)}-\frac{b \cos (a+b x)}{48 d^2 (c+d x)^2}-\frac{b \cos (3 a+3 b x)}{32 d^2 (c+d x)^2}+\frac{5 b \cos (5 a+5 b x)}{96 d^2 (c+d x)^2}-\frac{\sin (a+b x)}{24 d (c+d x)^3}-\frac{\sin (3 a+3 b x)}{48 d (c+d x)^3}+\frac{\sin (5 a+5 b x)}{48 d (c+d x)^3}","-\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{48 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}+\frac{125 b^3 \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{48 d^4}+\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}-\frac{125 b^3 \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^2 \sin (a+b x)}{48 d^3 (c+d x)}+\frac{3 b^2 \sin (3 a+3 b x)}{32 d^3 (c+d x)}-\frac{25 b^2 \sin (5 a+5 b x)}{96 d^3 (c+d x)}-\frac{b \cos (a+b x)}{48 d^2 (c+d x)^2}-\frac{b \cos (3 a+3 b x)}{32 d^2 (c+d x)^2}+\frac{5 b \cos (5 a+5 b x)}{96 d^2 (c+d x)^2}-\frac{\sin (a+b x)}{24 d (c+d x)^3}-\frac{\sin (3 a+3 b x)}{48 d (c+d x)^3}+\frac{\sin (5 a+5 b x)}{48 d (c+d x)^3}",1,"-(b*Cos[a + b*x])/(48*d^2*(c + d*x)^2) - (b*Cos[3*a + 3*b*x])/(32*d^2*(c + d*x)^2) + (5*b*Cos[5*a + 5*b*x])/(96*d^2*(c + d*x)^2) - (b^3*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(48*d^4) - (9*b^3*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(32*d^4) + (125*b^3*Cos[5*a - (5*b*c)/d]*CosIntegral[(5*b*c)/d + 5*b*x])/(96*d^4) - Sin[a + b*x]/(24*d*(c + d*x)^3) + (b^2*Sin[a + b*x])/(48*d^3*(c + d*x)) - Sin[3*a + 3*b*x]/(48*d*(c + d*x)^3) + (3*b^2*Sin[3*a + 3*b*x])/(32*d^3*(c + d*x)) + Sin[5*a + 5*b*x]/(48*d*(c + d*x)^3) - (25*b^2*Sin[5*a + 5*b*x])/(96*d^3*(c + d*x)) + (b^3*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(48*d^4) + (9*b^3*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(32*d^4) - (125*b^3*Sin[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(96*d^4)","A",20,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
97,0,0,0,0.1265642,"\int (c+d x)^m \cos (a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]*Cot[a + b*x],x]","\int (c+d x)^m \cos (a+b x) \cot (a+b x) \, dx","\text{Int}\left(\csc (a+b x) (c+d x)^m,x\right)+\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}",0,"(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) + Defer[Int][(c + d*x)^m*Csc[a + b*x], x]","A",0,0,0,0,-1,"{}"
98,1,333,0,0.2841334,"\int (c+d x)^4 \cos (a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]*Cot[a + b*x],x]","-\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}+\frac{24 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}-\frac{24 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}+\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{2 (c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","-\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}+\frac{24 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}-\frac{24 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}+\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{2 (c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^4*ArcTanh[E^(I*(a + b*x))])/b + (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 + ((4*I)*d*(c + d*x)^3*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((4*I)*d*(c + d*x)^3*PolyLog[2, E^(I*(a + b*x))])/b^2 - (12*d^2*(c + d*x)^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (12*d^2*(c + d*x)^2*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((24*I)*d^3*(c + d*x)*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((24*I)*d^3*(c + d*x)*PolyLog[4, E^(I*(a + b*x))])/b^4 + (24*d^4*PolyLog[5, -E^(I*(a + b*x))])/b^5 - (24*d^4*PolyLog[5, E^(I*(a + b*x))])/b^5 + (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",17,8,20,0.4000,1,"{4408, 3296, 2638, 4183, 2531, 6609, 2282, 6589}"
99,1,254,0,0.1983502,"\int (c+d x)^3 \cos (a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]*Cot[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{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{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{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{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 - (6*d^2*(c + d*x)*Cos[a + b*x])/b^3 + ((c + d*x)^3*Cos[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 + (6*d^3*Sin[a + b*x])/b^4 - (3*d*(c + d*x)^2*Sin[a + b*x])/b^2","A",14,8,20,0.4000,1,"{4408, 3296, 2637, 4183, 2531, 6609, 2282, 6589}"
100,1,171,0,0.1383333,"\int (c+d x)^2 \cos (a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]*Cot[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 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 (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 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 (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*d^2*Cos[a + b*x])/b^3 + ((c + d*x)^2*Cos[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 - (2*d*(c + d*x)*Sin[a + b*x])/b^2","A",11,7,20,0.3500,1,"{4408, 3296, 2638, 4183, 2531, 2282, 6589}"
101,1,94,0,0.06174,"\int (c+d x) \cos (a+b x) \cot (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]*Cot[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{d \sin (a+b x)}{b^2}+\frac{(c+d x) \cos (a+b x)}{b}-\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{d \sin (a+b x)}{b^2}+\frac{(c+d x) \cos (a+b x)}{b}-\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 + ((c + d*x)*Cos[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 - (d*Sin[a + b*x])/b^2","A",8,6,18,0.3333,1,"{4408, 3296, 2637, 4183, 2279, 2391}"
102,0,0,0,0.1066251,"\int \frac{\cos (a+b x) \cot (a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]*Cot[a + b*x])/(c + d*x),x]","\int \frac{\cos (a+b x) \cot (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc (a+b x)}{c+d x},x\right)-\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}",0,"-((CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d) - (Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d + Defer[Int][Csc[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
103,0,0,0,0.1306143,"\int \frac{\cos (a+b x) \cot (a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]*Cot[a + b*x])/(c + d*x)^2,x]","\int \frac{\cos (a+b x) \cot (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc (a+b x)}{(c+d x)^2},x\right)-\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)}",0,"-((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 + Defer[Int][Csc[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
104,0,0,0,0.0347689,"\int (c+d x)^m \cot ^2(a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x]^2,x]","\int (c+d x)^m \cot ^2(a+b x) \, dx","\text{Int}\left(\cot ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Cot[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
105,1,155,0,0.2288504,"\int (c+d x)^4 \cot ^2(a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x]^2,x]","-\frac{6 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{6 d^3 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^4 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^5}+\frac{4 d (c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^4 \cot (a+b x)}{b}-\frac{i (c+d x)^4}{b}-\frac{(c+d x)^5}{5 d}","-\frac{6 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^3}+\frac{6 d^3 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^4 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^5}+\frac{4 d (c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b^2}-\frac{(c+d x)^4 \cot (a+b x)}{b}-\frac{i (c+d x)^4}{b}-\frac{(c+d x)^5}{5 d}",1,"((-I)*(c + d*x)^4)/b - (c + d*x)^5/(5*d) - ((c + d*x)^4*Cot[a + b*x])/b + (4*d*(c + d*x)^3*Log[1 - E^((2*I)*(a + b*x))])/b^2 - ((6*I)*d^2*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^3 + (6*d^3*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/b^4 + ((3*I)*d^4*PolyLog[4, E^((2*I)*(a + b*x))])/b^5","A",8,8,16,0.5000,1,"{3720, 3717, 2190, 2531, 6609, 2282, 6589, 32}"
106,1,127,0,0.1972579,"\int (c+d x)^3 \cot ^2(a+b x) \, dx","Int[(c + d*x)^3*Cot[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{(c+d x)^4}{4 d}","-\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{(c+d x)^4}{4 d}",1,"((-I)*(c + d*x)^3)/b - (c + d*x)^4/(4*d) - ((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",7,7,16,0.4375,1,"{3720, 3717, 2190, 2531, 2282, 6589, 32}"
107,1,97,0,0.1296147,"\int (c+d x)^2 \cot ^2(a+b x) \, dx","Int[(c + d*x)^2*Cot[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{(c+d x)^3}{3 d}","-\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{(c+d x)^3}{3 d}",1,"((-I)*(c + d*x)^2)/b - (c + d*x)^3/(3*d) - ((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",6,6,16,0.3750,1,"{3720, 3717, 2190, 2279, 2391, 32}"
108,1,41,0,0.0261395,"\int (c+d x) \cot ^2(a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x]^2,x]","\frac{d \log (\sin (a+b x))}{b^2}-\frac{(c+d x) \cot (a+b x)}{b}-c x-\frac{d x^2}{2}","\frac{d \log (\sin (a+b x))}{b^2}-\frac{(c+d x) \cot (a+b x)}{b}-c x-\frac{d x^2}{2}",1,"-(c*x) - (d*x^2)/2 - ((c + d*x)*Cot[a + b*x])/b + (d*Log[Sin[a + b*x]])/b^2","A",3,2,14,0.1429,1,"{3720, 3475}"
109,0,0,0,0.0355474,"\int \frac{\cot ^2(a+b x)}{c+d x} \, dx","Int[Cot[a + b*x]^2/(c + d*x),x]","\int \frac{\cot ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Cot[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
110,0,0,0,0.0344833,"\int \frac{\cot ^2(a+b x)}{(c+d x)^2} \, dx","Int[Cot[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\cot ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Cot[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
111,0,0,0,0.0752131,"\int (c+d x)^m \cot ^2(a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x]^2*Csc[a + b*x],x]","\int (c+d x)^m \cot ^2(a+b x) \csc (a+b x) \, dx","\text{Int}\left(\csc ^3(a+b x) (c+d x)^m,x\right)-\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] + Defer[Int][(c + d*x)^m*Csc[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
112,1,416,0,0.5019591,"\int (c+d x)^4 \cot ^2(a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x]^2*Csc[a + b*x],x]","\frac{12 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^3 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}-\frac{6 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{12 d^4 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^5}+\frac{12 d^4 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^5}-\frac{12 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}+\frac{12 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}-\frac{12 d^2 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \csc (a+b x)}{b^2}+\frac{(c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \cot (a+b x) \csc (a+b x)}{2 b}","\frac{12 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^3 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}-\frac{6 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{12 d^4 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^5}+\frac{12 d^4 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^5}-\frac{12 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}+\frac{12 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}-\frac{12 d^2 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \csc (a+b x)}{b^2}+\frac{(c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \cot (a+b x) \csc (a+b x)}{2 b}",1,"(-12*d^2*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b^3 + ((c + d*x)^4*ArcTanh[E^(I*(a + b*x))])/b - (2*d*(c + d*x)^3*Csc[a + b*x])/b^2 - ((c + d*x)^4*Cot[a + b*x]*Csc[a + b*x])/(2*b) + ((12*I)*d^3*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^4 - ((2*I)*d*(c + d*x)^3*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((12*I)*d^3*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^4 + ((2*I)*d*(c + d*x)^3*PolyLog[2, E^(I*(a + b*x))])/b^2 - (12*d^4*PolyLog[3, -E^(I*(a + b*x))])/b^5 + (6*d^2*(c + d*x)^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (12*d^4*PolyLog[3, E^(I*(a + b*x))])/b^5 - (6*d^2*(c + d*x)^2*PolyLog[3, E^(I*(a + b*x))])/b^3 + ((12*I)*d^3*(c + d*x)*PolyLog[4, -E^(I*(a + b*x))])/b^4 - ((12*I)*d^3*(c + d*x)*PolyLog[4, E^(I*(a + b*x))])/b^4 - (12*d^4*PolyLog[5, -E^(I*(a + b*x))])/b^5 + (12*d^4*PolyLog[5, E^(I*(a + b*x))])/b^5","A",31,7,22,0.3182,1,"{4415, 4183, 2531, 6609, 2282, 6589, 4186}"
113,1,308,0,0.3442287,"\int (c+d x)^3 \cot ^2(a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^3*Cot[a + b*x]^2*Csc[a + b*x],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",25,9,22,0.4091,1,"{4415, 4183, 2531, 6609, 2282, 6589, 4186, 2279, 2391}"
114,1,179,0,0.2230153,"\int (c+d x)^2 \cot ^2(a+b x) \csc (a+b x) \, dx","Int[(c + d*x)^2*Cot[a + b*x]^2*Csc[a + b*x],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",17,7,22,0.3182,1,"{4415, 4183, 2531, 2282, 6589, 4186, 3770}"
115,1,108,0,0.1071973,"\int (c+d x) \cot ^2(a+b x) \csc (a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x]^2*Csc[a + b*x],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",12,5,20,0.2500,1,"{4415, 4183, 2279, 2391, 4185}"
116,0,0,0,0.0810282,"\int \frac{\cot ^2(a+b x) \csc (a+b x)}{c+d x} \, dx","Int[(Cot[a + b*x]^2*Csc[a + b*x])/(c + d*x),x]","\int \frac{\cot ^2(a+b x) \csc (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x)}{c+d x},x\right)-\text{Int}\left(\frac{\csc (a+b x)}{c+d x},x\right)",0,"-Defer[Int][Csc[a + b*x]/(c + d*x), x] + Defer[Int][Csc[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
117,0,0,0,0.0804008,"\int \frac{\cot ^2(a+b x) \csc (a+b x)}{(c+d x)^2} \, dx","Int[(Cot[a + b*x]^2*Csc[a + b*x])/(c + d*x)^2,x]","\int \frac{\cot ^2(a+b x) \csc (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x)}{(c+d x)^2},x\right)-\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] + Defer[Int][Csc[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
118,1,406,0,0.6668369,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^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)}{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{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)}{16 b^{7/2}}+\frac{15 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 (a+b x)}{8 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{72 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{12 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)}{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{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)}{16 b^{7/2}}+\frac{15 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 (a+b x)}{8 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{72 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{12 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(16*b^3) - ((c + d*x)^(5/2)*Cos[a + b*x])/(4*b) + (5*d^2*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(144*b^3) - ((c + d*x)^(5/2)*Cos[3*a + 3*b*x])/(12*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]])/(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)) + (15*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])/(8*b^2) + (5*d*(c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(72*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
119,1,353,0,0.5261999,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x],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{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)}{8 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)}{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{3 d \sqrt{c+d x} \sin (a+b x)}{8 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{24 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{12 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{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)}{8 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)}{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{3 d \sqrt{c+d x} \sin (a+b x)}{8 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{24 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{12 b}",1,"-((c + d*x)^(3/2)*Cos[a + b*x])/(4*b) - ((c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(12*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]])/(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)) - (3*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)) + (3*d*Sqrt[c + d*x]*Sin[a + b*x])/(8*b^2) + (d*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(24*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
120,1,304,0,0.4161395,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*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)}{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{\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{\sqrt{c+d x} \cos (a+b x)}{4 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 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)}{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{\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{\sqrt{c+d x} \cos (a+b x)}{4 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 b}",1,"-(Sqrt[c + d*x]*Cos[a + b*x])/(4*b) - (Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(12*b) + (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)) - (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",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
121,1,304,0,0.4191207,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*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)}{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{\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{\sqrt{c+d x} \cos (a+b x)}{4 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 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)}{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{\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{\sqrt{c+d x} \cos (a+b x)}{4 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{12 b}",1,"-(Sqrt[c + d*x]*Cos[a + b*x])/(4*b) - (Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(12*b) + (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)) - (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",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
122,1,353,0,0.52797,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x],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{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)}{8 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)}{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{3 d \sqrt{c+d x} \sin (a+b x)}{8 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{24 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{12 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{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)}{8 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)}{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{3 d \sqrt{c+d x} \sin (a+b x)}{8 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{24 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{12 b}",1,"-((c + d*x)^(3/2)*Cos[a + b*x])/(4*b) - ((c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(12*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]])/(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)) - (3*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)) + (3*d*Sqrt[c + d*x]*Sin[a + b*x])/(8*b^2) + (d*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(24*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
123,1,406,0,0.6271226,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^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)}{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{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)}{16 b^{7/2}}+\frac{15 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 (a+b x)}{8 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{72 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{12 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)}{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{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)}{16 b^{7/2}}+\frac{15 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 (a+b x)}{8 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{72 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{4 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{12 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(16*b^3) - ((c + d*x)^(5/2)*Cos[a + b*x])/(4*b) + (5*d^2*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(144*b^3) - ((c + d*x)^(5/2)*Cos[3*a + 3*b*x])/(12*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]])/(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)) + (15*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])/(8*b^2) + (5*d*(c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(72*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
124,1,228,0,0.3980631,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (4 a+4 b x)}{2048 b^3}-\frac{5 d (c+d x)^{3/2} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{7/2}}{28 d}","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (4 a+4 b x)}{2048 b^3}-\frac{5 d (c+d x)^{3/2} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{7/2}}{28 d}",1,"(c + d*x)^(7/2)/(28*d) - (5*d*(c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(256*b^2) - (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^2*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(2048*b^3) - ((c + d*x)^(5/2)*Sin[4*a + 4*b*x])/(32*b)","A",10,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
125,1,200,0,0.3287374,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 d \sqrt{c+d x} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{5/2}}{20 d}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 d \sqrt{c+d x} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{5/2}}{20 d}",1,"(c + d*x)^(5/2)/(20*d) - (3*d*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(256*b^2) + (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - ((c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(32*b)","A",9,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
126,1,174,0,0.2703687,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{c+d x} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{3/2}}{12 d}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{c+d x} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{3/2}}{12 d}",1,"(c + d*x)^(3/2)/(12*d) + (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(32*b)","A",8,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
127,1,174,0,0.2491623,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{c+d x} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{3/2}}{12 d}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{c+d x} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{3/2}}{12 d}",1,"(c + d*x)^(3/2)/(12*d) + (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(32*b)","A",8,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
128,1,200,0,0.3182298,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 d \sqrt{c+d x} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{5/2}}{20 d}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 d \sqrt{c+d x} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{5/2}}{20 d}",1,"(c + d*x)^(5/2)/(20*d) - (3*d*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(256*b^2) + (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - ((c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(32*b)","A",9,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
129,1,228,0,0.3776829,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^2*Sin[a + b*x]^2,x]","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (4 a+4 b x)}{2048 b^3}-\frac{5 d (c+d x)^{3/2} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{7/2}}{28 d}","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sin (4 a+4 b x)}{2048 b^3}-\frac{5 d (c+d x)^{3/2} \cos (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \sin (4 a+4 b x)}{32 b}+\frac{(c+d x)^{7/2}}{28 d}",1,"(c + d*x)^(7/2)/(28*d) - (5*d*(c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(256*b^2) - (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^2*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(2048*b^3) - ((c + d*x)^(5/2)*Sin[4*a + 4*b*x])/(32*b)","A",10,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
130,1,615,0,1.1530028,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^2*Sin[a + b*x]^3,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)}{32 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)}{576 b^{7/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 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)}{576 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)}{32 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{576 b^3}-\frac{3 d^2 \sqrt{c+d x} \cos (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{16 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \sin (5 a+5 b x)}{160 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{5/2} \cos (5 a+5 b x)}{80 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)}{32 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)}{576 b^{7/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 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)}{576 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)}{32 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{576 b^3}-\frac{3 d^2 \sqrt{c+d x} \cos (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{16 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \sin (5 a+5 b x)}{160 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{5/2} \cos (5 a+5 b x)}{80 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(32*b^3) - ((c + d*x)^(5/2)*Cos[a + b*x])/(8*b) + (5*d^2*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(576*b^3) - ((c + d*x)^(5/2)*Cos[3*a + 3*b*x])/(48*b) - (3*d^2*Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(1600*b^3) + ((c + d*x)^(5/2)*Cos[5*a + 5*b*x])/(80*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]])/(32*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]])/(576*b^(7/2)) + (3*d^(5/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1600*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(1600*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])/(576*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])/(32*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x])/(16*b^2) + (5*d*(c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(288*b^2) - (d*(c + d*x)^(3/2)*Sin[5*a + 5*b*x])/(160*b^2)","A",26,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
131,1,534,0,0.8793483,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\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)}{96 b^{5/2}}-\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)}{16 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)}{16 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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{16 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \sin (5 a+5 b x)}{800 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{3/2} \cos (5 a+5 b x)}{80 b}","\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\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)}{96 b^{5/2}}-\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)}{16 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)}{16 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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{16 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \sin (5 a+5 b x)}{800 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{3/2} \cos (5 a+5 b x)}{80 b}",1,"-((c + d*x)^(3/2)*Cos[a + b*x])/(8*b) - ((c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(48*b) + ((c + d*x)^(3/2)*Cos[5*a + 5*b*x])/(80*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]])/(16*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]])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(800*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(800*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])/(96*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])/(16*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[a + b*x])/(16*b^2) + (d*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(96*b^2) - (3*d*Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(800*b^2)","A",23,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
132,1,459,0,0.6705482,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*Sin[a + b*x]^3,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)}{8 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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 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)}{48 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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{8 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{48 b}+\frac{\sqrt{c+d x} \cos (5 a+5 b x)}{80 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)}{8 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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 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)}{48 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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{8 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{48 b}+\frac{\sqrt{c+d x} \cos (5 a+5 b x)}{80 b}",1,"-(Sqrt[c + d*x]*Cos[a + b*x])/(8*b) - (Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(48*b) + (Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(80*b) + (Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(8*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]])/(48*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(80*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])/(48*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])/(8*b^(3/2))","A",20,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
133,1,459,0,0.6581846,"\int \sqrt{c+d x} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2*Sin[a + b*x]^3,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)}{8 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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 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)}{48 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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{8 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{48 b}+\frac{\sqrt{c+d x} \cos (5 a+5 b x)}{80 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)}{8 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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 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)}{48 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)}{8 b^{3/2}}-\frac{\sqrt{c+d x} \cos (a+b x)}{8 b}-\frac{\sqrt{c+d x} \cos (3 a+3 b x)}{48 b}+\frac{\sqrt{c+d x} \cos (5 a+5 b x)}{80 b}",1,"-(Sqrt[c + d*x]*Cos[a + b*x])/(8*b) - (Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(48*b) + (Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(80*b) + (Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(8*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]])/(48*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(80*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])/(48*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])/(8*b^(3/2))","A",20,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
134,1,534,0,0.8013996,"\int (c+d x)^{3/2} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x]^3,x]","\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\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)}{96 b^{5/2}}-\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)}{16 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)}{16 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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{16 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \sin (5 a+5 b x)}{800 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{3/2} \cos (5 a+5 b x)}{80 b}","\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\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)}{96 b^{5/2}}-\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)}{16 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)}{16 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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (a+b x)}{16 b^2}+\frac{d \sqrt{c+d x} \sin (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \sin (5 a+5 b x)}{800 b^2}-\frac{(c+d x)^{3/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{3/2} \cos (5 a+5 b x)}{80 b}",1,"-((c + d*x)^(3/2)*Cos[a + b*x])/(8*b) - ((c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(48*b) + ((c + d*x)^(3/2)*Cos[5*a + 5*b*x])/(80*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]])/(16*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]])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(800*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(800*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])/(96*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])/(16*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[a + b*x])/(16*b^2) + (d*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(96*b^2) - (3*d*Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(800*b^2)","A",23,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
135,1,615,0,0.9528041,"\int (c+d x)^{5/2} \cos ^2(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^2*Sin[a + b*x]^3,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)}{32 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)}{576 b^{7/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 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)}{576 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)}{32 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{576 b^3}-\frac{3 d^2 \sqrt{c+d x} \cos (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{16 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \sin (5 a+5 b x)}{160 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{5/2} \cos (5 a+5 b x)}{80 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)}{32 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)}{576 b^{7/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 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)}{576 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)}{32 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \cos (3 a+3 b x)}{576 b^3}-\frac{3 d^2 \sqrt{c+d x} \cos (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \sin (a+b x)}{16 b^2}+\frac{5 d (c+d x)^{3/2} \sin (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \sin (5 a+5 b x)}{160 b^2}-\frac{(c+d x)^{5/2} \cos (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (3 a+3 b x)}{48 b}+\frac{(c+d x)^{5/2} \cos (5 a+5 b x)}{80 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[a + b*x])/(32*b^3) - ((c + d*x)^(5/2)*Cos[a + b*x])/(8*b) + (5*d^2*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(576*b^3) - ((c + d*x)^(5/2)*Cos[3*a + 3*b*x])/(48*b) - (3*d^2*Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(1600*b^3) + ((c + d*x)^(5/2)*Cos[5*a + 5*b*x])/(80*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]])/(32*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]])/(576*b^(7/2)) + (3*d^(5/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1600*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(1600*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])/(576*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])/(32*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[a + b*x])/(16*b^2) + (5*d*(c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(288*b^2) - (d*(c + d*x)^(3/2)*Sin[5*a + 5*b*x])/(160*b^2)","A",26,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
136,1,273,0,0.2881188,"\int (c+d x)^m \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}","-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{4 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{4 i b (c+d x)}{d}\right)}{b}-\frac{2^{-m-4} 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{2^{-2 (m+3)} e^{-4 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{4 i b (c+d x)}{d}\right)}{b}",1,"-((2^(-4 - 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)) - (2^(-4 - 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) - (E^((4*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*(((-I)*b*(c + d*x))/d)^m) - ((c + d*x)^m*Gamma[1 + m, ((4*I)*b*(c + d*x))/d])/(2^(2*(3 + m))*b*E^((4*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",8,3,22,0.1364,1,"{4406, 3308, 2181}"
137,1,260,0,0.2340007,"\int (c+d x)^4 \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{3 d^2 (c+d x)^2 \cos ^4(a+b x)}{16 b^3}+\frac{9 d^2 (c+d x)^2 \cos ^2(a+b x)}{16 b^3}-\frac{3 d^3 (c+d x) \sin (a+b x) \cos ^3(a+b x)}{32 b^4}-\frac{45 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{64 b^4}+\frac{d (c+d x)^3 \sin (a+b x) \cos ^3(a+b x)}{4 b^2}+\frac{3 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{8 b^2}-\frac{3 d^4 \cos ^4(a+b x)}{128 b^5}-\frac{45 d^4 \cos ^2(a+b x)}{128 b^5}-\frac{(c+d x)^4 \cos ^4(a+b x)}{4 b}-\frac{45 c d^3 x}{64 b^3}-\frac{45 d^4 x^2}{128 b^3}+\frac{3 (c+d x)^4}{32 b}","\frac{3 d^2 (c+d x)^2 \cos ^4(a+b x)}{16 b^3}+\frac{9 d^2 (c+d x)^2 \cos ^2(a+b x)}{16 b^3}-\frac{3 d^3 (c+d x) \sin (a+b x) \cos ^3(a+b x)}{32 b^4}-\frac{45 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{64 b^4}+\frac{d (c+d x)^3 \sin (a+b x) \cos ^3(a+b x)}{4 b^2}+\frac{3 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{8 b^2}-\frac{3 d^4 \cos ^4(a+b x)}{128 b^5}-\frac{45 d^4 \cos ^2(a+b x)}{128 b^5}-\frac{(c+d x)^4 \cos ^4(a+b x)}{4 b}-\frac{45 c d^3 x}{64 b^3}-\frac{45 d^4 x^2}{128 b^3}+\frac{3 (c+d x)^4}{32 b}",1,"(-45*c*d^3*x)/(64*b^3) - (45*d^4*x^2)/(128*b^3) + (3*(c + d*x)^4)/(32*b) - (45*d^4*Cos[a + b*x]^2)/(128*b^5) + (9*d^2*(c + d*x)^2*Cos[a + b*x]^2)/(16*b^3) - (3*d^4*Cos[a + b*x]^4)/(128*b^5) + (3*d^2*(c + d*x)^2*Cos[a + b*x]^4)/(16*b^3) - ((c + d*x)^4*Cos[a + b*x]^4)/(4*b) - (45*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(64*b^4) + (3*d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/(8*b^2) - (3*d^3*(c + d*x)*Cos[a + b*x]^3*Sin[a + b*x])/(32*b^4) + (d*(c + d*x)^3*Cos[a + b*x]^3*Sin[a + b*x])/(4*b^2)","A",9,4,22,0.1818,1,"{4405, 3311, 32, 3310}"
138,1,196,0,0.1608406,"\int (c+d x)^3 \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{3 d^2 (c+d x) \cos ^4(a+b x)}{32 b^3}+\frac{9 d^2 (c+d x) \cos ^2(a+b x)}{32 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos ^3(a+b x)}{16 b^2}+\frac{9 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{3 d^3 \sin (a+b x) \cos ^3(a+b x)}{128 b^4}-\frac{45 d^3 \sin (a+b x) \cos (a+b x)}{256 b^4}-\frac{(c+d x)^3 \cos ^4(a+b x)}{4 b}-\frac{45 d^3 x}{256 b^3}+\frac{3 (c+d x)^3}{32 b}","\frac{3 d^2 (c+d x) \cos ^4(a+b x)}{32 b^3}+\frac{9 d^2 (c+d x) \cos ^2(a+b x)}{32 b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos ^3(a+b x)}{16 b^2}+\frac{9 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{3 d^3 \sin (a+b x) \cos ^3(a+b x)}{128 b^4}-\frac{45 d^3 \sin (a+b x) \cos (a+b x)}{256 b^4}-\frac{(c+d x)^3 \cos ^4(a+b x)}{4 b}-\frac{45 d^3 x}{256 b^3}+\frac{3 (c+d x)^3}{32 b}",1,"(-45*d^3*x)/(256*b^3) + (3*(c + d*x)^3)/(32*b) + (9*d^2*(c + d*x)*Cos[a + b*x]^2)/(32*b^3) + (3*d^2*(c + d*x)*Cos[a + b*x]^4)/(32*b^3) - ((c + d*x)^3*Cos[a + b*x]^4)/(4*b) - (45*d^3*Cos[a + b*x]*Sin[a + b*x])/(256*b^4) + (9*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(32*b^2) - (3*d^3*Cos[a + b*x]^3*Sin[a + b*x])/(128*b^4) + (3*d*(c + d*x)^2*Cos[a + b*x]^3*Sin[a + b*x])/(16*b^2)","A",9,5,22,0.2273,1,"{4405, 3311, 32, 2635, 8}"
139,1,134,0,0.086674,"\int (c+d x)^2 \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{d (c+d x) \sin (a+b x) \cos ^3(a+b x)}{8 b^2}+\frac{3 d (c+d x) \sin (a+b x) \cos (a+b x)}{16 b^2}+\frac{d^2 \cos ^4(a+b x)}{32 b^3}+\frac{3 d^2 \cos ^2(a+b x)}{32 b^3}-\frac{(c+d x)^2 \cos ^4(a+b x)}{4 b}+\frac{3 c d x}{16 b}+\frac{3 d^2 x^2}{32 b}","\frac{d (c+d x) \sin (a+b x) \cos ^3(a+b x)}{8 b^2}+\frac{3 d (c+d x) \sin (a+b x) \cos (a+b x)}{16 b^2}+\frac{d^2 \cos ^4(a+b x)}{32 b^3}+\frac{3 d^2 \cos ^2(a+b x)}{32 b^3}-\frac{(c+d x)^2 \cos ^4(a+b x)}{4 b}+\frac{3 c d x}{16 b}+\frac{3 d^2 x^2}{32 b}",1,"(3*c*d*x)/(16*b) + (3*d^2*x^2)/(32*b) + (3*d^2*Cos[a + b*x]^2)/(32*b^3) + (d^2*Cos[a + b*x]^4)/(32*b^3) - ((c + d*x)^2*Cos[a + b*x]^4)/(4*b) + (3*d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(16*b^2) + (d*(c + d*x)*Cos[a + b*x]^3*Sin[a + b*x])/(8*b^2)","A",4,2,22,0.09091,1,"{4405, 3310}"
140,1,72,0,0.0470773,"\int (c+d x) \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{d \sin (a+b x) \cos ^3(a+b x)}{16 b^2}+\frac{3 d \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{(c+d x) \cos ^4(a+b x)}{4 b}+\frac{3 d x}{32 b}","\frac{d \sin (a+b x) \cos ^3(a+b x)}{16 b^2}+\frac{3 d \sin (a+b x) \cos (a+b x)}{32 b^2}-\frac{(c+d x) \cos ^4(a+b x)}{4 b}+\frac{3 d x}{32 b}",1,"(3*d*x)/(32*b) - ((c + d*x)*Cos[a + b*x]^4)/(4*b) + (3*d*Cos[a + b*x]*Sin[a + b*x])/(32*b^2) + (d*Cos[a + b*x]^3*Sin[a + b*x])/(16*b^2)","A",4,3,20,0.1500,1,"{4405, 2635, 8}"
141,1,129,0,0.2118128,"\int \frac{\cos ^3(a+b x) \sin (a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x])/(c + d*x),x]","\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}","\frac{\sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}+\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{4 d}+\frac{\cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{8 d}",1,"(CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/(8*d) + (CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(4*d) + (Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(4*d) + (Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(8*d)","A",8,4,22,0.1818,1,"{4406, 3303, 3299, 3302}"
142,1,179,0,0.2684763,"\int \frac{\cos ^3(a+b x) \sin (a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x])/(c + d*x)^2,x]","\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}+\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}-\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)}-\frac{\sin (4 a+4 b x)}{8 d (c+d x)}","\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}+\frac{b \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^2}-\frac{b \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{2 d^2}-\frac{\sin (2 a+2 b x)}{4 d (c+d x)}-\frac{\sin (4 a+4 b x)}{8 d (c+d x)}",1,"(b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(2*d^2) + (b*Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/(2*d^2) - Sin[2*a + 2*b*x]/(4*d*(c + d*x)) - Sin[4*a + 4*b*x]/(8*d*(c + d*x)) - (b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d^2) - (b*Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(2*d^2)","A",10,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
143,1,231,0,0.3291901,"\int \frac{\cos ^3(a+b x) \sin (a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x])/(c + d*x)^3,x]","-\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \cos (2 a+2 b x)}{4 d^2 (c+d x)}-\frac{b \cos (4 a+4 b x)}{4 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{8 d (c+d x)^2}-\frac{\sin (4 a+4 b x)}{16 d (c+d x)^2}","-\frac{b^2 \sin \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d^3}-\frac{b^2 \cos \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{d^3}-\frac{b \cos (2 a+2 b x)}{4 d^2 (c+d x)}-\frac{b \cos (4 a+4 b x)}{4 d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{8 d (c+d x)^2}-\frac{\sin (4 a+4 b x)}{16 d (c+d x)^2}",1,"-(b*Cos[2*a + 2*b*x])/(4*d^2*(c + d*x)) - (b*Cos[4*a + 4*b*x])/(4*d^2*(c + d*x)) - (b^2*CosIntegral[(4*b*c)/d + 4*b*x]*Sin[4*a - (4*b*c)/d])/d^3 - (b^2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(2*d^3) - Sin[2*a + 2*b*x]/(8*d*(c + d*x)^2) - Sin[4*a + 4*b*x]/(16*d*(c + d*x)^2) - (b^2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d^3) - (b^2*Cos[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/d^3","A",12,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
144,1,287,0,0.4511765,"\int \frac{\cos ^3(a+b x) \sin (a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x])/(c + d*x)^4,x]","-\frac{b^3 \cos \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{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^3 \sin \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{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^2 \sin (2 a+2 b x)}{6 d^3 (c+d x)}+\frac{b^2 \sin (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{12 d^2 (c+d x)^2}-\frac{b \cos (4 a+4 b x)}{12 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{12 d (c+d x)^3}-\frac{\sin (4 a+4 b x)}{24 d (c+d x)^3}","-\frac{b^3 \cos \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{4 b^3 \cos \left(4 a-\frac{4 b c}{d}\right) \text{CosIntegral}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^3 \sin \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{4 b^3 \sin \left(4 a-\frac{4 b c}{d}\right) \text{Si}\left(\frac{4 b c}{d}+4 b x\right)}{3 d^4}+\frac{b^2 \sin (2 a+2 b x)}{6 d^3 (c+d x)}+\frac{b^2 \sin (4 a+4 b x)}{3 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{12 d^2 (c+d x)^2}-\frac{b \cos (4 a+4 b x)}{12 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{12 d (c+d x)^3}-\frac{\sin (4 a+4 b x)}{24 d (c+d x)^3}",1,"-(b*Cos[2*a + 2*b*x])/(12*d^2*(c + d*x)^2) - (b*Cos[4*a + 4*b*x])/(12*d^2*(c + d*x)^2) - (b^3*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(3*d^4) - (4*b^3*Cos[4*a - (4*b*c)/d]*CosIntegral[(4*b*c)/d + 4*b*x])/(3*d^4) - Sin[2*a + 2*b*x]/(12*d*(c + d*x)^3) + (b^2*Sin[2*a + 2*b*x])/(6*d^3*(c + d*x)) - Sin[4*a + 4*b*x]/(24*d*(c + d*x)^3) + (b^2*Sin[4*a + 4*b*x])/(3*d^3*(c + d*x)) + (b^3*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(3*d^4) + (4*b^3*Sin[4*a - (4*b*c)/d]*SinIntegral[(4*b*c)/d + 4*b*x])/(3*d^4)","A",14,5,22,0.2273,1,"{4406, 3297, 3303, 3299, 3302}"
145,1,419,0,0.4347329,"\int (c+d x)^m \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{i 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)}{16 b}+\frac{i 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)}{32 b}+\frac{i 5^{-m-1} e^{5 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{5 i b (c+d x)}{d}\right)}{32 b}+\frac{i 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)}{16 b}-\frac{i 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)}{32 b}-\frac{i 5^{-m-1} e^{-5 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{5 i b (c+d x)}{d}\right)}{32 b}","-\frac{i 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)}{16 b}+\frac{i 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)}{32 b}+\frac{i 5^{-m-1} e^{5 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{5 i b (c+d x)}{d}\right)}{32 b}+\frac{i 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)}{16 b}-\frac{i 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)}{32 b}-\frac{i 5^{-m-1} e^{-5 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{5 i b (c+d x)}{d}\right)}{32 b}",1,"((-I/16)*E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) + ((I/16)*(c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + ((I/32)*3^(-1 - m)*E^((3*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-3*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - ((I/32)*3^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((3*I)*b*(c + d*x))/d])/(b*E^((3*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + ((I/32)*5^(-1 - m)*E^((5*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-5*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - ((I/32)*5^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((5*I)*b*(c + d*x))/d])/(b*E^((5*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",11,3,24,0.1250,1,"{4406, 3307, 2181}"
146,1,330,0,0.3683168,"\int (c+d x)^4 \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 d^2 (c+d x)^2 \sin (a+b x)}{2 b^3}+\frac{d^2 (c+d x)^2 \sin (3 a+3 b x)}{36 b^3}+\frac{3 d^2 (c+d x)^2 \sin (5 a+5 b x)}{500 b^3}-\frac{3 d^3 (c+d x) \cos (a+b x)}{b^4}+\frac{d^3 (c+d x) \cos (3 a+3 b x)}{54 b^4}+\frac{3 d^3 (c+d x) \cos (5 a+5 b x)}{1250 b^4}+\frac{d (c+d x)^3 \cos (a+b x)}{2 b^2}-\frac{d (c+d x)^3 \cos (3 a+3 b x)}{36 b^2}-\frac{d (c+d x)^3 \cos (5 a+5 b x)}{100 b^2}+\frac{3 d^4 \sin (a+b x)}{b^5}-\frac{d^4 \sin (3 a+3 b x)}{162 b^5}-\frac{3 d^4 \sin (5 a+5 b x)}{6250 b^5}+\frac{(c+d x)^4 \sin (a+b x)}{8 b}-\frac{(c+d x)^4 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^4 \sin (5 a+5 b x)}{80 b}","-\frac{3 d^2 (c+d x)^2 \sin (a+b x)}{2 b^3}+\frac{d^2 (c+d x)^2 \sin (3 a+3 b x)}{36 b^3}+\frac{3 d^2 (c+d x)^2 \sin (5 a+5 b x)}{500 b^3}-\frac{3 d^3 (c+d x) \cos (a+b x)}{b^4}+\frac{d^3 (c+d x) \cos (3 a+3 b x)}{54 b^4}+\frac{3 d^3 (c+d x) \cos (5 a+5 b x)}{1250 b^4}+\frac{d (c+d x)^3 \cos (a+b x)}{2 b^2}-\frac{d (c+d x)^3 \cos (3 a+3 b x)}{36 b^2}-\frac{d (c+d x)^3 \cos (5 a+5 b x)}{100 b^2}+\frac{3 d^4 \sin (a+b x)}{b^5}-\frac{d^4 \sin (3 a+3 b x)}{162 b^5}-\frac{3 d^4 \sin (5 a+5 b x)}{6250 b^5}+\frac{(c+d x)^4 \sin (a+b x)}{8 b}-\frac{(c+d x)^4 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^4 \sin (5 a+5 b x)}{80 b}",1,"(-3*d^3*(c + d*x)*Cos[a + b*x])/b^4 + (d*(c + d*x)^3*Cos[a + b*x])/(2*b^2) + (d^3*(c + d*x)*Cos[3*a + 3*b*x])/(54*b^4) - (d*(c + d*x)^3*Cos[3*a + 3*b*x])/(36*b^2) + (3*d^3*(c + d*x)*Cos[5*a + 5*b*x])/(1250*b^4) - (d*(c + d*x)^3*Cos[5*a + 5*b*x])/(100*b^2) + (3*d^4*Sin[a + b*x])/b^5 - (3*d^2*(c + d*x)^2*Sin[a + b*x])/(2*b^3) + ((c + d*x)^4*Sin[a + b*x])/(8*b) - (d^4*Sin[3*a + 3*b*x])/(162*b^5) + (d^2*(c + d*x)^2*Sin[3*a + 3*b*x])/(36*b^3) - ((c + d*x)^4*Sin[3*a + 3*b*x])/(48*b) - (3*d^4*Sin[5*a + 5*b*x])/(6250*b^5) + (3*d^2*(c + d*x)^2*Sin[5*a + 5*b*x])/(500*b^3) - ((c + d*x)^4*Sin[5*a + 5*b*x])/(80*b)","A",17,3,24,0.1250,1,"{4406, 3296, 2637}"
147,1,259,0,0.2726047,"\int (c+d x)^3 \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 d^2 (c+d x) \sin (a+b x)}{4 b^3}+\frac{d^2 (c+d x) \sin (3 a+3 b x)}{72 b^3}+\frac{3 d^2 (c+d x) \sin (5 a+5 b x)}{1000 b^3}+\frac{3 d (c+d x)^2 \cos (a+b x)}{8 b^2}-\frac{d (c+d x)^2 \cos (3 a+3 b x)}{48 b^2}-\frac{3 d (c+d x)^2 \cos (5 a+5 b x)}{400 b^2}-\frac{3 d^3 \cos (a+b x)}{4 b^4}+\frac{d^3 \cos (3 a+3 b x)}{216 b^4}+\frac{3 d^3 \cos (5 a+5 b x)}{5000 b^4}+\frac{(c+d x)^3 \sin (a+b x)}{8 b}-\frac{(c+d x)^3 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^3 \sin (5 a+5 b x)}{80 b}","-\frac{3 d^2 (c+d x) \sin (a+b x)}{4 b^3}+\frac{d^2 (c+d x) \sin (3 a+3 b x)}{72 b^3}+\frac{3 d^2 (c+d x) \sin (5 a+5 b x)}{1000 b^3}+\frac{3 d (c+d x)^2 \cos (a+b x)}{8 b^2}-\frac{d (c+d x)^2 \cos (3 a+3 b x)}{48 b^2}-\frac{3 d (c+d x)^2 \cos (5 a+5 b x)}{400 b^2}-\frac{3 d^3 \cos (a+b x)}{4 b^4}+\frac{d^3 \cos (3 a+3 b x)}{216 b^4}+\frac{3 d^3 \cos (5 a+5 b x)}{5000 b^4}+\frac{(c+d x)^3 \sin (a+b x)}{8 b}-\frac{(c+d x)^3 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^3 \sin (5 a+5 b x)}{80 b}",1,"(-3*d^3*Cos[a + b*x])/(4*b^4) + (3*d*(c + d*x)^2*Cos[a + b*x])/(8*b^2) + (d^3*Cos[3*a + 3*b*x])/(216*b^4) - (d*(c + d*x)^2*Cos[3*a + 3*b*x])/(48*b^2) + (3*d^3*Cos[5*a + 5*b*x])/(5000*b^4) - (3*d*(c + d*x)^2*Cos[5*a + 5*b*x])/(400*b^2) - (3*d^2*(c + d*x)*Sin[a + b*x])/(4*b^3) + ((c + d*x)^3*Sin[a + b*x])/(8*b) + (d^2*(c + d*x)*Sin[3*a + 3*b*x])/(72*b^3) - ((c + d*x)^3*Sin[3*a + 3*b*x])/(48*b) + (3*d^2*(c + d*x)*Sin[5*a + 5*b*x])/(1000*b^3) - ((c + d*x)^3*Sin[5*a + 5*b*x])/(80*b)","A",14,3,24,0.1250,1,"{4406, 3296, 2638}"
148,1,184,0,0.1899544,"\int (c+d x)^2 \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","\frac{d (c+d x) \cos (a+b x)}{4 b^2}-\frac{d (c+d x) \cos (3 a+3 b x)}{72 b^2}-\frac{d (c+d x) \cos (5 a+5 b x)}{200 b^2}-\frac{d^2 \sin (a+b x)}{4 b^3}+\frac{d^2 \sin (3 a+3 b x)}{216 b^3}+\frac{d^2 \sin (5 a+5 b x)}{1000 b^3}+\frac{(c+d x)^2 \sin (a+b x)}{8 b}-\frac{(c+d x)^2 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^2 \sin (5 a+5 b x)}{80 b}","\frac{d (c+d x) \cos (a+b x)}{4 b^2}-\frac{d (c+d x) \cos (3 a+3 b x)}{72 b^2}-\frac{d (c+d x) \cos (5 a+5 b x)}{200 b^2}-\frac{d^2 \sin (a+b x)}{4 b^3}+\frac{d^2 \sin (3 a+3 b x)}{216 b^3}+\frac{d^2 \sin (5 a+5 b x)}{1000 b^3}+\frac{(c+d x)^2 \sin (a+b x)}{8 b}-\frac{(c+d x)^2 \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^2 \sin (5 a+5 b x)}{80 b}",1,"(d*(c + d*x)*Cos[a + b*x])/(4*b^2) - (d*(c + d*x)*Cos[3*a + 3*b*x])/(72*b^2) - (d*(c + d*x)*Cos[5*a + 5*b*x])/(200*b^2) - (d^2*Sin[a + b*x])/(4*b^3) + ((c + d*x)^2*Sin[a + b*x])/(8*b) + (d^2*Sin[3*a + 3*b*x])/(216*b^3) - ((c + d*x)^2*Sin[3*a + 3*b*x])/(48*b) + (d^2*Sin[5*a + 5*b*x])/(1000*b^3) - ((c + d*x)^2*Sin[5*a + 5*b*x])/(80*b)","A",11,3,24,0.1250,1,"{4406, 3296, 2637}"
149,1,109,0,0.0939269,"\int (c+d x) \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","\frac{d \cos (a+b x)}{8 b^2}-\frac{d \cos (3 a+3 b x)}{144 b^2}-\frac{d \cos (5 a+5 b x)}{400 b^2}+\frac{(c+d x) \sin (a+b x)}{8 b}-\frac{(c+d x) \sin (3 a+3 b x)}{48 b}-\frac{(c+d x) \sin (5 a+5 b x)}{80 b}","\frac{d \cos (a+b x)}{8 b^2}-\frac{d \cos (3 a+3 b x)}{144 b^2}-\frac{d \cos (5 a+5 b x)}{400 b^2}+\frac{(c+d x) \sin (a+b x)}{8 b}-\frac{(c+d x) \sin (3 a+3 b x)}{48 b}-\frac{(c+d x) \sin (5 a+5 b x)}{80 b}",1,"(d*Cos[a + b*x])/(8*b^2) - (d*Cos[3*a + 3*b*x])/(144*b^2) - (d*Cos[5*a + 5*b*x])/(400*b^2) + ((c + d*x)*Sin[a + b*x])/(8*b) - ((c + d*x)*Sin[3*a + 3*b*x])/(48*b) - ((c + d*x)*Sin[5*a + 5*b*x])/(80*b)","A",8,3,22,0.1364,1,"{4406, 3296, 2638}"
150,1,185,0,0.2798522,"\int \frac{\cos ^3(a+b x) \sin ^2(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^2)/(c + d*x),x]","\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}-\frac{\cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}-\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}+\frac{\sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}","\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d}-\frac{\cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}-\frac{\cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}-\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d}+\frac{\sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d}+\frac{\sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d}",1,"(Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(8*d) - (Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(16*d) - (Cos[5*a - (5*b*c)/d]*CosIntegral[(5*b*c)/d + 5*b*x])/(16*d) - (Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d) + (Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(16*d) + (Sin[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(16*d)","A",11,4,24,0.1667,1,"{4406, 3303, 3299, 3302}"
151,1,257,0,0.3449436,"\int \frac{\cos ^3(a+b x) \sin ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^2)/(c + d*x)^2,x]","\frac{5 b \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}+\frac{3 b \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^2}-\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^2}+\frac{3 b \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d^2}+\frac{5 b \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{\cos (a+b x)}{8 d (c+d x)}+\frac{\cos (3 a+3 b x)}{16 d (c+d x)}+\frac{\cos (5 a+5 b x)}{16 d (c+d x)}","\frac{5 b \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}+\frac{3 b \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{16 d^2}-\frac{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{8 d^2}-\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{8 d^2}+\frac{3 b \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{16 d^2}+\frac{5 b \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{16 d^2}-\frac{\cos (a+b x)}{8 d (c+d x)}+\frac{\cos (3 a+3 b x)}{16 d (c+d x)}+\frac{\cos (5 a+5 b x)}{16 d (c+d x)}",1,"-Cos[a + b*x]/(8*d*(c + d*x)) + Cos[3*a + 3*b*x]/(16*d*(c + d*x)) + Cos[5*a + 5*b*x]/(16*d*(c + d*x)) + (5*b*CosIntegral[(5*b*c)/d + 5*b*x]*Sin[5*a - (5*b*c)/d])/(16*d^2) + (3*b*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(16*d^2) - (b*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(8*d^2) - (b*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(8*d^2) + (3*b*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(16*d^2) + (5*b*Cos[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(16*d^2)","A",14,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
152,1,338,0,0.4378001,"\int \frac{\cos ^3(a+b x) \sin ^2(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^2)/(c + d*x)^3,x]","-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{16 d^3}+\frac{9 b^2 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^3}+\frac{25 b^2 \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{16 d^3}-\frac{9 b^2 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^3}-\frac{25 b^2 \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}+\frac{b \sin (a+b x)}{16 d^2 (c+d x)}-\frac{3 b \sin (3 a+3 b x)}{32 d^2 (c+d x)}-\frac{5 b \sin (5 a+5 b x)}{32 d^2 (c+d x)}-\frac{\cos (a+b x)}{16 d (c+d x)^2}+\frac{\cos (3 a+3 b x)}{32 d (c+d x)^2}+\frac{\cos (5 a+5 b x)}{32 d (c+d x)^2}","-\frac{b^2 \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{16 d^3}+\frac{9 b^2 \cos \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^3}+\frac{25 b^2 \cos \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{16 d^3}-\frac{9 b^2 \sin \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^3}-\frac{25 b^2 \sin \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{32 d^3}+\frac{b \sin (a+b x)}{16 d^2 (c+d x)}-\frac{3 b \sin (3 a+3 b x)}{32 d^2 (c+d x)}-\frac{5 b \sin (5 a+5 b x)}{32 d^2 (c+d x)}-\frac{\cos (a+b x)}{16 d (c+d x)^2}+\frac{\cos (3 a+3 b x)}{32 d (c+d x)^2}+\frac{\cos (5 a+5 b x)}{32 d (c+d x)^2}",1,"-Cos[a + b*x]/(16*d*(c + d*x)^2) + Cos[3*a + 3*b*x]/(32*d*(c + d*x)^2) + Cos[5*a + 5*b*x]/(32*d*(c + d*x)^2) - (b^2*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(16*d^3) + (9*b^2*Cos[3*a - (3*b*c)/d]*CosIntegral[(3*b*c)/d + 3*b*x])/(32*d^3) + (25*b^2*Cos[5*a - (5*b*c)/d]*CosIntegral[(5*b*c)/d + 5*b*x])/(32*d^3) + (b*Sin[a + b*x])/(16*d^2*(c + d*x)) - (3*b*Sin[3*a + 3*b*x])/(32*d^2*(c + d*x)) - (5*b*Sin[5*a + 5*b*x])/(32*d^2*(c + d*x)) + (b^2*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(16*d^3) - (9*b^2*Sin[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(32*d^3) - (25*b^2*Sin[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(32*d^3)","A",17,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
153,1,413,0,0.5383889,"\int \frac{\cos ^3(a+b x) \sin ^2(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^2)/(c + d*x)^4,x]","-\frac{125 b^3 \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}-\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{48 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{48 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}-\frac{125 b^3 \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^2 \cos (a+b x)}{48 d^3 (c+d x)}-\frac{3 b^2 \cos (3 a+3 b x)}{32 d^3 (c+d x)}-\frac{25 b^2 \cos (5 a+5 b x)}{96 d^3 (c+d x)}+\frac{b \sin (a+b x)}{48 d^2 (c+d x)^2}-\frac{b \sin (3 a+3 b x)}{32 d^2 (c+d x)^2}-\frac{5 b \sin (5 a+5 b x)}{96 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{24 d (c+d x)^3}+\frac{\cos (3 a+3 b x)}{48 d (c+d x)^3}+\frac{\cos (5 a+5 b x)}{48 d (c+d x)^3}","-\frac{125 b^3 \sin \left(5 a-\frac{5 b c}{d}\right) \text{CosIntegral}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}-\frac{9 b^3 \sin \left(3 a-\frac{3 b c}{d}\right) \text{CosIntegral}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}+\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{48 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{48 d^4}-\frac{9 b^3 \cos \left(3 a-\frac{3 b c}{d}\right) \text{Si}\left(\frac{3 b c}{d}+3 b x\right)}{32 d^4}-\frac{125 b^3 \cos \left(5 a-\frac{5 b c}{d}\right) \text{Si}\left(\frac{5 b c}{d}+5 b x\right)}{96 d^4}+\frac{b^2 \cos (a+b x)}{48 d^3 (c+d x)}-\frac{3 b^2 \cos (3 a+3 b x)}{32 d^3 (c+d x)}-\frac{25 b^2 \cos (5 a+5 b x)}{96 d^3 (c+d x)}+\frac{b \sin (a+b x)}{48 d^2 (c+d x)^2}-\frac{b \sin (3 a+3 b x)}{32 d^2 (c+d x)^2}-\frac{5 b \sin (5 a+5 b x)}{96 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{24 d (c+d x)^3}+\frac{\cos (3 a+3 b x)}{48 d (c+d x)^3}+\frac{\cos (5 a+5 b x)}{48 d (c+d x)^3}",1,"-Cos[a + b*x]/(24*d*(c + d*x)^3) + (b^2*Cos[a + b*x])/(48*d^3*(c + d*x)) + Cos[3*a + 3*b*x]/(48*d*(c + d*x)^3) - (3*b^2*Cos[3*a + 3*b*x])/(32*d^3*(c + d*x)) + Cos[5*a + 5*b*x]/(48*d*(c + d*x)^3) - (25*b^2*Cos[5*a + 5*b*x])/(96*d^3*(c + d*x)) - (125*b^3*CosIntegral[(5*b*c)/d + 5*b*x]*Sin[5*a - (5*b*c)/d])/(96*d^4) - (9*b^3*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(32*d^4) + (b^3*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(48*d^4) + (b*Sin[a + b*x])/(48*d^2*(c + d*x)^2) - (b*Sin[3*a + 3*b*x])/(32*d^2*(c + d*x)^2) - (5*b*Sin[5*a + 5*b*x])/(96*d^2*(c + d*x)^2) + (b^3*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(48*d^4) - (9*b^3*Cos[3*a - (3*b*c)/d]*SinIntegral[(3*b*c)/d + 3*b*x])/(32*d^4) - (125*b^3*Cos[5*a - (5*b*c)/d]*SinIntegral[(5*b*c)/d + 5*b*x])/(96*d^4)","A",20,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
154,1,285,0,0.3169923,"\int (c+d x)^m \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","-\frac{3\ 2^{-m-7} 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{2^{-m-7} 3^{-m-1} e^{6 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{6 i b (c+d x)}{d}\right)}{b}-\frac{3\ 2^{-m-7} 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{2^{-m-7} 3^{-m-1} e^{-6 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{6 i b (c+d x)}{d}\right)}{b}","-\frac{3\ 2^{-m-7} 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{2^{-m-7} 3^{-m-1} e^{6 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{6 i b (c+d x)}{d}\right)}{b}-\frac{3\ 2^{-m-7} 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{2^{-m-7} 3^{-m-1} e^{-6 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{6 i b (c+d x)}{d}\right)}{b}",1,"(-3*2^(-7 - 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) - (3*2^(-7 - 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) + (2^(-7 - m)*3^(-1 - m)*E^((6*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-6*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) + (2^(-7 - m)*3^(-1 - m)*(c + d*x)^m*Gamma[1 + m, ((6*I)*b*(c + d*x))/d])/(b*E^((6*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",8,3,24,0.1250,1,"{4406, 3308, 2181}"
155,1,233,0,0.265973,"\int (c+d x)^4 \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","-\frac{9 d^3 (c+d x) \sin (2 a+2 b x)}{64 b^4}+\frac{d^3 (c+d x) \sin (6 a+6 b x)}{1728 b^4}+\frac{9 d^2 (c+d x)^2 \cos (2 a+2 b x)}{64 b^3}-\frac{d^2 (c+d x)^2 \cos (6 a+6 b x)}{576 b^3}+\frac{3 d (c+d x)^3 \sin (2 a+2 b x)}{32 b^2}-\frac{d (c+d x)^3 \sin (6 a+6 b x)}{288 b^2}-\frac{9 d^4 \cos (2 a+2 b x)}{128 b^5}+\frac{d^4 \cos (6 a+6 b x)}{10368 b^5}-\frac{3 (c+d x)^4 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^4 \cos (6 a+6 b x)}{192 b}","-\frac{9 d^3 (c+d x) \sin (2 a+2 b x)}{64 b^4}+\frac{d^3 (c+d x) \sin (6 a+6 b x)}{1728 b^4}+\frac{9 d^2 (c+d x)^2 \cos (2 a+2 b x)}{64 b^3}-\frac{d^2 (c+d x)^2 \cos (6 a+6 b x)}{576 b^3}+\frac{3 d (c+d x)^3 \sin (2 a+2 b x)}{32 b^2}-\frac{d (c+d x)^3 \sin (6 a+6 b x)}{288 b^2}-\frac{9 d^4 \cos (2 a+2 b x)}{128 b^5}+\frac{d^4 \cos (6 a+6 b x)}{10368 b^5}-\frac{3 (c+d x)^4 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^4 \cos (6 a+6 b x)}{192 b}",1,"(-9*d^4*Cos[2*a + 2*b*x])/(128*b^5) + (9*d^2*(c + d*x)^2*Cos[2*a + 2*b*x])/(64*b^3) - (3*(c + d*x)^4*Cos[2*a + 2*b*x])/(64*b) + (d^4*Cos[6*a + 6*b*x])/(10368*b^5) - (d^2*(c + d*x)^2*Cos[6*a + 6*b*x])/(576*b^3) + ((c + d*x)^4*Cos[6*a + 6*b*x])/(192*b) - (9*d^3*(c + d*x)*Sin[2*a + 2*b*x])/(64*b^4) + (3*d*(c + d*x)^3*Sin[2*a + 2*b*x])/(32*b^2) + (d^3*(c + d*x)*Sin[6*a + 6*b*x])/(1728*b^4) - (d*(c + d*x)^3*Sin[6*a + 6*b*x])/(288*b^2)","A",12,3,24,0.1250,1,"{4406, 3296, 2638}"
156,1,181,0,0.2189438,"\int (c+d x)^3 \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{9 d^2 (c+d x) \cos (2 a+2 b x)}{128 b^3}-\frac{d^2 (c+d x) \cos (6 a+6 b x)}{1152 b^3}+\frac{9 d (c+d x)^2 \sin (2 a+2 b x)}{128 b^2}-\frac{d (c+d x)^2 \sin (6 a+6 b x)}{384 b^2}-\frac{9 d^3 \sin (2 a+2 b x)}{256 b^4}+\frac{d^3 \sin (6 a+6 b x)}{6912 b^4}-\frac{3 (c+d x)^3 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^3 \cos (6 a+6 b x)}{192 b}","\frac{9 d^2 (c+d x) \cos (2 a+2 b x)}{128 b^3}-\frac{d^2 (c+d x) \cos (6 a+6 b x)}{1152 b^3}+\frac{9 d (c+d x)^2 \sin (2 a+2 b x)}{128 b^2}-\frac{d (c+d x)^2 \sin (6 a+6 b x)}{384 b^2}-\frac{9 d^3 \sin (2 a+2 b x)}{256 b^4}+\frac{d^3 \sin (6 a+6 b x)}{6912 b^4}-\frac{3 (c+d x)^3 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^3 \cos (6 a+6 b x)}{192 b}",1,"(9*d^2*(c + d*x)*Cos[2*a + 2*b*x])/(128*b^3) - (3*(c + d*x)^3*Cos[2*a + 2*b*x])/(64*b) - (d^2*(c + d*x)*Cos[6*a + 6*b*x])/(1152*b^3) + ((c + d*x)^3*Cos[6*a + 6*b*x])/(192*b) - (9*d^3*Sin[2*a + 2*b*x])/(256*b^4) + (9*d*(c + d*x)^2*Sin[2*a + 2*b*x])/(128*b^2) + (d^3*Sin[6*a + 6*b*x])/(6912*b^4) - (d*(c + d*x)^2*Sin[6*a + 6*b*x])/(384*b^2)","A",10,3,24,0.1250,1,"{4406, 3296, 2637}"
157,1,129,0,0.1437953,"\int (c+d x)^2 \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{3 d (c+d x) \sin (2 a+2 b x)}{64 b^2}-\frac{d (c+d x) \sin (6 a+6 b x)}{576 b^2}+\frac{3 d^2 \cos (2 a+2 b x)}{128 b^3}-\frac{d^2 \cos (6 a+6 b x)}{3456 b^3}-\frac{3 (c+d x)^2 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^2 \cos (6 a+6 b x)}{192 b}","\frac{3 d (c+d x) \sin (2 a+2 b x)}{64 b^2}-\frac{d (c+d x) \sin (6 a+6 b x)}{576 b^2}+\frac{3 d^2 \cos (2 a+2 b x)}{128 b^3}-\frac{d^2 \cos (6 a+6 b x)}{3456 b^3}-\frac{3 (c+d x)^2 \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^2 \cos (6 a+6 b x)}{192 b}",1,"(3*d^2*Cos[2*a + 2*b*x])/(128*b^3) - (3*(c + d*x)^2*Cos[2*a + 2*b*x])/(64*b) - (d^2*Cos[6*a + 6*b*x])/(3456*b^3) + ((c + d*x)^2*Cos[6*a + 6*b*x])/(192*b) + (3*d*(c + d*x)*Sin[2*a + 2*b*x])/(64*b^2) - (d*(c + d*x)*Sin[6*a + 6*b*x])/(576*b^2)","A",8,3,24,0.1250,1,"{4406, 3296, 2638}"
158,1,77,0,0.0744242,"\int (c+d x) \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{3 d \sin (2 a+2 b x)}{128 b^2}-\frac{d \sin (6 a+6 b x)}{1152 b^2}-\frac{3 (c+d x) \cos (2 a+2 b x)}{64 b}+\frac{(c+d x) \cos (6 a+6 b x)}{192 b}","\frac{3 d \sin (2 a+2 b x)}{128 b^2}-\frac{d \sin (6 a+6 b x)}{1152 b^2}-\frac{3 (c+d x) \cos (2 a+2 b x)}{64 b}+\frac{(c+d x) \cos (6 a+6 b x)}{192 b}",1,"(-3*(c + d*x)*Cos[2*a + 2*b*x])/(64*b) + ((c + d*x)*Cos[6*a + 6*b*x])/(192*b) + (3*d*Sin[2*a + 2*b*x])/(128*b^2) - (d*Sin[6*a + 6*b*x])/(1152*b^2)","A",6,3,22,0.1364,1,"{4406, 3296, 2637}"
159,1,129,0,0.2460711,"\int \frac{\cos ^3(a+b x) \sin ^3(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^3)/(c + d*x),x]","-\frac{\sin \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{32 d}+\frac{3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{32 d}+\frac{3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{32 d}-\frac{\cos \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{32 d}","-\frac{\sin \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{32 d}+\frac{3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{32 d}+\frac{3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{32 d}-\frac{\cos \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{32 d}",1,"-(CosIntegral[(6*b*c)/d + 6*b*x]*Sin[6*a - (6*b*c)/d])/(32*d) + (3*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(32*d) + (3*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(32*d) - (Cos[6*a - (6*b*c)/d]*SinIntegral[(6*b*c)/d + 6*b*x])/(32*d)","A",8,4,24,0.1667,1,"{4406, 3303, 3299, 3302}"
160,1,179,0,0.2970979,"\int \frac{\cos ^3(a+b x) \sin ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^3)/(c + d*x)^2,x]","\frac{3 b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^2}-\frac{3 b \cos \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^2}-\frac{3 b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^2}+\frac{3 b \sin \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^2}-\frac{3 \sin (2 a+2 b x)}{32 d (c+d x)}+\frac{\sin (6 a+6 b x)}{32 d (c+d x)}","\frac{3 b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^2}-\frac{3 b \cos \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^2}-\frac{3 b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^2}+\frac{3 b \sin \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^2}-\frac{3 \sin (2 a+2 b x)}{32 d (c+d x)}+\frac{\sin (6 a+6 b x)}{32 d (c+d x)}",1,"(3*b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(16*d^2) - (3*b*Cos[6*a - (6*b*c)/d]*CosIntegral[(6*b*c)/d + 6*b*x])/(16*d^2) - (3*Sin[2*a + 2*b*x])/(32*d*(c + d*x)) + Sin[6*a + 6*b*x]/(32*d*(c + d*x)) - (3*b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(16*d^2) + (3*b*Sin[6*a - (6*b*c)/d]*SinIntegral[(6*b*c)/d + 6*b*x])/(16*d^2)","A",10,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
161,1,235,0,0.3532232,"\int \frac{\cos ^3(a+b x) \sin ^3(a+b x)}{(c+d x)^3} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^3)/(c + d*x)^3,x]","\frac{9 b^2 \sin \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^3}-\frac{3 b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^3}-\frac{3 b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^3}+\frac{9 b^2 \cos \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^3}-\frac{3 b \cos (2 a+2 b x)}{32 d^2 (c+d x)}+\frac{3 b \cos (6 a+6 b x)}{32 d^2 (c+d x)}-\frac{3 \sin (2 a+2 b x)}{64 d (c+d x)^2}+\frac{\sin (6 a+6 b x)}{64 d (c+d x)^2}","\frac{9 b^2 \sin \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^3}-\frac{3 b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^3}-\frac{3 b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{16 d^3}+\frac{9 b^2 \cos \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{16 d^3}-\frac{3 b \cos (2 a+2 b x)}{32 d^2 (c+d x)}+\frac{3 b \cos (6 a+6 b x)}{32 d^2 (c+d x)}-\frac{3 \sin (2 a+2 b x)}{64 d (c+d x)^2}+\frac{\sin (6 a+6 b x)}{64 d (c+d x)^2}",1,"(-3*b*Cos[2*a + 2*b*x])/(32*d^2*(c + d*x)) + (3*b*Cos[6*a + 6*b*x])/(32*d^2*(c + d*x)) + (9*b^2*CosIntegral[(6*b*c)/d + 6*b*x]*Sin[6*a - (6*b*c)/d])/(16*d^3) - (3*b^2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(16*d^3) - (3*Sin[2*a + 2*b*x])/(64*d*(c + d*x)^2) + Sin[6*a + 6*b*x]/(64*d*(c + d*x)^2) - (3*b^2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(16*d^3) + (9*b^2*Cos[6*a - (6*b*c)/d]*SinIntegral[(6*b*c)/d + 6*b*x])/(16*d^3)","A",12,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
162,1,287,0,0.4192223,"\int \frac{\cos ^3(a+b x) \sin ^3(a+b x)}{(c+d x)^4} \, dx","Int[(Cos[a + b*x]^3*Sin[a + b*x]^3)/(c + d*x)^4,x]","-\frac{b^3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{8 d^4}+\frac{9 b^3 \cos \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{8 d^4}+\frac{b^3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{8 d^4}-\frac{9 b^3 \sin \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{8 d^4}+\frac{b^2 \sin (2 a+2 b x)}{16 d^3 (c+d x)}-\frac{3 b^2 \sin (6 a+6 b x)}{16 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{32 d^2 (c+d x)^2}+\frac{b \cos (6 a+6 b x)}{32 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{32 d (c+d x)^3}+\frac{\sin (6 a+6 b x)}{96 d (c+d x)^3}","-\frac{b^3 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{8 d^4}+\frac{9 b^3 \cos \left(6 a-\frac{6 b c}{d}\right) \text{CosIntegral}\left(\frac{6 b c}{d}+6 b x\right)}{8 d^4}+\frac{b^3 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{8 d^4}-\frac{9 b^3 \sin \left(6 a-\frac{6 b c}{d}\right) \text{Si}\left(\frac{6 b c}{d}+6 b x\right)}{8 d^4}+\frac{b^2 \sin (2 a+2 b x)}{16 d^3 (c+d x)}-\frac{3 b^2 \sin (6 a+6 b x)}{16 d^3 (c+d x)}-\frac{b \cos (2 a+2 b x)}{32 d^2 (c+d x)^2}+\frac{b \cos (6 a+6 b x)}{32 d^2 (c+d x)^2}-\frac{\sin (2 a+2 b x)}{32 d (c+d x)^3}+\frac{\sin (6 a+6 b x)}{96 d (c+d x)^3}",1,"-(b*Cos[2*a + 2*b*x])/(32*d^2*(c + d*x)^2) + (b*Cos[6*a + 6*b*x])/(32*d^2*(c + d*x)^2) - (b^3*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(8*d^4) + (9*b^3*Cos[6*a - (6*b*c)/d]*CosIntegral[(6*b*c)/d + 6*b*x])/(8*d^4) - Sin[2*a + 2*b*x]/(32*d*(c + d*x)^3) + (b^2*Sin[2*a + 2*b*x])/(16*d^3*(c + d*x)) + Sin[6*a + 6*b*x]/(96*d*(c + d*x)^3) - (3*b^2*Sin[6*a + 6*b*x])/(16*d^3*(c + d*x)) + (b^3*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(8*d^4) - (9*b^3*Sin[6*a - (6*b*c)/d]*SinIntegral[(6*b*c)/d + 6*b*x])/(8*d^4)","A",14,5,24,0.2083,1,"{4406, 3297, 3303, 3299, 3302}"
163,0,0,0,0.1720952,"\int (c+d x)^m \cos ^2(a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^2*Cot[a + b*x],x]","\int (c+d x)^m \cos ^2(a+b x) \cot (a+b x) \, dx","\text{Int}\left(\cot (a+b x) (c+d x)^m,x\right)+\frac{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{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}",0,"(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) + (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) + Defer[Int][(c + d*x)^m*Cot[a + b*x], x]","A",0,0,0,0,-1,"{}"
164,1,307,0,0.3398965,"\int (c+d x)^4 \cos ^2(a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^2*Cot[a + b*x],x]","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{3 d^2 (c+d x)^2 \sin ^2(a+b x)}{2 b^3}+\frac{3 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^4}-\frac{d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}-\frac{3 d^4 \sin ^2(a+b x)}{4 b^5}+\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \sin ^2(a+b x)}{2 b}-\frac{3 c d^3 x}{2 b^3}-\frac{3 d^4 x^2}{4 b^3}+\frac{(c+d x)^4}{4 b}-\frac{i (c+d x)^5}{5 d}","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{3 d^2 (c+d x)^2 \sin ^2(a+b x)}{2 b^3}+\frac{3 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^4}-\frac{d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}-\frac{3 d^4 \sin ^2(a+b x)}{4 b^5}+\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \sin ^2(a+b x)}{2 b}-\frac{3 c d^3 x}{2 b^3}-\frac{3 d^4 x^2}{4 b^3}+\frac{(c+d x)^4}{4 b}-\frac{i (c+d x)^5}{5 d}",1,"(-3*c*d^3*x)/(2*b^3) - (3*d^4*x^2)/(4*b^3) + (c + d*x)^4/(4*b) - ((I/5)*(c + d*x)^5)/d + ((c + d*x)^4*Log[1 - E^((2*I)*(a + b*x))])/b - ((2*I)*d*(c + d*x)^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 + ((3*I)*d^3*(c + d*x)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 - (3*d^4*PolyLog[5, E^((2*I)*(a + b*x))])/(2*b^5) + (3*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b^4) - (d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/b^2 - (3*d^4*Sin[a + b*x]^2)/(4*b^5) + (3*d^2*(c + d*x)^2*Sin[a + b*x]^2)/(2*b^3) - ((c + d*x)^4*Sin[a + b*x]^2)/(2*b)","A",13,11,22,0.5000,1,"{4408, 4404, 3311, 32, 3310, 3717, 2190, 2531, 6609, 2282, 6589}"
165,1,246,0,0.2780888,"\int (c+d x)^3 \cos ^2(a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^2*Cot[a + b*x],x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}+\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}-\frac{3 d^3 x}{8 b^3}+\frac{(c+d x)^3}{4 b}-\frac{i (c+d x)^4}{4 d}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}+\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}-\frac{3 d^3 x}{8 b^3}+\frac{(c+d x)^3}{4 b}-\frac{i (c+d x)^4}{4 d}",1,"(-3*d^3*x)/(8*b^3) + (c + d*x)^3/(4*b) - ((I/4)*(c + d*x)^4)/d + ((c + d*x)^3*Log[1 - E^((2*I)*(a + b*x))])/b - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) + (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 + (3*d^3*Cos[a + b*x]*Sin[a + b*x])/(8*b^4) - (3*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) + (3*d^2*(c + d*x)*Sin[a + b*x]^2)/(4*b^3) - ((c + d*x)^3*Sin[a + b*x]^2)/(2*b)","A",12,12,22,0.5455,1,"{4408, 4404, 3311, 32, 2635, 8, 3717, 2190, 2531, 6609, 2282, 6589}"
166,1,181,0,0.2269281,"\int (c+d x)^2 \cos ^2(a+b x) \cot (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^2*Cot[a + b*x],x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}+\frac{d^2 \sin ^2(a+b x)}{4 b^3}+\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}+\frac{c d x}{2 b}+\frac{d^2 x^2}{4 b}-\frac{i (c+d x)^3}{3 d}","-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}+\frac{d^2 \sin ^2(a+b x)}{4 b^3}+\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}+\frac{c d x}{2 b}+\frac{d^2 x^2}{4 b}-\frac{i (c+d x)^3}{3 d}",1,"(c*d*x)/(2*b) + (d^2*x^2)/(4*b) - ((I/3)*(c + d*x)^3)/d + ((c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b - (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b^2) + (d^2*Sin[a + b*x]^2)/(4*b^3) - ((c + d*x)^2*Sin[a + b*x]^2)/(2*b)","A",9,8,22,0.3636,1,"{4408, 4404, 3310, 3717, 2190, 2531, 2282, 6589}"
167,1,114,0,0.1279231,"\int (c+d x) \cos ^2(a+b x) \cot (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^2*Cot[a + b*x],x]","-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \sin ^2(a+b x)}{2 b}+\frac{d x}{4 b}-\frac{i (c+d x)^2}{2 d}","-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \sin ^2(a+b x)}{2 b}+\frac{d x}{4 b}-\frac{i (c+d x)^2}{2 d}",1,"(d*x)/(4*b) - ((I/2)*(c + d*x)^2)/d + ((c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b - ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) - ((c + d*x)*Sin[a + b*x]^2)/(2*b)","A",8,8,20,0.4000,1,"{4408, 4404, 2635, 8, 3717, 2190, 2279, 2391}"
168,0,0,0,0.1443134,"\int \frac{\cos ^2(a+b x) \cot (a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]^2*Cot[a + b*x])/(c + d*x),x]","\int \frac{\cos ^2(a+b x) \cot (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{c+d x},x\right)-\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}-\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}",0,"-(CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(2*d) - (Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d) + Defer[Int][Cot[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
169,0,0,0,0.1702997,"\int \frac{\cos ^2(a+b x) \cot (a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]^2*Cot[a + b*x])/(c + d*x)^2,x]","\int \frac{\cos ^2(a+b x) \cot (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot (a+b x)}{(c+d x)^2},x\right)-\frac{b \cos \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 \sin \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+2 b x)}{2 d (c+d x)}",0,"-((b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^2) + Sin[2*a + 2*b*x]/(2*d*(c + d*x)) + (b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2 + Defer[Int][Cot[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
170,0,0,0,0.239148,"\int (c+d x)^m \cos (a+b x) \cot ^2(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]*Cot[a + b*x]^2,x]","\int (c+d x)^m \cos (a+b x) \cot ^2(a+b x) \, dx","\text{Int}\left(\cot (a+b x) \csc (a+b x) (c+d x)^m,x\right)+\frac{i 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{i 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}",0,"((I/2)*E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - ((I/2)*(c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + Defer[Int][(c + d*x)^m*Cot[a + b*x]*Csc[a + b*x], x]","A",0,0,0,0,-1,"{}"
171,1,299,0,0.2926415,"\int (c+d x)^4 \cos (a+b x) \cot ^2(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]*Cot[a + b*x]^2,x]","-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{24 i d^4 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^5}+\frac{24 i d^4 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^5}+\frac{12 d^2 (c+d x)^2 \sin (a+b x)}{b^3}+\frac{24 d^3 (c+d x) \cos (a+b x)}{b^4}-\frac{4 d (c+d x)^3 \cos (a+b x)}{b^2}-\frac{8 d (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{24 d^4 \sin (a+b x)}{b^5}-\frac{(c+d x)^4 \sin (a+b x)}{b}-\frac{(c+d x)^4 \csc (a+b x)}{b}","-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{24 i d^4 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^5}+\frac{24 i d^4 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^5}+\frac{12 d^2 (c+d x)^2 \sin (a+b x)}{b^3}+\frac{24 d^3 (c+d x) \cos (a+b x)}{b^4}-\frac{4 d (c+d x)^3 \cos (a+b x)}{b^2}-\frac{8 d (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{24 d^4 \sin (a+b x)}{b^5}-\frac{(c+d x)^4 \sin (a+b x)}{b}-\frac{(c+d x)^4 \csc (a+b x)}{b}",1,"(-8*d*(c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b^2 + (24*d^3*(c + d*x)*Cos[a + b*x])/b^4 - (4*d*(c + d*x)^3*Cos[a + b*x])/b^2 - ((c + d*x)^4*Csc[a + b*x])/b + ((12*I)*d^2*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((12*I)*d^2*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^3 - (24*d^3*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^4 + (24*d^3*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^4 - ((24*I)*d^4*PolyLog[4, -E^(I*(a + b*x))])/b^5 + ((24*I)*d^4*PolyLog[4, E^(I*(a + b*x))])/b^5 - (24*d^4*Sin[a + b*x])/b^5 + (12*d^2*(c + d*x)^2*Sin[a + b*x])/b^3 - ((c + d*x)^4*Sin[a + b*x])/b","A",16,9,22,0.4091,1,"{4408, 3296, 2637, 4410, 4183, 2531, 6609, 2282, 6589}"
172,1,216,0,0.2222931,"\int (c+d x)^3 \cos (a+b x) \cot ^2(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]*Cot[a + b*x]^2,x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x) \sin (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cos (a+b x)}{b^2}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{6 d^3 \cos (a+b x)}{b^4}-\frac{(c+d x)^3 \sin (a+b x)}{b}-\frac{(c+d x)^3 \csc (a+b x)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x) \sin (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cos (a+b x)}{b^2}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{6 d^3 \cos (a+b x)}{b^4}-\frac{(c+d x)^3 \sin (a+b x)}{b}-\frac{(c+d x)^3 \csc (a+b x)}{b}",1,"(-6*d*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b^2 + (6*d^3*Cos[a + b*x])/b^4 - (3*d*(c + d*x)^2*Cos[a + b*x])/b^2 - ((c + d*x)^3*Csc[a + b*x])/b + ((6*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((6*I)*d^2*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^3 - (6*d^3*PolyLog[3, -E^(I*(a + b*x))])/b^4 + (6*d^3*PolyLog[3, E^(I*(a + b*x))])/b^4 + (6*d^2*(c + d*x)*Sin[a + b*x])/b^3 - ((c + d*x)^3*Sin[a + b*x])/b","A",13,8,22,0.3636,1,"{4408, 3296, 2638, 4410, 4183, 2531, 2282, 6589}"
173,1,139,0,0.14899,"\int (c+d x)^2 \cos (a+b x) \cot ^2(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]*Cot[a + b*x]^2,x]","\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \cos (a+b x)}{b^2}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{2 d^2 \sin (a+b x)}{b^3}-\frac{(c+d x)^2 \sin (a+b x)}{b}-\frac{(c+d x)^2 \csc (a+b x)}{b}","\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \cos (a+b x)}{b^2}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{2 d^2 \sin (a+b x)}{b^3}-\frac{(c+d x)^2 \sin (a+b x)}{b}-\frac{(c+d x)^2 \csc (a+b x)}{b}",1,"(-4*d*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b^2 - (2*d*(c + d*x)*Cos[a + b*x])/b^2 - ((c + d*x)^2*Csc[a + b*x])/b + ((2*I)*d^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 - ((2*I)*d^2*PolyLog[2, E^(I*(a + b*x))])/b^3 + (2*d^2*Sin[a + b*x])/b^3 - ((c + d*x)^2*Sin[a + b*x])/b","A",10,7,22,0.3182,1,"{4408, 3296, 2637, 4410, 4183, 2279, 2391}"
174,1,58,0,0.0631534,"\int (c+d x) \cos (a+b x) \cot ^2(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]*Cot[a + b*x]^2,x]","-\frac{d \cos (a+b x)}{b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \sin (a+b x)}{b}-\frac{(c+d x) \csc (a+b x)}{b}","-\frac{d \cos (a+b x)}{b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \sin (a+b x)}{b}-\frac{(c+d x) \csc (a+b x)}{b}",1,"-((d*ArcTanh[Cos[a + b*x]])/b^2) - (d*Cos[a + b*x])/b^2 - ((c + d*x)*Csc[a + b*x])/b - ((c + d*x)*Sin[a + b*x])/b","A",5,5,20,0.2500,1,"{4408, 3296, 2638, 4410, 3770}"
175,0,0,0,0.2136765,"\int \frac{\cos (a+b x) \cot ^2(a+b x)}{c+d x} \, dx","Int[(Cos[a + b*x]*Cot[a + b*x]^2)/(c + d*x),x]","\int \frac{\cos (a+b x) \cot ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc (a+b x)}{c+d x},x\right)-\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}",0,"-((Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d) + (Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d + Defer[Int][(Cot[a + b*x]*Csc[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
176,0,0,0,0.2563545,"\int \frac{\cos (a+b x) \cot ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Cos[a + b*x]*Cot[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\cos (a+b x) \cot ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot (a+b x) \csc (a+b x)}{(c+d x)^2},x\right)+\frac{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{\cos (a+b x)}{d (c+d x)}",0,"Cos[a + b*x]/(d*(c + d*x)) + (b*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d^2 + (b*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^2 + Defer[Int][(Cot[a + b*x]*Csc[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
177,0,0,0,0.0356774,"\int (c+d x)^m \cot ^3(a+b x) \, dx","Int[(c + d*x)^m*Cot[a + b*x]^3,x]","\int (c+d x)^m \cot ^3(a+b x) \, dx","\text{Int}\left(\cot ^3(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Cot[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
178,1,302,0,0.4623337,"\int (c+d x)^4 \cot ^3(a+b x) \, dx","Int[(c + d*x)^4*Cot[a + b*x]^3,x]","-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}-\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^5}+\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{6 d^2 (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \cot (a+b x)}{b^2}-\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \cot ^2(a+b x)}{2 b}-\frac{2 i d (c+d x)^3}{b^2}-\frac{(c+d x)^4}{2 b}+\frac{i (c+d x)^5}{5 d}","-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}-\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^5}+\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}+\frac{6 d^2 (c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \cot (a+b x)}{b^2}-\frac{(c+d x)^4 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^4 \cot ^2(a+b x)}{2 b}-\frac{2 i d (c+d x)^3}{b^2}-\frac{(c+d x)^4}{2 b}+\frac{i (c+d x)^5}{5 d}",1,"((-2*I)*d*(c + d*x)^3)/b^2 - (c + d*x)^4/(2*b) + ((I/5)*(c + d*x)^5)/d - (2*d*(c + d*x)^3*Cot[a + b*x])/b^2 - ((c + d*x)^4*Cot[a + b*x]^2)/(2*b) + (6*d^2*(c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b^3 - ((c + d*x)^4*Log[1 - E^((2*I)*(a + b*x))])/b - ((6*I)*d^3*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 + ((2*I)*d*(c + d*x)^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 + (3*d^4*PolyLog[3, E^((2*I)*(a + b*x))])/b^5 - (3*d^2*(c + d*x)^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 - ((3*I)*d^3*(c + d*x)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 + (3*d^4*PolyLog[5, E^((2*I)*(a + b*x))])/(2*b^5)","A",15,8,16,0.5000,1,"{3720, 3717, 2190, 2531, 2282, 6589, 32, 6609}"
179,1,256,0,0.3683764,"\int (c+d x)^3 \cot ^3(a+b x) \, dx","Int[(c + d*x)^3*Cot[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \cot ^2(a+b x)}{2 b}-\frac{3 i d (c+d x)^2}{2 b^2}-\frac{(c+d x)^3}{2 b}+\frac{i (c+d x)^4}{4 d}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \cot ^2(a+b x)}{2 b}-\frac{3 i d (c+d x)^2}{2 b^2}-\frac{(c+d x)^3}{2 b}+\frac{i (c+d x)^4}{4 d}",1,"(((-3*I)/2)*d*(c + d*x)^2)/b^2 - (c + d*x)^3/(2*b) + ((I/4)*(c + d*x)^4)/d - (3*d*(c + d*x)^2*Cot[a + b*x])/(2*b^2) - ((c + d*x)^3*Cot[a + b*x]^2)/(2*b) + (3*d^2*(c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b^3 - ((c + d*x)^3*Log[1 - E^((2*I)*(a + b*x))])/b - (((3*I)/2)*d^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",13,10,16,0.6250,1,"{3720, 3717, 2190, 2279, 2391, 32, 2531, 6609, 2282, 6589}"
180,1,168,0,0.2655089,"\int (c+d x)^2 \cot ^3(a+b x) \, dx","Int[(c + d*x)^2*Cot[a + b*x]^3,x]","\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \cot ^2(a+b x)}{2 b}-\frac{c d x}{b}-\frac{d^2 x^2}{2 b}+\frac{i (c+d x)^3}{3 d}","\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \cot ^2(a+b x)}{2 b}-\frac{c d x}{b}-\frac{d^2 x^2}{2 b}+\frac{i (c+d x)^3}{3 d}",1,"-((c*d*x)/b) - (d^2*x^2)/(2*b) + ((I/3)*(c + d*x)^3)/d - (d*(c + d*x)*Cot[a + b*x])/b^2 - ((c + d*x)^2*Cot[a + b*x]^2)/(2*b) - ((c + d*x)^2*Log[1 - E^((2*I)*(a + b*x))])/b + (d^2*Log[Sin[a + b*x]])/b^3 + (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3)","A",9,7,16,0.4375,1,"{3720, 3475, 3717, 2190, 2531, 2282, 6589}"
181,1,109,0,0.1282581,"\int (c+d x) \cot ^3(a+b x) \, dx","Int[(c + d*x)*Cot[a + b*x]^3,x]","\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \cot ^2(a+b x)}{2 b}-\frac{d x}{2 b}+\frac{i (c+d x)^2}{2 d}","\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \cot ^2(a+b x)}{2 b}-\frac{d x}{2 b}+\frac{i (c+d x)^2}{2 d}",1,"-(d*x)/(2*b) + ((I/2)*(c + d*x)^2)/d - (d*Cot[a + b*x])/(2*b^2) - ((c + d*x)*Cot[a + b*x]^2)/(2*b) - ((c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b + ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",7,7,14,0.5000,1,"{3720, 3473, 8, 3717, 2190, 2279, 2391}"
182,0,0,0,0.039856,"\int \frac{\cot ^3(a+b x)}{c+d x} \, dx","Int[Cot[a + b*x]^3/(c + d*x),x]","\int \frac{\cot ^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\cot ^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][Cot[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
183,0,0,0,0.0373215,"\int \frac{\cot ^3(a+b x)}{(c+d x)^2} \, dx","Int[Cot[a + b*x]^3/(c + d*x)^2,x]","\int \frac{\cot ^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\cot ^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Cot[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
184,1,407,0,0.7965758,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}+\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}+\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}+\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}+\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(128*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(8*b) + (15*d^2*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(2048*b^3) - ((c + d*x)^(5/2)*Cos[4*a + 4*b*x])/(32*b) - (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(256*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(256*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(32*b^2) + (5*d*(c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(256*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
185,1,351,0,0.5558082,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}+\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}+\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(8*b) - ((c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(32*b) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(64*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(64*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(32*b^2) + (3*d*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(256*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
186,1,299,0,0.4468113,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}-\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}-\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(8*b) - (Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(32*b) + (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(16*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(16*b^(3/2))","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
187,1,299,0,0.4549457,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x],x]","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}-\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}+\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \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)}{16 b^{3/2}}-\frac{\sqrt{c+d x} \cos (2 a+2 b x)}{8 b}-\frac{\sqrt{c+d x} \cos (4 a+4 b x)}{32 b}",1,"-(Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(8*b) - (Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(32*b) + (Sqrt[d]*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(3/2)) + (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(16*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(64*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(16*b^(3/2))","A",14,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
188,1,351,0,0.572442,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}+\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \sin \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \cos \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{512 b^{5/2}}-\frac{3 \sqrt{\pi } d^{3/2} \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)}{64 b^{5/2}}+\frac{3 d \sqrt{c+d x} \sin (2 a+2 b x)}{32 b^2}+\frac{3 d \sqrt{c+d x} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{3/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{3/2} \cos (4 a+4 b x)}{32 b}",1,"-((c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(8*b) - ((c + d*x)^(3/2)*Cos[4*a + 4*b*x])/(32*b) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(64*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/2]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(512*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(64*b^(5/2)) + (3*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(32*b^2) + (3*d*Sqrt[c + d*x]*Sin[4*a + 4*b*x])/(256*b^2)","A",16,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
189,1,407,0,0.6723663,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x],x]","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}+\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}+\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}","-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(4 a-\frac{4 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \sin \left(4 a-\frac{4 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{4096 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \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)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{128 b^3}+\frac{15 d^2 \sqrt{c+d x} \cos (4 a+4 b x)}{2048 b^3}+\frac{5 d (c+d x)^{3/2} \sin (2 a+2 b x)}{32 b^2}+\frac{5 d (c+d x)^{3/2} \sin (4 a+4 b x)}{256 b^2}-\frac{(c+d x)^{5/2} \cos (2 a+2 b x)}{8 b}-\frac{(c+d x)^{5/2} \cos (4 a+4 b x)}{32 b}",1,"(15*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(128*b^3) - ((c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(8*b) + (15*d^2*Sqrt[c + d*x]*Cos[4*a + 4*b*x])/(2048*b^3) - ((c + d*x)^(5/2)*Cos[4*a + 4*b*x])/(32*b) - (15*d^(5/2)*Sqrt[Pi/2]*Cos[4*a - (4*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(4096*b^(7/2)) - (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(256*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelS[(2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[4*a - (4*b*c)/d])/(4096*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(256*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(32*b^2) + (5*d*(c + d*x)^(3/2)*Sin[4*a + 4*b*x])/(256*b^2)","A",18,7,24,0.2917,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
190,1,615,0,1.1448455,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{32 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{576 b^3}+\frac{3 d^2 \sqrt{c+d x} \sin (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{16 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \cos (5 a+5 b x)}{160 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{5/2} \sin (5 a+5 b x)}{80 b}","-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{32 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{576 b^3}+\frac{3 d^2 \sqrt{c+d x} \sin (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{16 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \cos (5 a+5 b x)}{160 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{5/2} \sin (5 a+5 b x)}{80 b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(16*b^2) - (5*d*(c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(288*b^2) - (d*(c + d*x)^(3/2)*Cos[5*a + 5*b*x])/(160*b^2) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(32*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(576*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1600*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(1600*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(576*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(32*b^(7/2)) - (15*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(32*b^3) + ((c + d*x)^(5/2)*Sin[a + b*x])/(8*b) + (5*d^2*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(576*b^3) - ((c + d*x)^(5/2)*Sin[3*a + 3*b*x])/(48*b) + (3*d^2*Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(1600*b^3) - ((c + d*x)^(5/2)*Sin[5*a + 5*b*x])/(80*b)","A",26,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
191,1,534,0,0.8376157,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{16 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \cos (5 a+5 b x)}{800 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{3/2} \sin (5 a+5 b x)}{80 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{16 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \cos (5 a+5 b x)}{800 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{3/2} \sin (5 a+5 b x)}{80 b}",1,"(3*d*Sqrt[c + d*x]*Cos[a + b*x])/(16*b^2) - (d*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(96*b^2) - (3*d*Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(800*b^2) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(5/2)) + (d^(3/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(800*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(800*b^(5/2)) - (d^(3/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(16*b^(5/2)) + ((c + d*x)^(3/2)*Sin[a + b*x])/(8*b) - ((c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(48*b) - ((c + d*x)^(3/2)*Sin[5*a + 5*b*x])/(80*b)","A",23,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
192,1,459,0,0.6925948,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{8 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{48 b}-\frac{\sqrt{c+d x} \sin (5 a+5 b x)}{80 b}","\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{8 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{48 b}-\frac{\sqrt{c+d x} \sin (5 a+5 b x)}{80 b}",1,"-(Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(8*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(48*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(48*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(8*b^(3/2)) + (Sqrt[c + d*x]*Sin[a + b*x])/(8*b) - (Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(48*b) - (Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(80*b)","A",20,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
193,1,459,0,0.6715043,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{8 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{48 b}-\frac{\sqrt{c+d x} \sin (5 a+5 b x)}{80 b}","\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} \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^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sqrt{d} \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)}{48 b^{3/2}}+\frac{\sqrt{\frac{\pi }{10}} \sqrt{d} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{80 b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{8 b}-\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{48 b}-\frac{\sqrt{c+d x} \sin (5 a+5 b x)}{80 b}",1,"-(Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(8*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(48*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(80*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(48*b^(3/2)) - (Sqrt[d]*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(8*b^(3/2)) + (Sqrt[c + d*x]*Sin[a + b*x])/(8*b) - (Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(48*b) - (Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(80*b)","A",20,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
194,1,534,0,0.8579248,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{16 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \cos (5 a+5 b x)}{800 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{3/2} \sin (5 a+5 b x)}{80 b}","-\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \cos \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{3/2} \sin \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{800 b^{5/2}}-\frac{\sqrt{\frac{\pi }{6}} d^{3/2} \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)}{96 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} \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^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{16 b^2}-\frac{d \sqrt{c+d x} \cos (3 a+3 b x)}{96 b^2}-\frac{3 d \sqrt{c+d x} \cos (5 a+5 b x)}{800 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{3/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{3/2} \sin (5 a+5 b x)}{80 b}",1,"(3*d*Sqrt[c + d*x]*Cos[a + b*x])/(16*b^2) - (d*Sqrt[c + d*x]*Cos[3*a + 3*b*x])/(96*b^2) - (3*d*Sqrt[c + d*x]*Cos[5*a + 5*b*x])/(800*b^2) - (3*d^(3/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(5/2)) + (d^(3/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(800*b^(5/2)) - (3*d^(3/2)*Sqrt[Pi/10]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(800*b^(5/2)) - (d^(3/2)*Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(96*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(16*b^(5/2)) + ((c + d*x)^(3/2)*Sin[a + b*x])/(8*b) - ((c + d*x)^(3/2)*Sin[3*a + 3*b*x])/(48*b) - ((c + d*x)^(3/2)*Sin[5*a + 5*b*x])/(80*b)","A",23,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
195,1,615,0,1.015477,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x]^2,x]","-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{32 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{576 b^3}+\frac{3 d^2 \sqrt{c+d x} \sin (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{16 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \cos (5 a+5 b x)}{160 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{5/2} \sin (5 a+5 b x)}{80 b}","-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \sin \left(5 a-\frac{5 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{10}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \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)}{32 b^{7/2}}+\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{6}} d^{5/2} \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)}{576 b^{7/2}}-\frac{3 \sqrt{\frac{\pi }{10}} d^{5/2} \cos \left(5 a-\frac{5 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{10}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1600 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{32 b^3}+\frac{5 d^2 \sqrt{c+d x} \sin (3 a+3 b x)}{576 b^3}+\frac{3 d^2 \sqrt{c+d x} \sin (5 a+5 b x)}{1600 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{16 b^2}-\frac{5 d (c+d x)^{3/2} \cos (3 a+3 b x)}{288 b^2}-\frac{d (c+d x)^{3/2} \cos (5 a+5 b x)}{160 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{8 b}-\frac{(c+d x)^{5/2} \sin (3 a+3 b x)}{48 b}-\frac{(c+d x)^{5/2} \sin (5 a+5 b x)}{80 b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(16*b^2) - (5*d*(c + d*x)^(3/2)*Cos[3*a + 3*b*x])/(288*b^2) - (d*(c + d*x)^(3/2)*Cos[5*a + 5*b*x])/(160*b^2) + (15*d^(5/2)*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(32*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(576*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*Cos[5*a - (5*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1600*b^(7/2)) - (3*d^(5/2)*Sqrt[Pi/10]*FresnelC[(Sqrt[b]*Sqrt[10/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[5*a - (5*b*c)/d])/(1600*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/6]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(576*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(32*b^(7/2)) - (15*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(32*b^3) + ((c + d*x)^(5/2)*Sin[a + b*x])/(8*b) + (5*d^2*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(576*b^3) - ((c + d*x)^(5/2)*Sin[3*a + 3*b*x])/(48*b) + (3*d^2*Sqrt[c + d*x]*Sin[5*a + 5*b*x])/(1600*b^3) - ((c + d*x)^(5/2)*Sin[5*a + 5*b*x])/(80*b)","A",26,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
196,1,407,0,0.8968668,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}-\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}+\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{1024 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (6 a+6 b x)}{9216 b^3}+\frac{15 d (c+d x)^{3/2} \sin (2 a+2 b x)}{256 b^2}-\frac{5 d (c+d x)^{3/2} \sin (6 a+6 b x)}{2304 b^2}-\frac{3 (c+d x)^{5/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{5/2} \cos (6 a+6 b x)}{192 b}","\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}-\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}+\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{1024 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (6 a+6 b x)}{9216 b^3}+\frac{15 d (c+d x)^{3/2} \sin (2 a+2 b x)}{256 b^2}-\frac{5 d (c+d x)^{3/2} \sin (6 a+6 b x)}{2304 b^2}-\frac{3 (c+d x)^{5/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{5/2} \cos (6 a+6 b x)}{192 b}",1,"(45*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(1024*b^3) - (3*(c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(64*b) - (5*d^2*Sqrt[c + d*x]*Cos[6*a + 6*b*x])/(9216*b^3) + ((c + d*x)^(5/2)*Cos[6*a + 6*b*x])/(192*b) + (5*d^(5/2)*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(18432*b^(7/2)) - (45*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(2048*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/3]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(18432*b^(7/2)) + (45*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(2048*b^(7/2)) + (15*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(256*b^2) - (5*d*(c + d*x)^(3/2)*Sin[6*a + 6*b*x])/(2304*b^2)","A",18,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
197,1,351,0,0.6282849,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \sin \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \cos \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{9 d \sqrt{c+d x} \sin (2 a+2 b x)}{256 b^2}-\frac{d \sqrt{c+d x} \sin (6 a+6 b x)}{768 b^2}-\frac{3 (c+d x)^{3/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{3/2} \cos (6 a+6 b x)}{192 b}","\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \sin \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \cos \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{9 d \sqrt{c+d x} \sin (2 a+2 b x)}{256 b^2}-\frac{d \sqrt{c+d x} \sin (6 a+6 b x)}{768 b^2}-\frac{3 (c+d x)^{3/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{3/2} \cos (6 a+6 b x)}{192 b}",1,"(-3*(c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(64*b) + ((c + d*x)^(3/2)*Cos[6*a + 6*b*x])/(192*b) + (d^(3/2)*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1536*b^(5/2)) - (9*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(512*b^(5/2)) + (d^(3/2)*Sqrt[Pi/3]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(1536*b^(5/2)) - (9*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(512*b^(5/2)) + (9*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(256*b^2) - (d*Sqrt[c + d*x]*Sin[6*a + 6*b*x])/(768*b^2)","A",16,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
198,1,299,0,0.4576784,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}+\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b}+\frac{\sqrt{c+d x} \cos (6 a+6 b x)}{192 b}","-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}+\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b}+\frac{\sqrt{c+d x} \cos (6 a+6 b x)}{192 b}",1,"(-3*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(64*b) + (Sqrt[c + d*x]*Cos[6*a + 6*b*x])/(192*b) - (Sqrt[d]*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(384*b^(3/2)) + (3*Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/3]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(384*b^(3/2)) - (3*Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(3/2))","A",14,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
199,1,299,0,0.4481349,"\int \sqrt{c+d x} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}+\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b}+\frac{\sqrt{c+d x} \cos (6 a+6 b x)}{192 b}","-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}+\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{384 b^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{d} \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)}{128 b^{3/2}}-\frac{3 \sqrt{c+d x} \cos (2 a+2 b x)}{64 b}+\frac{\sqrt{c+d x} \cos (6 a+6 b x)}{192 b}",1,"(-3*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(64*b) + (Sqrt[c + d*x]*Cos[6*a + 6*b*x])/(192*b) - (Sqrt[d]*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(384*b^(3/2)) + (3*Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(3/2)) + (Sqrt[d]*Sqrt[Pi/3]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(384*b^(3/2)) - (3*Sqrt[d]*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(3/2))","A",14,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
200,1,351,0,0.5591802,"\int (c+d x)^{3/2} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \sin \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \cos \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{9 d \sqrt{c+d x} \sin (2 a+2 b x)}{256 b^2}-\frac{d \sqrt{c+d x} \sin (6 a+6 b x)}{768 b^2}-\frac{3 (c+d x)^{3/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{3/2} \cos (6 a+6 b x)}{192 b}","\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \sin \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} \cos \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{1536 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} \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)}{512 b^{5/2}}+\frac{9 d \sqrt{c+d x} \sin (2 a+2 b x)}{256 b^2}-\frac{d \sqrt{c+d x} \sin (6 a+6 b x)}{768 b^2}-\frac{3 (c+d x)^{3/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{3/2} \cos (6 a+6 b x)}{192 b}",1,"(-3*(c + d*x)^(3/2)*Cos[2*a + 2*b*x])/(64*b) + ((c + d*x)^(3/2)*Cos[6*a + 6*b*x])/(192*b) + (d^(3/2)*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(1536*b^(5/2)) - (9*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(512*b^(5/2)) + (d^(3/2)*Sqrt[Pi/3]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(1536*b^(5/2)) - (9*d^(3/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(512*b^(5/2)) + (9*d*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(256*b^2) - (d*Sqrt[c + d*x]*Sin[6*a + 6*b*x])/(768*b^2)","A",16,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
201,1,407,0,0.6693013,"\int (c+d x)^{5/2} \cos ^3(a+b x) \sin ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3*Sin[a + b*x]^3,x]","\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}-\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}+\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{1024 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (6 a+6 b x)}{9216 b^3}+\frac{15 d (c+d x)^{3/2} \sin (2 a+2 b x)}{256 b^2}-\frac{5 d (c+d x)^{3/2} \sin (6 a+6 b x)}{2304 b^2}-\frac{3 (c+d x)^{5/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{5/2} \cos (6 a+6 b x)}{192 b}","\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \cos \left(6 a-\frac{6 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{\frac{3}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}-\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} \sin \left(6 a-\frac{6 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{\frac{3}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{18432 b^{7/2}}+\frac{45 \sqrt{\pi } d^{5/2} \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)}{2048 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \cos (2 a+2 b x)}{1024 b^3}-\frac{5 d^2 \sqrt{c+d x} \cos (6 a+6 b x)}{9216 b^3}+\frac{15 d (c+d x)^{3/2} \sin (2 a+2 b x)}{256 b^2}-\frac{5 d (c+d x)^{3/2} \sin (6 a+6 b x)}{2304 b^2}-\frac{3 (c+d x)^{5/2} \cos (2 a+2 b x)}{64 b}+\frac{(c+d x)^{5/2} \cos (6 a+6 b x)}{192 b}",1,"(45*d^2*Sqrt[c + d*x]*Cos[2*a + 2*b*x])/(1024*b^3) - (3*(c + d*x)^(5/2)*Cos[2*a + 2*b*x])/(64*b) - (5*d^2*Sqrt[c + d*x]*Cos[6*a + 6*b*x])/(9216*b^3) + ((c + d*x)^(5/2)*Cos[6*a + 6*b*x])/(192*b) + (5*d^(5/2)*Sqrt[Pi/3]*Cos[6*a - (6*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(18432*b^(7/2)) - (45*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(2048*b^(7/2)) - (5*d^(5/2)*Sqrt[Pi/3]*FresnelS[(2*Sqrt[b]*Sqrt[3/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[6*a - (6*b*c)/d])/(18432*b^(7/2)) + (45*d^(5/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(2048*b^(7/2)) + (15*d*(c + d*x)^(3/2)*Sin[2*a + 2*b*x])/(256*b^2) - (5*d*(c + d*x)^(3/2)*Sin[6*a + 6*b*x])/(2304*b^2)","A",18,7,26,0.2692,1,"{4406, 3296, 3306, 3305, 3351, 3304, 3352}"
202,1,112,0,0.1851446,"\int x^3 \cos ^2(x) \cot ^2(x) \, dx","Int[x^3*Cos[x]^2*Cot[x]^2,x]","-3 i x \text{PolyLog}\left(2,e^{2 i x}\right)+\frac{3}{2} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{3 x^4}{8}-i x^3+\frac{3 x^2}{8}+3 x^2 \log \left(1-e^{2 i x}\right)-\frac{3}{4} x^2 \cos ^2(x)-x^3 \cot (x)-\frac{1}{2} x^3 \sin (x) \cos (x)+\frac{3 \cos ^2(x)}{8}+\frac{3}{4} x \sin (x) \cos (x)","-3 i x \text{PolyLog}\left(2,e^{2 i x}\right)+\frac{3}{2} \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{3 x^4}{8}-i x^3+\frac{3 x^2}{8}+3 x^2 \log \left(1-e^{2 i x}\right)-\frac{3}{4} x^2 \cos ^2(x)-x^3 \cot (x)-\frac{1}{2} x^3 \sin (x) \cos (x)+\frac{3 \cos ^2(x)}{8}+\frac{3}{4} x \sin (x) \cos (x)",1,"(3*x^2)/8 - I*x^3 - (3*x^4)/8 + (3*Cos[x]^2)/8 - (3*x^2*Cos[x]^2)/4 - x^3*Cot[x] + 3*x^2*Log[1 - E^((2*I)*x)] - (3*I)*x*PolyLog[2, E^((2*I)*x)] + (3*PolyLog[3, E^((2*I)*x)])/2 + (3*x*Cos[x]*Sin[x])/4 - (x^3*Cos[x]*Sin[x])/2","A",12,10,12,0.8333,1,"{4408, 3311, 30, 3310, 3720, 3717, 2190, 2531, 2282, 6589}"
203,1,83,0,0.1695144,"\int x^2 \cos ^2(x) \cot ^2(x) \, dx","Int[x^2*Cos[x]^2*Cot[x]^2,x]","-i \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{x^3}{2}-i x^2-x^2 \cot (x)-\frac{1}{2} x^2 \sin (x) \cos (x)+\frac{x}{4}+2 x \log \left(1-e^{2 i x}\right)-\frac{1}{2} x \cos ^2(x)+\frac{1}{4} \sin (x) \cos (x)","-i \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{x^3}{2}-i x^2-x^2 \cot (x)-\frac{1}{2} x^2 \sin (x) \cos (x)+\frac{x}{4}+2 x \log \left(1-e^{2 i x}\right)-\frac{1}{2} x \cos ^2(x)+\frac{1}{4} \sin (x) \cos (x)",1,"x/4 - I*x^2 - x^3/2 - (x*Cos[x]^2)/2 - x^2*Cot[x] + 2*x*Log[1 - E^((2*I)*x)] - I*PolyLog[2, E^((2*I)*x)] + (Cos[x]*Sin[x])/4 - (x^2*Cos[x]*Sin[x])/2","A",11,10,12,0.8333,1,"{4408, 3311, 30, 2635, 8, 3720, 3717, 2190, 2279, 2391}"
204,1,33,0,0.0546779,"\int x \cos ^2(x) \cot ^2(x) \, dx","Int[x*Cos[x]^2*Cot[x]^2,x]","-\frac{3 x^2}{4}-\frac{\cos ^2(x)}{4}-x \cot (x)+\log (\sin (x))-\frac{1}{2} x \sin (x) \cos (x)","-\frac{3 x^2}{4}-\frac{\cos ^2(x)}{4}-x \cot (x)+\log (\sin (x))-\frac{1}{2} x \sin (x) \cos (x)",1,"(-3*x^2)/4 - Cos[x]^2/4 - x*Cot[x] + Log[Sin[x]] - (x*Cos[x]*Sin[x])/2","A",6,5,10,0.5000,1,"{4408, 3310, 30, 3720, 3475}"
205,1,180,0,0.4006149,"\int x^3 \cos ^2(x) \cot ^3(x) \, dx","Int[x^3*Cos[x]^2*Cot[x]^3,x]","3 i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-3 x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{3}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{3}{2} i \text{PolyLog}\left(4,e^{2 i x}\right)+\frac{i x^4}{2}-\frac{3 x^3}{4}-\frac{3 i x^2}{2}-2 x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^3 \sin ^2(x)-\frac{1}{2} x^3 \cot ^2(x)-\frac{3}{2} x^2 \cot (x)+\frac{3}{4} x^2 \sin (x) \cos (x)+\frac{3 x}{8}+3 x \log \left(1-e^{2 i x}\right)-\frac{3}{4} x \sin ^2(x)-\frac{3}{8} \sin (x) \cos (x)","3 i x^2 \text{PolyLog}\left(2,e^{2 i x}\right)-3 x \text{PolyLog}\left(3,e^{2 i x}\right)-\frac{3}{2} i \text{PolyLog}\left(2,e^{2 i x}\right)-\frac{3}{2} i \text{PolyLog}\left(4,e^{2 i x}\right)+\frac{i x^4}{2}-\frac{3 x^3}{4}-\frac{3 i x^2}{2}-2 x^3 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^3 \sin ^2(x)-\frac{1}{2} x^3 \cot ^2(x)-\frac{3}{2} x^2 \cot (x)+\frac{3}{4} x^2 \sin (x) \cos (x)+\frac{3 x}{8}+3 x \log \left(1-e^{2 i x}\right)-\frac{3}{4} x \sin ^2(x)-\frac{3}{8} \sin (x) \cos (x)",1,"(3*x)/8 - ((3*I)/2)*x^2 - (3*x^3)/4 + (I/2)*x^4 - (3*x^2*Cot[x])/2 - (x^3*Cot[x]^2)/2 + 3*x*Log[1 - E^((2*I)*x)] - 2*x^3*Log[1 - E^((2*I)*x)] - ((3*I)/2)*PolyLog[2, E^((2*I)*x)] + (3*I)*x^2*PolyLog[2, E^((2*I)*x)] - 3*x*PolyLog[3, E^((2*I)*x)] - ((3*I)/2)*PolyLog[4, E^((2*I)*x)] - (3*Cos[x]*Sin[x])/8 + (3*x^2*Cos[x]*Sin[x])/4 - (3*x*Sin[x]^2)/4 + (x^3*Sin[x]^2)/2","A",26,15,12,1.250,1,"{4408, 3443, 3311, 30, 2635, 8, 3717, 2190, 2531, 6609, 2282, 6589, 3720, 2279, 2391}"
206,1,106,0,0.2783088,"\int x^2 \cos ^2(x) \cot ^3(x) \, dx","Int[x^2*Cos[x]^2*Cot[x]^3,x]","2 i x \text{PolyLog}\left(2,e^{2 i x}\right)-\text{PolyLog}\left(3,e^{2 i x}\right)+\frac{2 i x^3}{3}-\frac{3 x^2}{4}-2 x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \sin ^2(x)-\frac{1}{2} x^2 \cot ^2(x)-\frac{\sin ^2(x)}{4}-x \cot (x)+\log (\sin (x))+\frac{1}{2} x \sin (x) \cos (x)","2 i x \text{PolyLog}\left(2,e^{2 i x}\right)-\text{PolyLog}\left(3,e^{2 i x}\right)+\frac{2 i x^3}{3}-\frac{3 x^2}{4}-2 x^2 \log \left(1-e^{2 i x}\right)+\frac{1}{2} x^2 \sin ^2(x)-\frac{1}{2} x^2 \cot ^2(x)-\frac{\sin ^2(x)}{4}-x \cot (x)+\log (\sin (x))+\frac{1}{2} x \sin (x) \cos (x)",1,"(-3*x^2)/4 + ((2*I)/3)*x^3 - x*Cot[x] - (x^2*Cot[x]^2)/2 - 2*x^2*Log[1 - E^((2*I)*x)] + Log[Sin[x]] + (2*I)*x*PolyLog[2, E^((2*I)*x)] - PolyLog[3, E^((2*I)*x)] + (x*Cos[x]*Sin[x])/2 - Sin[x]^2/4 + (x^2*Sin[x]^2)/2","A",19,11,12,0.9167,1,"{4408, 3443, 3310, 30, 3717, 2190, 2531, 2282, 6589, 3720, 3475}"
207,1,73,0,0.1635919,"\int x \cos ^2(x) \cot ^3(x) \, dx","Int[x*Cos[x]^2*Cot[x]^3,x]","i \text{PolyLog}\left(2,e^{2 i x}\right)+i x^2-\frac{3 x}{4}-2 x \log \left(1-e^{2 i x}\right)+\frac{1}{2} x \sin ^2(x)-\frac{1}{2} x \cot ^2(x)-\frac{\cot (x)}{2}+\frac{1}{4} \sin (x) \cos (x)","i \text{PolyLog}\left(2,e^{2 i x}\right)+i x^2-\frac{3 x}{4}-2 x \log \left(1-e^{2 i x}\right)+\frac{1}{2} x \sin ^2(x)-\frac{1}{2} x \cot ^2(x)-\frac{\cot (x)}{2}+\frac{1}{4} \sin (x) \cos (x)",1,"(-3*x)/4 + I*x^2 - Cot[x]/2 - (x*Cot[x]^2)/2 - 2*x*Log[1 - E^((2*I)*x)] + I*PolyLog[2, E^((2*I)*x)] + (Cos[x]*Sin[x])/4 + (x*Sin[x]^2)/2","A",16,10,10,1.000,1,"{4408, 3443, 2635, 8, 3717, 2190, 2279, 2391, 3720, 3473}"
208,0,0,0,0.0177912,"\int (c+d x)^m \tan (a+b x) \, dx","Int[(c + d*x)^m*Tan[a + b*x],x]","\int (c+d x)^m \tan (a+b x) \, dx","\text{Int}\left(\tan (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Tan[a + b*x], x]","A",0,0,0,0,-1,"{}"
209,1,158,0,0.2095777,"\int (c+d x)^4 \tan (a+b x) \, dx","Int[(c + d*x)^4*Tan[a + b*x],x]","-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{(c+d x)^4 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^5}{5 d}","-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{(c+d x)^4 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^5}{5 d}",1,"((I/5)*(c + d*x)^5)/d - ((c + d*x)^4*Log[1 + E^((2*I)*(a + b*x))])/b + ((2*I)*d*(c + d*x)^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)^2*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 - ((3*I)*d^3*(c + d*x)*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (3*d^4*PolyLog[5, -E^((2*I)*(a + b*x))])/(2*b^5)","A",7,6,14,0.4286,1,"{3719, 2190, 2531, 6609, 2282, 6589}"
210,1,132,0,0.1827949,"\int (c+d x)^3 \tan (a+b x) \, dx","Int[(c + d*x)^3*Tan[a + b*x],x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^4}{4 d}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^4}{4 d}",1,"((I/4)*(c + d*x)^4)/d - ((c + d*x)^3*Log[1 + E^((2*I)*(a + b*x))])/b + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4","A",6,6,14,0.4286,1,"{3719, 2190, 2531, 6609, 2282, 6589}"
211,1,96,0,0.1529825,"\int (c+d x)^2 \tan (a+b x) \, dx","Int[(c + d*x)^2*Tan[a + b*x],x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^3}{3 d}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^3}{3 d}",1,"((I/3)*(c + d*x)^3)/d - ((c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b + (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3)","A",5,5,14,0.3571,1,"{3719, 2190, 2531, 2282, 6589}"
212,1,66,0,0.0925894,"\int (c+d x) \tan (a+b x) \, dx","Int[(c + d*x)*Tan[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^2}{2 d}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{i (c+d x)^2}{2 d}",1,"((I/2)*(c + d*x)^2)/d - ((c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b + ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2","A",4,4,12,0.3333,1,"{3719, 2190, 2279, 2391}"
213,0,0,0,0.0199929,"\int \frac{\tan (a+b x)}{c+d x} \, dx","Int[Tan[a + b*x]/(c + d*x),x]","\int \frac{\tan (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{c+d x},x\right)",0,"Defer[Int][Tan[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
214,0,0,0,0.0196721,"\int \frac{\tan (a+b x)}{(c+d x)^2} \, dx","Int[Tan[a + b*x]/(c + d*x)^2,x]","\int \frac{\tan (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Tan[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
215,0,0,0,0.135594,"\int (c+d x)^m \sin (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x]*Tan[a + b*x],x]","\int (c+d x)^m \sin (a+b x) \tan (a+b x) \, dx","\text{Int}\left(\sec (a+b x) (c+d x)^m,x\right)+\frac{i 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{i 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}",0,"((I/2)*E^(I*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) - ((I/2)*(c + d*x)^m*Gamma[1 + m, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m) + Defer[Int][(c + d*x)^m*Sec[a + b*x], x]","A",0,0,0,0,-1,"{}"
216,1,275,0,0.2149072,"\int (c+d x)^3 \sin (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x]*Tan[a + b*x],x]","-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x) \sin (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cos (a+b x)}{b^2}+\frac{6 d^3 \cos (a+b x)}{b^4}-\frac{(c+d x)^3 \sin (a+b x)}{b}-\frac{2 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}","-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}+\frac{6 d^2 (c+d x) \sin (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cos (a+b x)}{b^2}+\frac{6 d^3 \cos (a+b x)}{b^4}-\frac{(c+d x)^3 \sin (a+b x)}{b}-\frac{2 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((-2*I)*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b + (6*d^3*Cos[a + b*x])/b^4 - (3*d*(c + d*x)^2*Cos[a + b*x])/b^2 + ((3*I)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((3*I)*d*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - (6*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (6*d^2*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^3 - ((6*I)*d^3*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^4 + ((6*I)*d^3*PolyLog[4, I*E^(I*(a + b*x))])/b^4 + (6*d^2*(c + d*x)*Sin[a + b*x])/b^3 - ((c + d*x)^3*Sin[a + b*x])/b","A",14,8,20,0.4000,1,"{4407, 3296, 2638, 4181, 2531, 6609, 2282, 6589}"
217,1,186,0,0.146066,"\int (c+d x)^2 \sin (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x]*Tan[a + b*x],x]","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \cos (a+b x)}{b^2}+\frac{2 d^2 \sin (a+b x)}{b^3}-\frac{(c+d x)^2 \sin (a+b x)}{b}-\frac{2 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \cos (a+b x)}{b^2}+\frac{2 d^2 \sin (a+b x)}{b^3}-\frac{(c+d x)^2 \sin (a+b x)}{b}-\frac{2 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((-2*I)*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b - (2*d*(c + d*x)*Cos[a + b*x])/b^2 + ((2*I)*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - (2*d^2*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (2*d^2*PolyLog[3, I*E^(I*(a + b*x))])/b^3 + (2*d^2*Sin[a + b*x])/b^3 - ((c + d*x)^2*Sin[a + b*x])/b","A",11,7,20,0.3500,1,"{4407, 3296, 2637, 4181, 2531, 2282, 6589}"
218,1,103,0,0.0675388,"\int (c+d x) \sin (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x]*Tan[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{d \cos (a+b x)}{b^2}-\frac{(c+d x) \sin (a+b x)}{b}-\frac{2 i (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{d \cos (a+b x)}{b^2}-\frac{(c+d x) \sin (a+b x)}{b}-\frac{2 i (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((-2*I)*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b - (d*Cos[a + b*x])/b^2 + (I*d*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - (I*d*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - ((c + d*x)*Sin[a + b*x])/b","A",8,6,18,0.3333,1,"{4407, 3296, 2638, 4181, 2279, 2391}"
219,0,0,0,0.1100885,"\int \frac{\sin (a+b x) \tan (a+b x)}{c+d x} \, dx","Int[(Sin[a + b*x]*Tan[a + b*x])/(c + d*x),x]","\int \frac{\sin (a+b x) \tan (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\sec (a+b x)}{c+d x},x\right)-\frac{\cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}",0,"-((Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d) + (Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d + Defer[Int][Sec[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
220,0,0,0,0.1389039,"\int \frac{\sin (a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","Int[(Sin[a + b*x]*Tan[a + b*x])/(c + d*x)^2,x]","\int \frac{\sin (a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\sec (a+b x)}{(c+d x)^2},x\right)+\frac{b \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{b \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{\cos (a+b x)}{d (c+d x)}",0,"Cos[a + b*x]/(d*(c + d*x)) + (b*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d^2 + (b*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^2 + Defer[Int][Sec[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.1708345,"\int (c+d x)^m \sin ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x]^2*Tan[a + b*x],x]","\int (c+d x)^m \sin ^2(a+b x) \tan (a+b x) \, dx","\text{Int}\left(\tan (a+b x) (c+d x)^m,x\right)+\frac{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{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}",0,"(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) + (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) + Defer[Int][(c + d*x)^m*Tan[a + b*x], x]","A",0,0,0,0,-1,"{}"
222,1,251,0,0.2975386,"\int (c+d x)^3 \sin ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x]^2*Tan[a + b*x],x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}-\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}-\frac{3 d^3 x}{8 b^3}+\frac{(c+d x)^3}{4 b}+\frac{i (c+d x)^4}{4 d}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{4 b^2}+\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{8 b^4}-\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \sin ^2(a+b x)}{2 b}-\frac{3 d^3 x}{8 b^3}+\frac{(c+d x)^3}{4 b}+\frac{i (c+d x)^4}{4 d}",1,"(-3*d^3*x)/(8*b^3) + (c + d*x)^3/(4*b) + ((I/4)*(c + d*x)^4)/d - ((c + d*x)^3*Log[1 + E^((2*I)*(a + b*x))])/b + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (3*d^3*Cos[a + b*x]*Sin[a + b*x])/(8*b^4) - (3*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) + (3*d^2*(c + d*x)*Sin[a + b*x]^2)/(4*b^3) - ((c + d*x)^3*Sin[a + b*x]^2)/(2*b)","A",12,12,22,0.5455,1,"{4407, 4404, 3311, 32, 2635, 8, 3719, 2190, 2531, 6609, 2282, 6589}"
223,1,184,0,0.2280754,"\int (c+d x)^2 \sin ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x]^2*Tan[a + b*x],x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}+\frac{d^2 \sin ^2(a+b x)}{4 b^3}-\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}+\frac{c d x}{2 b}+\frac{d^2 x^2}{4 b}+\frac{i (c+d x)^3}{3 d}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \sin (a+b x) \cos (a+b x)}{2 b^2}+\frac{d^2 \sin ^2(a+b x)}{4 b^3}-\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \sin ^2(a+b x)}{2 b}+\frac{c d x}{2 b}+\frac{d^2 x^2}{4 b}+\frac{i (c+d x)^3}{3 d}",1,"(c*d*x)/(2*b) + (d^2*x^2)/(4*b) + ((I/3)*(c + d*x)^3)/d - ((c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b + (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) - (d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b^2) + (d^2*Sin[a + b*x]^2)/(4*b^3) - ((c + d*x)^2*Sin[a + b*x]^2)/(2*b)","A",9,8,22,0.3636,1,"{4407, 4404, 3310, 3719, 2190, 2531, 2282, 6589}"
224,1,115,0,0.1278515,"\int (c+d x) \sin ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x]^2*Tan[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}-\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \sin ^2(a+b x)}{2 b}+\frac{d x}{4 b}+\frac{i (c+d x)^2}{2 d}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \sin (a+b x) \cos (a+b x)}{4 b^2}-\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}-\frac{(c+d x) \sin ^2(a+b x)}{2 b}+\frac{d x}{4 b}+\frac{i (c+d x)^2}{2 d}",1,"(d*x)/(4*b) + ((I/2)*(c + d*x)^2)/d - ((c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b + ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (d*Cos[a + b*x]*Sin[a + b*x])/(4*b^2) - ((c + d*x)*Sin[a + b*x]^2)/(2*b)","A",8,8,20,0.4000,1,"{4407, 4404, 2635, 8, 3719, 2190, 2279, 2391}"
225,0,0,0,0.151151,"\int \frac{\sin ^2(a+b x) \tan (a+b x)}{c+d x} \, dx","Int[(Sin[a + b*x]^2*Tan[a + b*x])/(c + d*x),x]","\int \frac{\sin ^2(a+b x) \tan (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{c+d x},x\right)-\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}-\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}",0,"-(CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(2*d) - (Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d) + Defer[Int][Tan[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
226,0,0,0,0.1763261,"\int \frac{\sin ^2(a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","Int[(Sin[a + b*x]^2*Tan[a + b*x])/(c + d*x)^2,x]","\int \frac{\sin ^2(a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan (a+b x)}{(c+d x)^2},x\right)-\frac{b \cos \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 \sin \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+2 b x)}{2 d (c+d x)}",0,"-((b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^2) + Sin[2*a + 2*b*x]/(2*d*(c + d*x)) + (b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2 + Defer[Int][Tan[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
227,0,0,0,0.183179,"\int (c+d x)^m \csc (a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x],x]","\int (c+d x)^m \csc (a+b x) \sec (a+b x) \, dx","\text{Int}\left(\csc (a+b x) \sec (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x], x]","A",0,0,0,0,-1,"{}"
228,1,247,0,0.2290666,"\int (c+d x)^4 \csc (a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^4*Csc[a + b*x]*Sec[a + b*x],x]","-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}","-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^4*ArcTanh[E^((2*I)*(a + b*x))])/b + ((2*I)*d*(c + d*x)^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)^2*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 + (3*d^2*(c + d*x)^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 - ((3*I)*d^3*(c + d*x)*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + ((3*I)*d^3*(c + d*x)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 + (3*d^4*PolyLog[5, -E^((2*I)*(a + b*x))])/(2*b^5) - (3*d^4*PolyLog[5, E^((2*I)*(a + b*x))])/(2*b^5)","A",12,6,20,0.3000,1,"{4419, 4183, 2531, 6609, 2282, 6589}"
229,1,197,0,0.1662808,"\int (c+d x)^3 \csc (a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]*Sec[a + b*x],x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^3*ArcTanh[E^((2*I)*(a + b*x))])/b + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",10,6,20,0.3000,1,"{4419, 4183, 2531, 6609, 2282, 6589}"
230,1,127,0,0.1166446,"\int (c+d x)^2 \csc (a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]*Sec[a + b*x],x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)^2*ArcTanh[E^((2*I)*(a + b*x))])/b + (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3)","A",8,5,20,0.2500,1,"{4419, 4183, 2531, 2282, 6589}"
231,1,71,0,0.0555391,"\int (c+d x) \csc (a+b x) \sec (a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]*Sec[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}",1,"(-2*(c + d*x)*ArcTanh[E^((2*I)*(a + b*x))])/b + ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",6,4,18,0.2222,1,"{4419, 4183, 2279, 2391}"
232,0,0,0,0.04482,"\int \frac{\csc (a+b x) \sec (a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x])/(c + d*x),x]","\int \frac{\csc (a+b x) \sec (a+b x)}{c+d x} \, dx","2 \text{Int}\left(\frac{\csc (2 a+2 b x)}{c+d x},x\right)",0,"2*Defer[Int][Csc[2*a + 2*b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
233,0,0,0,0.0410168,"\int \frac{\csc (a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x])/(c + d*x)^2,x]","\int \frac{\csc (a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","2 \text{Int}\left(\frac{\csc (2 a+2 b x)}{(c+d x)^2},x\right)",0,"2*Defer[Int][Csc[2*a + 2*b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
234,0,0,0,0.1967168,"\int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x],x]","\int (c+d x)^m \csc ^2(a+b x) \sec (a+b x) \, dx","\text{Int}\left(\csc ^2(a+b x) \sec (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x], x]","A",0,0,0,0,-1,"{}"
235,1,350,0,0.6401347,"\int (c+d x)^3 \csc ^2(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^2*Sec[a + b*x],x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \csc (a+b x)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \csc (a+b x)}{b}",1,"((-2*I)*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b - (6*d*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b^2 - ((c + d*x)^3*Csc[a + b*x])/b + ((6*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^3 + ((3*I)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((3*I)*d*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - ((6*I)*d^2*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^3 - (6*d^3*PolyLog[3, -E^(I*(a + b*x))])/b^4 - (6*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (6*d^2*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^3 + (6*d^3*PolyLog[3, E^(I*(a + b*x))])/b^4 - ((6*I)*d^3*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^4 + ((6*I)*d^3*PolyLog[4, I*E^(I*(a + b*x))])/b^4","A",23,14,22,0.6364,1,"{2621, 321, 207, 4420, 6741, 12, 6742, 6273, 4181, 2531, 6609, 2282, 6589, 4183}"
236,1,226,0,0.383878,"\int (c+d x)^2 \csc ^2(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^2*Sec[a + b*x],x]","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{2 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \csc (a+b x)}{b}","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{2 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{4 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \csc (a+b x)}{b}",1,"((-2*I)*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b - (4*d*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b^2 - ((c + d*x)^2*Csc[a + b*x])/b + ((2*I)*d^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 + ((2*I)*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - ((2*I)*d^2*PolyLog[2, E^(I*(a + b*x))])/b^3 - (2*d^2*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (2*d^2*PolyLog[3, I*E^(I*(a + b*x))])/b^3","A",19,15,22,0.6818,1,"{2621, 321, 207, 4420, 6741, 12, 6742, 6273, 4181, 2531, 2282, 6589, 4183, 2279, 2391}"
237,1,131,0,0.1345384,"\int (c+d x) \csc ^2(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^2*Sec[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \csc (a+b x)}{b}+\frac{(c+d x) \tanh ^{-1}(\sin (a+b x))}{b}-\frac{2 i d x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{d x \tanh ^{-1}(\sin (a+b x))}{b}","\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{(c+d x) \csc (a+b x)}{b}+\frac{(c+d x) \tanh ^{-1}(\sin (a+b x))}{b}-\frac{2 i d x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{d x \tanh ^{-1}(\sin (a+b x))}{b}",1,"((-2*I)*d*x*ArcTan[E^(I*(a + b*x))])/b - (d*ArcTanh[Cos[a + b*x]])/b^2 - (d*x*ArcTanh[Sin[a + b*x]])/b + ((c + d*x)*ArcTanh[Sin[a + b*x]])/b - ((c + d*x)*Csc[a + b*x])/b + (I*d*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - (I*d*PolyLog[2, I*E^(I*(a + b*x))])/b^2","A",10,10,20,0.5000,1,"{2621, 321, 207, 4420, 6271, 12, 4181, 2279, 2391, 3770}"
238,0,0,0,0.1598464,"\int \frac{\csc ^2(a+b x) \sec (a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x])/(c + d*x),x]","\int \frac{\csc ^2(a+b x) \sec (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x) \sec (a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]^2*Sec[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
239,0,0,0,0.1898831,"\int \frac{\csc ^2(a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x])/(c + d*x)^2,x]","\int \frac{\csc ^2(a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x) \sec (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]^2*Sec[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
240,0,0,0,0.2367413,"\int (c+d x)^m \csc ^3(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x],x]","\int (c+d x)^m \csc ^3(a+b x) \sec (a+b x) \, dx","\text{Int}\left(\csc ^3(a+b x) \sec (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x], x]","A",0,0,0,0,-1,"{}"
241,1,325,0,0.8234504,"\int (c+d x)^3 \csc ^3(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^3*Sec[a + b*x],x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \cot ^2(a+b x)}{2 b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{3 i d (c+d x)^2}{2 b^2}-\frac{(c+d x)^3}{2 b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 d^2 (c+d x) \log \left(1-e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \cot (a+b x)}{2 b^2}-\frac{(c+d x)^3 \cot ^2(a+b x)}{2 b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{3 i d (c+d x)^2}{2 b^2}-\frac{(c+d x)^3}{2 b}",1,"(((-3*I)/2)*d*(c + d*x)^2)/b^2 - (c + d*x)^3/(2*b) - (2*(c + d*x)^3*ArcTanh[E^((2*I)*(a + b*x))])/b - (3*d*(c + d*x)^2*Cot[a + b*x])/(2*b^2) - ((c + d*x)^3*Cot[a + b*x]^2)/(2*b) + (3*d^2*(c + d*x)*Log[1 - E^((2*I)*(a + b*x))])/b^3 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (((3*I)/2)*d^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",22,18,22,0.8182,1,"{2620, 14, 4420, 6741, 12, 6742, 3720, 3717, 2190, 2279, 2391, 32, 2551, 4183, 2531, 6609, 2282, 6589}"
242,1,201,0,0.4425078,"\int (c+d x)^2 \csc ^3(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^3*Sec[a + b*x],x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \cot ^2(a+b x)}{2 b}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{c d x}{b}-\frac{d^2 x^2}{2 b}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \cot (a+b x)}{b^2}+\frac{d^2 \log (\sin (a+b x))}{b^3}-\frac{(c+d x)^2 \cot ^2(a+b x)}{2 b}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{c d x}{b}-\frac{d^2 x^2}{2 b}",1,"-((c*d*x)/b) - (d^2*x^2)/(2*b) - (2*(c + d*x)^2*ArcTanh[E^((2*I)*(a + b*x))])/b - (d*(c + d*x)*Cot[a + b*x])/b^2 - ((c + d*x)^2*Cot[a + b*x]^2)/(2*b) + (d^2*Log[Sin[a + b*x]])/b^3 + (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3)","A",17,13,22,0.5909,1,"{2620, 14, 4420, 6741, 12, 6742, 3720, 3475, 2551, 4183, 2531, 2282, 6589}"
243,1,141,0,0.1385705,"\int (c+d x) \csc ^3(a+b x) \sec (a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^3*Sec[a + b*x],x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \cot ^2(a+b x)}{2 b}+\frac{(c+d x) \log (\tan (a+b x))}{b}-\frac{2 d x \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{d x \log (\tan (a+b x))}{b}-\frac{d x}{2 b}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \cot (a+b x)}{2 b^2}-\frac{(c+d x) \cot ^2(a+b x)}{2 b}+\frac{(c+d x) \log (\tan (a+b x))}{b}-\frac{2 d x \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{d x \log (\tan (a+b x))}{b}-\frac{d x}{2 b}",1,"-(d*x)/(2*b) - (2*d*x*ArcTanh[E^((2*I)*(a + b*x))])/b - (d*Cot[a + b*x])/(2*b^2) - ((c + d*x)*Cot[a + b*x]^2)/(2*b) - (d*x*Log[Tan[a + b*x]])/b + ((c + d*x)*Log[Tan[a + b*x]])/b + ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",11,10,20,0.5000,1,"{2620, 14, 4420, 3473, 8, 2548, 12, 4183, 2279, 2391}"
244,0,0,0,0.1467449,"\int \frac{\csc ^3(a+b x) \sec (a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x])/(c + d*x),x]","\int \frac{\csc ^3(a+b x) \sec (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec (a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
245,0,0,0,0.1919782,"\int \frac{\csc ^3(a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x])/(c + d*x)^2,x]","\int \frac{\csc ^3(a+b x) \sec (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
246,0,0,0,0.1420172,"\int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^m*Sec[a + b*x]*Tan[a + b*x],x]","\int (c+d x)^m \sec (a+b x) \tan (a+b x) \, dx","\text{Int}\left(\tan (a+b x) \sec (a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Sec[a + b*x]*Tan[a + b*x], x]","A",0,0,0,0,-1,"{}"
247,1,227,0,0.1857137,"\int (c+d x)^4 \sec (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^4*Sec[a + b*x]*Tan[a + b*x],x]","\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{24 i d^4 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^5}-\frac{24 i d^4 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^5}+\frac{8 i d (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^4 \sec (a+b x)}{b}","\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{24 i d^4 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^5}-\frac{24 i d^4 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^5}+\frac{8 i d (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^4 \sec (a+b x)}{b}",1,"((8*I)*d*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b^2 - ((12*I)*d^2*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((12*I)*d^2*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + (24*d^3*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (24*d^3*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + ((24*I)*d^4*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^5 - ((24*I)*d^4*PolyLog[4, I*E^(I*(a + b*x))])/b^5 + ((c + d*x)^4*Sec[a + b*x])/b","A",10,6,20,0.3000,1,"{4409, 4181, 2531, 6609, 2282, 6589}"
248,1,159,0,0.1257662,"\int (c+d x)^3 \sec (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]*Tan[a + b*x],x]","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^3 \sec (a+b x)}{b}","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^3 \sec (a+b x)}{b}",1,"((6*I)*d*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b^2 - ((6*I)*d^2*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((6*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + (6*d^3*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (6*d^3*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + ((c + d*x)^3*Sec[a + b*x])/b","A",8,5,20,0.2500,1,"{4409, 4181, 2531, 2282, 6589}"
249,1,97,0,0.0684212,"\int (c+d x)^2 \sec (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]*Tan[a + b*x],x]","-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^2 \sec (a+b x)}{b}","-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^2 \sec (a+b x)}{b}",1,"((4*I)*d*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^2 - ((2*I)*d^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((2*I)*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + ((c + d*x)^2*Sec[a + b*x])/b","A",6,4,20,0.2000,1,"{4409, 4181, 2279, 2391}"
250,1,29,0,0.0193704,"\int (c+d x) \sec (a+b x) \tan (a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x]*Tan[a + b*x],x]","\frac{(c+d x) \sec (a+b x)}{b}-\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}","\frac{(c+d x) \sec (a+b x)}{b}-\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}",1,"-((d*ArcTanh[Sin[a + b*x]])/b^2) + ((c + d*x)*Sec[a + b*x])/b","A",2,2,18,0.1111,1,"{4409, 3770}"
251,0,0,0,0.0940087,"\int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx","Int[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x),x]","\int \frac{\sec (a+b x) \tan (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{c+d x},x\right)",0,"Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
252,0,0,0,0.1146171,"\int \frac{\sec (a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","Int[(Sec[a + b*x]*Tan[a + b*x])/(c + d*x)^2,x]","\int \frac{\sec (a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
253,0,0,0,0.0357392,"\int (c+d x)^m \tan ^2(a+b x) \, dx","Int[(c + d*x)^m*Tan[a + b*x]^2,x]","\int (c+d x)^m \tan ^2(a+b x) \, dx","\text{Int}\left(\tan ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Tan[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
254,1,128,0,0.2102689,"\int (c+d x)^3 \tan ^2(a+b x) \, dx","Int[(c + d*x)^3*Tan[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 \tan (a+b x)}{b}-\frac{i (c+d x)^3}{b}-\frac{(c+d x)^4}{4 d}","-\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 \tan (a+b x)}{b}-\frac{i (c+d x)^3}{b}-\frac{(c+d x)^4}{4 d}",1,"((-I)*(c + d*x)^3)/b - (c + d*x)^4/(4*d) + (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) + ((c + d*x)^3*Tan[a + b*x])/b","A",7,7,16,0.4375,1,"{3720, 3719, 2190, 2531, 2282, 6589, 32}"
255,1,96,0,0.1410865,"\int (c+d x)^2 \tan ^2(a+b x) \, dx","Int[(c + d*x)^2*Tan[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 \tan (a+b x)}{b}-\frac{i (c+d x)^2}{b}-\frac{(c+d x)^3}{3 d}","-\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 \tan (a+b x)}{b}-\frac{i (c+d x)^2}{b}-\frac{(c+d x)^3}{3 d}",1,"((-I)*(c + d*x)^2)/b - (c + d*x)^3/(3*d) + (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 + ((c + d*x)^2*Tan[a + b*x])/b","A",6,6,16,0.3750,1,"{3720, 3719, 2190, 2279, 2391, 32}"
256,1,40,0,0.0283952,"\int (c+d x) \tan ^2(a+b x) \, dx","Int[(c + d*x)*Tan[a + b*x]^2,x]","\frac{d \log (\cos (a+b x))}{b^2}+\frac{(c+d x) \tan (a+b x)}{b}-c x-\frac{d x^2}{2}","\frac{d \log (\cos (a+b x))}{b^2}+\frac{(c+d x) \tan (a+b x)}{b}-c x-\frac{d x^2}{2}",1,"-(c*x) - (d*x^2)/2 + (d*Log[Cos[a + b*x]])/b^2 + ((c + d*x)*Tan[a + b*x])/b","A",3,2,14,0.1429,1,"{3720, 3475}"
257,0,0,0,0.0398115,"\int \frac{\tan ^2(a+b x)}{c+d x} \, dx","Int[Tan[a + b*x]^2/(c + d*x),x]","\int \frac{\tan ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Tan[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
258,0,0,0,0.0385174,"\int \frac{\tan ^2(a+b x)}{(c+d x)^2} \, dx","Int[Tan[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\tan ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Tan[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
259,0,0,0,0.1571458,"\int (c+d x)^m \sin (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^m*Sin[a + b*x]*Tan[a + b*x]^2,x]","\int (c+d x)^m \sin (a+b x) \tan ^2(a+b x) \, dx","\text{Int}\left(\tan (a+b x) \sec (a+b x) (c+d x)^m,x\right)+\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}",0,"(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) + Defer[Int][(c + d*x)^m*Sec[a + b*x]*Tan[a + b*x], x]","A",0,0,0,0,-1,"{}"
260,1,228,0,0.2110203,"\int (c+d x)^3 \sin (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^3*Sin[a + b*x]*Tan[a + b*x]^2,x]","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\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 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{6 d^3 \sin (a+b x)}{b^4}+\frac{(c+d x)^3 \cos (a+b x)}{b}+\frac{(c+d x)^3 \sec (a+b x)}{b}","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\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 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{6 d^3 \sin (a+b x)}{b^4}+\frac{(c+d x)^3 \cos (a+b x)}{b}+\frac{(c+d x)^3 \sec (a+b x)}{b}",1,"((6*I)*d*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b^2 - (6*d^2*(c + d*x)*Cos[a + b*x])/b^3 + ((c + d*x)^3*Cos[a + b*x])/b - ((6*I)*d^2*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((6*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + (6*d^3*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (6*d^3*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + ((c + d*x)^3*Sec[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",13,8,22,0.3636,1,"{4407, 3296, 2637, 4409, 4181, 2531, 2282, 6589}"
261,1,145,0,0.1311278,"\int (c+d x)^2 \sin (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^2*Sin[a + b*x]*Tan[a + b*x]^2,x]","-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \sin (a+b x)}{b^2}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \cos (a+b x)}{b^3}+\frac{(c+d x)^2 \cos (a+b x)}{b}+\frac{(c+d x)^2 \sec (a+b x)}{b}","-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \sin (a+b x)}{b^2}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \cos (a+b x)}{b^3}+\frac{(c+d x)^2 \cos (a+b x)}{b}+\frac{(c+d x)^2 \sec (a+b x)}{b}",1,"((4*I)*d*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^2 - (2*d^2*Cos[a + b*x])/b^3 + ((c + d*x)^2*Cos[a + b*x])/b - ((2*I)*d^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((2*I)*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + ((c + d*x)^2*Sec[a + b*x])/b - (2*d*(c + d*x)*Sin[a + b*x])/b^2","A",10,7,22,0.3182,1,"{4407, 3296, 2638, 4409, 4181, 2279, 2391}"
262,1,56,0,0.0537627,"\int (c+d x) \sin (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)*Sin[a + b*x]*Tan[a + b*x]^2,x]","-\frac{d \sin (a+b x)}{b^2}-\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{(c+d x) \cos (a+b x)}{b}+\frac{(c+d x) \sec (a+b x)}{b}","-\frac{d \sin (a+b x)}{b^2}-\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{(c+d x) \cos (a+b x)}{b}+\frac{(c+d x) \sec (a+b x)}{b}",1,"-((d*ArcTanh[Sin[a + b*x]])/b^2) + ((c + d*x)*Cos[a + b*x])/b + ((c + d*x)*Sec[a + b*x])/b - (d*Sin[a + b*x])/b^2","A",5,5,20,0.2500,1,"{4407, 3296, 2637, 4409, 3770}"
263,0,0,0,0.1501454,"\int \frac{\sin (a+b x) \tan ^2(a+b x)}{c+d x} \, dx","Int[(Sin[a + b*x]*Tan[a + b*x]^2)/(c + d*x),x]","\int \frac{\sin (a+b x) \tan ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{c+d x},x\right)-\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}",0,"-((CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d) - (Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d + Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
264,0,0,0,0.1814049,"\int \frac{\sin (a+b x) \tan ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Sin[a + b*x]*Tan[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\sin (a+b x) \tan ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{(c+d x)^2},x\right)-\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)}",0,"-((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 + Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
265,0,0,0,0.2484597,"\int (c+d x)^m \csc (a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x]^2,x]","\int (c+d x)^m \csc (a+b x) \sec ^2(a+b x) \, dx","\text{Int}\left(\csc (a+b x) \sec ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
266,1,469,0,0.794557,"\int (c+d x)^4 \csc (a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^4*Csc[a + b*x]*Sec[a + b*x]^2,x]","\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}+\frac{24 i d^4 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^5}-\frac{24 i d^4 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^5}+\frac{24 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}-\frac{24 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}+\frac{8 i d (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^4 \sec (a+b x)}{b}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{24 d^3 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{24 i d^3 (c+d x) \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{12 i d^2 (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{12 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{4 i d (c+d x)^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}+\frac{24 i d^4 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^5}-\frac{24 i d^4 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^5}+\frac{24 d^4 \text{PolyLog}\left(5,-e^{i (a+b x)}\right)}{b^5}-\frac{24 d^4 \text{PolyLog}\left(5,e^{i (a+b x)}\right)}{b^5}+\frac{8 i d (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^4 \sec (a+b x)}{b}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((8*I)*d*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b^2 - (2*(c + d*x)^4*ArcTanh[E^(I*(a + b*x))])/b + ((4*I)*d*(c + d*x)^3*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((12*I)*d^2*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((12*I)*d^2*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((4*I)*d*(c + d*x)^3*PolyLog[2, E^(I*(a + b*x))])/b^2 - (12*d^2*(c + d*x)^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (24*d^3*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (24*d^3*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + (12*d^2*(c + d*x)^2*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((24*I)*d^3*(c + d*x)*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((24*I)*d^4*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^5 - ((24*I)*d^4*PolyLog[4, I*E^(I*(a + b*x))])/b^5 + ((24*I)*d^3*(c + d*x)*PolyLog[4, E^(I*(a + b*x))])/b^4 + (24*d^4*PolyLog[5, -E^(I*(a + b*x))])/b^5 - (24*d^4*PolyLog[5, E^(I*(a + b*x))])/b^5 + ((c + d*x)^4*Sec[a + b*x])/b","A",27,14,22,0.6364,1,"{2622, 321, 207, 4420, 6741, 12, 6742, 6273, 4183, 2531, 6609, 2282, 6589, 4181}"
267,1,343,0,0.5726265,"\int (c+d x)^3 \csc (a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]*Sec[a + b*x]^2,x]","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i 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{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 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i 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{6 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^3 \sec (a+b x)}{b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i 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{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 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i 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{6 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^3 \sec (a+b x)}{b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((6*I)*d*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b^2 - (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 - ((6*I)*d^2*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((6*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((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^3*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (6*d^3*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + (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 + ((c + d*x)^3*Sec[a + b*x])/b","A",23,14,22,0.6364,1,"{2622, 321, 207, 4420, 6741, 12, 6742, 6273, 4183, 2531, 6609, 2282, 6589, 4181}"
268,1,219,0,0.3773803,"\int (c+d x)^2 \csc (a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]*Sec[a + b*x]^2,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 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i 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 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^2 \sec (a+b x)}{b}-\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 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i 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 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{(c+d x)^2 \sec (a+b x)}{b}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((4*I)*d*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^2 - (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^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((2*I)*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((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 + ((c + d*x)^2*Sec[a + b*x])/b","A",19,15,22,0.6818,1,"{2622, 321, 207, 4420, 6741, 12, 6742, 6273, 4183, 2531, 2282, 6589, 4181, 2279, 2391}"
269,1,122,0,0.1304504,"\int (c+d x) \csc (a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]*Sec[a + b*x]^2,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{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{(c+d x) \sec (a+b x)}{b}-\frac{(c+d x) \tanh ^{-1}(\cos (a+b x))}{b}-\frac{2 d x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{d x \tanh ^{-1}(\cos (a+b x))}{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{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{c \sec (a+b x)}{b}-\frac{c \tanh ^{-1}(\cos (a+b x))}{b}+\frac{d x \sec (a+b x)}{b}-\frac{2 d x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-2*d*x*ArcTanh[E^(I*(a + b*x))])/b + (d*x*ArcTanh[Cos[a + b*x]])/b - ((c + d*x)*ArcTanh[Cos[a + b*x]])/b - (d*ArcTanh[Sin[a + b*x]])/b^2 + (I*d*PolyLog[2, -E^(I*(a + b*x))])/b^2 - (I*d*PolyLog[2, E^(I*(a + b*x))])/b^2 + ((c + d*x)*Sec[a + b*x])/b","A",10,10,20,0.5000,1,"{2622, 321, 207, 4420, 6271, 12, 4183, 2279, 2391, 3770}"
270,0,0,0,0.1532007,"\int \frac{\csc (a+b x) \sec ^2(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x]^2)/(c + d*x),x]","\int \frac{\csc (a+b x) \sec ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc (a+b x) \sec ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]*Sec[a + b*x]^2)/(c + d*x), x]","A",0,0,0,0,-1,"{}"
271,0,0,0,0.1803738,"\int \frac{\csc (a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\csc (a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc (a+b x) \sec ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]*Sec[a + b*x]^2)/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
272,0,0,0,0.1896492,"\int (c+d x)^m \csc ^2(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x]^2,x]","\int (c+d x)^m \csc ^2(a+b x) \sec ^2(a+b x) \, dx","\text{Int}\left(\csc ^2(a+b x) \sec ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
273,1,118,0,0.2801061,"\int (c+d x)^3 \csc ^2(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^2*Sec[a + b*x]^2,x]","-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(2,e^{4 i (a+b x)}\right)}{2 b^3}+\frac{3 d^3 \text{PolyLog}\left(3,e^{4 i (a+b x)}\right)}{8 b^4}+\frac{3 d (c+d x)^2 \log \left(1-e^{4 i (a+b x)}\right)}{b^2}-\frac{2 (c+d x)^3 \cot (2 a+2 b x)}{b}-\frac{2 i (c+d x)^3}{b}","-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(2,e^{4 i (a+b x)}\right)}{2 b^3}+\frac{3 d^3 \text{PolyLog}\left(3,e^{4 i (a+b x)}\right)}{8 b^4}+\frac{3 d (c+d x)^2 \log \left(1-e^{4 i (a+b x)}\right)}{b^2}-\frac{2 (c+d x)^3 \cot (2 a+2 b x)}{b}-\frac{2 i (c+d x)^3}{b}",1,"((-2*I)*(c + d*x)^3)/b - (2*(c + d*x)^3*Cot[2*a + 2*b*x])/b + (3*d*(c + d*x)^2*Log[1 - E^((4*I)*(a + b*x))])/b^2 - (((3*I)/2)*d^2*(c + d*x)*PolyLog[2, E^((4*I)*(a + b*x))])/b^3 + (3*d^3*PolyLog[3, E^((4*I)*(a + b*x))])/(8*b^4)","A",7,7,24,0.2917,1,"{4419, 4184, 3717, 2190, 2531, 2282, 6589}"
274,1,88,0,0.191444,"\int (c+d x)^2 \csc ^2(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^2*Sec[a + b*x]^2,x]","-\frac{i d^2 \text{PolyLog}\left(2,e^{4 i (a+b x)}\right)}{2 b^3}+\frac{2 d (c+d x) \log \left(1-e^{4 i (a+b x)}\right)}{b^2}-\frac{2 (c+d x)^2 \cot (2 a+2 b x)}{b}-\frac{2 i (c+d x)^2}{b}","-\frac{i d^2 \text{PolyLog}\left(2,e^{4 i (a+b x)}\right)}{2 b^3}+\frac{2 d (c+d x) \log \left(1-e^{4 i (a+b x)}\right)}{b^2}-\frac{2 (c+d x)^2 \cot (2 a+2 b x)}{b}-\frac{2 i (c+d x)^2}{b}",1,"((-2*I)*(c + d*x)^2)/b - (2*(c + d*x)^2*Cot[2*a + 2*b*x])/b + (2*d*(c + d*x)*Log[1 - E^((4*I)*(a + b*x))])/b^2 - ((I/2)*d^2*PolyLog[2, E^((4*I)*(a + b*x))])/b^3","A",6,6,24,0.2500,1,"{4419, 4184, 3717, 2190, 2279, 2391}"
275,1,35,0,0.0594156,"\int (c+d x) \csc ^2(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^2*Sec[a + b*x]^2,x]","\frac{d \log (\sin (2 a+2 b x))}{b^2}-\frac{2 (c+d x) \cot (2 a+2 b x)}{b}","\frac{d \log (\sin (2 a+2 b x))}{b^2}-\frac{2 (c+d x) \cot (2 a+2 b x)}{b}",1,"(-2*(c + d*x)*Cot[2*a + 2*b*x])/b + (d*Log[Sin[2*a + 2*b*x]])/b^2","A",3,3,22,0.1364,1,"{4419, 4184, 3475}"
276,0,0,0,0.0936632,"\int \frac{\csc ^2(a+b x) \sec ^2(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x]^2)/(c + d*x),x]","\int \frac{\csc ^2(a+b x) \sec ^2(a+b x)}{c+d x} \, dx","4 \text{Int}\left(\frac{\csc ^2(2 a+2 b x)}{c+d x},x\right)",0,"4*Defer[Int][Csc[2*a + 2*b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
277,0,0,0,0.0857983,"\int \frac{\csc ^2(a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\csc ^2(a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","4 \text{Int}\left(\frac{\csc ^2(2 a+2 b x)}{(c+d x)^2},x\right)",0,"4*Defer[Int][Csc[2*a + 2*b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
278,0,0,0,0.2152128,"\int (c+d x)^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\int (c+d x)^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx","\text{Int}\left(\csc ^3(a+b x) \sec ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
279,1,601,0,2.3126898,"\int (c+d x)^3 \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","-\frac{6 i c d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i c d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{9 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{6 i d^3 x \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^3 x \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{9 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{9 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{3 c^2 d \csc (a+b x)}{2 b^2}-\frac{3 c^2 d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{12 i c d^2 x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 c d^2 x \csc (a+b x)}{b^2}-\frac{3 c d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{6 i d^3 x^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 d^3 x^2 \csc (a+b x)}{2 b^2}-\frac{6 d^3 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 (c+d x)^3 \sec (a+b x)}{2 b}-\frac{3 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \csc ^2(a+b x) \sec (a+b x)}{2 b}","-\frac{6 i c d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i c d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{9 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{6 i d^3 x \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i d^3 x \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{9 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{9 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{3 c^2 d \csc (a+b x)}{2 b^2}-\frac{3 c^2 d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{12 i c d^2 x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 c d^2 x \csc (a+b x)}{b^2}-\frac{3 c d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{6 i d^3 x^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 d^3 x^2 \csc (a+b x)}{2 b^2}-\frac{6 d^3 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 (c+d x)^3 \sec (a+b x)}{2 b}-\frac{3 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^3 \csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"((12*I)*c*d^2*x*ArcTan[E^(I*(a + b*x))])/b^2 + ((6*I)*d^3*x^2*ArcTan[E^(I*(a + b*x))])/b^2 - (6*d^3*x*ArcTanh[E^(I*(a + b*x))])/b^3 - (3*(c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b - (3*c*d^2*ArcTanh[Cos[a + b*x]])/b^3 - (3*c^2*d*ArcTanh[Sin[a + b*x]])/b^2 - (3*c^2*d*Csc[a + b*x])/(2*b^2) - (3*c*d^2*x*Csc[a + b*x])/b^2 - (3*d^3*x^2*Csc[a + b*x])/(2*b^2) + ((3*I)*d^3*PolyLog[2, -E^(I*(a + b*x))])/b^4 + (((9*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((6*I)*c*d^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 - ((6*I)*d^3*x*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((6*I)*c*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 + ((6*I)*d^3*x*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((3*I)*d^3*PolyLog[2, E^(I*(a + b*x))])/b^4 - (((9*I)/2)*d*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^2 - (9*d^2*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (6*d^3*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (6*d^3*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + (9*d^2*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((9*I)*d^3*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((9*I)*d^3*PolyLog[4, E^(I*(a + b*x))])/b^4 + (3*(c + d*x)^3*Sec[a + b*x])/(2*b) - ((c + d*x)^3*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",64,24,24,1.000,1,"{2622, 288, 321, 207, 4420, 6688, 12, 6742, 6273, 4183, 2531, 6609, 2282, 6589, 4133, 453, 206, 4181, 2279, 2391, 2621, 6271, 3770, 14}"
280,1,305,0,0.8652437,"\int (c+d x)^2 \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{3 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{c d \csc (a+b x)}{b^2}-\frac{2 c d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{4 i d^2 x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{d^2 x \csc (a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{3 (c+d x)^2 \sec (a+b x)}{2 b}-\frac{3 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \csc ^2(a+b x) \sec (a+b x)}{2 b}","\frac{3 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{c d \csc (a+b x)}{b^2}-\frac{2 c d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{4 i d^2 x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{d^2 x \csc (a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{3 (c+d x)^2 \sec (a+b x)}{2 b}-\frac{3 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{(c+d x)^2 \csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"((4*I)*d^2*x*ArcTan[E^(I*(a + b*x))])/b^2 - (3*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b - (d^2*ArcTanh[Cos[a + b*x]])/b^3 - (2*c*d*ArcTanh[Sin[a + b*x]])/b^2 - (c*d*Csc[a + b*x])/b^2 - (d^2*x*Csc[a + b*x])/b^2 + ((3*I)*d*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((2*I)*d^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((2*I)*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((3*I)*d*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^2 - (3*d^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (3*d^2*PolyLog[3, E^(I*(a + b*x))])/b^3 + (3*(c + d*x)^2*Sec[a + b*x])/(2*b) - ((c + d*x)^2*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",36,22,24,0.9167,1,"{2622, 288, 321, 207, 4420, 6688, 12, 6742, 6273, 4183, 2531, 2282, 6589, 4133, 453, 206, 4181, 2279, 2391, 2621, 6271, 3770}"
281,1,174,0,0.1913782,"\int (c+d x) \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{3 i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 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{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{3 (c+d x) \sec (a+b x)}{2 b}-\frac{3 (c+d x) \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{(c+d x) \csc ^2(a+b x) \sec (a+b x)}{2 b}-\frac{3 d x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{3 d x \tanh ^{-1}(\cos (a+b x))}{2 b}","\frac{3 i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 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{d \tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{3 (c+d x) \sec (a+b x)}{2 b}-\frac{(c+d x) \csc ^2(a+b x) \sec (a+b x)}{2 b}-\frac{3 c \tanh ^{-1}(\cos (a+b x))}{2 b}-\frac{3 d x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-3*d*x*ArcTanh[E^(I*(a + b*x))])/b + (3*d*x*ArcTanh[Cos[a + b*x]])/(2*b) - (3*(c + d*x)*ArcTanh[Cos[a + b*x]])/(2*b) - (d*ArcTanh[Sin[a + b*x]])/b^2 - (d*Csc[a + b*x])/(2*b^2) + (((3*I)/2)*d*PolyLog[2, -E^(I*(a + b*x))])/b^2 - (((3*I)/2)*d*PolyLog[2, E^(I*(a + b*x))])/b^2 + (3*(c + d*x)*Sec[a + b*x])/(2*b) - ((c + d*x)*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",13,12,22,0.5455,1,"{2622, 288, 321, 207, 4420, 6271, 12, 4183, 2279, 2391, 3770, 2621}"
282,0,0,0,0.2011746,"\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^2)/(c + d*x),x]","\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x]^2)/(c + d*x), x]","A",0,0,0,0,-1,"{}"
283,0,0,0,0.2244293,"\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x]^2)/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
284,0,0,0,0.9236519,"\int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[x^m*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\int x^m \csc ^3(a+b x) \sec ^2(a+b x) \, dx","\text{Int}\left(x^m \csc ^3(a+b x) \sec ^2(a+b x),x\right)",0,"Defer[Int][x^m*Csc[a + b*x]^3*Sec[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
285,1,387,0,0.9600718,"\int x^3 \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[x^3*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{9 i x^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{9 i x^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{6 i x \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i x \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{9 x \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{9 x \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{3 i \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{6 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{9 i \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{9 i \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 i x^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 x^2 \csc (a+b x)}{2 b^2}-\frac{6 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 x^3 \sec (a+b x)}{2 b}-\frac{3 x^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x^3 \csc ^2(a+b x) \sec (a+b x)}{2 b}","\frac{9 i x^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{9 i x^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{6 i x \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{6 i x \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{9 x \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{9 x \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{3 i \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^4}-\frac{3 i \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^4}+\frac{6 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}-\frac{6 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}-\frac{9 i \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{9 i \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}+\frac{6 i x^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 x^2 \csc (a+b x)}{2 b^2}-\frac{6 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 x^3 \sec (a+b x)}{2 b}-\frac{3 x^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x^3 \csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"((6*I)*x^2*ArcTan[E^(I*(a + b*x))])/b^2 - (6*x*ArcTanh[E^(I*(a + b*x))])/b^3 - (3*x^3*ArcTanh[E^(I*(a + b*x))])/b - (3*x^2*Csc[a + b*x])/(2*b^2) + ((3*I)*PolyLog[2, -E^(I*(a + b*x))])/b^4 + (((9*I)/2)*x^2*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((6*I)*x*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((6*I)*x*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((3*I)*PolyLog[2, E^(I*(a + b*x))])/b^4 - (((9*I)/2)*x^2*PolyLog[2, E^(I*(a + b*x))])/b^2 - (9*x*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (6*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 - (6*PolyLog[3, I*E^(I*(a + b*x))])/b^4 + (9*x*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((9*I)*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((9*I)*PolyLog[4, E^(I*(a + b*x))])/b^4 + (3*x^3*Sec[a + b*x])/(2*b) - (x^3*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",40,18,20,0.9000,1,"{2622, 288, 321, 207, 4420, 14, 6273, 12, 4183, 2531, 6609, 2282, 6589, 6742, 4181, 2621, 2279, 2391}"
286,1,235,0,0.5374502,"\int x^2 \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[x^2*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{3 i x \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i x \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 i \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{x \csc (a+b x)}{b^2}-\frac{\tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{3 x^2 \sec (a+b x)}{2 b}-\frac{3 x^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x^2 \csc ^2(a+b x) \sec (a+b x)}{2 b}","\frac{3 i x \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i x \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{2 i \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}+\frac{2 i \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{4 i x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{x \csc (a+b x)}{b^2}-\frac{\tanh ^{-1}(\cos (a+b x))}{b^3}+\frac{3 x^2 \sec (a+b x)}{2 b}-\frac{3 x^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x^2 \csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"((4*I)*x*ArcTan[E^(I*(a + b*x))])/b^2 - (3*x^2*ArcTanh[E^(I*(a + b*x))])/b - ArcTanh[Cos[a + b*x]]/b^3 - (x*Csc[a + b*x])/b^2 + ((3*I)*x*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((2*I)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 + ((2*I)*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((3*I)*x*PolyLog[2, E^(I*(a + b*x))])/b^2 - (3*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (3*PolyLog[3, E^(I*(a + b*x))])/b^3 + (3*x^2*Sec[a + b*x])/(2*b) - (x^2*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",29,19,20,0.9500,1,"{2622, 288, 321, 207, 4420, 14, 6273, 12, 4183, 2531, 2282, 6589, 6742, 4181, 2279, 2391, 2621, 6271, 3770}"
287,1,126,0,0.1677002,"\int x \csc ^3(a+b x) \sec ^2(a+b x) \, dx","Int[x*Csc[a + b*x]^3*Sec[a + b*x]^2,x]","\frac{3 i \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{\csc (a+b x)}{2 b^2}-\frac{\tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{3 x \sec (a+b x)}{2 b}-\frac{3 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x \csc ^2(a+b x) \sec (a+b x)}{2 b}","\frac{3 i \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{2 b^2}-\frac{\csc (a+b x)}{2 b^2}-\frac{\tanh ^{-1}(\sin (a+b x))}{b^2}+\frac{3 x \sec (a+b x)}{2 b}-\frac{3 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{x \csc ^2(a+b x) \sec (a+b x)}{2 b}",1,"(-3*x*ArcTanh[E^(I*(a + b*x))])/b - ArcTanh[Sin[a + b*x]]/b^2 - Csc[a + b*x]/(2*b^2) + (((3*I)/2)*PolyLog[2, -E^(I*(a + b*x))])/b^2 - (((3*I)/2)*PolyLog[2, E^(I*(a + b*x))])/b^2 + (3*x*Sec[a + b*x])/(2*b) - (x*Csc[a + b*x]^2*Sec[a + b*x])/(2*b)","A",13,12,18,0.6667,1,"{2622, 288, 321, 207, 4420, 6271, 12, 4183, 2279, 2391, 3770, 2621}"
288,0,0,0,0.4998083,"\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^2)/x,x]","\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x]^2)/x, x]","A",0,0,0,0,-1,"{}"
289,0,0,0,0.5132826,"\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x^2} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^2)/x^2,x]","\int \frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\csc ^3(a+b x) \sec ^2(a+b x)}{x^2},x\right)",0,"Defer[Int][(Csc[a + b*x]^3*Sec[a + b*x]^2)/x^2, x]","A",0,0,0,0,-1,"{}"
290,0,0,0,0.1524406,"\int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^m*Sec[a + b*x]^2*Tan[a + b*x],x]","\int (c+d x)^m \sec ^2(a+b x) \tan (a+b x) \, dx","\text{Int}\left(\tan (a+b x) \sec ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Sec[a + b*x]^2*Tan[a + b*x], x]","A",0,0,0,0,-1,"{}"
291,1,139,0,0.2578885,"\int (c+d x)^4 \sec ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^4*Sec[a + b*x]^2*Tan[a + b*x],x]","\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^4 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^5}-\frac{6 d^2 (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \tan (a+b x)}{b^2}+\frac{(c+d x)^4 \sec ^2(a+b x)}{2 b}+\frac{2 i d (c+d x)^3}{b^2}","\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^4 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^5}-\frac{6 d^2 (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \tan (a+b x)}{b^2}+\frac{(c+d x)^4 \sec ^2(a+b x)}{2 b}+\frac{2 i d (c+d x)^3}{b^2}",1,"((2*I)*d*(c + d*x)^3)/b^2 - (6*d^2*(c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b^3 + ((6*I)*d^3*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 - (3*d^4*PolyLog[3, -E^((2*I)*(a + b*x))])/b^5 + ((c + d*x)^4*Sec[a + b*x]^2)/(2*b) - (2*d*(c + d*x)^3*Tan[a + b*x])/b^2","A",7,7,22,0.3182,1,"{4409, 4184, 3719, 2190, 2531, 2282, 6589}"
292,1,115,0,0.1736715,"\int (c+d x)^3 \sec ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]^2*Tan[a + b*x],x]","\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \sec ^2(a+b x)}{2 b}+\frac{3 i d (c+d x)^2}{2 b^2}","\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \sec ^2(a+b x)}{2 b}+\frac{3 i d (c+d x)^2}{2 b^2}",1,"(((3*I)/2)*d*(c + d*x)^2)/b^2 - (3*d^2*(c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b^3 + (((3*I)/2)*d^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 + ((c + d*x)^3*Sec[a + b*x]^2)/(2*b) - (3*d*(c + d*x)^2*Tan[a + b*x])/(2*b^2)","A",6,6,22,0.2727,1,"{4409, 4184, 3719, 2190, 2279, 2391}"
293,1,55,0,0.0615893,"\int (c+d x)^2 \sec ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]^2*Tan[a + b*x],x]","-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \sec ^2(a+b x)}{2 b}","-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \sec ^2(a+b x)}{2 b}",1,"-((d^2*Log[Cos[a + b*x]])/b^3) + ((c + d*x)^2*Sec[a + b*x]^2)/(2*b) - (d*(c + d*x)*Tan[a + b*x])/b^2","A",3,3,22,0.1364,1,"{4409, 4184, 3475}"
294,1,35,0,0.0316128,"\int (c+d x) \sec ^2(a+b x) \tan (a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x]^2*Tan[a + b*x],x]","\frac{(c+d x) \sec ^2(a+b x)}{2 b}-\frac{d \tan (a+b x)}{2 b^2}","\frac{(c+d x) \sec ^2(a+b x)}{2 b}-\frac{d \tan (a+b x)}{2 b^2}",1,"((c + d*x)*Sec[a + b*x]^2)/(2*b) - (d*Tan[a + b*x])/(2*b^2)","A",3,3,20,0.1500,1,"{4409, 3767, 8}"
295,0,0,0,0.1064422,"\int \frac{\sec ^2(a+b x) \tan (a+b x)}{c+d x} \, dx","Int[(Sec[a + b*x]^2*Tan[a + b*x])/(c + d*x),x]","\int \frac{\sec ^2(a+b x) \tan (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Sec[a + b*x]^2*Tan[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
296,0,0,0,0.1283107,"\int \frac{\sec ^2(a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","Int[(Sec[a + b*x]^2*Tan[a + b*x])/(c + d*x)^2,x]","\int \frac{\sec ^2(a+b x) \tan (a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan (a+b x) \sec ^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Sec[a + b*x]^2*Tan[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
297,0,0,0,0.0839489,"\int (c+d x)^m \sec (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^m*Sec[a + b*x]*Tan[a + b*x]^2,x]","\int (c+d x)^m \sec (a+b x) \tan ^2(a+b x) \, dx","\text{Int}\left(\sec ^3(a+b x) (c+d x)^m,x\right)-\text{Int}\left(\sec (a+b x) (c+d x)^m,x\right)",0,"-Defer[Int][(c + d*x)^m*Sec[a + b*x], x] + Defer[Int][(c + d*x)^m*Sec[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
298,1,337,0,0.4083324,"\int (c+d x)^3 \sec (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]*Tan[a + b*x]^2,x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}+\frac{i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x)^3 \tan (a+b x) \sec (a+b x)}{2 b}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}+\frac{i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x)^3 \tan (a+b x) \sec (a+b x)}{2 b}",1,"((-6*I)*d^2*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^3 + (I*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b + ((3*I)*d^3*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((3*I)*d^3*PolyLog[2, I*E^(I*(a + b*x))])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 - (3*d^2*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^3 + ((3*I)*d^3*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^4 - ((3*I)*d^3*PolyLog[4, I*E^(I*(a + b*x))])/b^4 - (3*d*(c + d*x)^2*Sec[a + b*x])/(2*b^2) + ((c + d*x)^3*Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",25,9,22,0.4091,1,"{4413, 4181, 2531, 6609, 2282, 6589, 4186, 2279, 2391}"
299,1,193,0,0.2711427,"\int (c+d x)^2 \sec (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]*Tan[a + b*x]^2,x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}-\frac{d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \sec (a+b x)}{b^2}+\frac{d^2 \tanh ^{-1}(\sin (a+b x))}{b^3}+\frac{i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x)^2 \tan (a+b x) \sec (a+b x)}{2 b}","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}-\frac{d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \sec (a+b x)}{b^2}+\frac{d^2 \tanh ^{-1}(\sin (a+b x))}{b^3}+\frac{i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x)^2 \tan (a+b x) \sec (a+b x)}{2 b}",1,"(I*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b + (d^2*ArcTanh[Sin[a + b*x]])/b^3 - (I*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 + (I*d*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^2 + (d^2*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 - (d^2*PolyLog[3, I*E^(I*(a + b*x))])/b^3 - (d*(c + d*x)*Sec[a + b*x])/b^2 + ((c + d*x)^2*Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",17,7,22,0.3182,1,"{4413, 4181, 2531, 2282, 6589, 4186, 3770}"
300,1,117,0,0.1292495,"\int (c+d x) \sec (a+b x) \tan ^2(a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x]*Tan[a + b*x]^2,x]","-\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}-\frac{d \sec (a+b x)}{2 b^2}+\frac{i (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x) \tan (a+b x) \sec (a+b x)}{2 b}","-\frac{i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}-\frac{d \sec (a+b x)}{2 b^2}+\frac{i (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}+\frac{(c+d x) \tan (a+b x) \sec (a+b x)}{2 b}",1,"(I*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b - ((I/2)*d*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 + ((I/2)*d*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - (d*Sec[a + b*x])/(2*b^2) + ((c + d*x)*Sec[a + b*x]*Tan[a + b*x])/(2*b)","A",12,5,20,0.2500,1,"{4413, 4181, 2279, 2391, 4185}"
301,0,0,0,0.0911012,"\int \frac{\sec (a+b x) \tan ^2(a+b x)}{c+d x} \, dx","Int[(Sec[a + b*x]*Tan[a + b*x]^2)/(c + d*x),x]","\int \frac{\sec (a+b x) \tan ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\sec ^3(a+b x)}{c+d x},x\right)-\text{Int}\left(\frac{\sec (a+b x)}{c+d x},x\right)",0,"-Defer[Int][Sec[a + b*x]/(c + d*x), x] + Defer[Int][Sec[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
302,0,0,0,0.0888488,"\int \frac{\sec (a+b x) \tan ^2(a+b x)}{(c+d x)^2} \, dx","Int[(Sec[a + b*x]*Tan[a + b*x]^2)/(c + d*x)^2,x]","\int \frac{\sec (a+b x) \tan ^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\sec ^3(a+b x)}{(c+d x)^2},x\right)-\text{Int}\left(\frac{\sec (a+b x)}{(c+d x)^2},x\right)",0,"-Defer[Int][Sec[a + b*x]/(c + d*x)^2, x] + Defer[Int][Sec[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
303,0,0,0,0.0348048,"\int (c+d x)^m \tan ^3(a+b x) \, dx","Int[(c + d*x)^m*Tan[a + b*x]^3,x]","\int (c+d x)^m \tan ^3(a+b x) \, dx","\text{Int}\left(\tan ^3(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Tan[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
304,1,259,0,0.3557069,"\int (c+d x)^3 \tan ^3(a+b x) \, dx","Int[(c + d*x)^3*Tan[a + b*x]^3,x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x)^3 \tan ^2(a+b x)}{2 b}+\frac{3 i d (c+d x)^2}{2 b^2}+\frac{(c+d x)^3}{2 b}-\frac{i (c+d x)^4}{4 d}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x)^3 \tan ^2(a+b x)}{2 b}+\frac{3 i d (c+d x)^2}{2 b^2}+\frac{(c+d x)^3}{2 b}-\frac{i (c+d x)^4}{4 d}",1,"(((3*I)/2)*d*(c + d*x)^2)/b^2 + (c + d*x)^3/(2*b) - ((I/4)*(c + d*x)^4)/d - (3*d^2*(c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b^3 + ((c + d*x)^3*Log[1 + E^((2*I)*(a + b*x))])/b + (((3*I)/2)*d^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 - (3*d*(c + d*x)^2*Tan[a + b*x])/(2*b^2) + ((c + d*x)^3*Tan[a + b*x]^2)/(2*b)","A",13,10,16,0.6250,1,"{3720, 3719, 2190, 2279, 2391, 32, 2531, 6609, 2282, 6589}"
305,1,169,0,0.2217488,"\int (c+d x)^2 \tan ^3(a+b x) \, dx","Int[(c + d*x)^2*Tan[a + b*x]^3,x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x)^2 \tan ^2(a+b x)}{2 b}+\frac{c d x}{b}+\frac{d^2 x^2}{2 b}-\frac{i (c+d x)^3}{3 d}","-\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x)^2 \tan ^2(a+b x)}{2 b}+\frac{c d x}{b}+\frac{d^2 x^2}{2 b}-\frac{i (c+d x)^3}{3 d}",1,"(c*d*x)/b + (d^2*x^2)/(2*b) - ((I/3)*(c + d*x)^3)/d + ((c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b - (d^2*Log[Cos[a + b*x]])/b^3 - (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) - (d*(c + d*x)*Tan[a + b*x])/b^2 + ((c + d*x)^2*Tan[a + b*x]^2)/(2*b)","A",9,7,16,0.4375,1,"{3720, 3475, 3719, 2190, 2531, 2282, 6589}"
306,1,108,0,0.116911,"\int (c+d x) \tan ^3(a+b x) \, dx","Int[(c + d*x)*Tan[a + b*x]^3,x]","-\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \tan (a+b x)}{2 b^2}+\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x) \tan ^2(a+b x)}{2 b}+\frac{d x}{2 b}-\frac{i (c+d x)^2}{2 d}","-\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \tan (a+b x)}{2 b^2}+\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{(c+d x) \tan ^2(a+b x)}{2 b}+\frac{d x}{2 b}-\frac{i (c+d x)^2}{2 d}",1,"(d*x)/(2*b) - ((I/2)*(c + d*x)^2)/d + ((c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b - ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (d*Tan[a + b*x])/(2*b^2) + ((c + d*x)*Tan[a + b*x]^2)/(2*b)","A",7,7,14,0.5000,1,"{3720, 3473, 8, 3719, 2190, 2279, 2391}"
307,0,0,0,0.0385794,"\int \frac{\tan ^3(a+b x)}{c+d x} \, dx","Int[Tan[a + b*x]^3/(c + d*x),x]","\int \frac{\tan ^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\tan ^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][Tan[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
308,0,0,0,0.0366005,"\int \frac{\tan ^3(a+b x)}{(c+d x)^2} \, dx","Int[Tan[a + b*x]^3/(c + d*x)^2,x]","\int \frac{\tan ^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tan ^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Tan[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
309,0,0,0,0.2686618,"\int (c+d x)^m \csc (a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x]^3,x]","\int (c+d x)^m \csc (a+b x) \sec ^3(a+b x) \, dx","\text{Int}\left(\csc (a+b x) \sec ^3(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]*Sec[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
310,1,399,0,0.9710337,"\int (c+d x)^4 \csc (a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^4*Csc[a + b*x]*Sec[a + b*x]^3,x]","\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^4}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^5}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}-\frac{6 d^2 (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \tan (a+b x)}{b^2}+\frac{(c+d x)^4 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{2 i d (c+d x)^3}{b^2}+\frac{(c+d x)^4}{2 b}","\frac{6 i d^3 (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^4}-\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{b^4}-\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^5}+\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{3 d^4 \text{PolyLog}\left(5,e^{2 i (a+b x)}\right)}{2 b^5}-\frac{6 d^2 (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x)^3 \tan (a+b x)}{b^2}+\frac{(c+d x)^4 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^4 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{2 i d (c+d x)^3}{b^2}+\frac{(c+d x)^4}{2 b}",1,"((2*I)*d*(c + d*x)^3)/b^2 + (c + d*x)^4/(2*b) - (2*(c + d*x)^4*ArcTanh[E^((2*I)*(a + b*x))])/b - (6*d^2*(c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b^3 + ((6*I)*d^3*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 + ((2*I)*d*(c + d*x)^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^4*PolyLog[3, -E^((2*I)*(a + b*x))])/b^5 - (3*d^2*(c + d*x)^2*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 + (3*d^2*(c + d*x)^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 - ((3*I)*d^3*(c + d*x)*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + ((3*I)*d^3*(c + d*x)*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 + (3*d^4*PolyLog[5, -E^((2*I)*(a + b*x))])/(2*b^5) - (3*d^4*PolyLog[5, E^((2*I)*(a + b*x))])/(2*b^5) - (2*d*(c + d*x)^3*Tan[a + b*x])/b^2 + ((c + d*x)^4*Tan[a + b*x]^2)/(2*b)","A",25,16,22,0.7273,1,"{2620, 14, 4420, 6741, 12, 6742, 2551, 4183, 2531, 6609, 2282, 6589, 3720, 3719, 2190, 32}"
311,1,325,0,0.6401406,"\int (c+d x)^3 \csc (a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]*Sec[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{3 i d (c+d x)^2}{2 b^2}+\frac{(c+d x)^3}{2 b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \tan (a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{3 i d (c+d x)^2}{2 b^2}+\frac{(c+d x)^3}{2 b}",1,"(((3*I)/2)*d*(c + d*x)^2)/b^2 + (c + d*x)^3/(2*b) - (2*(c + d*x)^3*ArcTanh[E^((2*I)*(a + b*x))])/b - (3*d^2*(c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b^3 + (((3*I)/2)*d^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (((3*I)/4)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4 - (3*d*(c + d*x)^2*Tan[a + b*x])/(2*b^2) + ((c + d*x)^3*Tan[a + b*x]^2)/(2*b)","A",22,18,22,0.8182,1,"{2620, 14, 4420, 6741, 12, 6742, 2551, 4183, 2531, 6609, 2282, 6589, 3720, 3719, 2190, 2279, 2391, 32}"
312,1,201,0,0.4139056,"\int (c+d x)^2 \csc (a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]*Sec[a + b*x]^3,x]","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{c d x}{b}+\frac{d^2 x^2}{2 b}","\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{2 b^3}-\frac{d (c+d x) \tan (a+b x)}{b^2}-\frac{d^2 \log (\cos (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^2(a+b x)}{2 b}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}+\frac{c d x}{b}+\frac{d^2 x^2}{2 b}",1,"(c*d*x)/b + (d^2*x^2)/(2*b) - (2*(c + d*x)^2*ArcTanh[E^((2*I)*(a + b*x))])/b - (d^2*Log[Cos[a + b*x]])/b^3 + (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (I*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/(2*b^3) - (d*(c + d*x)*Tan[a + b*x])/b^2 + ((c + d*x)^2*Tan[a + b*x]^2)/(2*b)","A",17,13,22,0.5909,1,"{2620, 14, 4420, 6741, 12, 6742, 2551, 4183, 2531, 2282, 6589, 3720, 3475}"
313,1,141,0,0.1352659,"\int (c+d x) \csc (a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]*Sec[a + b*x]^3,x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \tan (a+b x)}{2 b^2}+\frac{(c+d x) \tan ^2(a+b x)}{2 b}+\frac{(c+d x) \log (\tan (a+b x))}{b}-\frac{2 d x \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{d x \log (\tan (a+b x))}{b}+\frac{d x}{2 b}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^2}-\frac{d \tan (a+b x)}{2 b^2}+\frac{c \tan ^2(a+b x)}{2 b}+\frac{c \log (\tan (a+b x))}{b}+\frac{d x \tan ^2(a+b x)}{2 b}-\frac{2 d x \tanh ^{-1}\left(e^{2 i a+2 i b x}\right)}{b}+\frac{d x}{2 b}",1,"(d*x)/(2*b) - (2*d*x*ArcTanh[E^((2*I)*(a + b*x))])/b - (d*x*Log[Tan[a + b*x]])/b + ((c + d*x)*Log[Tan[a + b*x]])/b + ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((I/2)*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d*Tan[a + b*x])/(2*b^2) + ((c + d*x)*Tan[a + b*x]^2)/(2*b)","A",11,10,20,0.5000,1,"{2620, 14, 4420, 2548, 12, 4183, 2279, 2391, 3473, 8}"
314,0,0,0,0.1888985,"\int \frac{\csc (a+b x) \sec ^3(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x]^3)/(c + d*x),x]","\int \frac{\csc (a+b x) \sec ^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc (a+b x) \sec ^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]*Sec[a + b*x]^3)/(c + d*x), x]","A",0,0,0,0,-1,"{}"
315,0,0,0,0.2086931,"\int \frac{\csc (a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]*Sec[a + b*x]^3)/(c + d*x)^2,x]","\int \frac{\csc (a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc (a+b x) \sec ^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]*Sec[a + b*x]^3)/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
316,0,0,0,0.2328935,"\int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x]^3,x]","\int (c+d x)^m \csc ^2(a+b x) \sec ^3(a+b x) \, dx","\text{Int}\left(\csc ^2(a+b x) \sec ^3(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^2*Sec[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
317,1,486,0,1.2063499,"\int (c+d x)^3 \csc ^2(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^2*Sec[a + b*x]^3,x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}-\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{9 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{9 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{3 (c+d x)^3 \csc (a+b x)}{2 b}+\frac{(c+d x)^3 \csc (a+b x) \sec ^2(a+b x)}{2 b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{9 d^2 (c+d x) \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}-\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^4}-\frac{6 d^3 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^4}-\frac{9 i d^3 \text{PolyLog}\left(4,-i e^{i (a+b x)}\right)}{b^4}+\frac{9 i d^3 \text{PolyLog}\left(4,i e^{i (a+b x)}\right)}{b^4}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}-\frac{6 d (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{3 i (c+d x)^3 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{3 (c+d x)^3 \csc (a+b x)}{2 b}+\frac{(c+d x)^3 \csc (a+b x) \sec ^2(a+b x)}{2 b}",1,"((-6*I)*d^2*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^3 - ((3*I)*(c + d*x)^3*ArcTan[E^(I*(a + b*x))])/b - (6*d*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b^2 - (3*(c + d*x)^3*Csc[a + b*x])/(2*b) + ((6*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^3 + ((3*I)*d^3*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^4 + (((9*I)/2)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((3*I)*d^3*PolyLog[2, I*E^(I*(a + b*x))])/b^4 - (((9*I)/2)*d*(c + d*x)^2*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - ((6*I)*d^2*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^3 - (6*d^3*PolyLog[3, -E^(I*(a + b*x))])/b^4 - (9*d^2*(c + d*x)*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (9*d^2*(c + d*x)*PolyLog[3, I*E^(I*(a + b*x))])/b^3 + (6*d^3*PolyLog[3, E^(I*(a + b*x))])/b^4 - ((9*I)*d^3*PolyLog[4, (-I)*E^(I*(a + b*x))])/b^4 + ((9*I)*d^3*PolyLog[4, I*E^(I*(a + b*x))])/b^4 - (3*d*(c + d*x)^2*Sec[a + b*x])/(2*b^2) + ((c + d*x)^3*Csc[a + b*x]*Sec[a + b*x]^2)/(2*b)","A",44,19,24,0.7917,1,"{2621, 288, 321, 207, 4420, 6688, 12, 6742, 6273, 4181, 2531, 6609, 2282, 6589, 4183, 2622, 6741, 2279, 2391}"
318,1,341,0,0.6476495,"\int (c+d x)^2 \csc ^2(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^2*Sec[a + b*x]^3,x]","\frac{3 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \sec (a+b x)}{b^2}-\frac{6 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{d (c+d x) \tanh ^{-1}(\cos (a+b x))}{b^2}+\frac{2 d^2 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{d^2 \tanh ^{-1}(\sin (a+b x))}{b^3}-\frac{d^2 x \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{3 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{3 (c+d x)^2 \csc (a+b x)}{2 b}+\frac{(c+d x)^2 \csc (a+b x) \sec ^2(a+b x)}{2 b}","\frac{3 i d (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^3}-\frac{3 d^2 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^3}-\frac{d (c+d x) \sec (a+b x)}{b^2}-\frac{6 d (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{d (c+d x) \tanh ^{-1}(\cos (a+b x))}{b^2}+\frac{2 d^2 x \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{d^2 \tanh ^{-1}(\sin (a+b x))}{b^3}-\frac{d^2 x \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{3 i (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{3 (c+d x)^2 \csc (a+b x)}{2 b}+\frac{(c+d x)^2 \csc (a+b x) \sec ^2(a+b x)}{2 b}",1,"((-3*I)*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b + (2*d^2*x*ArcTanh[E^(I*(a + b*x))])/b^2 - (6*d*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b^2 - (d^2*x*ArcTanh[Cos[a + b*x]])/b^2 + (d*(c + d*x)*ArcTanh[Cos[a + b*x]])/b^2 + (d^2*ArcTanh[Sin[a + b*x]])/b^3 - (3*(c + d*x)^2*Csc[a + b*x])/(2*b) + ((2*I)*d^2*PolyLog[2, -E^(I*(a + b*x))])/b^3 + ((3*I)*d*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - ((3*I)*d*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - ((2*I)*d^2*PolyLog[2, E^(I*(a + b*x))])/b^3 - (3*d^2*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^3 + (3*d^2*PolyLog[3, I*E^(I*(a + b*x))])/b^3 - (d*(c + d*x)*Sec[a + b*x])/b^2 + ((c + d*x)^2*Csc[a + b*x]*Sec[a + b*x]^2)/(2*b)","A",31,19,24,0.7917,1,"{2621, 288, 321, 207, 4420, 6688, 12, 6742, 6273, 4181, 2531, 2282, 6589, 4183, 2279, 2391, 2622, 6271, 3770}"
319,1,182,0,0.1958674,"\int (c+d x) \csc ^2(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^2*Sec[a + b*x]^3,x]","\frac{3 i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}-\frac{d \sec (a+b x)}{2 b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{3 (c+d x) \csc (a+b x)}{2 b}+\frac{3 (c+d x) \tanh ^{-1}(\sin (a+b x))}{2 b}+\frac{(c+d x) \csc (a+b x) \sec ^2(a+b x)}{2 b}-\frac{3 i d x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}-\frac{3 d x \tanh ^{-1}(\sin (a+b x))}{2 b}","\frac{3 i d \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{2 b^2}-\frac{d \sec (a+b x)}{2 b^2}-\frac{d \tanh ^{-1}(\cos (a+b x))}{b^2}-\frac{3 (c+d x) \csc (a+b x)}{2 b}+\frac{(c+d x) \csc (a+b x) \sec ^2(a+b x)}{2 b}+\frac{3 c \tanh ^{-1}(\sin (a+b x))}{2 b}-\frac{3 i d x \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"((-3*I)*d*x*ArcTan[E^(I*(a + b*x))])/b - (d*ArcTanh[Cos[a + b*x]])/b^2 - (3*d*x*ArcTanh[Sin[a + b*x]])/(2*b) + (3*(c + d*x)*ArcTanh[Sin[a + b*x]])/(2*b) - (3*(c + d*x)*Csc[a + b*x])/(2*b) + (((3*I)/2)*d*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^2 - (((3*I)/2)*d*PolyLog[2, I*E^(I*(a + b*x))])/b^2 - (d*Sec[a + b*x])/(2*b^2) + ((c + d*x)*Csc[a + b*x]*Sec[a + b*x]^2)/(2*b)","A",13,12,22,0.5455,1,"{2621, 288, 321, 207, 4420, 6271, 12, 4181, 2279, 2391, 3770, 2622}"
320,0,0,0,0.1866199,"\int \frac{\csc ^2(a+b x) \sec ^3(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x]^3)/(c + d*x),x]","\int \frac{\csc ^2(a+b x) \sec ^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][(Csc[a + b*x]^2*Sec[a + b*x]^3)/(c + d*x), x]","A",0,0,0,0,-1,"{}"
321,0,0,0,0.1971327,"\int \frac{\csc ^2(a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^2*Sec[a + b*x]^3)/(c + d*x)^2,x]","\int \frac{\csc ^2(a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\csc ^2(a+b x) \sec ^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][(Csc[a + b*x]^2*Sec[a + b*x]^3)/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
322,0,0,0,0.2645783,"\int (c+d x)^m \csc ^3(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x]^3,x]","\int (c+d x)^m \csc ^3(a+b x) \sec ^3(a+b x) \, dx","\text{Int}\left(\csc ^3(a+b x) \sec ^3(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Csc[a + b*x]^3*Sec[a + b*x]^3, x]","A",0,0,0,0,-1,"{}"
323,1,318,0,0.32147,"\int (c+d x)^3 \csc ^3(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^3*Sec[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \csc (2 a+2 b x)}{b^2}-\frac{4 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x)^3 \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,e^{2 i (a+b x)}\right)}{2 b^4}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \csc (2 a+2 b x)}{b^2}-\frac{4 (c+d x)^3 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x)^3 \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}",1,"(-6*d^2*(c + d*x)*ArcTanh[E^((2*I)*(a + b*x))])/b^3 - (4*(c + d*x)^3*ArcTanh[E^((2*I)*(a + b*x))])/b - (3*d*(c + d*x)^2*Csc[2*a + 2*b*x])/b^2 - (2*(c + d*x)^3*Cot[2*a + 2*b*x]*Csc[2*a + 2*b*x])/b + (((3*I)/2)*d^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^4 + ((3*I)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (((3*I)/2)*d^3*PolyLog[2, E^((2*I)*(a + b*x))])/b^4 - ((3*I)*d*(c + d*x)^2*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 + (3*d^2*(c + d*x)*PolyLog[3, E^((2*I)*(a + b*x))])/b^3 - (((3*I)/2)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 + (((3*I)/2)*d^3*PolyLog[4, E^((2*I)*(a + b*x))])/b^4","A",16,9,24,0.3750,1,"{4419, 4186, 4183, 2279, 2391, 2531, 6609, 2282, 6589}"
324,1,190,0,0.2128356,"\int (c+d x)^2 \csc ^3(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^3*Sec[a + b*x]^3,x]","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \csc (2 a+2 b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (2 a+2 b x))}{b^3}-\frac{4 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x)^2 \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}","\frac{2 i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{2 i (a+b x)}\right)}{b^3}-\frac{2 d (c+d x) \csc (2 a+2 b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cos (2 a+2 b x))}{b^3}-\frac{4 (c+d x)^2 \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x)^2 \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}",1,"(-4*(c + d*x)^2*ArcTanh[E^((2*I)*(a + b*x))])/b - (d^2*ArcTanh[Cos[2*a + 2*b*x]])/b^3 - (2*d*(c + d*x)*Csc[2*a + 2*b*x])/b^2 - (2*(c + d*x)^2*Cot[2*a + 2*b*x]*Csc[2*a + 2*b*x])/b + ((2*I)*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - ((2*I)*d*(c + d*x)*PolyLog[2, E^((2*I)*(a + b*x))])/b^2 - (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 + (d^2*PolyLog[3, E^((2*I)*(a + b*x))])/b^3","A",10,7,24,0.2917,1,"{4419, 4186, 3770, 4183, 2531, 2282, 6589}"
325,1,110,0,0.1061727,"\int (c+d x) \csc ^3(a+b x) \sec ^3(a+b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^3*Sec[a + b*x]^3,x]","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d \csc (2 a+2 b x)}{b^2}-\frac{4 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x) \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}","\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{i d \text{PolyLog}\left(2,e^{2 i (a+b x)}\right)}{b^2}-\frac{d \csc (2 a+2 b x)}{b^2}-\frac{4 (c+d x) \tanh ^{-1}\left(e^{2 i (a+b x)}\right)}{b}-\frac{2 (c+d x) \cot (2 a+2 b x) \csc (2 a+2 b x)}{b}",1,"(-4*(c + d*x)*ArcTanh[E^((2*I)*(a + b*x))])/b - (d*Csc[2*a + 2*b*x])/b^2 - (2*(c + d*x)*Cot[2*a + 2*b*x]*Csc[2*a + 2*b*x])/b + (I*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 - (I*d*PolyLog[2, E^((2*I)*(a + b*x))])/b^2","A",7,5,22,0.2273,1,"{4419, 4185, 4183, 2279, 2391}"
326,0,0,0,0.0871065,"\int \frac{\csc ^3(a+b x) \sec ^3(a+b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^3)/(c + d*x),x]","\int \frac{\csc ^3(a+b x) \sec ^3(a+b x)}{c+d x} \, dx","8 \text{Int}\left(\frac{\csc ^3(2 a+2 b x)}{c+d x},x\right)",0,"8*Defer[Int][Csc[2*a + 2*b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
327,0,0,0,0.088088,"\int \frac{\csc ^3(a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^3*Sec[a + b*x]^3)/(c + d*x)^2,x]","\int \frac{\csc ^3(a+b x) \sec ^3(a+b x)}{(c+d x)^2} \, dx","8 \text{Int}\left(\frac{\csc ^3(2 a+2 b x)}{(c+d x)^2},x\right)",0,"8*Defer[Int][Csc[2*a + 2*b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
328,1,83,0,0.0535435,"\int x \cos ^{\frac{5}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Cos[a + b*x]^(5/2)*Sin[a + b*x],x]","\frac{20 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{147 b^2}+\frac{4 \sin (a+b x) \cos ^{\frac{5}{2}}(a+b x)}{49 b^2}+\frac{20 \sin (a+b x) \sqrt{\cos (a+b x)}}{147 b^2}-\frac{2 x \cos ^{\frac{7}{2}}(a+b x)}{7 b}","\frac{20 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{147 b^2}+\frac{4 \sin (a+b x) \cos ^{\frac{5}{2}}(a+b x)}{49 b^2}+\frac{20 \sin (a+b x) \sqrt{\cos (a+b x)}}{147 b^2}-\frac{2 x \cos ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(-2*x*Cos[a + b*x]^(7/2))/(7*b) + (20*EllipticF[(a + b*x)/2, 2])/(147*b^2) + (20*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(147*b^2) + (4*Cos[a + b*x]^(5/2)*Sin[a + b*x])/(49*b^2)","A",4,3,18,0.1667,1,"{3444, 2635, 2641}"
329,1,60,0,0.0397231,"\int x \cos ^{\frac{3}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Cos[a + b*x]^(3/2)*Sin[a + b*x],x]","\frac{12 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{25 b^2}+\frac{4 \sin (a+b x) \cos ^{\frac{3}{2}}(a+b x)}{25 b^2}-\frac{2 x \cos ^{\frac{5}{2}}(a+b x)}{5 b}","\frac{12 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{25 b^2}+\frac{4 \sin (a+b x) \cos ^{\frac{3}{2}}(a+b x)}{25 b^2}-\frac{2 x \cos ^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-2*x*Cos[a + b*x]^(5/2))/(5*b) + (12*EllipticE[(a + b*x)/2, 2])/(25*b^2) + (4*Cos[a + b*x]^(3/2)*Sin[a + b*x])/(25*b^2)","A",3,3,18,0.1667,1,"{3444, 2635, 2639}"
330,1,60,0,0.0388699,"\int x \sqrt{\cos (a+b x)} \sin (a+b x) \, dx","Int[x*Sqrt[Cos[a + b*x]]*Sin[a + b*x],x]","\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{9 b^2}+\frac{4 \sin (a+b x) \sqrt{\cos (a+b x)}}{9 b^2}-\frac{2 x \cos ^{\frac{3}{2}}(a+b x)}{3 b}","\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{9 b^2}+\frac{4 \sin (a+b x) \sqrt{\cos (a+b x)}}{9 b^2}-\frac{2 x \cos ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(-2*x*Cos[a + b*x]^(3/2))/(3*b) + (4*EllipticF[(a + b*x)/2, 2])/(9*b^2) + (4*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(9*b^2)","A",3,3,18,0.1667,1,"{3444, 2635, 2641}"
331,1,33,0,0.0262149,"\int \frac{x \sin (a+b x)}{\sqrt{\cos (a+b x)}} \, dx","Int[(x*Sin[a + b*x])/Sqrt[Cos[a + b*x]],x]","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}-\frac{2 x \sqrt{\cos (a+b x)}}{b}","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}-\frac{2 x \sqrt{\cos (a+b x)}}{b}",1,"(-2*x*Sqrt[Cos[a + b*x]])/b + (4*EllipticE[(a + b*x)/2, 2])/b^2","A",2,2,18,0.1111,1,"{3444, 2639}"
332,1,33,0,0.0256239,"\int \frac{x \sin (a+b x)}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Cos[a + b*x]^(3/2),x]","\frac{2 x}{b \sqrt{\cos (a+b x)}}-\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}","\frac{2 x}{b \sqrt{\cos (a+b x)}}-\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}",1,"(2*x)/(b*Sqrt[Cos[a + b*x]]) - (4*EllipticF[(a + b*x)/2, 2])/b^2","A",2,2,18,0.1111,1,"{3444, 2641}"
333,1,60,0,0.0360545,"\int \frac{x \sin (a+b x)}{\cos ^{\frac{5}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Cos[a + b*x]^(5/2),x]","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b^2}-\frac{4 \sin (a+b x)}{3 b^2 \sqrt{\cos (a+b x)}}+\frac{2 x}{3 b \cos ^{\frac{3}{2}}(a+b x)}","\frac{4 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b^2}-\frac{4 \sin (a+b x)}{3 b^2 \sqrt{\cos (a+b x)}}+\frac{2 x}{3 b \cos ^{\frac{3}{2}}(a+b x)}",1,"(2*x)/(3*b*Cos[a + b*x]^(3/2)) + (4*EllipticE[(a + b*x)/2, 2])/(3*b^2) - (4*Sin[a + b*x])/(3*b^2*Sqrt[Cos[a + b*x]])","A",3,3,18,0.1667,1,"{3444, 2636, 2639}"
334,1,60,0,0.0379388,"\int \frac{x \sin (a+b x)}{\cos ^{\frac{7}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Cos[a + b*x]^(7/2),x]","-\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{15 b^2}-\frac{4 \sin (a+b x)}{15 b^2 \cos ^{\frac{3}{2}}(a+b x)}+\frac{2 x}{5 b \cos ^{\frac{5}{2}}(a+b x)}","-\frac{4 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{15 b^2}-\frac{4 \sin (a+b x)}{15 b^2 \cos ^{\frac{3}{2}}(a+b x)}+\frac{2 x}{5 b \cos ^{\frac{5}{2}}(a+b x)}",1,"(2*x)/(5*b*Cos[a + b*x]^(5/2)) - (4*EllipticF[(a + b*x)/2, 2])/(15*b^2) - (4*Sin[a + b*x])/(15*b^2*Cos[a + b*x]^(3/2))","A",3,3,18,0.1667,1,"{3444, 2636, 2641}"
335,1,83,0,0.0484516,"\int \frac{x \sin (a+b x)}{\cos ^{\frac{9}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Cos[a + b*x]^(9/2),x]","\frac{12 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{35 b^2}-\frac{4 \sin (a+b x)}{35 b^2 \cos ^{\frac{5}{2}}(a+b x)}-\frac{12 \sin (a+b x)}{35 b^2 \sqrt{\cos (a+b x)}}+\frac{2 x}{7 b \cos ^{\frac{7}{2}}(a+b x)}","\frac{12 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{35 b^2}-\frac{4 \sin (a+b x)}{35 b^2 \cos ^{\frac{5}{2}}(a+b x)}-\frac{12 \sin (a+b x)}{35 b^2 \sqrt{\cos (a+b x)}}+\frac{2 x}{7 b \cos ^{\frac{7}{2}}(a+b x)}",1,"(2*x)/(7*b*Cos[a + b*x]^(7/2)) + (12*EllipticE[(a + b*x)/2, 2])/(35*b^2) - (4*Sin[a + b*x])/(35*b^2*Cos[a + b*x]^(5/2)) - (12*Sin[a + b*x])/(35*b^2*Sqrt[Cos[a + b*x]])","A",4,3,18,0.1667,1,"{3444, 2636, 2639}"
336,1,103,0,0.0620826,"\int x \sec ^{\frac{9}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Sec[a + b*x]^(9/2)*Sin[a + b*x],x]","-\frac{4 \sin (a+b x) \sec ^{\frac{5}{2}}(a+b x)}{35 b^2}-\frac{12 \sin (a+b x) \sqrt{\sec (a+b x)}}{35 b^2}+\frac{12 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{35 b^2}+\frac{2 x \sec ^{\frac{7}{2}}(a+b x)}{7 b}","-\frac{4 \sin (a+b x) \sec ^{\frac{5}{2}}(a+b x)}{35 b^2}-\frac{12 \sin (a+b x) \sqrt{\sec (a+b x)}}{35 b^2}+\frac{12 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{35 b^2}+\frac{2 x \sec ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(12*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(35*b^2) + (2*x*Sec[a + b*x]^(7/2))/(7*b) - (12*Sqrt[Sec[a + b*x]]*Sin[a + b*x])/(35*b^2) - (4*Sec[a + b*x]^(5/2)*Sin[a + b*x])/(35*b^2)","A",5,4,18,0.2222,1,"{4212, 3768, 3771, 2639}"
337,1,80,0,0.0488525,"\int x \sec ^{\frac{7}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Sec[a + b*x]^(7/2)*Sin[a + b*x],x]","-\frac{4 \sin (a+b x) \sec ^{\frac{3}{2}}(a+b x)}{15 b^2}-\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{15 b^2}+\frac{2 x \sec ^{\frac{5}{2}}(a+b x)}{5 b}","-\frac{4 \sin (a+b x) \sec ^{\frac{3}{2}}(a+b x)}{15 b^2}-\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{15 b^2}+\frac{2 x \sec ^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(15*b^2) + (2*x*Sec[a + b*x]^(5/2))/(5*b) - (4*Sec[a + b*x]^(3/2)*Sin[a + b*x])/(15*b^2)","A",4,4,18,0.2222,1,"{4212, 3768, 3771, 2641}"
338,1,80,0,0.0525987,"\int x \sec ^{\frac{5}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Sec[a + b*x]^(5/2)*Sin[a + b*x],x]","-\frac{4 \sin (a+b x) \sqrt{\sec (a+b x)}}{3 b^2}+\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b^2}+\frac{2 x \sec ^{\frac{3}{2}}(a+b x)}{3 b}","-\frac{4 \sin (a+b x) \sqrt{\sec (a+b x)}}{3 b^2}+\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b^2}+\frac{2 x \sec ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(4*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(3*b^2) + (2*x*Sec[a + b*x]^(3/2))/(3*b) - (4*Sqrt[Sec[a + b*x]]*Sin[a + b*x])/(3*b^2)","A",4,4,18,0.2222,1,"{4212, 3768, 3771, 2639}"
339,1,53,0,0.0358781,"\int x \sec ^{\frac{3}{2}}(a+b x) \sin (a+b x) \, dx","Int[x*Sec[a + b*x]^(3/2)*Sin[a + b*x],x]","\frac{2 x \sqrt{\sec (a+b x)}}{b}-\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}","\frac{2 x \sqrt{\sec (a+b x)}}{b}-\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}",1,"(2*x*Sqrt[Sec[a + b*x]])/b - (4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b^2","A",3,3,18,0.1667,1,"{4212, 3771, 2641}"
340,1,53,0,0.0366521,"\int x \sqrt{\sec (a+b x)} \sin (a+b x) \, dx","Int[x*Sqrt[Sec[a + b*x]]*Sin[a + b*x],x]","\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}-\frac{2 x}{b \sqrt{\sec (a+b x)}}","\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b^2}-\frac{2 x}{b \sqrt{\sec (a+b x)}}",1,"(-2*x)/(b*Sqrt[Sec[a + b*x]]) + (4*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/b^2","A",3,3,18,0.1667,1,"{4212, 3771, 2639}"
341,1,80,0,0.0456498,"\int \frac{x \sin (a+b x)}{\sqrt{\sec (a+b x)}} \, dx","Int[(x*Sin[a + b*x])/Sqrt[Sec[a + b*x]],x]","\frac{4 \sin (a+b x)}{9 b^2 \sqrt{\sec (a+b x)}}+\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{9 b^2}-\frac{2 x}{3 b \sec ^{\frac{3}{2}}(a+b x)}","\frac{4 \sin (a+b x)}{9 b^2 \sqrt{\sec (a+b x)}}+\frac{4 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{9 b^2}-\frac{2 x}{3 b \sec ^{\frac{3}{2}}(a+b x)}",1,"(-2*x)/(3*b*Sec[a + b*x]^(3/2)) + (4*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(9*b^2) + (4*Sin[a + b*x])/(9*b^2*Sqrt[Sec[a + b*x]])","A",4,4,18,0.2222,1,"{4212, 3769, 3771, 2641}"
342,1,80,0,0.0465426,"\int \frac{x \sin (a+b x)}{\sec ^{\frac{3}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Sec[a + b*x]^(3/2),x]","\frac{4 \sin (a+b x)}{25 b^2 \sec ^{\frac{3}{2}}(a+b x)}+\frac{12 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{25 b^2}-\frac{2 x}{5 b \sec ^{\frac{5}{2}}(a+b x)}","\frac{4 \sin (a+b x)}{25 b^2 \sec ^{\frac{3}{2}}(a+b x)}+\frac{12 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{25 b^2}-\frac{2 x}{5 b \sec ^{\frac{5}{2}}(a+b x)}",1,"(-2*x)/(5*b*Sec[a + b*x]^(5/2)) + (12*Sqrt[Cos[a + b*x]]*EllipticE[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(25*b^2) + (4*Sin[a + b*x])/(25*b^2*Sec[a + b*x]^(3/2))","A",4,4,18,0.2222,1,"{4212, 3769, 3771, 2639}"
343,1,103,0,0.0600873,"\int \frac{x \sin (a+b x)}{\sec ^{\frac{5}{2}}(a+b x)} \, dx","Int[(x*Sin[a + b*x])/Sec[a + b*x]^(5/2),x]","\frac{4 \sin (a+b x)}{49 b^2 \sec ^{\frac{5}{2}}(a+b x)}+\frac{20 \sin (a+b x)}{147 b^2 \sqrt{\sec (a+b x)}}+\frac{20 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{147 b^2}-\frac{2 x}{7 b \sec ^{\frac{7}{2}}(a+b x)}","\frac{4 \sin (a+b x)}{49 b^2 \sec ^{\frac{5}{2}}(a+b x)}+\frac{20 \sin (a+b x)}{147 b^2 \sqrt{\sec (a+b x)}}+\frac{20 \sqrt{\cos (a+b x)} \sqrt{\sec (a+b x)} F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{147 b^2}-\frac{2 x}{7 b \sec ^{\frac{7}{2}}(a+b x)}",1,"(-2*x)/(7*b*Sec[a + b*x]^(7/2)) + (20*Sqrt[Cos[a + b*x]]*EllipticF[(a + b*x)/2, 2]*Sqrt[Sec[a + b*x]])/(147*b^2) + (4*Sin[a + b*x])/(49*b^2*Sec[a + b*x]^(5/2)) + (20*Sin[a + b*x])/(147*b^2*Sqrt[Sec[a + b*x]])","A",5,4,18,0.2222,1,"{4212, 3769, 3771, 2641}"
344,1,88,0,0.0442303,"\int x \cos (a+b x) \sin ^{\frac{5}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Sin[a + b*x]^(5/2),x]","-\frac{20 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2}+\frac{4 \sin ^{\frac{5}{2}}(a+b x) \cos (a+b x)}{49 b^2}+\frac{20 \sqrt{\sin (a+b x)} \cos (a+b x)}{147 b^2}+\frac{2 x \sin ^{\frac{7}{2}}(a+b x)}{7 b}","-\frac{20 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2}+\frac{4 \sin ^{\frac{5}{2}}(a+b x) \cos (a+b x)}{49 b^2}+\frac{20 \sqrt{\sin (a+b x)} \cos (a+b x)}{147 b^2}+\frac{2 x \sin ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(-20*EllipticF[(a - Pi/2 + b*x)/2, 2])/(147*b^2) + (20*Cos[a + b*x]*Sqrt[Sin[a + b*x]])/(147*b^2) + (4*Cos[a + b*x]*Sin[a + b*x]^(5/2))/(49*b^2) + (2*x*Sin[a + b*x]^(7/2))/(7*b)","A",4,3,18,0.1667,1,"{3443, 2635, 2641}"
345,1,65,0,0.0323581,"\int x \cos (a+b x) \sin ^{\frac{3}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Sin[a + b*x]^(3/2),x]","-\frac{12 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2}+\frac{4 \sin ^{\frac{3}{2}}(a+b x) \cos (a+b x)}{25 b^2}+\frac{2 x \sin ^{\frac{5}{2}}(a+b x)}{5 b}","-\frac{12 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2}+\frac{4 \sin ^{\frac{3}{2}}(a+b x) \cos (a+b x)}{25 b^2}+\frac{2 x \sin ^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-12*EllipticE[(a - Pi/2 + b*x)/2, 2])/(25*b^2) + (4*Cos[a + b*x]*Sin[a + b*x]^(3/2))/(25*b^2) + (2*x*Sin[a + b*x]^(5/2))/(5*b)","A",3,3,18,0.1667,1,"{3443, 2635, 2639}"
346,1,65,0,0.0315743,"\int x \cos (a+b x) \sqrt{\sin (a+b x)} \, dx","Int[x*Cos[a + b*x]*Sqrt[Sin[a + b*x]],x]","-\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2}+\frac{4 \sqrt{\sin (a+b x)} \cos (a+b x)}{9 b^2}+\frac{2 x \sin ^{\frac{3}{2}}(a+b x)}{3 b}","-\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2}+\frac{4 \sqrt{\sin (a+b x)} \cos (a+b x)}{9 b^2}+\frac{2 x \sin ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(-4*EllipticF[(a - Pi/2 + b*x)/2, 2])/(9*b^2) + (4*Cos[a + b*x]*Sqrt[Sin[a + b*x]])/(9*b^2) + (2*x*Sin[a + b*x]^(3/2))/(3*b)","A",3,3,18,0.1667,1,"{3443, 2635, 2641}"
347,1,38,0,0.0222333,"\int \frac{x \cos (a+b x)}{\sqrt{\sin (a+b x)}} \, dx","Int[(x*Cos[a + b*x])/Sqrt[Sin[a + b*x]],x]","\frac{2 x \sqrt{\sin (a+b x)}}{b}-\frac{4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}","\frac{2 x \sqrt{\sin (a+b x)}}{b}-\frac{4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}",1,"(-4*EllipticE[(a - Pi/2 + b*x)/2, 2])/b^2 + (2*x*Sqrt[Sin[a + b*x]])/b","A",2,2,18,0.1111,1,"{3443, 2639}"
348,1,38,0,0.0229804,"\int \frac{x \cos (a+b x)}{\sin ^{\frac{3}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Sin[a + b*x]^(3/2),x]","\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}-\frac{2 x}{b \sqrt{\sin (a+b x)}}","\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}-\frac{2 x}{b \sqrt{\sin (a+b x)}}",1,"(4*EllipticF[(a - Pi/2 + b*x)/2, 2])/b^2 - (2*x)/(b*Sqrt[Sin[a + b*x]])","A",2,2,18,0.1111,1,"{3443, 2641}"
349,1,65,0,0.0319102,"\int \frac{x \cos (a+b x)}{\sin ^{\frac{5}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Sin[a + b*x]^(5/2),x]","-\frac{4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2}-\frac{4 \cos (a+b x)}{3 b^2 \sqrt{\sin (a+b x)}}-\frac{2 x}{3 b \sin ^{\frac{3}{2}}(a+b x)}","-\frac{4 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2}-\frac{4 \cos (a+b x)}{3 b^2 \sqrt{\sin (a+b x)}}-\frac{2 x}{3 b \sin ^{\frac{3}{2}}(a+b x)}",1,"(-4*EllipticE[(a - Pi/2 + b*x)/2, 2])/(3*b^2) - (2*x)/(3*b*Sin[a + b*x]^(3/2)) - (4*Cos[a + b*x])/(3*b^2*Sqrt[Sin[a + b*x]])","A",3,3,18,0.1667,1,"{3443, 2636, 2639}"
350,1,65,0,0.0339171,"\int \frac{x \cos (a+b x)}{\sin ^{\frac{7}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Sin[a + b*x]^(7/2),x]","\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2}-\frac{4 \cos (a+b x)}{15 b^2 \sin ^{\frac{3}{2}}(a+b x)}-\frac{2 x}{5 b \sin ^{\frac{5}{2}}(a+b x)}","\frac{4 F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2}-\frac{4 \cos (a+b x)}{15 b^2 \sin ^{\frac{3}{2}}(a+b x)}-\frac{2 x}{5 b \sin ^{\frac{5}{2}}(a+b x)}",1,"(4*EllipticF[(a - Pi/2 + b*x)/2, 2])/(15*b^2) - (2*x)/(5*b*Sin[a + b*x]^(5/2)) - (4*Cos[a + b*x])/(15*b^2*Sin[a + b*x]^(3/2))","A",3,3,18,0.1667,1,"{3443, 2636, 2641}"
351,1,88,0,0.0443534,"\int \frac{x \cos (a+b x)}{\sin ^{\frac{9}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Sin[a + b*x]^(9/2),x]","-\frac{12 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2}-\frac{4 \cos (a+b x)}{35 b^2 \sin ^{\frac{5}{2}}(a+b x)}-\frac{12 \cos (a+b x)}{35 b^2 \sqrt{\sin (a+b x)}}-\frac{2 x}{7 b \sin ^{\frac{7}{2}}(a+b x)}","-\frac{12 E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2}-\frac{4 \cos (a+b x)}{35 b^2 \sin ^{\frac{5}{2}}(a+b x)}-\frac{12 \cos (a+b x)}{35 b^2 \sqrt{\sin (a+b x)}}-\frac{2 x}{7 b \sin ^{\frac{7}{2}}(a+b x)}",1,"(-12*EllipticE[(a - Pi/2 + b*x)/2, 2])/(35*b^2) - (2*x)/(7*b*Sin[a + b*x]^(7/2)) - (4*Cos[a + b*x])/(35*b^2*Sin[a + b*x]^(5/2)) - (12*Cos[a + b*x])/(35*b^2*Sqrt[Sin[a + b*x]])","A",4,3,18,0.1667,1,"{3443, 2636, 2639}"
352,1,108,0,0.0576411,"\int x \cos (a+b x) \csc ^{\frac{9}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Csc[a + b*x]^(9/2),x]","-\frac{4 \cos (a+b x) \csc ^{\frac{5}{2}}(a+b x)}{35 b^2}-\frac{12 \cos (a+b x) \sqrt{\csc (a+b x)}}{35 b^2}-\frac{12 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2}-\frac{2 x \csc ^{\frac{7}{2}}(a+b x)}{7 b}","-\frac{4 \cos (a+b x) \csc ^{\frac{5}{2}}(a+b x)}{35 b^2}-\frac{12 \cos (a+b x) \sqrt{\csc (a+b x)}}{35 b^2}-\frac{12 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{35 b^2}-\frac{2 x \csc ^{\frac{7}{2}}(a+b x)}{7 b}",1,"(-12*Cos[a + b*x]*Sqrt[Csc[a + b*x]])/(35*b^2) - (4*Cos[a + b*x]*Csc[a + b*x]^(5/2))/(35*b^2) - (2*x*Csc[a + b*x]^(7/2))/(7*b) - (12*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(35*b^2)","A",5,4,18,0.2222,1,"{4213, 3768, 3771, 2639}"
353,1,85,0,0.0443634,"\int x \cos (a+b x) \csc ^{\frac{7}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Csc[a + b*x]^(7/2),x]","-\frac{4 \cos (a+b x) \csc ^{\frac{3}{2}}(a+b x)}{15 b^2}+\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2}-\frac{2 x \csc ^{\frac{5}{2}}(a+b x)}{5 b}","-\frac{4 \cos (a+b x) \csc ^{\frac{3}{2}}(a+b x)}{15 b^2}+\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{15 b^2}-\frac{2 x \csc ^{\frac{5}{2}}(a+b x)}{5 b}",1,"(-4*Cos[a + b*x]*Csc[a + b*x]^(3/2))/(15*b^2) - (2*x*Csc[a + b*x]^(5/2))/(5*b) + (4*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(15*b^2)","A",4,4,18,0.2222,1,"{4213, 3768, 3771, 2641}"
354,1,85,0,0.0401547,"\int x \cos (a+b x) \csc ^{\frac{5}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Csc[a + b*x]^(5/2),x]","-\frac{4 \cos (a+b x) \sqrt{\csc (a+b x)}}{3 b^2}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2}-\frac{2 x \csc ^{\frac{3}{2}}(a+b x)}{3 b}","-\frac{4 \cos (a+b x) \sqrt{\csc (a+b x)}}{3 b^2}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{3 b^2}-\frac{2 x \csc ^{\frac{3}{2}}(a+b x)}{3 b}",1,"(-4*Cos[a + b*x]*Sqrt[Csc[a + b*x]])/(3*b^2) - (2*x*Csc[a + b*x]^(3/2))/(3*b) - (4*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(3*b^2)","A",4,4,18,0.2222,1,"{4213, 3768, 3771, 2639}"
355,1,58,0,0.0320025,"\int x \cos (a+b x) \csc ^{\frac{3}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]*Csc[a + b*x]^(3/2),x]","\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}-\frac{2 x \sqrt{\csc (a+b x)}}{b}","\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}-\frac{2 x \sqrt{\csc (a+b x)}}{b}",1,"(-2*x*Sqrt[Csc[a + b*x]])/b + (4*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b^2","A",3,3,18,0.1667,1,"{4213, 3771, 2641}"
356,1,58,0,0.0319711,"\int x \cos (a+b x) \sqrt{\csc (a+b x)} \, dx","Int[x*Cos[a + b*x]*Sqrt[Csc[a + b*x]],x]","\frac{2 x}{b \sqrt{\csc (a+b x)}}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}","\frac{2 x}{b \sqrt{\csc (a+b x)}}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{b^2}",1,"(2*x)/(b*Sqrt[Csc[a + b*x]]) - (4*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/b^2","A",3,3,18,0.1667,1,"{4213, 3771, 2639}"
357,1,85,0,0.0442773,"\int \frac{x \cos (a+b x)}{\sqrt{\csc (a+b x)}} \, dx","Int[(x*Cos[a + b*x])/Sqrt[Csc[a + b*x]],x]","\frac{4 \cos (a+b x)}{9 b^2 \sqrt{\csc (a+b x)}}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2}+\frac{2 x}{3 b \csc ^{\frac{3}{2}}(a+b x)}","\frac{4 \cos (a+b x)}{9 b^2 \sqrt{\csc (a+b x)}}-\frac{4 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{9 b^2}+\frac{2 x}{3 b \csc ^{\frac{3}{2}}(a+b x)}",1,"(2*x)/(3*b*Csc[a + b*x]^(3/2)) + (4*Cos[a + b*x])/(9*b^2*Sqrt[Csc[a + b*x]]) - (4*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(9*b^2)","A",4,4,18,0.2222,1,"{4213, 3769, 3771, 2641}"
358,1,85,0,0.0437454,"\int \frac{x \cos (a+b x)}{\csc ^{\frac{3}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Csc[a + b*x]^(3/2),x]","\frac{4 \cos (a+b x)}{25 b^2 \csc ^{\frac{3}{2}}(a+b x)}-\frac{12 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2}+\frac{2 x}{5 b \csc ^{\frac{5}{2}}(a+b x)}","\frac{4 \cos (a+b x)}{25 b^2 \csc ^{\frac{3}{2}}(a+b x)}-\frac{12 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} E\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{25 b^2}+\frac{2 x}{5 b \csc ^{\frac{5}{2}}(a+b x)}",1,"(2*x)/(5*b*Csc[a + b*x]^(5/2)) + (4*Cos[a + b*x])/(25*b^2*Csc[a + b*x]^(3/2)) - (12*Sqrt[Csc[a + b*x]]*EllipticE[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(25*b^2)","A",4,4,18,0.2222,1,"{4213, 3769, 3771, 2639}"
359,1,108,0,0.0596252,"\int \frac{x \cos (a+b x)}{\csc ^{\frac{5}{2}}(a+b x)} \, dx","Int[(x*Cos[a + b*x])/Csc[a + b*x]^(5/2),x]","\frac{4 \cos (a+b x)}{49 b^2 \csc ^{\frac{5}{2}}(a+b x)}+\frac{20 \cos (a+b x)}{147 b^2 \sqrt{\csc (a+b x)}}-\frac{20 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2}+\frac{2 x}{7 b \csc ^{\frac{7}{2}}(a+b x)}","\frac{4 \cos (a+b x)}{49 b^2 \csc ^{\frac{5}{2}}(a+b x)}+\frac{20 \cos (a+b x)}{147 b^2 \sqrt{\csc (a+b x)}}-\frac{20 \sqrt{\sin (a+b x)} \sqrt{\csc (a+b x)} F\left(\left.\frac{1}{2} \left(a+b x-\frac{\pi }{2}\right)\right|2\right)}{147 b^2}+\frac{2 x}{7 b \csc ^{\frac{7}{2}}(a+b x)}",1,"(2*x)/(7*b*Csc[a + b*x]^(7/2)) + (4*Cos[a + b*x])/(49*b^2*Csc[a + b*x]^(5/2)) + (20*Cos[a + b*x])/(147*b^2*Sqrt[Csc[a + b*x]]) - (20*Sqrt[Csc[a + b*x]]*EllipticF[(a - Pi/2 + b*x)/2, 2]*Sqrt[Sin[a + b*x]])/(147*b^2)","A",5,4,18,0.2222,1,"{4213, 3769, 3771, 2641}"
360,1,31,0,0.0412594,"\int x \csc (x) \sin (3 x) \, dx","Int[x*Csc[x]*Sin[3*x],x]","\frac{x^2}{2}-\frac{\sin ^2(x)}{4}+\frac{3 \cos ^2(x)}{4}+2 x \sin (x) \cos (x)","\frac{x^2}{2}-\frac{\sin ^2(x)}{4}+\frac{3 \cos ^2(x)}{4}+2 x \sin (x) \cos (x)",1,"x^2/2 + (3*Cos[x]^2)/4 + 2*x*Cos[x]*Sin[x] - Sin[x]^2/4","A",6,3,8,0.3750,1,"{4431, 3310, 30}"
361,1,131,0,0.1880994,"\int (c+d x)^4 \csc (x) \sin (3 x) \, dx","Int[(c + d*x)^4*Csc[x]*Sin[3*x],x]","\frac{3}{2} d^3 \sin ^2(x) (c+d x)-\frac{9}{2} d^3 \cos ^2(x) (c+d x)-6 d^2 \sin (x) \cos (x) (c+d x)^2+\frac{(c+d x)^5}{5 d}-d (c+d x)^3-d \sin ^2(x) (c+d x)^3+3 d \cos ^2(x) (c+d x)^3+2 \sin (x) \cos (x) (c+d x)^4+\frac{3 d^4 x}{2}+3 d^4 \sin (x) \cos (x)","\frac{3}{2} d^3 \sin ^2(x) (c+d x)-\frac{9}{2} d^3 \cos ^2(x) (c+d x)-6 d^2 \sin (x) \cos (x) (c+d x)^2+\frac{(c+d x)^5}{5 d}-d (c+d x)^3-d \sin ^2(x) (c+d x)^3+3 d \cos ^2(x) (c+d x)^3+2 \sin (x) \cos (x) (c+d x)^4+\frac{3 d^4 x}{2}+3 d^4 \sin (x) \cos (x)",1,"(3*d^4*x)/2 - d*(c + d*x)^3 + (c + d*x)^5/(5*d) - (9*d^3*(c + d*x)*Cos[x]^2)/2 + 3*d*(c + d*x)^3*Cos[x]^2 + 3*d^4*Cos[x]*Sin[x] - 6*d^2*(c + d*x)^2*Cos[x]*Sin[x] + 2*(c + d*x)^4*Cos[x]*Sin[x] + (3*d^3*(c + d*x)*Sin[x]^2)/2 - d*(c + d*x)^3*Sin[x]^2","A",14,5,14,0.3571,1,"{4431, 3311, 32, 2635, 8}"
362,1,115,0,0.1413522,"\int (c+d x)^3 \csc (x) \sin (3 x) \, dx","Int[(c + d*x)^3*Csc[x]*Sin[3*x],x]","-\frac{3}{2} c d^2 x-3 d^2 \sin (x) \cos (x) (c+d x)+\frac{(c+d x)^4}{4 d}-\frac{3}{4} d \sin ^2(x) (c+d x)^2+\frac{9}{4} d \cos ^2(x) (c+d x)^2+2 \sin (x) \cos (x) (c+d x)^3-\frac{3 d^3 x^2}{4}+\frac{3}{8} d^3 \sin ^2(x)-\frac{9}{8} d^3 \cos ^2(x)","-\frac{3}{2} c d^2 x-3 d^2 \sin (x) \cos (x) (c+d x)+\frac{(c+d x)^4}{4 d}-\frac{3}{4} d \sin ^2(x) (c+d x)^2+\frac{9}{4} d \cos ^2(x) (c+d x)^2+2 \sin (x) \cos (x) (c+d x)^3-\frac{3 d^3 x^2}{4}+\frac{3}{8} d^3 \sin ^2(x)-\frac{9}{8} d^3 \cos ^2(x)",1,"(-3*c*d^2*x)/2 - (3*d^3*x^2)/4 + (c + d*x)^4/(4*d) - (9*d^3*Cos[x]^2)/8 + (9*d*(c + d*x)^2*Cos[x]^2)/4 - 3*d^2*(c + d*x)*Cos[x]*Sin[x] + 2*(c + d*x)^3*Cos[x]*Sin[x] + (3*d^3*Sin[x]^2)/8 - (3*d*(c + d*x)^2*Sin[x]^2)/4","A",10,4,14,0.2857,1,"{4431, 3311, 32, 3310}"
363,1,73,0,0.102692,"\int (c+d x)^2 \csc (x) \sin (3 x) \, dx","Int[(c + d*x)^2*Csc[x]*Sin[3*x],x]","\frac{(c+d x)^3}{3 d}-\frac{1}{2} d \sin ^2(x) (c+d x)+\frac{3}{2} d \cos ^2(x) (c+d x)+2 \sin (x) \cos (x) (c+d x)^2-\frac{d^2 x}{2}-d^2 \sin (x) \cos (x)","\frac{(c+d x)^3}{3 d}-\frac{1}{2} d \sin ^2(x) (c+d x)+\frac{3}{2} d \cos ^2(x) (c+d x)+2 \sin (x) \cos (x) (c+d x)^2-\frac{d^2 x}{2}-d^2 \sin (x) \cos (x)",1,"-(d^2*x)/2 + (c + d*x)^3/(3*d) + (3*d*(c + d*x)*Cos[x]^2)/2 - d^2*Cos[x]*Sin[x] + 2*(c + d*x)^2*Cos[x]*Sin[x] - (d*(c + d*x)*Sin[x]^2)/2","A",10,5,14,0.3571,1,"{4431, 3311, 32, 2635, 8}"
364,1,41,0,0.0563706,"\int (c+d x) \csc (x) \sin (3 x) \, dx","Int[(c + d*x)*Csc[x]*Sin[3*x],x]","2 \sin (x) \cos (x) (c+d x)+c x+\frac{d x^2}{2}-\frac{1}{4} d \sin ^2(x)+\frac{3}{4} d \cos ^2(x)","2 \sin (x) \cos (x) (c+d x)+c x+\frac{d x^2}{2}-\frac{1}{4} d \sin ^2(x)+\frac{3}{4} d \cos ^2(x)",1,"c*x + (d*x^2)/2 + (3*d*Cos[x]^2)/4 + 2*(c + d*x)*Cos[x]*Sin[x] - (d*Sin[x]^2)/4","A",6,2,12,0.1667,1,"{4431, 3310}"
365,1,57,0,0.2518518,"\int \frac{\csc (x) \sin (3 x)}{c+d x} \, dx","Int[(Csc[x]*Sin[3*x])/(c + d*x),x]","\frac{2 \cos \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d}+\frac{2 \sin \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d}+\frac{\log (c+d x)}{d}","\frac{2 \cos \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d}+\frac{2 \sin \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d}+\frac{\log (c+d x)}{d}",1,"(2*Cos[(2*c)/d]*CosIntegral[(2*c)/d + 2*x])/d + Log[c + d*x]/d + (2*Sin[(2*c)/d]*SinIntegral[(2*c)/d + 2*x])/d","A",12,5,14,0.3571,1,"{4431, 3312, 3303, 3299, 3302}"
366,1,78,0,0.2379263,"\int \frac{\csc (x) \sin (3 x)}{(c+d x)^2} \, dx","Int[(Csc[x]*Sin[3*x])/(c + d*x)^2,x]","\frac{4 \sin \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d^2}-\frac{4 \cos \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d^2}+\frac{\sin ^2(x)}{d (c+d x)}-\frac{3 \cos ^2(x)}{d (c+d x)}","\frac{4 \sin \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d^2}-\frac{4 \cos \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d^2}+\frac{\sin ^2(x)}{d (c+d x)}-\frac{3 \cos ^2(x)}{d (c+d x)}",1,"(-3*Cos[x]^2)/(d*(c + d*x)) + (4*CosIntegral[(2*c)/d + 2*x]*Sin[(2*c)/d])/d^2 + Sin[x]^2/(d*(c + d*x)) - (4*Cos[(2*c)/d]*SinIntegral[(2*c)/d + 2*x])/d^2","A",12,6,14,0.4286,1,"{4431, 3313, 12, 3303, 3299, 3302}"
367,1,99,0,0.3285647,"\int \frac{\csc (x) \sin (3 x)}{(c+d x)^3} \, dx","Int[(Csc[x]*Sin[3*x])/(c + d*x)^3,x]","-\frac{4 \cos \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d^3}-\frac{4 \sin \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d^3}+\frac{4 \sin (x) \cos (x)}{d^2 (c+d x)}+\frac{\sin ^2(x)}{2 d (c+d x)^2}-\frac{3 \cos ^2(x)}{2 d (c+d x)^2}","-\frac{4 \cos \left(\frac{2 c}{d}\right) \text{CosIntegral}\left(\frac{2 c}{d}+2 x\right)}{d^3}-\frac{4 \sin \left(\frac{2 c}{d}\right) \text{Si}\left(\frac{2 c}{d}+2 x\right)}{d^3}+\frac{4 \sin (x) \cos (x)}{d^2 (c+d x)}+\frac{\sin ^2(x)}{2 d (c+d x)^2}-\frac{3 \cos ^2(x)}{2 d (c+d x)^2}",1,"(-3*Cos[x]^2)/(2*d*(c + d*x)^2) - (4*Cos[(2*c)/d]*CosIntegral[(2*c)/d + 2*x])/d^3 + (4*Cos[x]*Sin[x])/(d^2*(c + d*x)) + Sin[x]^2/(2*d*(c + d*x)^2) - (4*Sin[(2*c)/d]*SinIntegral[(2*c)/d + 2*x])/d^3","A",16,7,14,0.5000,1,"{4431, 3314, 31, 3312, 3303, 3299, 3302}"
368,1,198,0,0.2518293,"\int (c+d x)^4 \csc (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^4*Csc[a + b*x]*Sin[3*a + 3*b*x],x]","\frac{3 d^3 (c+d x) \sin ^2(a+b x)}{2 b^4}-\frac{9 d^3 (c+d x) \cos ^2(a+b x)}{2 b^4}-\frac{6 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b^3}-\frac{d (c+d x)^3 \sin ^2(a+b x)}{b^2}+\frac{3 d (c+d x)^3 \cos ^2(a+b x)}{b^2}+\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{b^5}+\frac{2 (c+d x)^4 \sin (a+b x) \cos (a+b x)}{b}-\frac{d (c+d x)^3}{b^2}+\frac{3 d^4 x}{2 b^4}+\frac{(c+d x)^5}{5 d}","\frac{3 d^3 (c+d x) \sin ^2(a+b x)}{2 b^4}-\frac{9 d^3 (c+d x) \cos ^2(a+b x)}{2 b^4}-\frac{6 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b^3}-\frac{d (c+d x)^3 \sin ^2(a+b x)}{b^2}+\frac{3 d (c+d x)^3 \cos ^2(a+b x)}{b^2}+\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{b^5}+\frac{2 (c+d x)^4 \sin (a+b x) \cos (a+b x)}{b}-\frac{d (c+d x)^3}{b^2}+\frac{3 d^4 x}{2 b^4}+\frac{(c+d x)^5}{5 d}",1,"(3*d^4*x)/(2*b^4) - (d*(c + d*x)^3)/b^2 + (c + d*x)^5/(5*d) - (9*d^3*(c + d*x)*Cos[a + b*x]^2)/(2*b^4) + (3*d*(c + d*x)^3*Cos[a + b*x]^2)/b^2 + (3*d^4*Cos[a + b*x]*Sin[a + b*x])/b^5 - (6*d^2*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/b^3 + (2*(c + d*x)^4*Cos[a + b*x]*Sin[a + b*x])/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",14,5,23,0.2174,1,"{4431, 3311, 32, 2635, 8}"
369,1,171,0,0.1836623,"\int (c+d x)^3 \csc (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]*Sin[3*a + 3*b*x],x]","-\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \sin ^2(a+b x)}{4 b^2}+\frac{9 d (c+d x)^2 \cos ^2(a+b x)}{4 b^2}+\frac{3 d^3 \sin ^2(a+b x)}{8 b^4}-\frac{9 d^3 \cos ^2(a+b x)}{8 b^4}+\frac{2 (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b}-\frac{3 c d^2 x}{2 b^2}-\frac{3 d^3 x^2}{4 b^2}+\frac{(c+d x)^4}{4 d}","-\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \sin ^2(a+b x)}{4 b^2}+\frac{9 d (c+d x)^2 \cos ^2(a+b x)}{4 b^2}+\frac{3 d^3 \sin ^2(a+b x)}{8 b^4}-\frac{9 d^3 \cos ^2(a+b x)}{8 b^4}+\frac{2 (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b}-\frac{3 c d^2 x}{2 b^2}-\frac{3 d^3 x^2}{4 b^2}+\frac{(c+d x)^4}{4 d}",1,"(-3*c*d^2*x)/(2*b^2) - (3*d^3*x^2)/(4*b^2) + (c + d*x)^4/(4*d) - (9*d^3*Cos[a + b*x]^2)/(8*b^4) + (9*d*(c + d*x)^2*Cos[a + b*x]^2)/(4*b^2) - (3*d^2*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/b^3 + (2*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/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",10,4,23,0.1739,1,"{4431, 3311, 32, 3310}"
370,1,112,0,0.1359503,"\int (c+d x)^2 \csc (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]*Sin[3*a + 3*b*x],x]","-\frac{d (c+d x) \sin ^2(a+b x)}{2 b^2}+\frac{3 d (c+d x) \cos ^2(a+b x)}{2 b^2}-\frac{d^2 \sin (a+b x) \cos (a+b x)}{b^3}+\frac{2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b}-\frac{d^2 x}{2 b^2}+\frac{(c+d x)^3}{3 d}","-\frac{d (c+d x) \sin ^2(a+b x)}{2 b^2}+\frac{3 d (c+d x) \cos ^2(a+b x)}{2 b^2}-\frac{d^2 \sin (a+b x) \cos (a+b x)}{b^3}+\frac{2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b}-\frac{d^2 x}{2 b^2}+\frac{(c+d x)^3}{3 d}",1,"-(d^2*x)/(2*b^2) + (c + d*x)^3/(3*d) + (3*d*(c + d*x)*Cos[a + b*x]^2)/(2*b^2) - (d^2*Cos[a + b*x]*Sin[a + b*x])/b^3 + (2*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/b - (d*(c + d*x)*Sin[a + b*x]^2)/(2*b^2)","A",10,5,23,0.2174,1,"{4431, 3311, 32, 2635, 8}"
371,1,66,0,0.0682019,"\int (c+d x) \csc (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)*Csc[a + b*x]*Sin[3*a + 3*b*x],x]","-\frac{d \sin ^2(a+b x)}{4 b^2}+\frac{3 d \cos ^2(a+b x)}{4 b^2}+\frac{2 (c+d x) \sin (a+b x) \cos (a+b x)}{b}+c x+\frac{d x^2}{2}","-\frac{d \sin ^2(a+b x)}{4 b^2}+\frac{3 d \cos ^2(a+b x)}{4 b^2}+\frac{2 (c+d x) \sin (a+b x) \cos (a+b x)}{b}+c x+\frac{d x^2}{2}",1,"c*x + (d*x^2)/2 + (3*d*Cos[a + b*x]^2)/(4*b^2) + (2*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/b - (d*Sin[a + b*x]^2)/(4*b^2)","A",6,2,21,0.09524,1,"{4431, 3310}"
372,1,71,0,0.2810175,"\int \frac{\csc (a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","Int[(Csc[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x),x]","\frac{2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d}-\frac{2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d}+\frac{\log (c+d x)}{d}","\frac{2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d}-\frac{2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d}+\frac{\log (c+d x)}{d}",1,"(2*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d + Log[c + d*x]/d - (2*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d","A",12,5,23,0.2174,1,"{4431, 3312, 3303, 3299, 3302}"
373,1,102,0,0.2761826,"\int \frac{\csc (a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x)^2,x]","-\frac{4 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{4 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{3 \cos ^2(a+b x)}{d (c+d x)}","-\frac{4 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{4 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{3 \cos ^2(a+b x)}{d (c+d x)}",1,"(-3*Cos[a + b*x]^2)/(d*(c + d*x)) - (4*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)) - (4*b*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2","A",12,6,23,0.2609,1,"{4431, 3313, 12, 3303, 3299, 3302}"
374,1,136,0,0.3742168,"\int \frac{\csc (a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","Int[(Csc[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x)^3,x]","-\frac{4 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{4 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{4 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{3 \cos ^2(a+b x)}{2 d (c+d x)^2}","-\frac{4 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{4 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{4 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{3 \cos ^2(a+b x)}{2 d (c+d x)^2}",1,"(-3*Cos[a + b*x]^2)/(2*d*(c + d*x)^2) - (4*b^2*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^3 + (4*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) + (4*b^2*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^3","A",16,7,23,0.3043,1,"{4431, 3314, 31, 3312, 3303, 3299, 3302}"
375,1,205,0,0.3798931,"\int \frac{\csc (a+b x) \sin (3 a+3 b x)}{(c+d x)^4} \, dx","Int[(Csc[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x)^4,x]","\frac{8 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{8 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{2 b^2 \cos ^2(a+b x)}{d^3 (c+d x)}+\frac{4 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{\cos ^2(a+b x)}{d (c+d x)^3}-\frac{2 b^2}{3 d^3 (c+d x)}","\frac{8 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{8 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{2 b^2 \cos ^2(a+b x)}{d^3 (c+d x)}+\frac{4 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{\cos ^2(a+b x)}{d (c+d x)^3}-\frac{2 b^2}{3 d^3 (c+d x)}",1,"(-2*b^2)/(3*d^3*(c + d*x)) - Cos[a + b*x]^2/(d*(c + d*x)^3) + (2*b^2*Cos[a + b*x]^2)/(d^3*(c + d*x)) + (8*b^3*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/(3*d^4) + (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)) + (8*b^3*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(3*d^4)","A",16,8,23,0.3478,1,"{4431, 3314, 32, 3313, 12, 3303, 3299, 3302}"
376,1,255,0,0.3470595,"\int (c+d x)^3 \csc ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^3*Csc[a + b*x]^2*Sin[3*a + 3*b*x],x]","-\frac{18 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{18 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{18 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{18 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{24 d^2 (c+d x) \cos (a+b x)}{b^3}-\frac{12 d (c+d x)^2 \sin (a+b x)}{b^2}+\frac{24 d^3 \sin (a+b x)}{b^4}+\frac{4 (c+d x)^3 \cos (a+b x)}{b}-\frac{6 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","-\frac{18 d^2 (c+d x) \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{18 d^2 (c+d x) \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}+\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{9 i d (c+d x)^2 \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{18 i d^3 \text{PolyLog}\left(4,-e^{i (a+b x)}\right)}{b^4}+\frac{18 i d^3 \text{PolyLog}\left(4,e^{i (a+b x)}\right)}{b^4}-\frac{24 d^2 (c+d x) \cos (a+b x)}{b^3}-\frac{12 d (c+d x)^2 \sin (a+b x)}{b^2}+\frac{24 d^3 \sin (a+b x)}{b^4}+\frac{4 (c+d x)^3 \cos (a+b x)}{b}-\frac{6 (c+d x)^3 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-6*(c + d*x)^3*ArcTanh[E^(I*(a + b*x))])/b - (24*d^2*(c + d*x)*Cos[a + b*x])/b^3 + (4*(c + d*x)^3*Cos[a + b*x])/b + ((9*I)*d*(c + d*x)^2*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((9*I)*d*(c + d*x)^2*PolyLog[2, E^(I*(a + b*x))])/b^2 - (18*d^2*(c + d*x)*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (18*d^2*(c + d*x)*PolyLog[3, E^(I*(a + b*x))])/b^3 - ((18*I)*d^3*PolyLog[4, -E^(I*(a + b*x))])/b^4 + ((18*I)*d^3*PolyLog[4, E^(I*(a + b*x))])/b^4 + (24*d^3*Sin[a + b*x])/b^4 - (12*d*(c + d*x)^2*Sin[a + b*x])/b^2","A",20,9,25,0.3600,1,"{4431, 4408, 3296, 2637, 4183, 2531, 6609, 2282, 6589}"
377,1,172,0,0.2287927,"\int (c+d x)^2 \csc ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^2*Csc[a + b*x]^2*Sin[3*a + 3*b*x],x]","\frac{6 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{6 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{6 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{8 d (c+d x) \sin (a+b x)}{b^2}-\frac{8 d^2 \cos (a+b x)}{b^3}+\frac{4 (c+d x)^2 \cos (a+b x)}{b}-\frac{6 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{6 i d (c+d x) \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{6 i d (c+d x) \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{6 d^2 \text{PolyLog}\left(3,-e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 \text{PolyLog}\left(3,e^{i (a+b x)}\right)}{b^3}-\frac{8 d (c+d x) \sin (a+b x)}{b^2}-\frac{8 d^2 \cos (a+b x)}{b^3}+\frac{4 (c+d x)^2 \cos (a+b x)}{b}-\frac{6 (c+d x)^2 \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-6*(c + d*x)^2*ArcTanh[E^(I*(a + b*x))])/b - (8*d^2*Cos[a + b*x])/b^3 + (4*(c + d*x)^2*Cos[a + b*x])/b + ((6*I)*d*(c + d*x)*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((6*I)*d*(c + d*x)*PolyLog[2, E^(I*(a + b*x))])/b^2 - (6*d^2*PolyLog[3, -E^(I*(a + b*x))])/b^3 + (6*d^2*PolyLog[3, E^(I*(a + b*x))])/b^3 - (8*d*(c + d*x)*Sin[a + b*x])/b^2","A",16,8,25,0.3200,1,"{4431, 4408, 3296, 2638, 4183, 2531, 2282, 6589}"
378,1,95,0,0.1088553,"\int (c+d x) \csc ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)*Csc[a + b*x]^2*Sin[3*a + 3*b*x],x]","\frac{3 i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{4 d \sin (a+b x)}{b^2}+\frac{4 (c+d x) \cos (a+b x)}{b}-\frac{6 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{3 i d \text{PolyLog}\left(2,-e^{i (a+b x)}\right)}{b^2}-\frac{3 i d \text{PolyLog}\left(2,e^{i (a+b x)}\right)}{b^2}-\frac{4 d \sin (a+b x)}{b^2}+\frac{4 (c+d x) \cos (a+b x)}{b}-\frac{6 (c+d x) \tanh ^{-1}\left(e^{i (a+b x)}\right)}{b}",1,"(-6*(c + d*x)*ArcTanh[E^(I*(a + b*x))])/b + (4*(c + d*x)*Cos[a + b*x])/b + ((3*I)*d*PolyLog[2, -E^(I*(a + b*x))])/b^2 - ((3*I)*d*PolyLog[2, E^(I*(a + b*x))])/b^2 - (4*d*Sin[a + b*x])/b^2","A",12,7,23,0.3043,1,"{4431, 4408, 3296, 2637, 4183, 2279, 2391}"
379,0,0,0,0.2104003,"\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","Int[(Csc[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x),x]","\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","3 \text{Int}\left(\frac{\csc (a+b x)}{c+d x},x\right)-\frac{4 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}-\frac{4 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}",0,"(-4*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d - (4*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d + 3*Defer[Int][Csc[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
380,0,0,0,0.2830364,"\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","Int[(Csc[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x)^2,x]","\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","3 \text{Int}\left(\frac{\csc (a+b x)}{(c+d x)^2},x\right)-\frac{4 b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{4 b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{4 \sin (a+b x)}{d (c+d x)}",0,"(-4*b*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d^2 + (4*Sin[a + b*x])/(d*(c + d*x)) + (4*b*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^2 + 3*Defer[Int][Csc[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
381,0,0,0,0.3283235,"\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","Int[(Csc[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x)^3,x]","\int \frac{\csc ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","3 \text{Int}\left(\frac{\csc (a+b x)}{(c+d x)^3},x\right)+\frac{2 b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^3}+\frac{2 b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^3}+\frac{2 b \cos (a+b x)}{d^2 (c+d x)}+\frac{2 \sin (a+b x)}{d (c+d x)^2}",0,"(2*b*Cos[a + b*x])/(d^2*(c + d*x)) + (2*b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d^3 + (2*Sin[a + b*x])/(d*(c + d*x)^2) + (2*b^2*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^3 + 3*Defer[Int][Csc[a + b*x]/(c + d*x)^3, x]","A",0,0,0,0,-1,"{}"
382,1,299,0,0.5031253,"\int (c+d x)^4 \sec (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^4*Sec[a + b*x]*Sin[3*a + 3*b*x],x]","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{6 d^2 (c+d x)^2 \sin ^2(a+b x)}{b^3}-\frac{6 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{b^4}+\frac{4 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}+\frac{3 d^4 \sin ^2(a+b x)}{b^5}+\frac{(c+d x)^4 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^4 \sin ^2(a+b x)}{b}+\frac{6 c d^3 x}{b^3}+\frac{3 d^4 x^2}{b^3}-\frac{(c+d x)^4}{b}-\frac{i (c+d x)^5}{5 d}","\frac{3 d^2 (c+d x)^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 i d^3 (c+d x) \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{b^4}-\frac{2 i d (c+d x)^3 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}-\frac{3 d^4 \text{PolyLog}\left(5,-e^{2 i (a+b x)}\right)}{2 b^5}-\frac{6 d^2 (c+d x)^2 \sin ^2(a+b x)}{b^3}-\frac{6 d^3 (c+d x) \sin (a+b x) \cos (a+b x)}{b^4}+\frac{4 d (c+d x)^3 \sin (a+b x) \cos (a+b x)}{b^2}+\frac{3 d^4 \sin ^2(a+b x)}{b^5}+\frac{(c+d x)^4 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^4 \sin ^2(a+b x)}{b}+\frac{6 c d^3 x}{b^3}+\frac{3 d^4 x^2}{b^3}-\frac{(c+d x)^4}{b}-\frac{i (c+d x)^5}{5 d}",1,"(6*c*d^3*x)/b^3 + (3*d^4*x^2)/b^3 - (c + d*x)^4/b - ((I/5)*(c + d*x)^5)/d + ((c + d*x)^4*Log[1 + E^((2*I)*(a + b*x))])/b - ((2*I)*d*(c + d*x)^3*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)^2*PolyLog[3, -E^((2*I)*(a + b*x))])/b^3 + ((3*I)*d^3*(c + d*x)*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 - (3*d^4*PolyLog[5, -E^((2*I)*(a + b*x))])/(2*b^5) - (6*d^3*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/b^4 + (4*d*(c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/b^2 + (3*d^4*Sin[a + b*x]^2)/b^5 - (6*d^2*(c + d*x)^2*Sin[a + b*x]^2)/b^3 + (2*(c + d*x)^4*Sin[a + b*x]^2)/b","A",20,12,23,0.5217,1,"{4431, 4404, 3311, 32, 3310, 4407, 3719, 2190, 2531, 6609, 2282, 6589}"
383,1,242,0,0.4455136,"\int (c+d x)^3 \sec (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]*Sin[3*a + 3*b*x],x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b^2}-\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{2 b^4}+\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^3 \sin ^2(a+b x)}{b}+\frac{3 d^3 x}{2 b^3}-\frac{(c+d x)^3}{b}-\frac{i (c+d x)^4}{4 d}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(4,-e^{2 i (a+b x)}\right)}{4 b^4}-\frac{3 d^2 (c+d x) \sin ^2(a+b x)}{b^3}+\frac{3 d (c+d x)^2 \sin (a+b x) \cos (a+b x)}{b^2}-\frac{3 d^3 \sin (a+b x) \cos (a+b x)}{2 b^4}+\frac{(c+d x)^3 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^3 \sin ^2(a+b x)}{b}+\frac{3 d^3 x}{2 b^3}-\frac{(c+d x)^3}{b}-\frac{i (c+d x)^4}{4 d}",1,"(3*d^3*x)/(2*b^3) - (c + d*x)^3/b - ((I/4)*(c + d*x)^4)/d + ((c + d*x)^3*Log[1 + E^((2*I)*(a + b*x))])/b - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (((3*I)/4)*d^3*PolyLog[4, -E^((2*I)*(a + b*x))])/b^4 - (3*d^3*Cos[a + b*x]*Sin[a + b*x])/(2*b^4) + (3*d*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/b^2 - (3*d^2*(c + d*x)*Sin[a + b*x]^2)/b^3 + (2*(c + d*x)^3*Sin[a + b*x]^2)/b","A",19,13,23,0.5652,1,"{4431, 4404, 3311, 32, 2635, 8, 4407, 3719, 2190, 2531, 6609, 2282, 6589}"
384,1,173,0,0.3282733,"\int (c+d x)^2 \sec (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]*Sin[3*a + 3*b*x],x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{2 d (c+d x) \sin (a+b x) \cos (a+b x)}{b^2}-\frac{d^2 \sin ^2(a+b x)}{b^3}+\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^2 \sin ^2(a+b x)}{b}-\frac{2 c d x}{b}-\frac{d^2 x^2}{b}-\frac{i (c+d x)^3}{3 d}","-\frac{i d (c+d x) \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{b^2}+\frac{d^2 \text{PolyLog}\left(3,-e^{2 i (a+b x)}\right)}{2 b^3}+\frac{2 d (c+d x) \sin (a+b x) \cos (a+b x)}{b^2}-\frac{d^2 \sin ^2(a+b x)}{b^3}+\frac{(c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x)^2 \sin ^2(a+b x)}{b}-\frac{2 c d x}{b}-\frac{d^2 x^2}{b}-\frac{i (c+d x)^3}{3 d}",1,"(-2*c*d*x)/b - (d^2*x^2)/b - ((I/3)*(c + d*x)^3)/d + ((c + d*x)^2*Log[1 + E^((2*I)*(a + b*x))])/b - (I*d*(c + d*x)*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (d^2*PolyLog[3, -E^((2*I)*(a + b*x))])/(2*b^3) + (2*d*(c + d*x)*Cos[a + b*x]*Sin[a + b*x])/b^2 - (d^2*Sin[a + b*x]^2)/b^3 + (2*(c + d*x)^2*Sin[a + b*x]^2)/b","A",14,9,23,0.3913,1,"{4431, 4404, 3310, 4407, 3719, 2190, 2531, 2282, 6589}"
385,1,107,0,0.1801707,"\int (c+d x) \sec (a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)*Sec[a + b*x]*Sin[3*a + 3*b*x],x]","-\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{d \sin (a+b x) \cos (a+b x)}{b^2}+\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x) \sin ^2(a+b x)}{b}-\frac{d x}{b}-\frac{i (c+d x)^2}{2 d}","-\frac{i d \text{PolyLog}\left(2,-e^{2 i (a+b x)}\right)}{2 b^2}+\frac{d \sin (a+b x) \cos (a+b x)}{b^2}+\frac{(c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b}+\frac{2 (c+d x) \sin ^2(a+b x)}{b}-\frac{d x}{b}-\frac{i (c+d x)^2}{2 d}",1,"-((d*x)/b) - ((I/2)*(c + d*x)^2)/d + ((c + d*x)*Log[1 + E^((2*I)*(a + b*x))])/b - ((I/2)*d*PolyLog[2, -E^((2*I)*(a + b*x))])/b^2 + (d*Cos[a + b*x]*Sin[a + b*x])/b^2 + (2*(c + d*x)*Sin[a + b*x]^2)/b","A",13,9,21,0.4286,1,"{4431, 4404, 2635, 8, 4407, 3719, 2190, 2279, 2391}"
386,0,0,0,0.2990711,"\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","Int[(Sec[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x),x]","\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","-\text{Int}\left(\frac{\tan (a+b x)}{c+d x},x\right)+\frac{2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d}+\frac{2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d}",0,"(2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/d + (2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d - Defer[Int][Tan[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
387,0,0,0,0.3419349,"\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","Int[(Sec[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x)^2,x]","\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","-\text{Int}\left(\frac{\tan (a+b x)}{(c+d x)^2},x\right)+\frac{4 b \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{4 b \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{2 \sin (2 a+2 b x)}{d (c+d x)}",0,"(4*b*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^2 - (2*Sin[2*a + 2*b*x])/(d*(c + d*x)) - (4*b*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2 - Defer[Int][Tan[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
388,0,0,0,0.3977789,"\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","Int[(Sec[a + b*x]*Sin[3*a + 3*b*x])/(c + d*x)^3,x]","\int \frac{\sec (a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","-\text{Int}\left(\frac{\tan (a+b x)}{(c+d x)^3},x\right)-\frac{4 b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{4 b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{2 b \cos (2 a+2 b x)}{d^2 (c+d x)}-\frac{\sin (2 a+2 b x)}{d (c+d x)^2}",0,"(-2*b*Cos[2*a + 2*b*x])/(d^2*(c + d*x)) - (4*b^2*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/d^3 - Sin[2*a + 2*b*x]/(d*(c + d*x)^2) - (4*b^2*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^3 - Defer[Int][Tan[a + b*x]/(c + d*x)^3, x]","A",0,0,0,0,-1,"{}"
389,1,230,0,0.3299638,"\int (c+d x)^3 \sec ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]^2*Sin[3*a + 3*b*x],x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}+\frac{24 d^2 (c+d x) \cos (a+b x)}{b^3}+\frac{12 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{24 d^3 \sin (a+b x)}{b^4}-\frac{4 (c+d x)^3 \cos (a+b x)}{b}-\frac{(c+d x)^3 \sec (a+b x)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}-\frac{6 d^3 \text{PolyLog}\left(3,-i e^{i (a+b x)}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(3,i e^{i (a+b x)}\right)}{b^4}+\frac{24 d^2 (c+d x) \cos (a+b x)}{b^3}+\frac{12 d (c+d x)^2 \sin (a+b x)}{b^2}-\frac{6 i d (c+d x)^2 \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}-\frac{24 d^3 \sin (a+b x)}{b^4}-\frac{4 (c+d x)^3 \cos (a+b x)}{b}-\frac{(c+d x)^3 \sec (a+b x)}{b}",1,"((-6*I)*d*(c + d*x)^2*ArcTan[E^(I*(a + b*x))])/b^2 + (24*d^2*(c + d*x)*Cos[a + b*x])/b^3 - (4*(c + d*x)^3*Cos[a + b*x])/b + ((6*I)*d^2*(c + d*x)*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 - ((6*I)*d^2*(c + d*x)*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - (6*d^3*PolyLog[3, (-I)*E^(I*(a + b*x))])/b^4 + (6*d^3*PolyLog[3, I*E^(I*(a + b*x))])/b^4 - ((c + d*x)^3*Sec[a + b*x])/b - (24*d^3*Sin[a + b*x])/b^4 + (12*d*(c + d*x)^2*Sin[a + b*x])/b^2","A",19,9,25,0.3600,1,"{4431, 3296, 2637, 4407, 4409, 4181, 2531, 2282, 6589}"
390,1,147,0,0.2124814,"\int (c+d x)^2 \sec ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]^2*Sin[3*a + 3*b*x],x]","\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{8 d (c+d x) \sin (a+b x)}{b^2}-\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{8 d^2 \cos (a+b x)}{b^3}-\frac{4 (c+d x)^2 \cos (a+b x)}{b}-\frac{(c+d x)^2 \sec (a+b x)}{b}","\frac{2 i d^2 \text{PolyLog}\left(2,-i e^{i (a+b x)}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(2,i e^{i (a+b x)}\right)}{b^3}+\frac{8 d (c+d x) \sin (a+b x)}{b^2}-\frac{4 i d (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^2}+\frac{8 d^2 \cos (a+b x)}{b^3}-\frac{4 (c+d x)^2 \cos (a+b x)}{b}-\frac{(c+d x)^2 \sec (a+b x)}{b}",1,"((-4*I)*d*(c + d*x)*ArcTan[E^(I*(a + b*x))])/b^2 + (8*d^2*Cos[a + b*x])/b^3 - (4*(c + d*x)^2*Cos[a + b*x])/b + ((2*I)*d^2*PolyLog[2, (-I)*E^(I*(a + b*x))])/b^3 - ((2*I)*d^2*PolyLog[2, I*E^(I*(a + b*x))])/b^3 - ((c + d*x)^2*Sec[a + b*x])/b + (8*d*(c + d*x)*Sin[a + b*x])/b^2","A",15,8,25,0.3200,1,"{4431, 3296, 2638, 4407, 4409, 4181, 2279, 2391}"
391,1,57,0,0.0914535,"\int (c+d x) \sec ^2(a+b x) \sin (3 a+3 b x) \, dx","Int[(c + d*x)*Sec[a + b*x]^2*Sin[3*a + 3*b*x],x]","\frac{4 d \sin (a+b x)}{b^2}+\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}-\frac{4 (c+d x) \cos (a+b x)}{b}-\frac{(c+d x) \sec (a+b x)}{b}","\frac{4 d \sin (a+b x)}{b^2}+\frac{d \tanh ^{-1}(\sin (a+b x))}{b^2}-\frac{4 (c+d x) \cos (a+b x)}{b}-\frac{(c+d x) \sec (a+b x)}{b}",1,"(d*ArcTanh[Sin[a + b*x]])/b^2 - (4*(c + d*x)*Cos[a + b*x])/b - ((c + d*x)*Sec[a + b*x])/b + (4*d*Sin[a + b*x])/b^2","A",9,6,23,0.2609,1,"{4431, 3296, 2637, 4407, 4409, 3770}"
392,0,0,0,0.2662077,"\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","Int[(Sec[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x),x]","\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{c+d x} \, dx","-\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{c+d x},x\right)+\frac{4 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d}+\frac{4 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d}",0,"(4*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d + (4*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d - Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x), x]","A",0,0,0,0,-1,"{}"
393,0,0,0,0.3442184,"\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","Int[(Sec[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x)^2,x]","\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^2} \, dx","-\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{(c+d x)^2},x\right)+\frac{4 b \cos \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{4 b \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{4 \sin (a+b x)}{d (c+d x)}",0,"(4*b*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d^2 - (4*Sin[a + b*x])/(d*(c + d*x)) - (4*b*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^2 - Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
394,0,0,0,0.4362261,"\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","Int[(Sec[a + b*x]^2*Sin[3*a + 3*b*x])/(c + d*x)^3,x]","\int \frac{\sec ^2(a+b x) \sin (3 a+3 b x)}{(c+d x)^3} \, dx","-\text{Int}\left(\frac{\tan (a+b x) \sec (a+b x)}{(c+d x)^3},x\right)-\frac{2 b^2 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{d^3}-\frac{2 b^2 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{d^3}-\frac{2 b \cos (a+b x)}{d^2 (c+d x)}-\frac{2 \sin (a+b x)}{d (c+d x)^2}",0,"(-2*b*Cos[a + b*x])/(d^2*(c + d*x)) - (2*b^2*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/d^3 - (2*Sin[a + b*x])/(d*(c + d*x)^2) - (2*b^2*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d^3 - Defer[Int][(Sec[a + b*x]*Tan[a + b*x])/(c + d*x)^3, x]","A",0,0,0,0,-1,"{}"
395,1,57,0,0.0674738,"\int x \cos (2 x) \sec (x) \, dx","Int[x*Cos[2*x]*Sec[x],x]","-i \text{PolyLog}\left(2,-i e^{i x}\right)+i \text{PolyLog}\left(2,i e^{i x}\right)+2 x \sin (x)+2 \cos (x)+2 i x \tan ^{-1}\left(e^{i x}\right)","-i \text{PolyLog}\left(2,-i e^{i x}\right)+i \text{PolyLog}\left(2,i e^{i x}\right)+2 x \sin (x)+2 \cos (x)+2 i x \tan ^{-1}\left(e^{i x}\right)",1,"(2*I)*x*ArcTan[E^(I*x)] + 2*Cos[x] - I*PolyLog[2, (-I)*E^(I*x)] + I*PolyLog[2, I*E^(I*x)] + 2*x*Sin[x]","A",12,7,8,0.8750,1,"{4431, 3296, 2638, 4407, 4181, 2279, 2391}"
396,1,14,0,0.0331439,"\int x \cos (2 x) \sec ^2(x) \, dx","Int[x*Cos[2*x]*Sec[x]^2,x]","x^2-x \tan (x)-\log (\cos (x))","x^2-x \tan (x)-\log (\cos (x))",1,"x^2 - Log[Cos[x]] - x*Tan[x]","A",5,4,10,0.4000,1,"{4431, 3720, 3475, 30}"
397,1,67,0,0.1372465,"\int x \cos (2 x) \sec ^3(x) \, dx","Int[x*Cos[2*x]*Sec[x]^3,x]","\frac{3}{2} i \text{PolyLog}\left(2,-i e^{i x}\right)-\frac{3}{2} i \text{PolyLog}\left(2,i e^{i x}\right)-3 i x \tan ^{-1}\left(e^{i x}\right)+\frac{\sec (x)}{2}-\frac{1}{2} x \tan (x) \sec (x)","\frac{3}{2} i \text{PolyLog}\left(2,-i e^{i x}\right)-\frac{3}{2} i \text{PolyLog}\left(2,i e^{i x}\right)-3 i x \tan ^{-1}\left(e^{i x}\right)+\frac{\sec (x)}{2}-\frac{1}{2} x \tan (x) \sec (x)",1,"(-3*I)*x*ArcTan[E^(I*x)] + ((3*I)/2)*PolyLog[2, (-I)*E^(I*x)] - ((3*I)/2)*PolyLog[2, I*E^(I*x)] + Sec[x]/2 - (x*Sec[x]*Tan[x])/2","A",19,6,10,0.6000,1,"{4431, 4181, 2279, 2391, 4413, 4185}"