1,1,91,0,0.0932382,"\int (c+d x)^4 \cos (a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x],x]","-\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{24 d^4 \sin (a+b x)}{b^5}+\frac{(c+d x)^4 \sin (a+b x)}{b}","-\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{24 d^4 \sin (a+b x)}{b^5}+\frac{(c+d x)^4 \sin (a+b x)}{b}",1,"(-24*d^3*(c + d*x)*Cos[a + b*x])/b^4 + (4*d*(c + d*x)^3*Cos[a + b*x])/b^2 + (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",5,2,14,0.1429,1,"{3296, 2637}"
2,1,70,0,0.0655573,"\int (c+d x)^3 \cos (a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x],x]","-\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{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}",1,"(-6*d^3*Cos[a + b*x])/b^4 + (3*d*(c + d*x)^2*Cos[a + b*x])/b^2 - (6*d^2*(c + d*x)*Sin[a + b*x])/b^3 + ((c + d*x)^3*Sin[a + b*x])/b","A",4,2,14,0.1429,1,"{3296, 2638}"
3,1,49,0,0.0406137,"\int (c+d x)^2 \cos (a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x],x]","\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 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}",1,"(2*d*(c + d*x)*Cos[a + b*x])/b^2 - (2*d^2*Sin[a + b*x])/b^3 + ((c + d*x)^2*Sin[a + b*x])/b","A",3,2,14,0.1429,1,"{3296, 2637}"
4,1,27,0,0.0164785,"\int (c+d x) \cos (a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x],x]","\frac{d \cos (a+b x)}{b^2}+\frac{(c+d x) \sin (a+b x)}{b}","\frac{d \cos (a+b x)}{b^2}+\frac{(c+d x) \sin (a+b x)}{b}",1,"(d*Cos[a + b*x])/b^2 + ((c + d*x)*Sin[a + b*x])/b","A",2,2,12,0.1667,1,"{3296, 2638}"
5,1,52,0,0.0983092,"\int \frac{\cos (a+b x)}{c+d x} \, dx","Int[Cos[a + b*x]/(c + d*x),x]","\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}","\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}",1,"(Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/d - (Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/d","A",3,3,14,0.2143,1,"{3303, 3299, 3302}"
6,1,73,0,0.1097969,"\int \frac{\cos (a+b x)}{(c+d x)^2} \, dx","Int[Cos[a + b*x]/(c + d*x)^2,x]","-\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)}","-\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)}",1,"-(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","A",4,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
7,1,104,0,0.1382536,"\int \frac{\cos (a+b x)}{(c+d x)^3} \, dx","Int[Cos[a + b*x]/(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)}{2 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{2 d^3}+\frac{b \sin (a+b x)}{2 d^2 (c+d x)}-\frac{\cos (a+b x)}{2 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)}{2 d^3}+\frac{b^2 \sin \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{2 d^3}+\frac{b \sin (a+b x)}{2 d^2 (c+d x)}-\frac{\cos (a+b x)}{2 d (c+d x)^2}",1,"-Cos[a + b*x]/(2*d*(c + d*x)^2) - (b^2*Cos[a - (b*c)/d]*CosIntegral[(b*c)/d + b*x])/(2*d^3) + (b*Sin[a + b*x])/(2*d^2*(c + d*x)) + (b^2*Sin[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(2*d^3)","A",5,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
8,1,127,0,0.1592486,"\int \frac{\cos (a+b x)}{(c+d x)^4} \, dx","Int[Cos[a + b*x]/(c + d*x)^4,x]","\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{6 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{6 d^4}+\frac{b^2 \cos (a+b x)}{6 d^3 (c+d x)}+\frac{b \sin (a+b x)}{6 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{3 d (c+d x)^3}","\frac{b^3 \sin \left(a-\frac{b c}{d}\right) \text{CosIntegral}\left(\frac{b c}{d}+b x\right)}{6 d^4}+\frac{b^3 \cos \left(a-\frac{b c}{d}\right) \text{Si}\left(\frac{b c}{d}+b x\right)}{6 d^4}+\frac{b^2 \cos (a+b x)}{6 d^3 (c+d x)}+\frac{b \sin (a+b x)}{6 d^2 (c+d x)^2}-\frac{\cos (a+b x)}{3 d (c+d x)^3}",1,"-Cos[a + b*x]/(3*d*(c + d*x)^3) + (b^2*Cos[a + b*x])/(6*d^3*(c + d*x)) + (b^3*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(6*d^4) + (b*Sin[a + b*x])/(6*d^2*(c + d*x)^2) + (b^3*Cos[a - (b*c)/d]*SinIntegral[(b*c)/d + b*x])/(6*d^4)","A",6,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
9,1,161,0,0.101873,"\int (c+d x)^4 \cos ^2(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^2,x]","-\frac{3 d^3 (c+d x) \cos ^2(a+b x)}{2 b^4}-\frac{3 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b^3}+\frac{d (c+d x)^3 \cos ^2(a+b x)}{b^2}+\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{4 b^5}+\frac{(c+d x)^4 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}+\frac{3 d^4 x}{4 b^4}+\frac{(c+d x)^5}{10 d}","-\frac{3 d^3 (c+d x) \cos ^2(a+b x)}{2 b^4}-\frac{3 d^2 (c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b^3}+\frac{d (c+d x)^3 \cos ^2(a+b x)}{b^2}+\frac{3 d^4 \sin (a+b x) \cos (a+b x)}{4 b^5}+\frac{(c+d x)^4 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}+\frac{3 d^4 x}{4 b^4}+\frac{(c+d x)^5}{10 d}",1,"(3*d^4*x)/(4*b^4) - (d*(c + d*x)^3)/(2*b^2) + (c + d*x)^5/(10*d) - (3*d^3*(c + d*x)*Cos[a + b*x]^2)/(2*b^4) + (d*(c + d*x)^3*Cos[a + b*x]^2)/b^2 + (3*d^4*Cos[a + b*x]*Sin[a + b*x])/(4*b^5) - (3*d^2*(c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(2*b^3) + ((c + d*x)^4*Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",6,4,16,0.2500,1,"{3311, 32, 2635, 8}"
10,1,134,0,0.073885,"\int (c+d x)^3 \cos ^2(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^2,x]","-\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \cos ^2(a+b x)}{4 b^2}-\frac{3 d^3 \cos ^2(a+b x)}{8 b^4}+\frac{(c+d x)^3 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 c d^2 x}{4 b^2}-\frac{3 d^3 x^2}{8 b^2}+\frac{(c+d x)^4}{8 d}","-\frac{3 d^2 (c+d x) \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{3 d (c+d x)^2 \cos ^2(a+b x)}{4 b^2}-\frac{3 d^3 \cos ^2(a+b x)}{8 b^4}+\frac{(c+d x)^3 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 c d^2 x}{4 b^2}-\frac{3 d^3 x^2}{8 b^2}+\frac{(c+d x)^4}{8 d}",1,"(-3*c*d^2*x)/(4*b^2) - (3*d^3*x^2)/(8*b^2) + (c + d*x)^4/(8*d) - (3*d^3*Cos[a + b*x]^2)/(8*b^4) + (3*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])/(4*b^3) + ((c + d*x)^3*Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",4,3,16,0.1875,1,"{3311, 32, 3310}"
11,1,95,0,0.0527312,"\int (c+d x)^2 \cos ^2(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^2,x]","\frac{d (c+d x) \cos ^2(a+b x)}{2 b^2}-\frac{d^2 \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{(c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d^2 x}{4 b^2}+\frac{(c+d x)^3}{6 d}","\frac{d (c+d x) \cos ^2(a+b x)}{2 b^2}-\frac{d^2 \sin (a+b x) \cos (a+b x)}{4 b^3}+\frac{(c+d x)^2 \sin (a+b x) \cos (a+b x)}{2 b}-\frac{d^2 x}{4 b^2}+\frac{(c+d x)^3}{6 d}",1,"-(d^2*x)/(4*b^2) + (c + d*x)^3/(6*d) + (d*(c + d*x)*Cos[a + b*x]^2)/(2*b^2) - (d^2*Cos[a + b*x]*Sin[a + b*x])/(4*b^3) + ((c + d*x)^2*Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",4,4,16,0.2500,1,"{3311, 32, 2635, 8}"
12,1,55,0,0.0246872,"\int (c+d x) \cos ^2(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^2,x]","\frac{d \cos ^2(a+b x)}{4 b^2}+\frac{(c+d x) \sin (a+b x) \cos (a+b x)}{2 b}+\frac{c x}{2}+\frac{d x^2}{4}","\frac{d \cos ^2(a+b x)}{4 b^2}+\frac{(c+d x) \sin (a+b x) \cos (a+b x)}{2 b}+\frac{c x}{2}+\frac{d x^2}{4}",1,"(c*x)/2 + (d*x^2)/4 + (d*Cos[a + b*x]^2)/(4*b^2) + ((c + d*x)*Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",2,1,14,0.07143,1,"{3310}"
13,1,78,0,0.1533843,"\int \frac{\cos ^2(a+b x)}{c+d x} \, dx","Int[Cos[a + b*x]^2/(c + d*x),x]","\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}-\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\log (c+d x)}{2 d}","\frac{\cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}-\frac{\sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\log (c+d x)}{2 d}",1,"(Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/(2*d) + Log[c + d*x]/(2*d) - (Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/(2*d)","A",5,4,16,0.2500,1,"{3312, 3303, 3299, 3302}"
14,1,83,0,0.1342639,"\int \frac{\cos ^2(a+b x)}{(c+d x)^2} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^2,x]","-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\cos ^2(a+b x)}{d (c+d x)}","-\frac{b \sin \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{b \cos \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\cos ^2(a+b x)}{d (c+d x)}",1,"-(Cos[a + b*x]^2/(d*(c + d*x))) - (b*CosIntegral[(2*b*c)/d + 2*b*x]*Sin[2*a - (2*b*c)/d])/d^2 - (b*Cos[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^2","A",5,5,16,0.3125,1,"{3313, 12, 3303, 3299, 3302}"
15,1,112,0,0.1968532,"\int \frac{\cos ^2(a+b x)}{(c+d x)^3} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^3,x]","-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b \sin (a+b x) \cos (a+b x)}{d^2 (c+d x)}-\frac{\cos ^2(a+b x)}{2 d (c+d x)^2}","-\frac{b^2 \cos \left(2 a-\frac{2 b c}{d}\right) \text{CosIntegral}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b^2 \sin \left(2 a-\frac{2 b c}{d}\right) \text{Si}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b \sin (a+b x) \cos (a+b x)}{d^2 (c+d x)}-\frac{\cos ^2(a+b x)}{2 d (c+d x)^2}",1,"-Cos[a + b*x]^2/(2*d*(c + d*x)^2) - (b^2*Cos[2*a - (2*b*c)/d]*CosIntegral[(2*b*c)/d + 2*b*x])/d^3 + (b*Cos[a + b*x]*Sin[a + b*x])/(d^2*(c + d*x)) + (b^2*Sin[2*a - (2*b*c)/d]*SinIntegral[(2*b*c)/d + 2*b*x])/d^3","A",7,6,16,0.3750,1,"{3314, 31, 3312, 3303, 3299, 3302}"
16,1,225,0,0.2543487,"\int (c+d x)^4 \cos ^3(a+b x) \, dx","Int[(c + d*x)^4*Cos[a + b*x]^3,x]","-\frac{80 d^2 (c+d x)^2 \sin (a+b x)}{9 b^3}-\frac{8 d^3 (c+d x) \cos ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \cos (a+b x)}{9 b^4}-\frac{4 d^2 (c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{9 b^3}+\frac{4 d (c+d x)^3 \cos ^3(a+b x)}{9 b^2}+\frac{8 d (c+d x)^3 \cos (a+b x)}{3 b^2}-\frac{8 d^4 \sin ^3(a+b x)}{81 b^5}+\frac{488 d^4 \sin (a+b x)}{27 b^5}+\frac{2 (c+d x)^4 \sin (a+b x)}{3 b}+\frac{(c+d x)^4 \sin (a+b x) \cos ^2(a+b x)}{3 b}","-\frac{80 d^2 (c+d x)^2 \sin (a+b x)}{9 b^3}-\frac{8 d^3 (c+d x) \cos ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \cos (a+b x)}{9 b^4}-\frac{4 d^2 (c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{9 b^3}+\frac{4 d (c+d x)^3 \cos ^3(a+b x)}{9 b^2}+\frac{8 d (c+d x)^3 \cos (a+b x)}{3 b^2}-\frac{8 d^4 \sin ^3(a+b x)}{81 b^5}+\frac{488 d^4 \sin (a+b x)}{27 b^5}+\frac{2 (c+d x)^4 \sin (a+b x)}{3 b}+\frac{(c+d x)^4 \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(-160*d^3*(c + d*x)*Cos[a + b*x])/(9*b^4) + (8*d*(c + d*x)^3*Cos[a + b*x])/(3*b^2) - (8*d^3*(c + d*x)*Cos[a + b*x]^3)/(27*b^4) + (4*d*(c + d*x)^3*Cos[a + b*x]^3)/(9*b^2) + (488*d^4*Sin[a + b*x])/(27*b^5) - (80*d^2*(c + d*x)^2*Sin[a + b*x])/(9*b^3) + (2*(c + d*x)^4*Sin[a + b*x])/(3*b) - (4*d^2*(c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x])/(9*b^3) + ((c + d*x)^4*Cos[a + b*x]^2*Sin[a + b*x])/(3*b) - (8*d^4*Sin[a + b*x]^3)/(81*b^5)","A",12,4,16,0.2500,1,"{3311, 3296, 2637, 2633}"
17,1,175,0,0.156228,"\int (c+d x)^3 \cos ^3(a+b x) \, dx","Int[(c + d*x)^3*Cos[a + b*x]^3,x]","-\frac{40 d^2 (c+d x) \sin (a+b x)}{9 b^3}-\frac{2 d^2 (c+d x) \sin (a+b x) \cos ^2(a+b x)}{9 b^3}+\frac{d (c+d x)^2 \cos ^3(a+b x)}{3 b^2}+\frac{2 d (c+d x)^2 \cos (a+b x)}{b^2}-\frac{2 d^3 \cos ^3(a+b x)}{27 b^4}-\frac{40 d^3 \cos (a+b x)}{9 b^4}+\frac{2 (c+d x)^3 \sin (a+b x)}{3 b}+\frac{(c+d x)^3 \sin (a+b x) \cos ^2(a+b x)}{3 b}","-\frac{40 d^2 (c+d x) \sin (a+b x)}{9 b^3}-\frac{2 d^2 (c+d x) \sin (a+b x) \cos ^2(a+b x)}{9 b^3}+\frac{d (c+d x)^2 \cos ^3(a+b x)}{3 b^2}+\frac{2 d (c+d x)^2 \cos (a+b x)}{b^2}-\frac{2 d^3 \cos ^3(a+b x)}{27 b^4}-\frac{40 d^3 \cos (a+b x)}{9 b^4}+\frac{2 (c+d x)^3 \sin (a+b x)}{3 b}+\frac{(c+d x)^3 \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(-40*d^3*Cos[a + b*x])/(9*b^4) + (2*d*(c + d*x)^2*Cos[a + b*x])/b^2 - (2*d^3*Cos[a + b*x]^3)/(27*b^4) + (d*(c + d*x)^2*Cos[a + b*x]^3)/(3*b^2) - (40*d^2*(c + d*x)*Sin[a + b*x])/(9*b^3) + (2*(c + d*x)^3*Sin[a + b*x])/(3*b) - (2*d^2*(c + d*x)*Cos[a + b*x]^2*Sin[a + b*x])/(9*b^3) + ((c + d*x)^3*Cos[a + b*x]^2*Sin[a + b*x])/(3*b)","A",8,4,16,0.2500,1,"{3311, 3296, 2638, 3310}"
18,1,123,0,0.0967742,"\int (c+d x)^2 \cos ^3(a+b x) \, dx","Int[(c + d*x)^2*Cos[a + b*x]^3,x]","\frac{2 d (c+d x) \cos ^3(a+b x)}{9 b^2}+\frac{4 d (c+d x) \cos (a+b x)}{3 b^2}+\frac{2 d^2 \sin ^3(a+b x)}{27 b^3}-\frac{14 d^2 \sin (a+b x)}{9 b^3}+\frac{2 (c+d x)^2 \sin (a+b x)}{3 b}+\frac{(c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{3 b}","\frac{2 d (c+d x) \cos ^3(a+b x)}{9 b^2}+\frac{4 d (c+d x) \cos (a+b x)}{3 b^2}+\frac{2 d^2 \sin ^3(a+b x)}{27 b^3}-\frac{14 d^2 \sin (a+b x)}{9 b^3}+\frac{2 (c+d x)^2 \sin (a+b x)}{3 b}+\frac{(c+d x)^2 \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(4*d*(c + d*x)*Cos[a + b*x])/(3*b^2) + (2*d*(c + d*x)*Cos[a + b*x]^3)/(9*b^2) - (14*d^2*Sin[a + b*x])/(9*b^3) + (2*(c + d*x)^2*Sin[a + b*x])/(3*b) + ((c + d*x)^2*Cos[a + b*x]^2*Sin[a + b*x])/(3*b) + (2*d^2*Sin[a + b*x]^3)/(27*b^3)","A",6,4,16,0.2500,1,"{3311, 3296, 2637, 2633}"
19,1,75,0,0.0417872,"\int (c+d x) \cos ^3(a+b x) \, dx","Int[(c + d*x)*Cos[a + b*x]^3,x]","\frac{d \cos ^3(a+b x)}{9 b^2}+\frac{2 d \cos (a+b x)}{3 b^2}+\frac{2 (c+d x) \sin (a+b x)}{3 b}+\frac{(c+d x) \sin (a+b x) \cos ^2(a+b x)}{3 b}","\frac{d \cos ^3(a+b x)}{9 b^2}+\frac{2 d \cos (a+b x)}{3 b^2}+\frac{2 (c+d x) \sin (a+b x)}{3 b}+\frac{(c+d x) \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(2*d*Cos[a + b*x])/(3*b^2) + (d*Cos[a + b*x]^3)/(9*b^2) + (2*(c + d*x)*Sin[a + b*x])/(3*b) + ((c + d*x)*Cos[a + b*x]^2*Sin[a + b*x])/(3*b)","A",3,3,14,0.2143,1,"{3310, 3296, 2638}"
20,1,121,0,0.2440365,"\int \frac{\cos ^3(a+b x)}{c+d x} \, dx","Int[Cos[a + b*x]^3/(c + d*x),x]","\frac{3 \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{3 \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{3 \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{3 \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,"(3*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) - (3*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",8,4,16,0.2500,1,"{3312, 3303, 3299, 3302}"
21,1,145,0,0.225448,"\int \frac{\cos ^3(a+b x)}{(c+d x)^2} \, dx","Int[Cos[a + b*x]^3/(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{3 b \sin \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(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 ^3(a+b x)}{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{3 b \sin \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(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 ^3(a+b x)}{d (c+d x)}",1,"-(Cos[a + b*x]^3/(d*(c + d*x))) - (3*b*CosIntegral[(3*b*c)/d + 3*b*x]*Sin[3*a - (3*b*c)/d])/(4*d^2) - (3*b*CosIntegral[(b*c)/d + b*x]*Sin[a - (b*c)/d])/(4*d^2) - (3*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",8,4,16,0.2500,1,"{3313, 3303, 3299, 3302}"
22,1,184,0,0.3448207,"\int \frac{\cos ^3(a+b x)}{(c+d x)^3} \, dx","Int[Cos[a + b*x]^3/(c + d*x)^3,x]","-\frac{3 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{3 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{3 b \sin (a+b x) \cos ^2(a+b x)}{2 d^2 (c+d x)}-\frac{\cos ^3(a+b x)}{2 d (c+d x)^2}","-\frac{3 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{3 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{3 b \sin (a+b x) \cos ^2(a+b x)}{2 d^2 (c+d x)}-\frac{\cos ^3(a+b x)}{2 d (c+d x)^2}",1,"-Cos[a + b*x]^3/(2*d*(c + d*x)^2) - (3*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) + (3*b*Cos[a + b*x]^2*Sin[a + b*x])/(2*d^2*(c + d*x)) + (3*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",12,5,16,0.3125,1,"{3314, 3303, 3299, 3302, 3312}"
23,1,172,0,0.1540061,"\int x^3 \cos ^4(a+b x) \, dx","Int[x^3*Cos[a + b*x]^4,x]","\frac{3 x^2 \cos ^4(a+b x)}{16 b^2}+\frac{9 x^2 \cos ^2(a+b x)}{16 b^2}-\frac{3 \cos ^4(a+b x)}{128 b^4}-\frac{45 \cos ^2(a+b x)}{128 b^4}-\frac{3 x \sin (a+b x) \cos ^3(a+b x)}{32 b^3}-\frac{45 x \sin (a+b x) \cos (a+b x)}{64 b^3}+\frac{x^3 \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x^3 \sin (a+b x) \cos (a+b x)}{8 b}-\frac{45 x^2}{128 b^2}+\frac{3 x^4}{32}","\frac{3 x^2 \cos ^4(a+b x)}{16 b^2}+\frac{9 x^2 \cos ^2(a+b x)}{16 b^2}-\frac{3 \cos ^4(a+b x)}{128 b^4}-\frac{45 \cos ^2(a+b x)}{128 b^4}-\frac{3 x \sin (a+b x) \cos ^3(a+b x)}{32 b^3}-\frac{45 x \sin (a+b x) \cos (a+b x)}{64 b^3}+\frac{x^3 \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x^3 \sin (a+b x) \cos (a+b x)}{8 b}-\frac{45 x^2}{128 b^2}+\frac{3 x^4}{32}",1,"(-45*x^2)/(128*b^2) + (3*x^4)/32 - (45*Cos[a + b*x]^2)/(128*b^4) + (9*x^2*Cos[a + b*x]^2)/(16*b^2) - (3*Cos[a + b*x]^4)/(128*b^4) + (3*x^2*Cos[a + b*x]^4)/(16*b^2) - (45*x*Cos[a + b*x]*Sin[a + b*x])/(64*b^3) + (3*x^3*Cos[a + b*x]*Sin[a + b*x])/(8*b) - (3*x*Cos[a + b*x]^3*Sin[a + b*x])/(32*b^3) + (x^3*Cos[a + b*x]^3*Sin[a + b*x])/(4*b)","A",8,3,12,0.2500,1,"{3311, 30, 3310}"
24,1,134,0,0.1082891,"\int x^2 \cos ^4(a+b x) \, dx","Int[x^2*Cos[a + b*x]^4,x]","\frac{x \cos ^4(a+b x)}{8 b^2}+\frac{3 x \cos ^2(a+b x)}{8 b^2}-\frac{\sin (a+b x) \cos ^3(a+b x)}{32 b^3}-\frac{15 \sin (a+b x) \cos (a+b x)}{64 b^3}+\frac{x^2 \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x^2 \sin (a+b x) \cos (a+b x)}{8 b}-\frac{15 x}{64 b^2}+\frac{x^3}{8}","\frac{x \cos ^4(a+b x)}{8 b^2}+\frac{3 x \cos ^2(a+b x)}{8 b^2}-\frac{\sin (a+b x) \cos ^3(a+b x)}{32 b^3}-\frac{15 \sin (a+b x) \cos (a+b x)}{64 b^3}+\frac{x^2 \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x^2 \sin (a+b x) \cos (a+b x)}{8 b}-\frac{15 x}{64 b^2}+\frac{x^3}{8}",1,"(-15*x)/(64*b^2) + x^3/8 + (3*x*Cos[a + b*x]^2)/(8*b^2) + (x*Cos[a + b*x]^4)/(8*b^2) - (15*Cos[a + b*x]*Sin[a + b*x])/(64*b^3) + (3*x^2*Cos[a + b*x]*Sin[a + b*x])/(8*b) - (Cos[a + b*x]^3*Sin[a + b*x])/(32*b^3) + (x^2*Cos[a + b*x]^3*Sin[a + b*x])/(4*b)","A",8,4,12,0.3333,1,"{3311, 30, 2635, 8}"
25,1,80,0,0.0474994,"\int x \cos ^4(a+b x) \, dx","Int[x*Cos[a + b*x]^4,x]","\frac{\cos ^4(a+b x)}{16 b^2}+\frac{3 \cos ^2(a+b x)}{16 b^2}+\frac{x \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x^2}{16}","\frac{\cos ^4(a+b x)}{16 b^2}+\frac{3 \cos ^2(a+b x)}{16 b^2}+\frac{x \sin (a+b x) \cos ^3(a+b x)}{4 b}+\frac{3 x \sin (a+b x) \cos (a+b x)}{8 b}+\frac{3 x^2}{16}",1,"(3*x^2)/16 + (3*Cos[a + b*x]^2)/(16*b^2) + Cos[a + b*x]^4/(16*b^2) + (3*x*Cos[a + b*x]*Sin[a + b*x])/(8*b) + (x*Cos[a + b*x]^3*Sin[a + b*x])/(4*b)","A",3,2,10,0.2000,1,"{3310, 30}"
26,1,59,0,0.1575709,"\int \frac{\cos ^4(a+b x)}{x} \, dx","Int[Cos[a + b*x]^4/x,x]","\frac{1}{2} \cos (2 a) \text{CosIntegral}(2 b x)+\frac{1}{8} \cos (4 a) \text{CosIntegral}(4 b x)-\frac{1}{2} \sin (2 a) \text{Si}(2 b x)-\frac{1}{8} \sin (4 a) \text{Si}(4 b x)+\frac{3 \log (x)}{8}","\frac{1}{2} \cos (2 a) \text{CosIntegral}(2 b x)+\frac{1}{8} \cos (4 a) \text{CosIntegral}(4 b x)-\frac{1}{2} \sin (2 a) \text{Si}(2 b x)-\frac{1}{8} \sin (4 a) \text{Si}(4 b x)+\frac{3 \log (x)}{8}",1,"(Cos[2*a]*CosIntegral[2*b*x])/2 + (Cos[4*a]*CosIntegral[4*b*x])/8 + (3*Log[x])/8 - (Sin[2*a]*SinIntegral[2*b*x])/2 - (Sin[4*a]*SinIntegral[4*b*x])/8","A",8,4,12,0.3333,1,"{3312, 3303, 3299, 3302}"
27,1,66,0,0.1509964,"\int \frac{\cos ^4(a+b x)}{x^2} \, dx","Int[Cos[a + b*x]^4/x^2,x]","-b \sin (2 a) \text{CosIntegral}(2 b x)-\frac{1}{2} b \sin (4 a) \text{CosIntegral}(4 b x)-b \cos (2 a) \text{Si}(2 b x)-\frac{1}{2} b \cos (4 a) \text{Si}(4 b x)-\frac{\cos ^4(a+b x)}{x}","-b \sin (2 a) \text{CosIntegral}(2 b x)-\frac{1}{2} b \sin (4 a) \text{CosIntegral}(4 b x)-b \cos (2 a) \text{Si}(2 b x)-\frac{1}{2} b \cos (4 a) \text{Si}(4 b x)-\frac{\cos ^4(a+b x)}{x}",1,"-(Cos[a + b*x]^4/x) - b*CosIntegral[2*b*x]*Sin[2*a] - (b*CosIntegral[4*b*x]*Sin[4*a])/2 - b*Cos[2*a]*SinIntegral[2*b*x] - (b*Cos[4*a]*SinIntegral[4*b*x])/2","A",8,4,12,0.3333,1,"{3313, 3303, 3299, 3302}"
28,1,90,0,0.2968952,"\int \frac{\cos ^4(a+b x)}{x^3} \, dx","Int[Cos[a + b*x]^4/x^3,x]","-b^2 \cos (2 a) \text{CosIntegral}(2 b x)-b^2 \cos (4 a) \text{CosIntegral}(4 b x)+b^2 \sin (2 a) \text{Si}(2 b x)+b^2 \sin (4 a) \text{Si}(4 b x)-\frac{\cos ^4(a+b x)}{2 x^2}+\frac{2 b \sin (a+b x) \cos ^3(a+b x)}{x}","-b^2 \cos (2 a) \text{CosIntegral}(2 b x)-b^2 \cos (4 a) \text{CosIntegral}(4 b x)+b^2 \sin (2 a) \text{Si}(2 b x)+b^2 \sin (4 a) \text{Si}(4 b x)-\frac{\cos ^4(a+b x)}{2 x^2}+\frac{2 b \sin (a+b x) \cos ^3(a+b x)}{x}",1,"-Cos[a + b*x]^4/(2*x^2) - b^2*Cos[2*a]*CosIntegral[2*b*x] - b^2*Cos[4*a]*CosIntegral[4*b*x] + (2*b*Cos[a + b*x]^3*Sin[a + b*x])/x + b^2*Sin[2*a]*SinIntegral[2*b*x] + b^2*Sin[4*a]*SinIntegral[4*b*x]","A",14,5,12,0.4167,1,"{3314, 3312, 3303, 3299, 3302}"
29,1,205,0,0.1573901,"\int (c+d x)^3 \sec (a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x],x]","-\frac{6 d^2 (c+d x) \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{Li}_4\left(-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{Li}_4\left(i e^{i (a+b x)}\right)}{b^4}-\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{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{6 d^2 (c+d x) \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{6 i d^3 \text{Li}_4\left(-i e^{i (a+b x)}\right)}{b^4}+\frac{6 i d^3 \text{Li}_4\left(i e^{i (a+b x)}\right)}{b^4}-\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 + ((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","A",9,5,14,0.3571,1,"{4181, 2531, 6609, 2282, 6589}"
30,1,137,0,0.0920892,"\int (c+d x)^2 \sec (a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x],x]","\frac{2 i d (c+d x) \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}-\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{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{2 i d (c+d x) \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{2 d^2 \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{2 d^2 \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}-\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*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","A",7,4,14,0.2857,1,"{4181, 2531, 2282, 6589}"
31,1,75,0,0.0415003,"\int (c+d x) \sec (a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x],x]","\frac{i d \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{2 i (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b}","\frac{i d \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{i d \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\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 + (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",5,3,12,0.2500,1,"{4181, 2279, 2391}"
32,0,0,0,0.0224226,"\int \frac{\sec (a+b x)}{c+d x} \, dx","Int[Sec[a + b*x]/(c + d*x),x]","\int \frac{\sec (a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\sec (a+b x)}{c+d x},x\right)",0,"Defer[Int][Sec[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
33,1,114,0,0.2153411,"\int (c+d x)^3 \sec ^2(a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]^2,x]","-\frac{3 i d^2 (c+d x) \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^3 \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{(c+d x)^3 \tan (a+b x)}{b}-\frac{i (c+d x)^3}{b}","-\frac{3 i d^2 (c+d x) \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^3}+\frac{3 d (c+d x)^2 \log \left(1+e^{2 i (a+b x)}\right)}{b^2}+\frac{3 d^3 \text{Li}_3\left(-e^{2 i (a+b x)}\right)}{2 b^4}+\frac{(c+d x)^3 \tan (a+b x)}{b}-\frac{i (c+d x)^3}{b}",1,"((-I)*(c + d*x)^3)/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) + ((c + d*x)^3*Tan[a + b*x])/b","A",6,6,16,0.3750,1,"{4184, 3719, 2190, 2531, 2282, 6589}"
34,1,82,0,0.1341782,"\int (c+d x)^2 \sec ^2(a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]^2,x]","\frac{2 d (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^2}-\frac{i d^2 \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^3}+\frac{(c+d x)^2 \tan (a+b x)}{b}-\frac{i (c+d x)^2}{b}","\frac{2 d (c+d x) \log \left(1+e^{2 i (a+b x)}\right)}{b^2}-\frac{i d^2 \text{Li}_2\left(-e^{2 i (a+b x)}\right)}{b^3}+\frac{(c+d x)^2 \tan (a+b x)}{b}-\frac{i (c+d x)^2}{b}",1,"((-I)*(c + d*x)^2)/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 + ((c + d*x)^2*Tan[a + b*x])/b","A",5,5,16,0.3125,1,"{4184, 3719, 2190, 2279, 2391}"
35,1,28,0,0.0273841,"\int (c+d x) \sec ^2(a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x]^2,x]","\frac{d \log (\cos (a+b x))}{b^2}+\frac{(c+d x) \tan (a+b x)}{b}","\frac{d \log (\cos (a+b x))}{b^2}+\frac{(c+d x) \tan (a+b x)}{b}",1,"(d*Log[Cos[a + b*x]])/b^2 + ((c + d*x)*Tan[a + b*x])/b","A",2,2,14,0.1429,1,"{4184, 3475}"
36,0,0,0,0.0390762,"\int \frac{\sec ^2(a+b x)}{c+d x} \, dx","Int[Sec[a + b*x]^2/(c + d*x),x]","\int \frac{\sec ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\sec ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sec[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
37,1,337,0,0.2688086,"\int (c+d x)^3 \sec ^3(a+b x) \, dx","Int[(c + d*x)^3*Sec[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}+\frac{3 i d^3 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{Li}_4\left(-i e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{Li}_4\left(i e^{i (a+b x)}\right)}{b^4}-\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{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}-\frac{6 i d^2 (c+d x) \tan ^{-1}\left(e^{i (a+b x)}\right)}{b^3}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{i (a+b x)}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \sec (a+b x)}{2 b^2}+\frac{3 i d^3 \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^4}-\frac{3 i d^3 \text{Li}_4\left(-i e^{i (a+b x)}\right)}{b^4}+\frac{3 i d^3 \text{Li}_4\left(i e^{i (a+b x)}\right)}{b^4}-\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",15,8,16,0.5000,1,"{4186, 4181, 2279, 2391, 2531, 6609, 2282, 6589}"
38,1,193,0,0.1427984,"\int (c+d x)^2 \sec ^3(a+b x) \, dx","Int[(c + d*x)^2*Sec[a + b*x]^3,x]","\frac{i d (c+d x) \text{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{d (c+d x) \sec (a+b x)}{b^2}-\frac{d^2 \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{d^2 \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}+\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{Li}_2\left(-i e^{i (a+b x)}\right)}{b^2}-\frac{i d (c+d x) \text{Li}_2\left(i e^{i (a+b x)}\right)}{b^2}-\frac{d (c+d x) \sec (a+b x)}{b^2}-\frac{d^2 \text{Li}_3\left(-i e^{i (a+b x)}\right)}{b^3}+\frac{d^2 \text{Li}_3\left(i e^{i (a+b x)}\right)}{b^3}+\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",9,6,16,0.3750,1,"{4186, 3770, 4181, 2531, 2282, 6589}"
39,1,117,0,0.0688011,"\int (c+d x) \sec ^3(a+b x) \, dx","Int[(c + d*x)*Sec[a + b*x]^3,x]","\frac{i d \text{Li}_2\left(-i e^{i (a+b x)}\right)}{2 b^2}-\frac{i d \text{Li}_2\left(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{Li}_2\left(-i e^{i (a+b x)}\right)}{2 b^2}-\frac{i d \text{Li}_2\left(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",6,4,14,0.2857,1,"{4185, 4181, 2279, 2391}"
40,0,0,0,0.0382456,"\int \frac{\sec ^2(a+b x)}{c+d x} \, dx","Int[Sec[a + b*x]^2/(c + d*x),x]","\int \frac{\sec ^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\sec ^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sec[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
41,1,194,0,0.4227343,"\int (c+d x)^{5/2} \cos (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x],x]","\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)}{4 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)}{4 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{4 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{2 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{b}","\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)}{4 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)}{4 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (a+b x)}{4 b^3}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{2 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x)}{b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(2*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]])/(4*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])/(4*b^(7/2)) - (15*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(4*b^3) + ((c + d*x)^(5/2)*Sin[a + b*x])/b","A",8,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
42,1,169,0,0.23601,"\int (c+d x)^{3/2} \cos (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x],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)}{2 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)}{2 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{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)}{2 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)}{2 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x)}{b}",1,"(3*d*Sqrt[c + d*x]*Cos[a + b*x])/(2*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]])/(2*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])/(2*b^(5/2)) + ((c + d*x)^(3/2)*Sin[a + b*x])/b","A",7,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
43,1,142,0,0.1715139,"\int \sqrt{c+d x} \cos (a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x],x]","-\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)}{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)}{b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{b}","-\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)}{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)}{b^{3/2}}+\frac{\sqrt{c+d x} \sin (a+b x)}{b}",1,"-((Sqrt[d]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/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])/b^(3/2) + (Sqrt[c + d*x]*Sin[a + b*x])/b","A",6,6,16,0.3750,1,"{3296, 3306, 3305, 3351, 3304, 3352}"
44,1,118,0,0.1339678,"\int \frac{\cos (a+b x)}{\sqrt{c+d x}} \, dx","Int[Cos[a + b*x]/Sqrt[c + d*x],x]","\frac{\sqrt{2 \pi } \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)}{\sqrt{b} \sqrt{d}}-\frac{\sqrt{2 \pi } \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}","\frac{\sqrt{2 \pi } \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)}{\sqrt{b} \sqrt{d}}-\frac{\sqrt{2 \pi } \sin \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{\sqrt{b} \sqrt{d}}",1,"(Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(Sqrt[b]*Sqrt[d]) - (Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(Sqrt[b]*Sqrt[d])","A",5,5,16,0.3125,1,"{3306, 3305, 3351, 3304, 3352}"
45,1,139,0,0.1856698,"\int \frac{\cos (a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(3/2),x]","-\frac{2 \sqrt{2 \pi } \sqrt{b} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{2 \pi } \sqrt{b} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cos (a+b x)}{d \sqrt{c+d x}}","-\frac{2 \sqrt{2 \pi } \sqrt{b} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{2 \pi } \sqrt{b} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cos (a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cos[a + b*x])/(d*Sqrt[c + d*x]) - (2*Sqrt[b]*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (2*Sqrt[b]*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(3/2)","A",6,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
46,1,168,0,0.2623338,"\int \frac{\cos (a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(5/2),x]","-\frac{4 \sqrt{2 \pi } b^{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)}{3 d^{5/2}}+\frac{4 \sqrt{2 \pi } b^{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)}{3 d^{5/2}}+\frac{4 b \sin (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cos (a+b x)}{3 d (c+d x)^{3/2}}","-\frac{4 \sqrt{2 \pi } b^{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)}{3 d^{5/2}}+\frac{4 \sqrt{2 \pi } b^{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)}{3 d^{5/2}}+\frac{4 b \sin (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cos (a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cos[a + b*x])/(3*d*(c + d*x)^(3/2)) - (4*b^(3/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) + (4*b^(3/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(3*d^(5/2)) + (4*b*Sin[a + b*x])/(3*d^2*Sqrt[c + d*x])","A",7,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
47,1,193,0,0.296318,"\int \frac{\cos (a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(7/2),x]","\frac{8 \sqrt{2 \pi } b^{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)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{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)}{15 d^{7/2}}+\frac{8 b^2 \cos (a+b x)}{15 d^3 \sqrt{c+d x}}+\frac{4 b \sin (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cos (a+b x)}{5 d (c+d x)^{5/2}}","\frac{8 \sqrt{2 \pi } b^{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)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{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)}{15 d^{7/2}}+\frac{8 b^2 \cos (a+b x)}{15 d^3 \sqrt{c+d x}}+\frac{4 b \sin (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cos (a+b x)}{5 d (c+d x)^{5/2}}",1,"(-2*Cos[a + b*x])/(5*d*(c + d*x)^(5/2)) + (8*b^2*Cos[a + b*x])/(15*d^3*Sqrt[c + d*x]) + (8*b^(5/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) + (8*b^(5/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(15*d^(7/2)) + (4*b*Sin[a + b*x])/(15*d^2*(c + d*x)^(3/2))","A",8,6,16,0.3750,1,"{3297, 3306, 3305, 3351, 3304, 3352}"
48,1,231,0,0.4347738,"\int (c+d x)^{5/2} \cos ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^2,x]","\frac{15 \sqrt{\pi } d^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{128 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \cos ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{5 d (c+d x)^{3/2}}{16 b^2}+\frac{(c+d x)^{7/2}}{7 d}","\frac{15 \sqrt{\pi } d^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{128 b^{7/2}}+\frac{15 \sqrt{\pi } d^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{128 b^{7/2}}-\frac{15 d^2 \sqrt{c+d x} \sin (2 a+2 b x)}{64 b^3}+\frac{5 d (c+d x)^{3/2} \cos ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{5/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{5 d (c+d x)^{3/2}}{16 b^2}+\frac{(c+d x)^{7/2}}{7 d}",1,"(-5*d*(c + d*x)^(3/2))/(16*b^2) + (c + d*x)^(7/2)/(7*d) + (5*d*(c + d*x)^(3/2)*Cos[a + b*x]^2)/(8*b^2) + (15*d^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(128*b^(7/2)) + (15*d^(5/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(128*b^(7/2)) + ((c + d*x)^(5/2)*Cos[a + b*x]*Sin[a + b*x])/(2*b) - (15*d^2*Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(64*b^3)","A",10,9,18,0.5000,1,"{3311, 32, 3312, 3296, 3306, 3305, 3351, 3304, 3352}"
49,1,203,0,0.3421561,"\int (c+d x)^{3/2} \cos ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^2,x]","-\frac{3 \sqrt{\pi } d^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{32 b^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 d \sqrt{c+d x}}{16 b^2}+\frac{(c+d x)^{5/2}}{5 d}","-\frac{3 \sqrt{\pi } d^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{32 b^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{32 b^{5/2}}+\frac{3 d \sqrt{c+d x} \cos ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{3/2} \sin (a+b x) \cos (a+b x)}{2 b}-\frac{3 d \sqrt{c+d x}}{16 b^2}+\frac{(c+d x)^{5/2}}{5 d}",1,"(-3*d*Sqrt[c + d*x])/(16*b^2) + (c + d*x)^(5/2)/(5*d) + (3*d*Sqrt[c + d*x]*Cos[a + b*x]^2)/(8*b^2) - (3*d^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(32*b^(5/2)) + (3*d^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(32*b^(5/2)) + ((c + d*x)^(3/2)*Cos[a + b*x]*Sin[a + b*x])/(2*b)","A",9,8,18,0.4444,1,"{3311, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
50,1,158,0,0.2783287,"\int \sqrt{c+d x} \cos ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^2,x]","-\frac{\sqrt{\pi } \sqrt{d} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{8 b^{3/2}}+\frac{\sqrt{c+d x} \sin (2 a+2 b x)}{4 b}+\frac{(c+d x)^{3/2}}{3 d}","-\frac{\sqrt{\pi } \sqrt{d} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{8 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{8 b^{3/2}}+\frac{\sqrt{c+d x} \sin (2 a+2 b x)}{4 b}+\frac{(c+d x)^{3/2}}{3 d}",1,"(c + d*x)^(3/2)/(3*d) - (Sqrt[d]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(8*b^(3/2)) - (Sqrt[d]*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(8*b^(3/2)) + (Sqrt[c + d*x]*Sin[2*a + 2*b*x])/(4*b)","A",8,7,18,0.3889,1,"{3312, 3296, 3306, 3305, 3351, 3304, 3352}"
51,1,130,0,0.2432247,"\int \frac{\cos ^2(a+b x)}{\sqrt{c+d x}} \, dx","Int[Cos[a + b*x]^2/Sqrt[c + d*x],x]","\frac{\sqrt{\pi } \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\pi } \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{c+d x}}{d}","\frac{\sqrt{\pi } \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\pi } \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{c+d x}}{d}",1,"Sqrt[c + d*x]/d + (Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(2*Sqrt[b]*Sqrt[d]) - (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(2*Sqrt[b]*Sqrt[d])","A",7,6,18,0.3333,1,"{3312, 3306, 3305, 3351, 3304, 3352}"
52,1,135,0,0.2577044,"\int \frac{\cos ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^(3/2),x]","-\frac{2 \sqrt{\pi } \sqrt{b} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{\pi } \sqrt{b} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{d^{3/2}}-\frac{2 \cos ^2(a+b x)}{d \sqrt{c+d x}}","-\frac{2 \sqrt{\pi } \sqrt{b} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sqrt{\pi } \sqrt{b} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{d^{3/2}}-\frac{2 \cos ^2(a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cos[a + b*x]^2)/(d*Sqrt[c + d*x]) - (2*Sqrt[b]*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/d^(3/2) - (2*Sqrt[b]*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/d^(3/2)","A",7,7,18,0.3889,1,"{3313, 12, 3306, 3305, 3351, 3304, 3352}"
53,1,170,0,0.3121774,"\int \frac{\cos ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^(5/2),x]","-\frac{8 \sqrt{\pi } b^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{3 d^{5/2}}+\frac{8 \sqrt{\pi } b^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{3 d^{5/2}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cos ^2(a+b x)}{3 d (c+d x)^{3/2}}","-\frac{8 \sqrt{\pi } b^{3/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{3 d^{5/2}}+\frac{8 \sqrt{\pi } b^{3/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{3 d^{5/2}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cos ^2(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cos[a + b*x]^2)/(3*d*(c + d*x)^(3/2)) - (8*b^(3/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(3*d^(5/2)) + (8*b^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(3*d^(5/2)) + (8*b*Cos[a + b*x]*Sin[a + b*x])/(3*d^2*Sqrt[c + d*x])","A",9,8,18,0.4444,1,"{3314, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
54,1,216,0,0.3244994,"\int \frac{\cos ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^(7/2),x]","\frac{32 \sqrt{\pi } b^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{15 d^{7/2}}+\frac{32 \sqrt{\pi } b^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{15 d^{7/2}}+\frac{32 b^2 \cos ^2(a+b x)}{15 d^3 \sqrt{c+d x}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cos ^2(a+b x)}{5 d (c+d x)^{5/2}}-\frac{16 b^2}{15 d^3 \sqrt{c+d x}}","\frac{32 \sqrt{\pi } b^{5/2} \sin \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{15 d^{7/2}}+\frac{32 \sqrt{\pi } b^{5/2} \cos \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{15 d^{7/2}}+\frac{32 b^2 \cos ^2(a+b x)}{15 d^3 \sqrt{c+d x}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cos ^2(a+b x)}{5 d (c+d x)^{5/2}}-\frac{16 b^2}{15 d^3 \sqrt{c+d x}}",1,"(-16*b^2)/(15*d^3*Sqrt[c + d*x]) - (2*Cos[a + b*x]^2)/(5*d*(c + d*x)^(5/2)) + (32*b^2*Cos[a + b*x]^2)/(15*d^3*Sqrt[c + d*x]) + (32*b^(5/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(15*d^(7/2)) + (32*b^(5/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(15*d^(7/2)) + (8*b*Cos[a + b*x]*Sin[a + b*x])/(15*d^2*(c + d*x)^(3/2))","A",9,9,18,0.5000,1,"{3314, 32, 3313, 12, 3306, 3305, 3351, 3304, 3352}"
55,1,247,0,0.4071354,"\int \frac{\cos ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Int[Cos[a + b*x]^2/(c + d*x)^(9/2),x]","\frac{128 \sqrt{\pi } b^{7/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{105 d^{9/2}}-\frac{128 \sqrt{\pi } b^{7/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{105 d^{9/2}}+\frac{32 b^2 \cos ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{128 b^3 \sin (a+b x) \cos (a+b x)}{105 d^4 \sqrt{c+d x}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \cos ^2(a+b x)}{7 d (c+d x)^{7/2}}-\frac{16 b^2}{105 d^3 (c+d x)^{3/2}}","\frac{128 \sqrt{\pi } b^{7/2} \cos \left(2 a-\frac{2 b c}{d}\right) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{\pi } \sqrt{d}}\right)}{105 d^{9/2}}-\frac{128 \sqrt{\pi } b^{7/2} \sin \left(2 a-\frac{2 b c}{d}\right) S\left(\frac{2 \sqrt{b} \sqrt{c+d x}}{\sqrt{d} \sqrt{\pi }}\right)}{105 d^{9/2}}+\frac{32 b^2 \cos ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{128 b^3 \sin (a+b x) \cos (a+b x)}{105 d^4 \sqrt{c+d x}}+\frac{8 b \sin (a+b x) \cos (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \cos ^2(a+b x)}{7 d (c+d x)^{7/2}}-\frac{16 b^2}{105 d^3 (c+d x)^{3/2}}",1,"(-16*b^2)/(105*d^3*(c + d*x)^(3/2)) - (2*Cos[a + b*x]^2)/(7*d*(c + d*x)^(7/2)) + (32*b^2*Cos[a + b*x]^2)/(105*d^3*(c + d*x)^(3/2)) + (128*b^(7/2)*Sqrt[Pi]*Cos[2*a - (2*b*c)/d]*FresnelC[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])])/(105*d^(9/2)) - (128*b^(7/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*Sqrt[c + d*x])/(Sqrt[d]*Sqrt[Pi])]*Sin[2*a - (2*b*c)/d])/(105*d^(9/2)) + (8*b*Cos[a + b*x]*Sin[a + b*x])/(35*d^2*(c + d*x)^(5/2)) - (128*b^3*Cos[a + b*x]*Sin[a + b*x])/(105*d^4*Sqrt[c + d*x])","A",11,8,18,0.4444,1,"{3314, 32, 3312, 3306, 3305, 3351, 3304, 3352}"
56,1,410,0,1.1390157,"\int (c+d x)^{5/2} \cos ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cos[a + b*x]^3,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{45 \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{45 \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{45 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 ^3(a+b x)}{18 b^2}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{3 b^2}+\frac{2 (c+d x)^{5/2} \sin (a+b x)}{3 b}+\frac{(c+d x)^{5/2} \sin (a+b x) \cos ^2(a+b x)}{3 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{45 \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{45 \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{45 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 ^3(a+b x)}{18 b^2}+\frac{5 d (c+d x)^{3/2} \cos (a+b x)}{3 b^2}+\frac{2 (c+d x)^{5/2} \sin (a+b x)}{3 b}+\frac{(c+d x)^{5/2} \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(5*d*(c + d*x)^(3/2)*Cos[a + b*x])/(3*b^2) + (5*d*(c + d*x)^(3/2)*Cos[a + b*x]^3)/(18*b^2) + (45*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)) + (45*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)) - (45*d^2*Sqrt[c + d*x]*Sin[a + b*x])/(16*b^3) + (2*(c + d*x)^(5/2)*Sin[a + b*x])/(3*b) + ((c + d*x)^(5/2)*Cos[a + b*x]^2*Sin[a + b*x])/(3*b) - (5*d^2*Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(144*b^3)","A",23,8,18,0.4444,1,"{3311, 3296, 3306, 3305, 3351, 3304, 3352, 3312}"
57,1,354,0,0.9906697,"\int (c+d x)^{3/2} \cos ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cos[a + b*x]^3,x]","-\frac{9 \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{9 \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{d \sqrt{c+d x} \cos ^3(a+b x)}{6 b^2}+\frac{d \sqrt{c+d x} \cos (a+b x)}{b^2}+\frac{2 (c+d x)^{3/2} \sin (a+b x)}{3 b}+\frac{(c+d x)^{3/2} \sin (a+b x) \cos ^2(a+b x)}{3 b}","-\frac{9 \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{9 \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{d \sqrt{c+d x} \cos ^3(a+b x)}{6 b^2}+\frac{d \sqrt{c+d x} \cos (a+b x)}{b^2}+\frac{2 (c+d x)^{3/2} \sin (a+b x)}{3 b}+\frac{(c+d x)^{3/2} \sin (a+b x) \cos ^2(a+b x)}{3 b}",1,"(d*Sqrt[c + d*x]*Cos[a + b*x])/b^2 + (d*Sqrt[c + d*x]*Cos[a + b*x]^3)/(6*b^2) - (9*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)) + (9*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)) + (2*(c + d*x)^(3/2)*Sin[a + b*x])/(3*b) + ((c + d*x)^(3/2)*Cos[a + b*x]^2*Sin[a + b*x])/(3*b)","A",20,8,18,0.4444,1,"{3311, 3296, 3306, 3305, 3351, 3304, 3352, 3312}"
58,1,304,0,0.4844693,"\int \sqrt{c+d x} \cos ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cos[a + b*x]^3,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{3 \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{3 \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{3 \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{3 \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{3 \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{3 \sqrt{c+d x} \sin (a+b x)}{4 b}+\frac{\sqrt{c+d x} \sin (3 a+3 b x)}{12 b}",1,"(-3*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)) - (3*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)) + (3*Sqrt[c + d*x]*Sin[a + b*x])/(4*b) + (Sqrt[c + d*x]*Sin[3*a + 3*b*x])/(12*b)","A",14,7,18,0.3889,1,"{3312, 3296, 3306, 3305, 3351, 3304, 3352}"
59,1,257,0,0.4174,"\int \frac{\cos ^3(a+b x)}{\sqrt{c+d x}} \, dx","Int[Cos[a + b*x]^3/Sqrt[c + d*x],x]","\frac{3 \sqrt{\frac{\pi }{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)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{6}} \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)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\frac{\pi }{6}} \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)}{2 \sqrt{b} \sqrt{d}}-\frac{3 \sqrt{\frac{\pi }{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)}{2 \sqrt{b} \sqrt{d}}","\frac{3 \sqrt{\frac{\pi }{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)}{2 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{6}} \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)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\frac{\pi }{6}} \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)}{2 \sqrt{b} \sqrt{d}}-\frac{3 \sqrt{\frac{\pi }{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)}{2 \sqrt{b} \sqrt{d}}",1,"(3*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d]) + (Sqrt[Pi/6]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d]) - (Sqrt[Pi/6]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(2*Sqrt[b]*Sqrt[d]) - (3*Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(2*Sqrt[b]*Sqrt[d])","A",12,6,18,0.3333,1,"{3312, 3306, 3305, 3351, 3304, 3352}"
60,1,271,0,0.5641461,"\int \frac{\cos ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cos[a + b*x]^3/(c + d*x)^(3/2),x]","-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cos ^3(a+b x)}{d \sqrt{c+d x}}","-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin \left(3 a-\frac{3 b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{6}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \sin \left(a-\frac{b c}{d}\right) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sqrt{b} \cos \left(a-\frac{b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{\sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos \left(3 a-\frac{3 b c}{d}\right) S\left(\frac{\sqrt{b} \sqrt{\frac{6}{\pi }} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cos ^3(a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cos[a + b*x]^3)/(d*Sqrt[c + d*x]) - (3*Sqrt[b]*Sqrt[Pi/2]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (Sqrt[b]*Sqrt[(3*Pi)/2]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (Sqrt[b]*Sqrt[(3*Pi)/2]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/d^(3/2) - (3*Sqrt[b]*Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(3/2)","A",12,6,18,0.3333,1,"{3313, 3306, 3305, 3351, 3304, 3352}"
61,1,292,0,0.7376455,"\int \frac{\cos ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cos[a + b*x]^3/(c + d*x)^(5/2),x]","-\frac{\sqrt{2 \pi } b^{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)}{d^{5/2}}-\frac{\sqrt{6 \pi } b^{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)}{d^{5/2}}+\frac{\sqrt{6 \pi } b^{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)}{d^{5/2}}+\frac{\sqrt{2 \pi } b^{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)}{d^{5/2}}+\frac{4 b \sin (a+b x) \cos ^2(a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \cos ^3(a+b x)}{3 d (c+d x)^{3/2}}","-\frac{\sqrt{2 \pi } b^{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)}{d^{5/2}}-\frac{\sqrt{6 \pi } b^{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)}{d^{5/2}}+\frac{\sqrt{6 \pi } b^{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)}{d^{5/2}}+\frac{\sqrt{2 \pi } b^{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)}{d^{5/2}}+\frac{4 b \sin (a+b x) \cos ^2(a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \cos ^3(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cos[a + b*x]^3)/(3*d*(c + d*x)^(3/2)) - (b^(3/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(5/2) - (b^(3/2)*Sqrt[6*Pi]*Cos[3*a - (3*b*c)/d]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/d^(5/2) + (b^(3/2)*Sqrt[6*Pi]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/d^(5/2) + (b^(3/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/d^(5/2) + (4*b*Cos[a + b*x]^2*Sin[a + b*x])/(d^2*Sqrt[c + d*x])","A",18,7,18,0.3889,1,"{3314, 3306, 3305, 3351, 3304, 3352, 3312}"
62,1,356,0,0.8314033,"\int \frac{\cos ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cos[a + b*x]^3/(c + d*x)^(7/2),x]","\frac{6 \sqrt{6 \pi } b^{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)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{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)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{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)}{5 d^{7/2}}+\frac{6 \sqrt{6 \pi } b^{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)}{5 d^{7/2}}+\frac{24 b^2 \cos ^3(a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{16 b^2 \cos (a+b x)}{5 d^3 \sqrt{c+d x}}+\frac{4 b \sin (a+b x) \cos ^2(a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \cos ^3(a+b x)}{5 d (c+d x)^{5/2}}","\frac{6 \sqrt{6 \pi } b^{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)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{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)}{5 d^{7/2}}+\frac{2 \sqrt{2 \pi } b^{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)}{5 d^{7/2}}+\frac{6 \sqrt{6 \pi } b^{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)}{5 d^{7/2}}+\frac{24 b^2 \cos ^3(a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{16 b^2 \cos (a+b x)}{5 d^3 \sqrt{c+d x}}+\frac{4 b \sin (a+b x) \cos ^2(a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \cos ^3(a+b x)}{5 d (c+d x)^{5/2}}",1,"(-16*b^2*Cos[a + b*x])/(5*d^3*Sqrt[c + d*x]) - (2*Cos[a + b*x]^3)/(5*d*(c + d*x)^(5/2)) + (24*b^2*Cos[a + b*x]^3)/(5*d^3*Sqrt[c + d*x]) + (2*b^(5/2)*Sqrt[2*Pi]*Cos[a - (b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) + (6*b^(5/2)*Sqrt[6*Pi]*Cos[3*a - (3*b*c)/d]*FresnelS[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) + (6*b^(5/2)*Sqrt[6*Pi]*FresnelC[(Sqrt[b]*Sqrt[6/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[3*a - (3*b*c)/d])/(5*d^(7/2)) + (2*b^(5/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi]*Sqrt[c + d*x])/Sqrt[d]]*Sin[a - (b*c)/d])/(5*d^(7/2)) + (4*b*Cos[a + b*x]^2*Sin[a + b*x])/(5*d^2*(c + d*x)^(3/2))","A",19,8,18,0.4444,1,"{3314, 3297, 3306, 3305, 3351, 3304, 3352, 3313}"
63,1,49,0,0.0572119,"\int x^{3/2} \cos (x) \, dx","Int[x^(3/2)*Cos[x],x]","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)+x^{3/2} \sin (x)+\frac{3}{2} \sqrt{x} \cos (x)","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)+x^{3/2} \sin (x)+\frac{3}{2} \sqrt{x} \cos (x)",1,"(3*Sqrt[x]*Cos[x])/2 - (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*Sqrt[x]])/2 + x^(3/2)*Sin[x]","A",4,3,8,0.3750,1,"{3296, 3304, 3352}"
64,1,36,0,0.034927,"\int \sqrt{x} \cos (x) \, dx","Int[Sqrt[x]*Cos[x],x]","\sqrt{x} \sin (x)-\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)","\sqrt{x} \sin (x)-\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)",1,"-(Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]) + Sqrt[x]*Sin[x]","A",3,3,8,0.3750,1,"{3296, 3305, 3351}"
65,1,24,0,0.019832,"\int \frac{\cos (x)}{\sqrt{x}} \, dx","Int[Cos[x]/Sqrt[x],x]","\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)","\sqrt{2 \pi } \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)",1,"Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*Sqrt[x]]","A",2,2,8,0.2500,1,"{3304, 3352}"
66,1,35,0,0.0366712,"\int \frac{\cos (x)}{x^{3/2}} \, dx","Int[Cos[x]/x^(3/2),x]","-2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)-\frac{2 \cos (x)}{\sqrt{x}}","-2 \sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} \sqrt{x}\right)-\frac{2 \cos (x)}{\sqrt{x}}",1,"(-2*Cos[x])/Sqrt[x] - 2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]","A",3,3,8,0.3750,1,"{3297, 3305, 3351}"
67,1,183,0,0.2403998,"\int (c+d x)^{4/3} \cos (a+b x) \, dx","Int[(c + d*x)^(4/3)*Cos[a + b*x],x]","\frac{2 i d^2 e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{9 b^3 (c+d x)^{2/3}}-\frac{2 i d^2 e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{9 b^3 (c+d x)^{2/3}}+\frac{4 d \sqrt[3]{c+d x} \cos (a+b x)}{3 b^2}+\frac{(c+d x)^{4/3} \sin (a+b x)}{b}","\frac{2 i d^2 e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{9 b^3 (c+d x)^{2/3}}-\frac{2 i d^2 e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{9 b^3 (c+d x)^{2/3}}+\frac{4 d \sqrt[3]{c+d x} \cos (a+b x)}{3 b^2}+\frac{(c+d x)^{4/3} \sin (a+b x)}{b}",1,"(4*d*(c + d*x)^(1/3)*Cos[a + b*x])/(3*b^2) + (((2*I)/9)*d^2*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(2/3)*Gamma[1/3, ((-I)*b*(c + d*x))/d])/(b^3*(c + d*x)^(2/3)) - (((2*I)/9)*d^2*((I*b*(c + d*x))/d)^(2/3)*Gamma[1/3, (I*b*(c + d*x))/d])/(b^3*E^(I*(a - (b*c)/d))*(c + d*x)^(2/3)) + ((c + d*x)^(4/3)*Sin[a + b*x])/b","A",5,3,16,0.1875,1,"{3296, 3307, 2181}"
68,1,152,0,0.1489578,"\int (c+d x)^{2/3} \cos (a+b x) \, dx","Int[(c + d*x)^(2/3)*Cos[a + b*x],x]","\frac{d e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{3 b^2 \sqrt[3]{c+d x}}+\frac{d e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{3 b^2 \sqrt[3]{c+d x}}+\frac{(c+d x)^{2/3} \sin (a+b x)}{b}","\frac{d e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{3 b^2 \sqrt[3]{c+d x}}+\frac{d e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{3 b^2 \sqrt[3]{c+d x}}+\frac{(c+d x)^{2/3} \sin (a+b x)}{b}",1,"(d*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(1/3)*Gamma[2/3, ((-I)*b*(c + d*x))/d])/(3*b^2*(c + d*x)^(1/3)) + (d*((I*b*(c + d*x))/d)^(1/3)*Gamma[2/3, (I*b*(c + d*x))/d])/(3*b^2*E^(I*(a - (b*c)/d))*(c + d*x)^(1/3)) + ((c + d*x)^(2/3)*Sin[a + b*x])/b","A",4,3,16,0.1875,1,"{3296, 3308, 2181}"
69,1,152,0,0.1617463,"\int \sqrt[3]{c+d x} \cos (a+b x) \, dx","Int[(c + d*x)^(1/3)*Cos[a + b*x],x]","\frac{d e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{6 b^2 (c+d x)^{2/3}}+\frac{d e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{6 b^2 (c+d x)^{2/3}}+\frac{\sqrt[3]{c+d x} \sin (a+b x)}{b}","\frac{d e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{6 b^2 (c+d x)^{2/3}}+\frac{d e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{6 b^2 (c+d x)^{2/3}}+\frac{\sqrt[3]{c+d x} \sin (a+b x)}{b}",1,"(d*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(2/3)*Gamma[1/3, ((-I)*b*(c + d*x))/d])/(6*b^2*(c + d*x)^(2/3)) + (d*((I*b*(c + d*x))/d)^(2/3)*Gamma[1/3, (I*b*(c + d*x))/d])/(6*b^2*E^(I*(a - (b*c)/d))*(c + d*x)^(2/3)) + ((c + d*x)^(1/3)*Sin[a + b*x])/b","A",4,3,16,0.1875,1,"{3296, 3308, 2181}"
70,1,135,0,0.1162293,"\int \frac{\cos (a+b x)}{\sqrt[3]{c+d x}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(1/3),x]","\frac{i e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{2 b \sqrt[3]{c+d x}}-\frac{i e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{2 b \sqrt[3]{c+d x}}","\frac{i e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{2 b \sqrt[3]{c+d x}}-\frac{i e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{2 b \sqrt[3]{c+d x}}",1,"((-I/2)*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(1/3)*Gamma[2/3, ((-I)*b*(c + d*x))/d])/(b*(c + d*x)^(1/3)) + ((I/2)*((I*b*(c + d*x))/d)^(1/3)*Gamma[2/3, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*(c + d*x)^(1/3))","A",3,2,16,0.1250,1,"{3307, 2181}"
71,1,135,0,0.1195841,"\int \frac{\cos (a+b x)}{(c+d x)^{2/3}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(2/3),x]","\frac{i e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{2 b (c+d x)^{2/3}}-\frac{i e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{2 b (c+d x)^{2/3}}","\frac{i e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{2 b (c+d x)^{2/3}}-\frac{i e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{2 b (c+d x)^{2/3}}",1,"((-I/2)*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(2/3)*Gamma[1/3, ((-I)*b*(c + d*x))/d])/(b*(c + d*x)^(2/3)) + ((I/2)*((I*b*(c + d*x))/d)^(2/3)*Gamma[1/3, (I*b*(c + d*x))/d])/(b*E^(I*(a - (b*c)/d))*(c + d*x)^(2/3))","A",3,2,16,0.1250,1,"{3307, 2181}"
72,1,151,0,0.1462387,"\int \frac{\cos (a+b x)}{(c+d x)^{4/3}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(4/3),x]","\frac{3 e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{2 d \sqrt[3]{c+d x}}+\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{2 d \sqrt[3]{c+d x}}-\frac{3 \cos (a+b x)}{d \sqrt[3]{c+d x}}","\frac{3 e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{2 d \sqrt[3]{c+d x}}+\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{2 d \sqrt[3]{c+d x}}-\frac{3 \cos (a+b x)}{d \sqrt[3]{c+d x}}",1,"(-3*Cos[a + b*x])/(d*(c + d*x)^(1/3)) + (3*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(1/3)*Gamma[2/3, ((-I)*b*(c + d*x))/d])/(2*d*(c + d*x)^(1/3)) + (3*((I*b*(c + d*x))/d)^(1/3)*Gamma[2/3, (I*b*(c + d*x))/d])/(2*d*E^(I*(a - (b*c)/d))*(c + d*x)^(1/3))","A",4,3,16,0.1875,1,"{3297, 3308, 2181}"
73,1,153,0,0.1546808,"\int \frac{\cos (a+b x)}{(c+d x)^{5/3}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(5/3),x]","\frac{3 e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{4 d (c+d x)^{2/3}}+\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{4 d (c+d x)^{2/3}}-\frac{3 \cos (a+b x)}{2 d (c+d x)^{2/3}}","\frac{3 e^{i \left(a-\frac{b c}{d}\right)} \left(-\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},-\frac{i b (c+d x)}{d}\right)}{4 d (c+d x)^{2/3}}+\frac{3 e^{-i \left(a-\frac{b c}{d}\right)} \left(\frac{i b (c+d x)}{d}\right)^{2/3} \text{Gamma}\left(\frac{1}{3},\frac{i b (c+d x)}{d}\right)}{4 d (c+d x)^{2/3}}-\frac{3 \cos (a+b x)}{2 d (c+d x)^{2/3}}",1,"(-3*Cos[a + b*x])/(2*d*(c + d*x)^(2/3)) + (3*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(2/3)*Gamma[1/3, ((-I)*b*(c + d*x))/d])/(4*d*(c + d*x)^(2/3)) + (3*((I*b*(c + d*x))/d)^(2/3)*Gamma[1/3, (I*b*(c + d*x))/d])/(4*d*E^(I*(a - (b*c)/d))*(c + d*x)^(2/3))","A",4,3,16,0.1875,1,"{3297, 3308, 2181}"
74,1,182,0,0.2040468,"\int \frac{\cos (a+b x)}{(c+d x)^{7/3}} \, dx","Int[Cos[a + b*x]/(c + d*x)^(7/3),x]","\frac{9 i b e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{8 d^2 \sqrt[3]{c+d x}}-\frac{9 i b e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{8 d^2 \sqrt[3]{c+d x}}+\frac{9 b \sin (a+b x)}{4 d^2 \sqrt[3]{c+d x}}-\frac{3 \cos (a+b x)}{4 d (c+d x)^{4/3}}","\frac{9 i b e^{i \left(a-\frac{b c}{d}\right)} \sqrt[3]{-\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},-\frac{i b (c+d x)}{d}\right)}{8 d^2 \sqrt[3]{c+d x}}-\frac{9 i b e^{-i \left(a-\frac{b c}{d}\right)} \sqrt[3]{\frac{i b (c+d x)}{d}} \text{Gamma}\left(\frac{2}{3},\frac{i b (c+d x)}{d}\right)}{8 d^2 \sqrt[3]{c+d x}}+\frac{9 b \sin (a+b x)}{4 d^2 \sqrt[3]{c+d x}}-\frac{3 \cos (a+b x)}{4 d (c+d x)^{4/3}}",1,"(-3*Cos[a + b*x])/(4*d*(c + d*x)^(4/3)) + (((9*I)/8)*b*E^(I*(a - (b*c)/d))*(((-I)*b*(c + d*x))/d)^(1/3)*Gamma[2/3, ((-I)*b*(c + d*x))/d])/(d^2*(c + d*x)^(1/3)) - (((9*I)/8)*b*((I*b*(c + d*x))/d)^(1/3)*Gamma[2/3, (I*b*(c + d*x))/d])/(d^2*E^(I*(a - (b*c)/d))*(c + d*x)^(1/3)) + (9*b*Sin[a + b*x])/(4*d^2*(c + d*x)^(1/3))","A",5,3,16,0.1875,1,"{3297, 3307, 2181}"
75,0,0,0,0.0173204,"\int x \sqrt{\cos (a+b x)} \, dx","Int[x*Sqrt[Cos[a + b*x]],x]","\int x \sqrt{\cos (a+b x)} \, dx","\text{Int}\left(x \sqrt{\cos (a+b x)},x\right)",0,"Defer[Int][x*Sqrt[Cos[a + b*x]], x]","A",0,0,0,0,-1,"{}"
76,1,16,0,0.008924,"\int \sqrt{\cos (a+b x)} \, dx","Int[Sqrt[Cos[a + b*x]],x]","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*EllipticE[(a + b*x)/2, 2])/b","A",1,1,10,0.1000,1,"{2639}"
77,0,0,0,0.0288276,"\int \frac{\sqrt{\cos (a+b x)}}{x} \, dx","Int[Sqrt[Cos[a + b*x]]/x,x]","\int \frac{\sqrt{\cos (a+b x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt{\cos (a+b x)}}{x},x\right)",0,"Defer[Int][Sqrt[Cos[a + b*x]]/x, x]","A",0,0,0,0,-1,"{}"
78,0,0,0,0.0377989,"\int x \cos ^{\frac{3}{2}}(a+b x) \, dx","Int[x*Cos[a + b*x]^(3/2),x]","\int x \cos ^{\frac{3}{2}}(a+b x) \, dx","\frac{1}{3} \text{Int}\left(\frac{x}{\sqrt{\cos (a+b x)}},x\right)+\frac{4 \cos ^{\frac{3}{2}}(a+b x)}{9 b^2}+\frac{2 x \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}",0,"(4*Cos[a + b*x]^(3/2))/(9*b^2) + (2*x*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(3*b) + Defer[Int][x/Sqrt[Cos[a + b*x]], x]/3","A",0,0,0,0,-1,"{}"
79,1,42,0,0.0203448,"\int \cos ^{\frac{3}{2}}(a+b x) \, dx","Int[Cos[a + b*x]^(3/2),x]","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}+\frac{2 \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{3 b}+\frac{2 \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}",1,"(2*EllipticF[(a + b*x)/2, 2])/(3*b) + (2*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(3*b)","A",2,2,10,0.2000,1,"{2635, 2641}"
80,0,0,0,0.0279345,"\int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx","Int[Cos[a + b*x]^(3/2)/x,x]","\int \frac{\cos ^{\frac{3}{2}}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\cos ^{\frac{3}{2}}(a+b x)}{x},x\right)",0,"Defer[Int][Cos[a + b*x]^(3/2)/x, x]","A",0,0,0,0,-1,"{}"
81,1,42,0,0.0586445,"\int \left(-\frac{x}{3 \sqrt{\cos (a+b x)}}+x \cos ^{\frac{3}{2}}(a+b x)\right) \, dx","Int[-x/(3*Sqrt[Cos[a + b*x]]) + x*Cos[a + b*x]^(3/2),x]","\frac{4 \cos ^{\frac{3}{2}}(a+b x)}{9 b^2}+\frac{2 x \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}","\frac{4 \cos ^{\frac{3}{2}}(a+b x)}{9 b^2}+\frac{2 x \sin (a+b x) \sqrt{\cos (a+b x)}}{3 b}",1,"(4*Cos[a + b*x]^(3/2))/(9*b^2) + (2*x*Sqrt[Cos[a + b*x]]*Sin[a + b*x])/(3*b)","A",2,1,28,0.03571,1,"{3310}"
82,0,0,0,0.0768357,"\int \frac{\cos ^{\frac{3}{2}}(x)}{x^3} \, dx","Int[Cos[x]^(3/2)/x^3,x]","\int \frac{\cos ^{\frac{3}{2}}(x)}{x^3} \, dx","-\frac{9}{8} \text{Int}\left(\frac{\cos ^{\frac{3}{2}}(x)}{x},x\right)+\frac{3}{8} \text{Int}\left(\frac{1}{x \sqrt{\cos (x)}},x\right)-\frac{\cos ^{\frac{3}{2}}(x)}{2 x^2}+\frac{3 \sin (x) \sqrt{\cos (x)}}{4 x}",0,"-Cos[x]^(3/2)/(2*x^2) + (3*Sqrt[Cos[x]]*Sin[x])/(4*x) + (3*Defer[Int][1/(x*Sqrt[Cos[x]]), x])/8 - (9*Defer[Int][Cos[x]^(3/2)/x, x])/8","A",0,0,0,0,-1,"{}"
83,0,0,0,0.0165909,"\int \frac{x}{\sqrt{\cos (a+b x)}} \, dx","Int[x/Sqrt[Cos[a + b*x]],x]","\int \frac{x}{\sqrt{\cos (a+b x)}} \, dx","\text{Int}\left(\frac{x}{\sqrt{\cos (a+b x)}},x\right)",0,"Defer[Int][x/Sqrt[Cos[a + b*x]], x]","A",0,0,0,0,-1,"{}"
84,1,16,0,0.0091666,"\int \frac{1}{\sqrt{\cos (a+b x)}} \, dx","Int[1/Sqrt[Cos[a + b*x]],x]","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 F\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(2*EllipticF[(a + b*x)/2, 2])/b","A",1,1,10,0.1000,1,"{2641}"
85,0,0,0,0.0284183,"\int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx","Int[1/(x*Sqrt[Cos[a + b*x]]),x]","\int \frac{1}{x \sqrt{\cos (a+b x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{\cos (a+b x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[Cos[a + b*x]]), x]","A",0,0,0,0,-1,"{}"
86,0,0,0,0.0363469,"\int \frac{x}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","Int[x/Cos[a + b*x]^(3/2),x]","\int \frac{x}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","-\text{Int}\left(x \sqrt{\cos (a+b x)},x\right)+\frac{4 \sqrt{\cos (a+b x)}}{b^2}+\frac{2 x \sin (a+b x)}{b \sqrt{\cos (a+b x)}}",0,"(4*Sqrt[Cos[a + b*x]])/b^2 + (2*x*Sin[a + b*x])/(b*Sqrt[Cos[a + b*x]]) - Defer[Int][x*Sqrt[Cos[a + b*x]], x]","A",0,0,0,0,-1,"{}"
87,1,38,0,0.0170415,"\int \frac{1}{\cos ^{\frac{3}{2}}(a+b x)} \, dx","Int[Cos[a + b*x]^(-3/2),x]","\frac{2 \sin (a+b x)}{b \sqrt{\cos (a+b x)}}-\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}","\frac{2 \sin (a+b x)}{b \sqrt{\cos (a+b x)}}-\frac{2 E\left(\left.\frac{1}{2} (a+b x)\right|2\right)}{b}",1,"(-2*EllipticE[(a + b*x)/2, 2])/b + (2*Sin[a + b*x])/(b*Sqrt[Cos[a + b*x]])","A",2,2,10,0.2000,1,"{2636, 2639}"
88,0,0,0,0.0275547,"\int \frac{1}{x \cos ^{\frac{3}{2}}(a+b x)} \, dx","Int[1/(x*Cos[a + b*x]^(3/2)),x]","\int \frac{1}{x \cos ^{\frac{3}{2}}(a+b x)} \, dx","\text{Int}\left(\frac{1}{x \cos ^{\frac{3}{2}}(a+b x)},x\right)",0,"Defer[Int][1/(x*Cos[a + b*x]^(3/2)), x]","A",0,0,0,0,-1,"{}"
89,1,38,0,0.055347,"\int \left(\frac{x}{\cos ^{\frac{3}{2}}(a+b x)}+x \sqrt{\cos (a+b x)}\right) \, dx","Int[x/Cos[a + b*x]^(3/2) + x*Sqrt[Cos[a + b*x]],x]","\frac{4 \sqrt{\cos (a+b x)}}{b^2}+\frac{2 x \sin (a+b x)}{b \sqrt{\cos (a+b x)}}","\frac{4 \sqrt{\cos (a+b x)}}{b^2}+\frac{2 x \sin (a+b x)}{b \sqrt{\cos (a+b x)}}",1,"(4*Sqrt[Cos[a + b*x]])/b^2 + (2*x*Sin[a + b*x])/(b*Sqrt[Cos[a + b*x]])","A",2,1,25,0.04000,1,"{3315}"
90,1,20,0,0.042698,"\int \left(\frac{x}{\cos ^{\frac{3}{2}}(x)}+x \sqrt{\cos (x)}\right) \, dx","Int[x/Cos[x]^(3/2) + x*Sqrt[Cos[x]],x]","4 \sqrt{\cos (x)}+\frac{2 x \sin (x)}{\sqrt{\cos (x)}}","4 \sqrt{\cos (x)}+\frac{2 x \sin (x)}{\sqrt{\cos (x)}}",1,"4*Sqrt[Cos[x]] + (2*x*Sin[x])/Sqrt[Cos[x]]","A",2,1,17,0.05882,1,"{3315}"
91,1,24,0,0.0459401,"\int \left(\frac{x}{\cos ^{\frac{5}{2}}(x)}-\frac{x}{3 \sqrt{\cos (x)}}\right) \, dx","Int[x/Cos[x]^(5/2) - x/(3*Sqrt[Cos[x]]),x]","\frac{2 x \sin (x)}{3 \cos ^{\frac{3}{2}}(x)}-\frac{4}{3 \sqrt{\cos (x)}}","\frac{2 x \sin (x)}{3 \cos ^{\frac{3}{2}}(x)}-\frac{4}{3 \sqrt{\cos (x)}}",1,"-4/(3*Sqrt[Cos[x]]) + (2*x*Sin[x])/(3*Cos[x]^(3/2))","A",2,1,20,0.05000,1,"{3315}"
92,1,47,0,0.0610706,"\int \left(\frac{x}{\cos ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\cos (x)}\right) \, dx","Int[x/Cos[x]^(7/2) + (3*x*Sqrt[Cos[x]])/5,x]","-\frac{4}{15 \cos ^{\frac{3}{2}}(x)}+\frac{12 \sqrt{\cos (x)}}{5}+\frac{2 x \sin (x)}{5 \cos ^{\frac{5}{2}}(x)}+\frac{6 x \sin (x)}{5 \sqrt{\cos (x)}}","-\frac{4}{15 \cos ^{\frac{3}{2}}(x)}+\frac{12 \sqrt{\cos (x)}}{5}+\frac{2 x \sin (x)}{5 \cos ^{\frac{5}{2}}(x)}+\frac{6 x \sin (x)}{5 \sqrt{\cos (x)}}",1,"-4/(15*Cos[x]^(3/2)) + (12*Sqrt[Cos[x]])/5 + (2*x*Sin[x])/(5*Cos[x]^(5/2)) + (6*x*Sin[x])/(5*Sqrt[Cos[x]])","A",3,1,20,0.05000,1,"{3315}"
93,1,32,0,0.0859179,"\int \left(\frac{x^2}{\cos ^{\frac{3}{2}}(x)}+x^2 \sqrt{\cos (x)}\right) \, dx","Int[x^2/Cos[x]^(3/2) + x^2*Sqrt[Cos[x]],x]","\frac{2 x^2 \sin (x)}{\sqrt{\cos (x)}}+8 x \sqrt{\cos (x)}-16 E\left(\left.\frac{x}{2}\right|2\right)","\frac{2 x^2 \sin (x)}{\sqrt{\cos (x)}}+8 x \sqrt{\cos (x)}-16 E\left(\left.\frac{x}{2}\right|2\right)",1,"8*x*Sqrt[Cos[x]] - 16*EllipticE[x/2, 2] + (2*x^2*Sin[x])/Sqrt[Cos[x]]","A",3,2,21,0.09524,1,"{3316, 2639}"
94,1,24,0,0.0814213,"\int \left(\frac{x}{\sec ^{\frac{3}{2}}(x)}-\frac{1}{3} x \sqrt{\sec (x)}\right) \, dx","Int[x/Sec[x]^(3/2) - (x*Sqrt[Sec[x]])/3,x]","\frac{4}{9 \sec ^{\frac{3}{2}}(x)}+\frac{2 x \sin (x)}{3 \sqrt{\sec (x)}}","\frac{4}{9 \sec ^{\frac{3}{2}}(x)}+\frac{2 x \sin (x)}{3 \sqrt{\sec (x)}}",1,"4/(9*Sec[x]^(3/2)) + (2*x*Sin[x])/(3*Sqrt[Sec[x]])","A",4,2,20,0.1000,1,"{4187, 4189}"
95,1,24,0,0.0791018,"\int \left(\frac{x}{\sec ^{\frac{5}{2}}(x)}-\frac{3 x}{5 \sqrt{\sec (x)}}\right) \, dx","Int[x/Sec[x]^(5/2) - (3*x)/(5*Sqrt[Sec[x]]),x]","\frac{4}{25 \sec ^{\frac{5}{2}}(x)}+\frac{2 x \sin (x)}{5 \sec ^{\frac{3}{2}}(x)}","\frac{4}{25 \sec ^{\frac{5}{2}}(x)}+\frac{2 x \sin (x)}{5 \sec ^{\frac{3}{2}}(x)}",1,"4/(25*Sec[x]^(5/2)) + (2*x*Sin[x])/(5*Sec[x]^(3/2))","A",4,2,20,0.1000,1,"{4187, 4189}"
96,1,47,0,0.0943382,"\int \left(\frac{x}{\sec ^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\sec (x)}\right) \, dx","Int[x/Sec[x]^(7/2) - (5*x*Sqrt[Sec[x]])/21,x]","\frac{20}{63 \sec ^{\frac{3}{2}}(x)}+\frac{4}{49 \sec ^{\frac{7}{2}}(x)}+\frac{2 x \sin (x)}{7 \sec ^{\frac{5}{2}}(x)}+\frac{10 x \sin (x)}{21 \sqrt{\sec (x)}}","\frac{20}{63 \sec ^{\frac{3}{2}}(x)}+\frac{4}{49 \sec ^{\frac{7}{2}}(x)}+\frac{2 x \sin (x)}{7 \sec ^{\frac{5}{2}}(x)}+\frac{10 x \sin (x)}{21 \sqrt{\sec (x)}}",1,"4/(49*Sec[x]^(7/2)) + 20/(63*Sec[x]^(3/2)) + (2*x*Sin[x])/(7*Sec[x]^(5/2)) + (10*x*Sin[x])/(21*Sqrt[Sec[x]])","A",5,2,20,0.1000,1,"{4187, 4189}"
97,1,62,0,0.1536356,"\int \left(\frac{x^2}{\sec ^{\frac{3}{2}}(x)}-\frac{1}{3} x^2 \sqrt{\sec (x)}\right) \, dx","Int[x^2/Sec[x]^(3/2) - (x^2*Sqrt[Sec[x]])/3,x]","\frac{2 x^2 \sin (x)}{3 \sqrt{\sec (x)}}+\frac{8 x}{9 \sec ^{\frac{3}{2}}(x)}-\frac{16 \sin (x)}{27 \sqrt{\sec (x)}}-\frac{16}{27} \sqrt{\cos (x)} \sqrt{\sec (x)} F\left(\left.\frac{x}{2}\right|2\right)","\frac{2 x^2 \sin (x)}{3 \sqrt{\sec (x)}}+\frac{8 x}{9 \sec ^{\frac{3}{2}}(x)}-\frac{16 \sin (x)}{27 \sqrt{\sec (x)}}-\frac{16}{27} \sqrt{\cos (x)} \sqrt{\sec (x)} F\left(\left.\frac{x}{2}\right|2\right)",1,"(8*x)/(9*Sec[x]^(3/2)) - (16*Sqrt[Cos[x]]*EllipticF[x/2, 2]*Sqrt[Sec[x]])/27 - (16*Sin[x])/(27*Sqrt[Sec[x]]) + (2*x^2*Sin[x])/(3*Sqrt[Sec[x]])","A",7,5,24,0.2083,1,"{4188, 4189, 3769, 3771, 2641}"
98,0,0,0,0.041328,"\int (c+d x)^m (b \cos (e+f x))^n \, dx","Int[(c + d*x)^m*(b*Cos[e + f*x])^n,x]","\int (c+d x)^m (b \cos (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (b \cos (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(b*Cos[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
99,1,275,0,0.3040029,"\int (c+d x)^m \cos ^3(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^3,x]","-\frac{3 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{3 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{3 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{3 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,"(((-3*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) + (((3*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",8,3,16,0.1875,1,"{3312, 3307, 2181}"
100,1,162,0,0.2133585,"\int (c+d x)^m \cos ^2(a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x]^2,x]","-\frac{i 2^{-m-3} e^{2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{i 2^{-m-3} e^{-2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{2 d (m+1)}","-\frac{i 2^{-m-3} e^{2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{i 2^{-m-3} e^{-2 i \left(a-\frac{b c}{d}\right)} (c+d x)^m \left(\frac{i b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{2 i b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{2 d (m+1)}",1,"(c + d*x)^(1 + m)/(2*d*(1 + m)) - (I*2^(-3 - m)*E^((2*I)*(a - (b*c)/d))*(c + d*x)^m*Gamma[1 + m, ((-2*I)*b*(c + d*x))/d])/(b*(((-I)*b*(c + d*x))/d)^m) + (I*2^(-3 - m)*(c + d*x)^m*Gamma[1 + m, ((2*I)*b*(c + d*x))/d])/(b*E^((2*I)*(a - (b*c)/d))*((I*b*(c + d*x))/d)^m)","A",5,3,16,0.1875,1,"{3312, 3307, 2181}"
101,1,131,0,0.0973537,"\int (c+d x)^m \cos (a+b x) \, dx","Int[(c + d*x)^m*Cos[a + b*x],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)}{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}","\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}",1,"((-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)","A",3,2,14,0.1429,1,"{3307, 2181}"
102,0,0,0,0.0188455,"\int (c+d x)^m \sec (a+b x) \, dx","Int[(c + d*x)^m*Sec[a + b*x],x]","\int (c+d x)^m \sec (a+b x) \, dx","\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]","A",0,0,0,0,-1,"{}"
103,0,0,0,0.0354351,"\int (c+d x)^m \sec ^2(a+b x) \, dx","Int[(c + d*x)^m*Sec[a + b*x]^2,x]","\int (c+d x)^m \sec ^2(a+b x) \, dx","\text{Int}\left(\sec ^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Sec[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
104,1,75,0,0.0797813,"\int x^{3+m} \cos (a+b x) \, dx","Int[x^(3 + m)*Cos[a + b*x],x]","-\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+4,-i b x)}{2 b^4}-\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+4,i b x)}{2 b^4}","-\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+4,-i b x)}{2 b^4}-\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+4,i b x)}{2 b^4}",1,"-(E^(I*a)*x^m*Gamma[4 + m, (-I)*b*x])/(2*b^4*((-I)*b*x)^m) - (x^m*Gamma[4 + m, I*b*x])/(2*b^4*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
105,1,79,0,0.0770637,"\int x^{2+m} \cos (a+b x) \, dx","Int[x^(2 + m)*Cos[a + b*x],x]","\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+3,-i b x)}{2 b^3}-\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+3,i b x)}{2 b^3}","\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+3,-i b x)}{2 b^3}-\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+3,i b x)}{2 b^3}",1,"((I/2)*E^(I*a)*x^m*Gamma[3 + m, (-I)*b*x])/(b^3*((-I)*b*x)^m) - ((I/2)*x^m*Gamma[3 + m, I*b*x])/(b^3*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
106,1,75,0,0.0766376,"\int x^{1+m} \cos (a+b x) \, dx","Int[x^(1 + m)*Cos[a + b*x],x]","\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+2,-i b x)}{2 b^2}+\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+2,i b x)}{2 b^2}","\frac{e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+2,-i b x)}{2 b^2}+\frac{e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+2,i b x)}{2 b^2}",1,"(E^(I*a)*x^m*Gamma[2 + m, (-I)*b*x])/(2*b^2*((-I)*b*x)^m) + (x^m*Gamma[2 + m, I*b*x])/(2*b^2*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
107,1,79,0,0.0713828,"\int x^m \cos (a+b x) \, dx","Int[x^m*Cos[a + b*x],x]","\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+1,i b x)}{2 b}-\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+1,-i b x)}{2 b}","\frac{i e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m+1,i b x)}{2 b}-\frac{i e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m+1,-i b x)}{2 b}",1,"((-I/2)*E^(I*a)*x^m*Gamma[1 + m, (-I)*b*x])/(b*((-I)*b*x)^m) + ((I/2)*x^m*Gamma[1 + m, I*b*x])/(b*E^(I*a)*(I*b*x)^m)","A",3,2,10,0.2000,1,"{3307, 2181}"
108,1,65,0,0.0731398,"\int x^{-1+m} \cos (a+b x) \, dx","Int[x^(-1 + m)*Cos[a + b*x],x]","-\frac{1}{2} e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m,-i b x)-\frac{1}{2} e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m,i b x)","-\frac{1}{2} e^{i a} x^m (-i b x)^{-m} \text{Gamma}(m,-i b x)-\frac{1}{2} e^{-i a} x^m (i b x)^{-m} \text{Gamma}(m,i b x)",1,"-(E^(I*a)*x^m*Gamma[m, (-I)*b*x])/(2*((-I)*b*x)^m) - (x^m*Gamma[m, I*b*x])/(2*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
109,1,75,0,0.0742731,"\int x^{-2+m} \cos (a+b x) \, dx","Int[x^(-2 + m)*Cos[a + b*x],x]","\frac{1}{2} i e^{i a} b x^m (-i b x)^{-m} \text{Gamma}(m-1,-i b x)-\frac{1}{2} i e^{-i a} b x^m (i b x)^{-m} \text{Gamma}(m-1,i b x)","\frac{1}{2} i e^{i a} b x^m (-i b x)^{-m} \text{Gamma}(m-1,-i b x)-\frac{1}{2} i e^{-i a} b x^m (i b x)^{-m} \text{Gamma}(m-1,i b x)",1,"((I/2)*b*E^(I*a)*x^m*Gamma[-1 + m, (-I)*b*x])/((-I)*b*x)^m - ((I/2)*b*x^m*Gamma[-1 + m, I*b*x])/(E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
110,1,75,0,0.074068,"\int x^{-3+m} \cos (a+b x) \, dx","Int[x^(-3 + m)*Cos[a + b*x],x]","\frac{1}{2} e^{i a} b^2 x^m (-i b x)^{-m} \text{Gamma}(m-2,-i b x)+\frac{1}{2} e^{-i a} b^2 x^m (i b x)^{-m} \text{Gamma}(m-2,i b x)","\frac{1}{2} e^{i a} b^2 x^m (-i b x)^{-m} \text{Gamma}(m-2,-i b x)+\frac{1}{2} e^{-i a} b^2 x^m (i b x)^{-m} \text{Gamma}(m-2,i b x)",1,"(b^2*E^(I*a)*x^m*Gamma[-2 + m, (-I)*b*x])/(2*((-I)*b*x)^m) + (b^2*x^m*Gamma[-2 + m, I*b*x])/(2*E^(I*a)*(I*b*x)^m)","A",3,2,12,0.1667,1,"{3307, 2181}"
111,1,99,0,0.1566643,"\int x^{3+m} \cos ^2(a+b x) \, dx","Int[x^(3 + m)*Cos[a + b*x]^2,x]","-\frac{e^{2 i a} 2^{-m-6} x^m (-i b x)^{-m} \text{Gamma}(m+4,-2 i b x)}{b^4}-\frac{e^{-2 i a} 2^{-m-6} x^m (i b x)^{-m} \text{Gamma}(m+4,2 i b x)}{b^4}+\frac{x^{m+4}}{2 (m+4)}","-\frac{e^{2 i a} 2^{-m-6} x^m (-i b x)^{-m} \text{Gamma}(m+4,-2 i b x)}{b^4}-\frac{e^{-2 i a} 2^{-m-6} x^m (i b x)^{-m} \text{Gamma}(m+4,2 i b x)}{b^4}+\frac{x^{m+4}}{2 (m+4)}",1,"x^(4 + m)/(2*(4 + m)) - (2^(-6 - m)*E^((2*I)*a)*x^m*Gamma[4 + m, (-2*I)*b*x])/(b^4*((-I)*b*x)^m) - (2^(-6 - m)*x^m*Gamma[4 + m, (2*I)*b*x])/(b^4*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
112,1,103,0,0.1436539,"\int x^{2+m} \cos ^2(a+b x) \, dx","Int[x^(2 + m)*Cos[a + b*x]^2,x]","\frac{i e^{2 i a} 2^{-m-5} x^m (-i b x)^{-m} \text{Gamma}(m+3,-2 i b x)}{b^3}-\frac{i e^{-2 i a} 2^{-m-5} x^m (i b x)^{-m} \text{Gamma}(m+3,2 i b x)}{b^3}+\frac{x^{m+3}}{2 (m+3)}","\frac{i e^{2 i a} 2^{-m-5} x^m (-i b x)^{-m} \text{Gamma}(m+3,-2 i b x)}{b^3}-\frac{i e^{-2 i a} 2^{-m-5} x^m (i b x)^{-m} \text{Gamma}(m+3,2 i b x)}{b^3}+\frac{x^{m+3}}{2 (m+3)}",1,"x^(3 + m)/(2*(3 + m)) + (I*2^(-5 - m)*E^((2*I)*a)*x^m*Gamma[3 + m, (-2*I)*b*x])/(b^3*((-I)*b*x)^m) - (I*2^(-5 - m)*x^m*Gamma[3 + m, (2*I)*b*x])/(b^3*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
113,1,97,0,0.1374782,"\int x^{1+m} \cos ^2(a+b x) \, dx","Int[x^(1 + m)*Cos[a + b*x]^2,x]","\frac{e^{2 i a} 2^{-m-4} x^m (-i b x)^{-m} \text{Gamma}(m+2,-2 i b x)}{b^2}+\frac{e^{-2 i a} 2^{-m-4} x^m (i b x)^{-m} \text{Gamma}(m+2,2 i b x)}{b^2}+\frac{x^{m+2}}{2 (m+2)}","\frac{e^{2 i a} 2^{-m-4} x^m (-i b x)^{-m} \text{Gamma}(m+2,-2 i b x)}{b^2}+\frac{e^{-2 i a} 2^{-m-4} x^m (i b x)^{-m} \text{Gamma}(m+2,2 i b x)}{b^2}+\frac{x^{m+2}}{2 (m+2)}",1,"x^(2 + m)/(2*(2 + m)) + (2^(-4 - m)*E^((2*I)*a)*x^m*Gamma[2 + m, (-2*I)*b*x])/(b^2*((-I)*b*x)^m) + (2^(-4 - m)*x^m*Gamma[2 + m, (2*I)*b*x])/(b^2*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
114,1,103,0,0.1329418,"\int x^m \cos ^2(a+b x) \, dx","Int[x^m*Cos[a + b*x]^2,x]","-\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \text{Gamma}(m+1,-2 i b x)}{b}+\frac{i e^{-2 i a} 2^{-m-3} x^m (i b x)^{-m} \text{Gamma}(m+1,2 i b x)}{b}+\frac{x^{m+1}}{2 (m+1)}","-\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \text{Gamma}(m+1,-2 i b x)}{b}+\frac{i e^{-2 i a} 2^{-m-3} x^m (i b x)^{-m} \text{Gamma}(m+1,2 i b x)}{b}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) - (I*2^(-3 - m)*E^((2*I)*a)*x^m*Gamma[1 + m, (-2*I)*b*x])/(b*((-I)*b*x)^m) + (I*2^(-3 - m)*x^m*Gamma[1 + m, (2*I)*b*x])/(b*E^((2*I)*a)*(I*b*x)^m)","A",5,3,12,0.2500,1,"{3312, 3307, 2181}"
115,1,85,0,0.1264211,"\int x^{-1+m} \cos ^2(a+b x) \, dx","Int[x^(-1 + m)*Cos[a + b*x]^2,x]","e^{2 i a} \left(-2^{-m-2}\right) x^m (-i b x)^{-m} \text{Gamma}(m,-2 i b x)-e^{-2 i a} 2^{-m-2} x^m (i b x)^{-m} \text{Gamma}(m,2 i b x)+\frac{x^m}{2 m}","e^{2 i a} \left(-2^{-m-2}\right) x^m (-i b x)^{-m} \text{Gamma}(m,-2 i b x)-e^{-2 i a} 2^{-m-2} x^m (i b x)^{-m} \text{Gamma}(m,2 i b x)+\frac{x^m}{2 m}",1,"x^m/(2*m) - (2^(-2 - m)*E^((2*I)*a)*x^m*Gamma[m, (-2*I)*b*x])/((-I)*b*x)^m - (2^(-2 - m)*x^m*Gamma[m, (2*I)*b*x])/(E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
116,1,101,0,0.1379882,"\int x^{-2+m} \cos ^2(a+b x) \, dx","Int[x^(-2 + m)*Cos[a + b*x]^2,x]","i e^{2 i a} b 2^{-m-1} x^m (-i b x)^{-m} \text{Gamma}(m-1,-2 i b x)-i e^{-2 i a} b 2^{-m-1} x^m (i b x)^{-m} \text{Gamma}(m-1,2 i b x)-\frac{x^{m-1}}{2 (1-m)}","i e^{2 i a} b 2^{-m-1} x^m (-i b x)^{-m} \text{Gamma}(m-1,-2 i b x)-i e^{-2 i a} b 2^{-m-1} x^m (i b x)^{-m} \text{Gamma}(m-1,2 i b x)-\frac{x^{m-1}}{2 (1-m)}",1,"-x^(-1 + m)/(2*(1 - m)) + (I*2^(-1 - m)*b*E^((2*I)*a)*x^m*Gamma[-1 + m, (-2*I)*b*x])/((-I)*b*x)^m - (I*2^(-1 - m)*b*x^m*Gamma[-1 + m, (2*I)*b*x])/(E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
117,1,95,0,0.1418949,"\int x^{-3+m} \cos ^2(a+b x) \, dx","Int[x^(-3 + m)*Cos[a + b*x]^2,x]","e^{2 i a} b^2 2^{-m} x^m (-i b x)^{-m} \text{Gamma}(m-2,-2 i b x)+e^{-2 i a} b^2 2^{-m} x^m (i b x)^{-m} \text{Gamma}(m-2,2 i b x)-\frac{x^{m-2}}{2 (2-m)}","e^{2 i a} b^2 2^{-m} x^m (-i b x)^{-m} \text{Gamma}(m-2,-2 i b x)+e^{-2 i a} b^2 2^{-m} x^m (i b x)^{-m} \text{Gamma}(m-2,2 i b x)-\frac{x^{m-2}}{2 (2-m)}",1,"-x^(-2 + m)/(2*(2 - m)) + (b^2*E^((2*I)*a)*x^m*Gamma[-2 + m, (-2*I)*b*x])/(2^m*((-I)*b*x)^m) + (b^2*x^m*Gamma[-2 + m, (2*I)*b*x])/(2^m*E^((2*I)*a)*(I*b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
118,1,89,0,0.1152071,"\int (c+d x)^3 (a+a \cos (e+f x)) \, dx","Int[(c + d*x)^3*(a + a*Cos[e + f*x]),x]","-\frac{6 a d^2 (c+d x) \sin (e+f x)}{f^3}+\frac{3 a d (c+d x)^2 \cos (e+f x)}{f^2}+\frac{a (c+d x)^3 \sin (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \cos (e+f x)}{f^4}","-\frac{6 a d^2 (c+d x) \sin (e+f x)}{f^3}+\frac{3 a d (c+d x)^2 \cos (e+f x)}{f^2}+\frac{a (c+d x)^3 \sin (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \cos (e+f x)}{f^4}",1,"(a*(c + d*x)^4)/(4*d) - (6*a*d^3*Cos[e + f*x])/f^4 + (3*a*d*(c + d*x)^2*Cos[e + f*x])/f^2 - (6*a*d^2*(c + d*x)*Sin[e + f*x])/f^3 + (a*(c + d*x)^3*Sin[e + f*x])/f","A",6,3,18,0.1667,1,"{3317, 3296, 2638}"
119,1,67,0,0.0845239,"\int (c+d x)^2 (a+a \cos (e+f x)) \, dx","Int[(c + d*x)^2*(a + a*Cos[e + f*x]),x]","\frac{2 a d (c+d x) \cos (e+f x)}{f^2}+\frac{a (c+d x)^2 \sin (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}-\frac{2 a d^2 \sin (e+f x)}{f^3}","\frac{2 a d (c+d x) \cos (e+f x)}{f^2}+\frac{a (c+d x)^2 \sin (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}-\frac{2 a d^2 \sin (e+f x)}{f^3}",1,"(a*(c + d*x)^3)/(3*d) + (2*a*d*(c + d*x)*Cos[e + f*x])/f^2 - (2*a*d^2*Sin[e + f*x])/f^3 + (a*(c + d*x)^2*Sin[e + f*x])/f","A",5,3,18,0.1667,1,"{3317, 3296, 2637}"
120,1,44,0,0.0423506,"\int (c+d x) (a+a \cos (e+f x)) \, dx","Int[(c + d*x)*(a + a*Cos[e + f*x]),x]","\frac{a (c+d x) \sin (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}+\frac{a d \cos (e+f x)}{f^2}","\frac{a (c+d x) \sin (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}+\frac{a d \cos (e+f x)}{f^2}",1,"(a*(c + d*x)^2)/(2*d) + (a*d*Cos[e + f*x])/f^2 + (a*(c + d*x)*Sin[e + f*x])/f","A",4,3,16,0.1875,1,"{3317, 3296, 2638}"
121,1,65,0,0.1497457,"\int \frac{a+a \cos (e+f x)}{c+d x} \, dx","Int[(a + a*Cos[e + f*x])/(c + d*x),x]","\frac{a \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d}-\frac{a \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{a \log (c+d x)}{d}","\frac{a \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d}-\frac{a \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}+\frac{a \log (c+d x)}{d}",1,"(a*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d + (a*Log[c + d*x])/d - (a*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3299, 3302}"
122,1,89,0,0.1633086,"\int \frac{a+a \cos (e+f x)}{(c+d x)^2} \, dx","Int[(a + a*Cos[e + f*x])/(c + d*x)^2,x]","-\frac{a f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^2}-\frac{a f \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \cos (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}","-\frac{a f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^2}-\frac{a f \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \cos (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}",1,"-(a/(d*(c + d*x))) - (a*Cos[e + f*x])/(d*(c + d*x)) - (a*f*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d^2 - (a*f*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3299, 3302}"
123,1,237,0,0.2607173,"\int (c+d x)^3 (a+a \cos (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + a*Cos[e + f*x])^2,x]","-\frac{12 a^2 d^2 (c+d x) \sin (e+f x)}{f^3}-\frac{3 a^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 a^2 c d^2 x}{4 f^2}+\frac{3 a^2 d (c+d x)^2 \cos ^2(e+f x)}{4 f^2}+\frac{6 a^2 d (c+d x)^2 \cos (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^3 \sin (e+f x)}{f}+\frac{a^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{3 a^2 (c+d x)^4}{8 d}-\frac{3 a^2 d^3 \cos ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \cos (e+f x)}{f^4}-\frac{3 a^2 d^3 x^2}{8 f^2}","-\frac{12 a^2 d^2 (c+d x) \sin (e+f x)}{f^3}-\frac{3 a^2 d^2 (c+d x) \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{3 a^2 c d^2 x}{4 f^2}+\frac{3 a^2 d (c+d x)^2 \cos ^2(e+f x)}{4 f^2}+\frac{6 a^2 d (c+d x)^2 \cos (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^3 \sin (e+f x)}{f}+\frac{a^2 (c+d x)^3 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{3 a^2 (c+d x)^4}{8 d}-\frac{3 a^2 d^3 \cos ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \cos (e+f x)}{f^4}-\frac{3 a^2 d^3 x^2}{8 f^2}",1,"(-3*a^2*c*d^2*x)/(4*f^2) - (3*a^2*d^3*x^2)/(8*f^2) + (3*a^2*(c + d*x)^4)/(8*d) - (12*a^2*d^3*Cos[e + f*x])/f^4 + (6*a^2*d*(c + d*x)^2*Cos[e + f*x])/f^2 - (3*a^2*d^3*Cos[e + f*x]^2)/(8*f^4) + (3*a^2*d*(c + d*x)^2*Cos[e + f*x]^2)/(4*f^2) - (12*a^2*d^2*(c + d*x)*Sin[e + f*x])/f^3 + (2*a^2*(c + d*x)^3*Sin[e + f*x])/f - (3*a^2*d^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) + (a^2*(c + d*x)^3*Cos[e + f*x]*Sin[e + f*x])/(2*f)","A",10,6,20,0.3000,1,"{3317, 3296, 2638, 3311, 32, 3310}"
124,1,168,0,0.1791488,"\int (c+d x)^2 (a+a \cos (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + a*Cos[e + f*x])^2,x]","\frac{a^2 d (c+d x) \cos ^2(e+f x)}{2 f^2}+\frac{4 a^2 d (c+d x) \cos (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^2 \sin (e+f x)}{f}+\frac{a^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^3}{2 d}-\frac{4 a^2 d^2 \sin (e+f x)}{f^3}-\frac{a^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{a^2 d^2 x}{4 f^2}","\frac{a^2 d (c+d x) \cos ^2(e+f x)}{2 f^2}+\frac{4 a^2 d (c+d x) \cos (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^2 \sin (e+f x)}{f}+\frac{a^2 (c+d x)^2 \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^3}{2 d}-\frac{4 a^2 d^2 \sin (e+f x)}{f^3}-\frac{a^2 d^2 \sin (e+f x) \cos (e+f x)}{4 f^3}-\frac{a^2 d^2 x}{4 f^2}",1,"-(a^2*d^2*x)/(4*f^2) + (a^2*(c + d*x)^3)/(2*d) + (4*a^2*d*(c + d*x)*Cos[e + f*x])/f^2 + (a^2*d*(c + d*x)*Cos[e + f*x]^2)/(2*f^2) - (4*a^2*d^2*Sin[e + f*x])/f^3 + (2*a^2*(c + d*x)^2*Sin[e + f*x])/f - (a^2*d^2*Cos[e + f*x]*Sin[e + f*x])/(4*f^3) + (a^2*(c + d*x)^2*Cos[e + f*x]*Sin[e + f*x])/(2*f)","A",9,7,20,0.3500,1,"{3317, 3296, 2637, 3311, 32, 2635, 8}"
125,1,118,0,0.0973405,"\int (c+d x) (a+a \cos (e+f x))^2 \, dx","Int[(c + d*x)*(a + a*Cos[e + f*x])^2,x]","\frac{2 a^2 (c+d x) \sin (e+f x)}{f}+\frac{a^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{1}{2} a^2 c x+\frac{a^2 d \cos ^2(e+f x)}{4 f^2}+\frac{2 a^2 d \cos (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2","\frac{2 a^2 (c+d x) \sin (e+f x)}{f}+\frac{a^2 (c+d x) \sin (e+f x) \cos (e+f x)}{2 f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{1}{2} a^2 c x+\frac{a^2 d \cos ^2(e+f x)}{4 f^2}+\frac{2 a^2 d \cos (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2",1,"(a^2*c*x)/2 + (a^2*d*x^2)/4 + (a^2*(c + d*x)^2)/(2*d) + (2*a^2*d*Cos[e + f*x])/f^2 + (a^2*d*Cos[e + f*x]^2)/(4*f^2) + (2*a^2*(c + d*x)*Sin[e + f*x])/f + (a^2*(c + d*x)*Cos[e + f*x]*Sin[e + f*x])/(2*f)","A",6,4,18,0.2222,1,"{3317, 3296, 2638, 3310}"
126,1,145,0,0.3379658,"\int \frac{(a+a \cos (e+f x))^2}{c+d x} \, dx","Int[(a + a*Cos[e + f*x])^2/(c + d*x),x]","\frac{2 a^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d}+\frac{a^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}-\frac{2 a^2 \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}-\frac{a^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{3 a^2 \log (c+d x)}{2 d}","\frac{2 a^2 \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \cos \left(e-\frac{c f}{d}\right)}{d}+\frac{a^2 \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \cos \left(2 e-\frac{2 c f}{d}\right)}{2 d}-\frac{2 a^2 \sin \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d}-\frac{a^2 \sin \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{3 a^2 \log (c+d x)}{2 d}",1,"(2*a^2*Cos[e - (c*f)/d]*CosIntegral[(c*f)/d + f*x])/d + (a^2*Cos[2*e - (2*c*f)/d]*CosIntegral[(2*c*f)/d + 2*f*x])/(2*d) + (3*a^2*Log[c + d*x])/(2*d) - (2*a^2*Sin[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d - (a^2*Sin[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/(2*d)","A",9,5,20,0.2500,1,"{3318, 3312, 3303, 3299, 3302}"
127,1,159,0,0.3166482,"\int \frac{(a+a \cos (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + a*Cos[e + f*x])^2/(c + d*x)^2,x]","-\frac{a^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}-\frac{2 a^2 f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a^2 f \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{4 a^2 \cos ^4\left(\frac{e}{2}+\frac{f x}{2}\right)}{d (c+d x)}","-\frac{a^2 f \text{CosIntegral}\left(\frac{2 c f}{d}+2 f x\right) \sin \left(2 e-\frac{2 c f}{d}\right)}{d^2}-\frac{2 a^2 f \text{CosIntegral}\left(\frac{c f}{d}+f x\right) \sin \left(e-\frac{c f}{d}\right)}{d^2}-\frac{2 a^2 f \cos \left(e-\frac{c f}{d}\right) \text{Si}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a^2 f \cos \left(2 e-\frac{2 c f}{d}\right) \text{Si}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{4 a^2 \cos ^4\left(\frac{e}{2}+\frac{f x}{2}\right)}{d (c+d x)}",1,"(-4*a^2*Cos[e/2 + (f*x)/2]^4)/(d*(c + d*x)) - (a^2*f*CosIntegral[(2*c*f)/d + 2*f*x]*Sin[2*e - (2*c*f)/d])/d^2 - (2*a^2*f*CosIntegral[(c*f)/d + f*x]*Sin[e - (c*f)/d])/d^2 - (2*a^2*f*Cos[e - (c*f)/d]*SinIntegral[(c*f)/d + f*x])/d^2 - (a^2*f*Cos[2*e - (2*c*f)/d]*SinIntegral[(2*c*f)/d + 2*f*x])/d^2","A",9,5,20,0.2500,1,"{3318, 3313, 3303, 3299, 3302}"
128,1,134,0,0.281878,"\int \frac{(c+d x)^3}{a+a \cos (e+f x)} \, dx","Int[(c + d*x)^3/(a + a*Cos[e + f*x]),x]","-\frac{12 i d^2 (c+d x) \text{Li}_2\left(-e^{i (e+f x)}\right)}{a f^3}+\frac{6 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^3}{a f}+\frac{12 d^3 \text{Li}_3\left(-e^{i (e+f x)}\right)}{a f^4}","-\frac{12 i d^2 (c+d x) \text{Li}_2\left(-e^{i (e+f x)}\right)}{a f^3}+\frac{6 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^3}{a f}+\frac{12 d^3 \text{Li}_3\left(-e^{i (e+f x)}\right)}{a f^4}",1,"((-I)*(c + d*x)^3)/(a*f) + (6*d*(c + d*x)^2*Log[1 + E^(I*(e + f*x))])/(a*f^2) - ((12*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(e + f*x))])/(a*f^3) + (12*d^3*PolyLog[3, -E^(I*(e + f*x))])/(a*f^4) + ((c + d*x)^3*Tan[e/2 + (f*x)/2])/(a*f)","A",7,7,20,0.3500,1,"{3318, 4184, 3719, 2190, 2531, 2282, 6589}"
129,1,101,0,0.1986895,"\int \frac{(c+d x)^2}{a+a \cos (e+f x)} \, dx","Int[(c + d*x)^2/(a + a*Cos[e + f*x]),x]","\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^2}{a f}-\frac{4 i d^2 \text{Li}_2\left(-e^{i (e+f x)}\right)}{a f^3}","\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{a f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^2}{a f}-\frac{4 i d^2 \text{Li}_2\left(-e^{i (e+f x)}\right)}{a f^3}",1,"((-I)*(c + d*x)^2)/(a*f) + (4*d*(c + d*x)*Log[1 + E^(I*(e + f*x))])/(a*f^2) - ((4*I)*d^2*PolyLog[2, -E^(I*(e + f*x))])/(a*f^3) + ((c + d*x)^2*Tan[e/2 + (f*x)/2])/(a*f)","A",6,6,20,0.3000,1,"{3318, 4184, 3719, 2190, 2279, 2391}"
130,1,49,0,0.0641462,"\int \frac{c+d x}{a+a \cos (e+f x)} \, dx","Int[(c + d*x)/(a + a*Cos[e + f*x]),x]","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}",1,"(2*d*Log[Cos[e/2 + (f*x)/2]])/(a*f^2) + ((c + d*x)*Tan[e/2 + (f*x)/2])/(a*f)","A",3,3,18,0.1667,1,"{3318, 4184, 3475}"
131,0,0,0,0.0596785,"\int \frac{1}{(c+d x) (a+a \cos (e+f x))} \, dx","Int[1/((c + d*x)*(a + a*Cos[e + f*x])),x]","\int \frac{1}{(c+d x) (a+a \cos (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \cos (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Cos[e + f*x])), x]","A",0,0,0,0,-1,"{}"
132,0,0,0,0.0565067,"\int \frac{1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + a*Cos[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+a \cos (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \cos (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Cos[e + f*x])), x]","A",0,0,0,0,-1,"{}"
133,1,271,0,0.3667192,"\int \frac{(c+d x)^3}{(a+a \cos (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + a*Cos[e + f*x])^2,x]","-\frac{4 i d^2 (c+d x) \text{Li}_2\left(-e^{i (e+f x)}\right)}{a^2 f^3}+\frac{2 d^2 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a^2 f^3}+\frac{2 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{i (c+d x)^3}{3 a^2 f}+\frac{4 d^3 \text{Li}_3\left(-e^{i (e+f x)}\right)}{a^2 f^4}+\frac{4 d^3 \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a^2 f^4}","-\frac{4 i d^2 (c+d x) \text{Li}_2\left(-e^{i (e+f x)}\right)}{a^2 f^3}+\frac{2 d^2 (c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{a^2 f^3}+\frac{2 d (c+d x)^2 \log \left(1+e^{i (e+f x)}\right)}{a^2 f^2}-\frac{d (c+d x)^2 \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{i (c+d x)^3}{3 a^2 f}+\frac{4 d^3 \text{Li}_3\left(-e^{i (e+f x)}\right)}{a^2 f^4}+\frac{4 d^3 \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a^2 f^4}",1,"((-I/3)*(c + d*x)^3)/(a^2*f) + (2*d*(c + d*x)^2*Log[1 + E^(I*(e + f*x))])/(a^2*f^2) + (4*d^3*Log[Cos[e/2 + (f*x)/2]])/(a^2*f^4) - ((4*I)*d^2*(c + d*x)*PolyLog[2, -E^(I*(e + f*x))])/(a^2*f^3) + (4*d^3*PolyLog[3, -E^(I*(e + f*x))])/(a^2*f^4) - (d*(c + d*x)^2*Sec[e/2 + (f*x)/2]^2)/(2*a^2*f^2) + (2*d^2*(c + d*x)*Tan[e/2 + (f*x)/2])/(a^2*f^3) + ((c + d*x)^3*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^3*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",10,9,20,0.4500,1,"{3318, 4186, 4184, 3475, 3719, 2190, 2531, 2282, 6589}"
134,1,212,0,0.2555284,"\int \frac{(c+d x)^2}{(a+a \cos (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + a*Cos[e + f*x])^2,x]","\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{i (c+d x)^2}{3 a^2 f}-\frac{4 i d^2 \text{Li}_2\left(-e^{i (e+f x)}\right)}{3 a^2 f^3}+\frac{2 d^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^3}","\frac{4 d (c+d x) \log \left(1+e^{i (e+f x)}\right)}{3 a^2 f^2}-\frac{d (c+d x) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{i (c+d x)^2}{3 a^2 f}-\frac{4 i d^2 \text{Li}_2\left(-e^{i (e+f x)}\right)}{3 a^2 f^3}+\frac{2 d^2 \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^3}",1,"((-I/3)*(c + d*x)^2)/(a^2*f) + (4*d*(c + d*x)*Log[1 + E^(I*(e + f*x))])/(3*a^2*f^2) - (((4*I)/3)*d^2*PolyLog[2, -E^(I*(e + f*x))])/(a^2*f^3) - (d*(c + d*x)*Sec[e/2 + (f*x)/2]^2)/(3*a^2*f^2) + (2*d^2*Tan[e/2 + (f*x)/2])/(3*a^2*f^3) + ((c + d*x)^2*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^2*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",9,9,20,0.4500,1,"{3318, 4186, 3767, 8, 4184, 3719, 2190, 2279, 2391}"
135,1,123,0,0.0946936,"\int \frac{c+d x}{(a+a \cos (e+f x))^2} \, dx","Int[(c + d*x)/(a + a*Cos[e + f*x])^2,x]","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{d \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}","\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tan \left(\frac{e}{2}+\frac{f x}{2}\right) \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}-\frac{d \sec ^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}+\frac{2 d \log \left(\cos \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}",1,"(2*d*Log[Cos[e/2 + (f*x)/2]])/(3*a^2*f^2) - (d*Sec[e/2 + (f*x)/2]^2)/(6*a^2*f^2) + ((c + d*x)*Tan[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)*Sec[e/2 + (f*x)/2]^2*Tan[e/2 + (f*x)/2])/(6*a^2*f)","A",4,4,18,0.2222,1,"{3318, 4185, 4184, 3475}"
136,0,0,0,0.0541021,"\int \frac{1}{(c+d x) (a+a \cos (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + a*Cos[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+a \cos (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \cos (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Cos[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
137,0,0,0,0.0521773,"\int \frac{1}{(c+d x)^2 (a+a \cos (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + a*Cos[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+a \cos (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \cos (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Cos[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
138,1,133,0,0.2837055,"\int \frac{(c+d x)^3}{a-a \cos (e+f x)} \, dx","Int[(c + d*x)^3/(a - a*Cos[e + f*x]),x]","-\frac{12 i d^2 (c+d x) \text{Li}_2\left(e^{i (e+f x)}\right)}{a f^3}+\frac{6 d (c+d x)^2 \log \left(1-e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^3}{a f}+\frac{12 d^3 \text{Li}_3\left(e^{i (e+f x)}\right)}{a f^4}","-\frac{12 i d^2 (c+d x) \text{Li}_2\left(e^{i (e+f x)}\right)}{a f^3}+\frac{6 d (c+d x)^2 \log \left(1-e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^3 \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^3}{a f}+\frac{12 d^3 \text{Li}_3\left(e^{i (e+f x)}\right)}{a f^4}",1,"((-I)*(c + d*x)^3)/(a*f) - ((c + d*x)^3*Cot[e/2 + (f*x)/2])/(a*f) + (6*d*(c + d*x)^2*Log[1 - E^(I*(e + f*x))])/(a*f^2) - ((12*I)*d^2*(c + d*x)*PolyLog[2, E^(I*(e + f*x))])/(a*f^3) + (12*d^3*PolyLog[3, E^(I*(e + f*x))])/(a*f^4)","A",7,7,21,0.3333,1,"{3318, 4184, 3717, 2190, 2531, 2282, 6589}"
139,1,102,0,0.2029758,"\int \frac{(c+d x)^2}{a-a \cos (e+f x)} \, dx","Int[(c + d*x)^2/(a - a*Cos[e + f*x]),x]","\frac{4 d (c+d x) \log \left(1-e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^2}{a f}-\frac{4 i d^2 \text{Li}_2\left(e^{i (e+f x)}\right)}{a f^3}","\frac{4 d (c+d x) \log \left(1-e^{i (e+f x)}\right)}{a f^2}-\frac{(c+d x)^2 \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{i (c+d x)^2}{a f}-\frac{4 i d^2 \text{Li}_2\left(e^{i (e+f x)}\right)}{a f^3}",1,"((-I)*(c + d*x)^2)/(a*f) - ((c + d*x)^2*Cot[e/2 + (f*x)/2])/(a*f) + (4*d*(c + d*x)*Log[1 - E^(I*(e + f*x))])/(a*f^2) - ((4*I)*d^2*PolyLog[2, E^(I*(e + f*x))])/(a*f^3)","A",6,6,21,0.2857,1,"{3318, 4184, 3717, 2190, 2279, 2391}"
140,1,50,0,0.0652033,"\int \frac{c+d x}{a-a \cos (e+f x)} \, dx","Int[(c + d*x)/(a - a*Cos[e + f*x]),x]","\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}","\frac{2 d \log \left(\sin \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}-\frac{(c+d x) \cot \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}",1,"-(((c + d*x)*Cot[e/2 + (f*x)/2])/(a*f)) + (2*d*Log[Sin[e/2 + (f*x)/2]])/(a*f^2)","A",3,3,19,0.1579,1,"{3318, 4184, 3475}"
141,0,0,0,0.062457,"\int \frac{1}{(c+d x) (a-a \cos (e+f x))} \, dx","Int[1/((c + d*x)*(a - a*Cos[e + f*x])),x]","\int \frac{1}{(c+d x) (a-a \cos (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a-a \cos (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a - a*Cos[e + f*x])), x]","A",0,0,0,0,-1,"{}"
142,0,0,0,0.057798,"\int \frac{1}{(c+d x)^2 (a-a \cos (e+f x))} \, dx","Int[1/((c + d*x)^2*(a - a*Cos[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a-a \cos (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a-a \cos (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a - a*Cos[e + f*x])), x]","A",0,0,0,0,-1,"{}"
143,1,110,0,0.1339527,"\int x^3 \sqrt{a+a \cos (c+d x)} \, dx","Int[x^3*Sqrt[a + a*Cos[c + d*x]],x]","\frac{12 x^2 \sqrt{a \cos (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \cos (c+d x)+a}}{d^4}-\frac{48 x \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d^3}+\frac{2 x^3 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}","\frac{12 x^2 \sqrt{a \cos (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \cos (c+d x)+a}}{d^4}-\frac{48 x \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d^3}+\frac{2 x^3 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}",1,"(-96*Sqrt[a + a*Cos[c + d*x]])/d^4 + (12*x^2*Sqrt[a + a*Cos[c + d*x]])/d^2 - (48*x*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/d^3 + (2*x^3*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/d","A",5,3,18,0.1667,1,"{3319, 3296, 2638}"
144,1,88,0,0.1124305,"\int x^2 \sqrt{a+a \cos (c+d x)} \, dx","Int[x^2*Sqrt[a + a*Cos[c + d*x]],x]","\frac{8 x \sqrt{a \cos (c+d x)+a}}{d^2}-\frac{16 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d^3}+\frac{2 x^2 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}","\frac{8 x \sqrt{a \cos (c+d x)+a}}{d^2}-\frac{16 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d^3}+\frac{2 x^2 \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}",1,"(8*x*Sqrt[a + a*Cos[c + d*x]])/d^2 - (16*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/d^3 + (2*x^2*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/d","A",4,3,18,0.1667,1,"{3319, 3296, 2637}"
145,1,53,0,0.0608678,"\int x \sqrt{a+a \cos (c+d x)} \, dx","Int[x*Sqrt[a + a*Cos[c + d*x]],x]","\frac{4 \sqrt{a \cos (c+d x)+a}}{d^2}+\frac{2 x \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}","\frac{4 \sqrt{a \cos (c+d x)+a}}{d^2}+\frac{2 x \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{d}",1,"(4*Sqrt[a + a*Cos[c + d*x]])/d^2 + (2*x*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/d","A",3,3,16,0.1875,1,"{3319, 3296, 2638}"
146,1,26,0,0.0131807,"\int \sqrt{a+a \cos (c+d x)} \, dx","Int[Sqrt[a + a*Cos[c + d*x]],x]","\frac{2 a \sin (c+d x)}{d \sqrt{a \cos (c+d x)+a}}","\frac{2 a \sin (c+d x)}{d \sqrt{a \cos (c+d x)+a}}",1,"(2*a*Sin[c + d*x])/(d*Sqrt[a + a*Cos[c + d*x]])","A",1,1,14,0.07143,1,"{2646}"
147,1,84,0,0.1213112,"\int \frac{\sqrt{a+a \cos (c+d x)}}{x} \, dx","Int[Sqrt[a + a*Cos[c + d*x]]/x,x]","\cos \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\sin \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}","\cos \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\sin \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}",1,"Cos[c/2]*Sqrt[a + a*Cos[c + d*x]]*CosIntegral[(d*x)/2]*Sec[c/2 + (d*x)/2] - Sqrt[a + a*Cos[c + d*x]]*Sec[c/2 + (d*x)/2]*Sin[c/2]*SinIntegral[(d*x)/2]","A",4,4,18,0.2222,1,"{3319, 3303, 3299, 3302}"
148,1,110,0,0.133418,"\int \frac{\sqrt{a+a \cos (c+d x)}}{x^2} \, dx","Int[Sqrt[a + a*Cos[c + d*x]]/x^2,x]","-\frac{1}{2} d \sin \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{1}{2} d \cos \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{\sqrt{a \cos (c+d x)+a}}{x}","-\frac{1}{2} d \sin \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{1}{2} d \cos \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{\sqrt{a \cos (c+d x)+a}}{x}",1,"-(Sqrt[a + a*Cos[c + d*x]]/x) - (d*Sqrt[a + a*Cos[c + d*x]]*CosIntegral[(d*x)/2]*Sec[c/2 + (d*x)/2]*Sin[c/2])/2 - (d*Cos[c/2]*Sqrt[a + a*Cos[c + d*x]]*Sec[c/2 + (d*x)/2]*SinIntegral[(d*x)/2])/2","A",5,5,18,0.2778,1,"{3319, 3297, 3303, 3299, 3302}"
149,1,151,0,0.1617127,"\int \frac{\sqrt{a+a \cos (c+d x)}}{x^3} \, dx","Int[Sqrt[a + a*Cos[c + d*x]]/x^3,x]","-\frac{1}{8} d^2 \cos \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}+\frac{1}{8} d^2 \sin \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{\sqrt{a \cos (c+d x)+a}}{2 x^2}+\frac{d \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{4 x}","-\frac{1}{8} d^2 \cos \left(\frac{c}{2}\right) \text{CosIntegral}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}+\frac{1}{8} d^2 \sin \left(\frac{c}{2}\right) \text{Si}\left(\frac{d x}{2}\right) \sec \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}-\frac{\sqrt{a \cos (c+d x)+a}}{2 x^2}+\frac{d \tan \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cos (c+d x)+a}}{4 x}",1,"-Sqrt[a + a*Cos[c + d*x]]/(2*x^2) - (d^2*Cos[c/2]*Sqrt[a + a*Cos[c + d*x]]*CosIntegral[(d*x)/2]*Sec[c/2 + (d*x)/2])/8 + (d^2*Sqrt[a + a*Cos[c + d*x]]*Sec[c/2 + (d*x)/2]*Sin[c/2]*SinIntegral[(d*x)/2])/8 + (d*Sqrt[a + a*Cos[c + d*x]]*Tan[c/2 + (d*x)/2])/(4*x)","A",6,5,18,0.2778,1,"{3319, 3297, 3303, 3299, 3302}"
150,1,68,0,0.1108375,"\int x^3 \sqrt{a+a \cos (x)} \, dx","Int[x^3*Sqrt[a + a*Cos[x]],x]","12 x^2 \sqrt{a \cos (x)+a}+2 x^3 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-96 \sqrt{a \cos (x)+a}-48 x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","12 x^2 \sqrt{a \cos (x)+a}+2 x^3 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-96 \sqrt{a \cos (x)+a}-48 x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"-96*Sqrt[a + a*Cos[x]] + 12*x^2*Sqrt[a + a*Cos[x]] - 48*x*Sqrt[a + a*Cos[x]]*Tan[x/2] + 2*x^3*Sqrt[a + a*Cos[x]]*Tan[x/2]","A",5,3,14,0.2143,1,"{3319, 3296, 2638}"
151,1,53,0,0.0959995,"\int x^2 \sqrt{a+a \cos (x)} \, dx","Int[x^2*Sqrt[a + a*Cos[x]],x]","2 x^2 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+8 x \sqrt{a \cos (x)+a}-16 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","2 x^2 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+8 x \sqrt{a \cos (x)+a}-16 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"8*x*Sqrt[a + a*Cos[x]] - 16*Sqrt[a + a*Cos[x]]*Tan[x/2] + 2*x^2*Sqrt[a + a*Cos[x]]*Tan[x/2]","A",4,3,14,0.2143,1,"{3319, 3296, 2637}"
152,1,32,0,0.0500326,"\int x \sqrt{a+a \cos (x)} \, dx","Int[x*Sqrt[a + a*Cos[x]],x]","4 \sqrt{a \cos (x)+a}+2 x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","4 \sqrt{a \cos (x)+a}+2 x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"4*Sqrt[a + a*Cos[x]] + 2*x*Sqrt[a + a*Cos[x]]*Tan[x/2]","A",3,3,12,0.2500,1,"{3319, 3296, 2638}"
153,1,15,0,0.0111368,"\int \sqrt{a+a \cos (x)} \, dx","Int[Sqrt[a + a*Cos[x]],x]","\frac{2 a \sin (x)}{\sqrt{a \cos (x)+a}}","\frac{2 a \sin (x)}{\sqrt{a \cos (x)+a}}",1,"(2*a*Sin[x])/Sqrt[a + a*Cos[x]]","A",1,1,10,0.1000,1,"{2646}"
154,1,23,0,0.087079,"\int \frac{\sqrt{a+a \cos (x)}}{x} \, dx","Int[Sqrt[a + a*Cos[x]]/x,x]","\text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","\text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"Sqrt[a + a*Cos[x]]*CosIntegral[x/2]*Sec[x/2]","A",2,2,14,0.1429,1,"{3319, 3302}"
155,1,42,0,0.0906291,"\int \frac{\sqrt{a+a \cos (x)}}{x^2} \, dx","Int[Sqrt[a + a*Cos[x]]/x^2,x]","-\frac{1}{2} \text{Si}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{\sqrt{a \cos (x)+a}}{x}","-\frac{1}{2} \text{Si}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{\sqrt{a \cos (x)+a}}{x}",1,"-(Sqrt[a + a*Cos[x]]/x) - (Sqrt[a + a*Cos[x]]*Sec[x/2]*SinIntegral[x/2])/2","A",3,3,14,0.2143,1,"{3319, 3297, 3299}"
156,1,67,0,0.1061452,"\int \frac{\sqrt{a+a \cos (x)}}{x^3} \, dx","Int[Sqrt[a + a*Cos[x]]/x^3,x]","-\frac{1}{8} \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{\sqrt{a \cos (x)+a}}{2 x^2}+\frac{\tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{4 x}","-\frac{1}{8} \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{\sqrt{a \cos (x)+a}}{2 x^2}+\frac{\tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{4 x}",1,"-Sqrt[a + a*Cos[x]]/(2*x^2) - (Sqrt[a + a*Cos[x]]*CosIntegral[x/2]*Sec[x/2])/8 + (Sqrt[a + a*Cos[x]]*Tan[x/2])/(4*x)","A",4,3,14,0.2143,1,"{3319, 3297, 3302}"
157,1,72,0,0.1147636,"\int x^3 \sqrt{a-a \cos (x)} \, dx","Int[x^3*Sqrt[a - a*Cos[x]],x]","12 x^2 \sqrt{a-a \cos (x)}-2 x^3 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-96 \sqrt{a-a \cos (x)}+48 x \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}","12 x^2 \sqrt{a-a \cos (x)}-2 x^3 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-96 \sqrt{a-a \cos (x)}+48 x \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}",1,"-96*Sqrt[a - a*Cos[x]] + 12*x^2*Sqrt[a - a*Cos[x]] + 48*x*Sqrt[a - a*Cos[x]]*Cot[x/2] - 2*x^3*Sqrt[a - a*Cos[x]]*Cot[x/2]","A",5,3,15,0.2000,1,"{3319, 3296, 2637}"
158,1,56,0,0.0983111,"\int x^2 \sqrt{a-a \cos (x)} \, dx","Int[x^2*Sqrt[a - a*Cos[x]],x]","-2 x^2 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}+8 x \sqrt{a-a \cos (x)}+16 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}","-2 x^2 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}+8 x \sqrt{a-a \cos (x)}+16 \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}",1,"8*x*Sqrt[a - a*Cos[x]] + 16*Sqrt[a - a*Cos[x]]*Cot[x/2] - 2*x^2*Sqrt[a - a*Cos[x]]*Cot[x/2]","A",4,3,15,0.2000,1,"{3319, 3296, 2638}"
159,1,34,0,0.0507503,"\int x \sqrt{a-a \cos (x)} \, dx","Int[x*Sqrt[a - a*Cos[x]],x]","4 \sqrt{a-a \cos (x)}-2 x \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}","4 \sqrt{a-a \cos (x)}-2 x \cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}",1,"4*Sqrt[a - a*Cos[x]] - 2*x*Sqrt[a - a*Cos[x]]*Cot[x/2]","A",3,3,13,0.2308,1,"{3319, 3296, 2637}"
160,1,16,0,0.011432,"\int \sqrt{a-a \cos (x)} \, dx","Int[Sqrt[a - a*Cos[x]],x]","-\frac{2 a \sin (x)}{\sqrt{a-a \cos (x)}}","-\frac{2 a \sin (x)}{\sqrt{a-a \cos (x)}}",1,"(-2*a*Sin[x])/Sqrt[a - a*Cos[x]]","A",1,1,11,0.09091,1,"{2646}"
161,1,24,0,0.087634,"\int \frac{\sqrt{a-a \cos (x)}}{x} \, dx","Int[Sqrt[a - a*Cos[x]]/x,x]","\text{Si}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}","\text{Si}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}",1,"Sqrt[a - a*Cos[x]]*Csc[x/2]*SinIntegral[x/2]","A",2,2,15,0.1333,1,"{3319, 3299}"
162,1,44,0,0.0917802,"\int \frac{\sqrt{a-a \cos (x)}}{x^2} \, dx","Int[Sqrt[a - a*Cos[x]]/x^2,x]","\frac{1}{2} \text{CosIntegral}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-\frac{\sqrt{a-a \cos (x)}}{x}","\frac{1}{2} \text{CosIntegral}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-\frac{\sqrt{a-a \cos (x)}}{x}",1,"-(Sqrt[a - a*Cos[x]]/x) + (Sqrt[a - a*Cos[x]]*CosIntegral[x/2]*Csc[x/2])/2","A",3,3,15,0.2000,1,"{3319, 3297, 3302}"
163,1,70,0,0.1057476,"\int \frac{\sqrt{a-a \cos (x)}}{x^3} \, dx","Int[Sqrt[a - a*Cos[x]]/x^3,x]","-\frac{1}{8} \text{Si}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-\frac{\sqrt{a-a \cos (x)}}{2 x^2}-\frac{\cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}}{4 x}","-\frac{1}{8} \text{Si}\left(\frac{x}{2}\right) \csc \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}-\frac{\sqrt{a-a \cos (x)}}{2 x^2}-\frac{\cot \left(\frac{x}{2}\right) \sqrt{a-a \cos (x)}}{4 x}",1,"-Sqrt[a - a*Cos[x]]/(2*x^2) - (Sqrt[a - a*Cos[x]]*Cot[x/2])/(4*x) - (Sqrt[a - a*Cos[x]]*Csc[x/2]*SinIntegral[x/2])/8","A",4,3,15,0.2000,1,"{3319, 3297, 3299}"
164,1,185,0,0.1832166,"\int x^3 (a+a \cos (x))^{3/2} \, dx","Int[x^3*(a + a*Cos[x])^(3/2),x]","\frac{8}{3} a x^2 \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+16 a x^2 \sqrt{a \cos (x)+a}+\frac{4}{3} a x^3 \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x^3 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{64}{27} a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{1280}{9} a \sqrt{a \cos (x)+a}-\frac{32}{9} a x \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{640}{9} a x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","\frac{8}{3} a x^2 \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+16 a x^2 \sqrt{a \cos (x)+a}+\frac{4}{3} a x^3 \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x^3 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{64}{27} a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{1280}{9} a \sqrt{a \cos (x)+a}-\frac{32}{9} a x \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{640}{9} a x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"(-1280*a*Sqrt[a + a*Cos[x]])/9 + 16*a*x^2*Sqrt[a + a*Cos[x]] - (64*a*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/27 + (8*a*x^2*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/3 - (32*a*x*Cos[x/2]*Sqrt[a + a*Cos[x]]*Sin[x/2])/9 + (4*a*x^3*Cos[x/2]*Sqrt[a + a*Cos[x]]*Sin[x/2])/3 - (640*a*x*Sqrt[a + a*Cos[x]]*Tan[x/2])/9 + (8*a*x^3*Sqrt[a + a*Cos[x]]*Tan[x/2])/3","A",9,5,14,0.3571,1,"{3319, 3311, 3296, 2638, 3310}"
165,1,145,0,0.1442655,"\int x^2 (a+a \cos (x))^{3/2} \, dx","Int[x^2*(a + a*Cos[x])^(3/2),x]","\frac{4}{3} a x^2 \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x^2 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{16}{9} a x \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{32}{3} a x \sqrt{a \cos (x)+a}-\frac{224}{9} a \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{32}{27} a \sin ^2\left(\frac{x}{2}\right) \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","\frac{4}{3} a x^2 \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x^2 \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{16}{9} a x \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{32}{3} a x \sqrt{a \cos (x)+a}-\frac{224}{9} a \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{32}{27} a \sin ^2\left(\frac{x}{2}\right) \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"(32*a*x*Sqrt[a + a*Cos[x]])/3 + (16*a*x*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/9 + (4*a*x^2*Cos[x/2]*Sqrt[a + a*Cos[x]]*Sin[x/2])/3 - (224*a*Sqrt[a + a*Cos[x]]*Tan[x/2])/9 + (8*a*x^2*Sqrt[a + a*Cos[x]]*Tan[x/2])/3 + (32*a*Sqrt[a + a*Cos[x]]*Sin[x/2]^2*Tan[x/2])/27","A",7,5,14,0.3571,1,"{3319, 3311, 3296, 2637, 2633}"
166,1,89,0,0.0720092,"\int x (a+a \cos (x))^{3/2} \, dx","Int[x*(a + a*Cos[x])^(3/2),x]","\frac{8}{9} a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{16}{3} a \sqrt{a \cos (x)+a}+\frac{4}{3} a x \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","\frac{8}{9} a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{16}{3} a \sqrt{a \cos (x)+a}+\frac{4}{3} a x \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{8}{3} a x \tan \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"(16*a*Sqrt[a + a*Cos[x]])/3 + (8*a*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/9 + (4*a*x*Cos[x/2]*Sqrt[a + a*Cos[x]]*Sin[x/2])/3 + (8*a*x*Sqrt[a + a*Cos[x]]*Tan[x/2])/3","A",4,4,12,0.3333,1,"{3319, 3310, 3296, 2638}"
167,1,55,0,0.1276674,"\int \frac{(a+a \cos (x))^{3/2}}{x} \, dx","Int[(a + a*Cos[x])^(3/2)/x,x]","\frac{3}{2} a \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{1}{2} a \text{CosIntegral}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}","\frac{3}{2} a \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}+\frac{1}{2} a \text{CosIntegral}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}",1,"(3*a*Sqrt[a + a*Cos[x]]*CosIntegral[x/2]*Sec[x/2])/2 + (a*Sqrt[a + a*Cos[x]]*CosIntegral[(3*x)/2]*Sec[x/2])/2","A",5,3,14,0.2143,1,"{3319, 3312, 3302}"
168,1,79,0,0.12649,"\int \frac{(a+a \cos (x))^{3/2}}{x^2} \, dx","Int[(a + a*Cos[x])^(3/2)/x^2,x]","-\frac{3}{4} a \text{Si}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{3}{4} a \text{Si}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{2 a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{x}","-\frac{3}{4} a \text{Si}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{3}{4} a \text{Si}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{2 a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{x}",1,"(-2*a*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/x - (3*a*Sqrt[a + a*Cos[x]]*Sec[x/2]*SinIntegral[x/2])/4 - (3*a*Sqrt[a + a*Cos[x]]*Sec[x/2]*SinIntegral[(3*x)/2])/4","A",5,3,14,0.2143,1,"{3319, 3313, 3299}"
169,1,109,0,0.1654692,"\int \frac{(a+a \cos (x))^{3/2}}{x^3} \, dx","Int[(a + a*Cos[x])^(3/2)/x^3,x]","-\frac{3}{16} a \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{9}{16} a \text{CosIntegral}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{x^2}+\frac{3 a \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{2 x}","-\frac{3}{16} a \text{CosIntegral}\left(\frac{x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{9}{16} a \text{CosIntegral}\left(\frac{3 x}{2}\right) \sec \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}-\frac{a \cos ^2\left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{x^2}+\frac{3 a \sin \left(\frac{x}{2}\right) \cos \left(\frac{x}{2}\right) \sqrt{a \cos (x)+a}}{2 x}",1,"-((a*Cos[x/2]^2*Sqrt[a + a*Cos[x]])/x^2) - (3*a*Sqrt[a + a*Cos[x]]*CosIntegral[x/2]*Sec[x/2])/16 - (9*a*Sqrt[a + a*Cos[x]]*CosIntegral[(3*x)/2]*Sec[x/2])/16 + (3*a*Cos[x/2]*Sqrt[a + a*Cos[x]]*Sin[x/2])/(2*x)","A",7,4,14,0.2857,1,"{3319, 3314, 3302, 3312}"
170,1,374,0,0.2116367,"\int \frac{x^3}{\sqrt{a+a \cos (c+d x)}} \, dx","Int[x^3/Sqrt[a + a*Cos[c + d*x]],x]","\frac{12 i x^2 \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{12 i x^2 \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{48 x \text{Li}_3\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}+\frac{48 x \text{Li}_3\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}-\frac{96 i \text{Li}_4\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cos (c+d x)+a}}+\frac{96 i \text{Li}_4\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x^3 \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}","\frac{12 i x^2 \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{12 i x^2 \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{48 x \text{Li}_3\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}+\frac{48 x \text{Li}_3\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}-\frac{96 i \text{Li}_4\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cos (c+d x)+a}}+\frac{96 i \text{Li}_4\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x^3 \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}",1,"((-4*I)*x^3*ArcTan[E^((I/2)*(c + d*x))]*Cos[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cos[c + d*x]]) + ((12*I)*x^2*Cos[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]]) - ((12*I)*x^2*Cos[c/2 + (d*x)/2]*PolyLog[2, I*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]]) - (48*x*Cos[c/2 + (d*x)/2]*PolyLog[3, (-I)*E^((I/2)*(c + d*x))])/(d^3*Sqrt[a + a*Cos[c + d*x]]) + (48*x*Cos[c/2 + (d*x)/2]*PolyLog[3, I*E^((I/2)*(c + d*x))])/(d^3*Sqrt[a + a*Cos[c + d*x]]) - ((96*I)*Cos[c/2 + (d*x)/2]*PolyLog[4, (-I)*E^((I/2)*(c + d*x))])/(d^4*Sqrt[a + a*Cos[c + d*x]]) + ((96*I)*Cos[c/2 + (d*x)/2]*PolyLog[4, I*E^((I/2)*(c + d*x))])/(d^4*Sqrt[a + a*Cos[c + d*x]])","A",10,6,18,0.3333,1,"{3319, 4181, 2531, 6609, 2282, 6589}"
171,1,262,0,0.1673952,"\int \frac{x^2}{\sqrt{a+a \cos (c+d x)}} \, dx","Int[x^2/Sqrt[a + a*Cos[c + d*x]],x]","\frac{8 i x \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{8 i x \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{16 \text{Li}_3\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}+\frac{16 \text{Li}_3\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x^2 \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}","\frac{8 i x \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{8 i x \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{16 \text{Li}_3\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}+\frac{16 \text{Li}_3\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x^2 \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}",1,"((-4*I)*x^2*ArcTan[E^((I/2)*(c + d*x))]*Cos[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cos[c + d*x]]) + ((8*I)*x*Cos[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]]) - ((8*I)*x*Cos[c/2 + (d*x)/2]*PolyLog[2, I*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]]) - (16*Cos[c/2 + (d*x)/2]*PolyLog[3, (-I)*E^((I/2)*(c + d*x))])/(d^3*Sqrt[a + a*Cos[c + d*x]]) + (16*Cos[c/2 + (d*x)/2]*PolyLog[3, I*E^((I/2)*(c + d*x))])/(d^3*Sqrt[a + a*Cos[c + d*x]])","A",8,5,18,0.2778,1,"{3319, 4181, 2531, 2282, 6589}"
172,1,156,0,0.0856533,"\int \frac{x}{\sqrt{a+a \cos (c+d x)}} \, dx","Int[x/Sqrt[a + a*Cos[c + d*x]],x]","\frac{4 i \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{4 i \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}","\frac{4 i \text{Li}_2\left(-i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{4 i \text{Li}_2\left(i e^{\frac{1}{2} i (c+d x)}\right) \cos \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cos (c+d x)+a}}-\frac{4 i x \cos \left(\frac{c}{2}+\frac{d x}{2}\right) \tan ^{-1}\left(e^{\frac{1}{2} i (c+d x)}\right)}{d \sqrt{a \cos (c+d x)+a}}",1,"((-4*I)*x*ArcTan[E^((I/2)*(c + d*x))]*Cos[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cos[c + d*x]]) + ((4*I)*Cos[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]]) - ((4*I)*Cos[c/2 + (d*x)/2]*PolyLog[2, I*E^((I/2)*(c + d*x))])/(d^2*Sqrt[a + a*Cos[c + d*x]])","A",6,4,16,0.2500,1,"{3319, 4181, 2279, 2391}"
173,1,46,0,0.0216911,"\int \frac{1}{\sqrt{a+a \cos (c+d x)}} \, dx","Int[1/Sqrt[a + a*Cos[c + d*x]],x]","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{\sqrt{a} d}","\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (c+d x)}{\sqrt{2} \sqrt{a \cos (c+d x)+a}}\right)}{\sqrt{a} d}",1,"(Sqrt[2]*ArcTanh[(Sqrt[a]*Sin[c + d*x])/(Sqrt[2]*Sqrt[a + a*Cos[c + d*x]])])/(Sqrt[a]*d)","A",2,2,14,0.1429,1,"{2649, 206}"
174,0,0,0,0.0685169,"\int \frac{1}{x \sqrt{a+a \cos (c+d x)}} \, dx","Int[1/(x*Sqrt[a + a*Cos[c + d*x]]),x]","\int \frac{1}{x \sqrt{a+a \cos (c+d x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a \cos (c+d x)+a}},x\right)",0,"Defer[Int][1/(x*Sqrt[a + a*Cos[c + d*x]]), x]","A",0,0,0,0,-1,"{}"
175,1,235,0,0.1733087,"\int \frac{x^3}{\sqrt{a-a \cos (x)}} \, dx","Int[x^3/Sqrt[a - a*Cos[x]],x]","\frac{12 i x^2 \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{12 i x^2 \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{48 x \text{Li}_3\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{48 x \text{Li}_3\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{96 i \text{Li}_4\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{96 i \text{Li}_4\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x^3 \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}","\frac{12 i x^2 \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{12 i x^2 \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{48 x \text{Li}_3\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{48 x \text{Li}_3\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{96 i \text{Li}_4\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{96 i \text{Li}_4\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x^3 \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}",1,"(-4*x^3*ArcTanh[E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + ((12*I)*x^2*PolyLog[2, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - ((12*I)*x^2*PolyLog[2, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - (48*x*PolyLog[3, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + (48*x*PolyLog[3, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - ((96*I)*PolyLog[4, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + ((96*I)*PolyLog[4, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]]","A",10,6,15,0.4000,1,"{3319, 4183, 2531, 6609, 2282, 6589}"
176,1,163,0,0.1411943,"\int \frac{x^2}{\sqrt{a-a \cos (x)}} \, dx","Int[x^2/Sqrt[a - a*Cos[x]],x]","\frac{8 i x \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{8 i x \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{16 \text{Li}_3\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{16 \text{Li}_3\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x^2 \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}","\frac{8 i x \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{8 i x \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{16 \text{Li}_3\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}+\frac{16 \text{Li}_3\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x^2 \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}",1,"(-4*x^2*ArcTanh[E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + ((8*I)*x*PolyLog[2, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - ((8*I)*x*PolyLog[2, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - (16*PolyLog[3, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + (16*PolyLog[3, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]]","A",8,5,15,0.3333,1,"{3319, 4183, 2531, 2282, 6589}"
177,1,97,0,0.0784426,"\int \frac{x}{\sqrt{a-a \cos (x)}} \, dx","Int[x/Sqrt[a - a*Cos[x]],x]","\frac{4 i \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 i \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}","\frac{4 i \text{Li}_2\left(-e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 i \text{Li}_2\left(e^{\frac{i x}{2}}\right) \sin \left(\frac{x}{2}\right)}{\sqrt{a-a \cos (x)}}-\frac{4 x \sin \left(\frac{x}{2}\right) \tanh ^{-1}\left(e^{\frac{i x}{2}}\right)}{\sqrt{a-a \cos (x)}}",1,"(-4*x*ArcTanh[E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] + ((4*I)*PolyLog[2, -E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]] - ((4*I)*PolyLog[2, E^((I/2)*x)]*Sin[x/2])/Sqrt[a - a*Cos[x]]","A",6,4,13,0.3077,1,"{3319, 4183, 2279, 2391}"
178,1,37,0,0.0204732,"\int \frac{1}{\sqrt{a-a \cos (x)}} \, dx","Int[1/Sqrt[a - a*Cos[x]],x]","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (x)}{\sqrt{2} \sqrt{a-a \cos (x)}}\right)}{\sqrt{a}}","-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{a} \sin (x)}{\sqrt{2} \sqrt{a-a \cos (x)}}\right)}{\sqrt{a}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[a]*Sin[x])/(Sqrt[2]*Sqrt[a - a*Cos[x]])])/Sqrt[a])","A",2,2,11,0.1818,1,"{2649, 206}"
179,0,0,0,0.0772828,"\int \frac{1}{x \sqrt{a-a \cos (x)}} \, dx","Int[1/(x*Sqrt[a - a*Cos[x]]),x]","\int \frac{1}{x \sqrt{a-a \cos (x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a-a \cos (x)}},x\right)",0,"Defer[Int][1/(x*Sqrt[a - a*Cos[x]]), x]","A",0,0,0,0,-1,"{}"
180,1,423,0,0.2595348,"\int \frac{x^3}{(a+a \cos (x))^{3/2}} \, dx","Int[x^3/(a + a*Cos[x])^(3/2),x]","\frac{3 i x^2 \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{3 i x^2 \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{12 x \text{Li}_3\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{12 x \text{Li}_3\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{24 i \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{24 i \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{24 i \text{Li}_4\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{24 i \text{Li}_4\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{3 x^2}{a \sqrt{a \cos (x)+a}}-\frac{i x^3 \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x^3 \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}-\frac{24 i x \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}","\frac{3 i x^2 \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{3 i x^2 \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{12 x \text{Li}_3\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{12 x \text{Li}_3\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{24 i \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{24 i \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{24 i \text{Li}_4\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{24 i \text{Li}_4\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{3 x^2}{a \sqrt{a \cos (x)+a}}-\frac{i x^3 \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x^3 \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}-\frac{24 i x \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}",1,"(-3*x^2)/(a*Sqrt[a + a*Cos[x]]) - ((24*I)*x*ArcTan[E^((I/2)*x)]*Cos[x/2])/(a*Sqrt[a + a*Cos[x]]) - (I*x^3*ArcTan[E^((I/2)*x)]*Cos[x/2])/(a*Sqrt[a + a*Cos[x]]) + ((24*I)*Cos[x/2]*PolyLog[2, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + ((3*I)*x^2*Cos[x/2]*PolyLog[2, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - ((24*I)*Cos[x/2]*PolyLog[2, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - ((3*I)*x^2*Cos[x/2]*PolyLog[2, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - (12*x*Cos[x/2]*PolyLog[3, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + (12*x*Cos[x/2]*PolyLog[3, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - ((24*I)*Cos[x/2]*PolyLog[4, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + ((24*I)*Cos[x/2]*PolyLog[4, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + (x^3*Tan[x/2])/(2*a*Sqrt[a + a*Cos[x]])","A",16,9,14,0.6429,1,"{3319, 4186, 4181, 2279, 2391, 2531, 6609, 2282, 6589}"
181,1,257,0,0.188985,"\int \frac{x^2}{(a+a \cos (x))^{3/2}} \, dx","Int[x^2/(a + a*Cos[x])^(3/2),x]","\frac{2 i x \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{2 i x \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{4 \text{Li}_3\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{4 \text{Li}_3\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{i x^2 \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x^2 \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}-\frac{2 x}{a \sqrt{a \cos (x)+a}}+\frac{4 \cos \left(\frac{x}{2}\right) \tanh ^{-1}\left(\sin \left(\frac{x}{2}\right)\right)}{a \sqrt{a \cos (x)+a}}","\frac{2 i x \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{2 i x \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{4 \text{Li}_3\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}+\frac{4 \text{Li}_3\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{i x^2 \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x^2 \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}-\frac{2 x}{a \sqrt{a \cos (x)+a}}+\frac{4 \cos \left(\frac{x}{2}\right) \tanh ^{-1}\left(\sin \left(\frac{x}{2}\right)\right)}{a \sqrt{a \cos (x)+a}}",1,"(-2*x)/(a*Sqrt[a + a*Cos[x]]) - (I*x^2*ArcTan[E^((I/2)*x)]*Cos[x/2])/(a*Sqrt[a + a*Cos[x]]) + (4*ArcTanh[Sin[x/2]]*Cos[x/2])/(a*Sqrt[a + a*Cos[x]]) + ((2*I)*x*Cos[x/2]*PolyLog[2, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - ((2*I)*x*Cos[x/2]*PolyLog[2, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - (4*Cos[x/2]*PolyLog[3, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + (4*Cos[x/2]*PolyLog[3, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + (x^2*Tan[x/2])/(2*a*Sqrt[a + a*Cos[x]])","A",10,7,14,0.5000,1,"{3319, 4186, 3770, 4181, 2531, 2282, 6589}"
182,1,150,0,0.11658,"\int \frac{x}{(a+a \cos (x))^{3/2}} \, dx","Int[x/(a + a*Cos[x])^(3/2),x]","\frac{i \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{i \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{1}{a \sqrt{a \cos (x)+a}}-\frac{i x \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}","\frac{i \text{Li}_2\left(-i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{i \text{Li}_2\left(i e^{\frac{i x}{2}}\right) \cos \left(\frac{x}{2}\right)}{a \sqrt{a \cos (x)+a}}-\frac{1}{a \sqrt{a \cos (x)+a}}-\frac{i x \cos \left(\frac{x}{2}\right) \tan ^{-1}\left(e^{\frac{i x}{2}}\right)}{a \sqrt{a \cos (x)+a}}+\frac{x \tan \left(\frac{x}{2}\right)}{2 a \sqrt{a \cos (x)+a}}",1,"-(1/(a*Sqrt[a + a*Cos[x]])) - (I*x*ArcTan[E^((I/2)*x)]*Cos[x/2])/(a*Sqrt[a + a*Cos[x]]) + (I*Cos[x/2]*PolyLog[2, (-I)*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) - (I*Cos[x/2]*PolyLog[2, I*E^((I/2)*x)])/(a*Sqrt[a + a*Cos[x]]) + (x*Tan[x/2])/(2*a*Sqrt[a + a*Cos[x]])","A",7,5,12,0.4167,1,"{3319, 4185, 4181, 2279, 2391}"
183,0,0,0,0.0786225,"\int \frac{1}{x (a+a \cos (x))^{3/2}} \, dx","Int[1/(x*(a + a*Cos[x])^(3/2)),x]","\int \frac{1}{x (a+a \cos (x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x (a \cos (x)+a)^{3/2}},x\right)",0,"Defer[Int][1/(x*(a + a*Cos[x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
184,0,0,0,0.0648875,"\int \frac{\sqrt[3]{a+a \cos (c+d x)}}{x} \, dx","Int[(a + a*Cos[c + d*x])^(1/3)/x,x]","\int \frac{\sqrt[3]{a+a \cos (c+d x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt[3]{a \cos (c+d x)+a}}{x},x\right)",0,"Defer[Int][(a + a*Cos[c + d*x])^(1/3)/x, x]","A",0,0,0,0,-1,"{}"
185,1,383,0,0.558972,"\int \frac{x^3}{a+b \cos (x)} \, dx","Int[x^3/(a + b*Cos[x]),x]","-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{6 i x \text{Li}_3\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{6 i x \text{Li}_3\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{6 \text{Li}_4\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{6 \text{Li}_4\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{i x^3 \log \left(1+\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{i x^3 \log \left(1+\frac{b e^{i x}}{\sqrt{a^2-b^2}+a}\right)}{\sqrt{a^2-b^2}}","-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{6 i x \text{Li}_3\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{6 i x \text{Li}_3\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{6 \text{Li}_4\left(-\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{6 \text{Li}_4\left(-\frac{b e^{i x}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-\frac{i x^3 \log \left(1+\frac{b e^{i x}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{i x^3 \log \left(1+\frac{b e^{i x}}{\sqrt{a^2-b^2}+a}\right)}{\sqrt{a^2-b^2}}",1,"((-I)*x^3*Log[1 + (b*E^(I*x))/(a - Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] + (I*x^3*Log[1 + (b*E^(I*x))/(a + Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] - (3*x^2*PolyLog[2, -((b*E^(I*x))/(a - Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2] + (3*x^2*PolyLog[2, -((b*E^(I*x))/(a + Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2] - ((6*I)*x*PolyLog[3, -((b*E^(I*x))/(a - Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2] + ((6*I)*x*PolyLog[3, -((b*E^(I*x))/(a + Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2] + (6*PolyLog[4, -((b*E^(I*x))/(a - Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2] - (6*PolyLog[4, -((b*E^(I*x))/(a + Sqrt[a^2 - b^2]))])/Sqrt[a^2 - b^2]","A",12,7,12,0.5833,1,"{3321, 2264, 2190, 2531, 6609, 2282, 6589}"
186,1,329,0,0.6629181,"\int \frac{x^2}{a+b \cos (c+d x)} \, dx","Int[x^2/(a + b*Cos[c + d*x]),x]","-\frac{2 x \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{2 x \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{2 i \text{Li}_3\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}+\frac{2 i \text{Li}_3\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}-\frac{i x^2 \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}+\frac{i x^2 \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \sqrt{a^2-b^2}}","-\frac{2 x \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{2 x \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{2 i \text{Li}_3\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}+\frac{2 i \text{Li}_3\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}-\frac{i x^2 \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}+\frac{i x^2 \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \sqrt{a^2-b^2}}",1,"((-I)*x^2*Log[1 + (b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) + (I*x^2*Log[1 + (b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) - (2*x*PolyLog[2, -((b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2]))])/(Sqrt[a^2 - b^2]*d^2) + (2*x*PolyLog[2, -((b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2]))])/(Sqrt[a^2 - b^2]*d^2) - ((2*I)*PolyLog[3, -((b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2]))])/(Sqrt[a^2 - b^2]*d^3) + ((2*I)*PolyLog[3, -((b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2]))])/(Sqrt[a^2 - b^2]*d^3)","A",10,6,16,0.3750,1,"{3321, 2264, 2190, 2531, 2282, 6589}"
187,1,214,0,0.4001711,"\int \frac{x}{a+b \cos (c+d x)} \, dx","Int[x/(a + b*Cos[c + d*x]),x]","-\frac{\text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{\text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{i x \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}+\frac{i x \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \sqrt{a^2-b^2}}","-\frac{\text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{\text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{i x \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}+\frac{i x \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \sqrt{a^2-b^2}}",1,"((-I)*x*Log[1 + (b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) + (I*x*Log[1 + (b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) - PolyLog[2, -((b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2]))]/(Sqrt[a^2 - b^2]*d^2) + PolyLog[2, -((b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2]))]/(Sqrt[a^2 - b^2]*d^2)","A",8,5,14,0.3571,1,"{3321, 2264, 2190, 2279, 2391}"
188,0,0,0,0.0485615,"\int \frac{1}{x (a+b \cos (x))} \, dx","Int[1/(x*(a + b*Cos[x])),x]","\int \frac{1}{x (a+b \cos (x))} \, dx","\text{Int}\left(\frac{1}{x (a+b \cos (x))},x\right)",0,"Defer[Int][1/(x*(a + b*Cos[x])), x]","A",0,0,0,0,-1,"{}"
189,1,296,0,0.5226428,"\int \frac{e+f x}{(a+b \cos (c+d x))^2} \, dx","Int[(e + f*x)/(a + b*Cos[c + d*x])^2,x]","-\frac{a f \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a f \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{f \log (a+b \cos (c+d x))}{d^2 \left(a^2-b^2\right)}-\frac{i a (e+f x) \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{i a (e+f x) \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{b (e+f x) \sin (c+d x)}{d \left(a^2-b^2\right) (a+b \cos (c+d x))}","-\frac{a f \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a f \text{Li}_2\left(-\frac{b e^{i (c+d x)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{f \log (a+b \cos (c+d x))}{d^2 \left(a^2-b^2\right)}-\frac{i a (e+f x) \log \left(1+\frac{b e^{i (c+d x)}}{a-\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{i a (e+f x) \log \left(1+\frac{b e^{i (c+d x)}}{\sqrt{a^2-b^2}+a}\right)}{d \left(a^2-b^2\right)^{3/2}}-\frac{b (e+f x) \sin (c+d x)}{d \left(a^2-b^2\right) (a+b \cos (c+d x))}",1,"((-I)*a*(e + f*x)*Log[1 + (b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + (I*a*(e + f*x)*Log[1 + (b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - (f*Log[a + b*Cos[c + d*x]])/((a^2 - b^2)*d^2) - (a*f*PolyLog[2, -((b*E^(I*(c + d*x)))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*d^2) + (a*f*PolyLog[2, -((b*E^(I*(c + d*x)))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*d^2) - (b*(e + f*x)*Sin[c + d*x])/((a^2 - b^2)*d*(a + b*Cos[c + d*x]))","A",11,8,18,0.4444,1,"{3324, 3321, 2264, 2190, 2279, 2391, 2668, 31}"