1,1,34,0,0.0317191,"\int x^3 \cos \left(a+b x^2\right) \, dx","Int[x^3*Cos[a + b*x^2],x]","\frac{\cos \left(a+b x^2\right)}{2 b^2}+\frac{x^2 \sin \left(a+b x^2\right)}{2 b}","\frac{\cos \left(a+b x^2\right)}{2 b^2}+\frac{x^2 \sin \left(a+b x^2\right)}{2 b}",1,"Cos[a + b*x^2]/(2*b^2) + (x^2*Sin[a + b*x^2])/(2*b)","A",3,3,12,0.2500,1,"{3380, 3296, 2638}"
2,1,91,0,0.0694239,"\int x^2 \cos \left(a+b x^2\right) \, dx","Int[x^2*Cos[a + b*x^2],x]","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{2 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{2 b^{3/2}}+\frac{x \sin \left(a+b x^2\right)}{2 b}","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{2 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{2 b^{3/2}}+\frac{x \sin \left(a+b x^2\right)}{2 b}",1,"-(Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(2*b^(3/2)) - (Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(2*b^(3/2)) + (x*Sin[a + b*x^2])/(2*b)","A",4,4,12,0.3333,1,"{3386, 3353, 3352, 3351}"
3,1,15,0,0.0143389,"\int x \cos \left(a+b x^2\right) \, dx","Int[x*Cos[a + b*x^2],x]","\frac{\sin \left(a+b x^2\right)}{2 b}","\frac{\sin \left(a+b x^2\right)}{2 b}",1,"Sin[a + b*x^2]/(2*b)","A",2,2,10,0.2000,1,"{3380, 2637}"
4,1,70,0,0.0214534,"\int \cos \left(a+b x^2\right) \, dx","Int[Cos[a + b*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{b}}","\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{b}}",1,"(Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] - (Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/Sqrt[b]","A",3,3,8,0.3750,1,"{3354, 3352, 3351}"
5,1,25,0,0.0289689,"\int \frac{\cos \left(a+b x^2\right)}{x} \, dx","Int[Cos[a + b*x^2]/x,x]","\frac{1}{2} \cos (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{2} \sin (a) \text{Si}\left(b x^2\right)","\frac{1}{2} \cos (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{2} \sin (a) \text{Si}\left(b x^2\right)",1,"(Cos[a]*CosIntegral[b*x^2])/2 - (Sin[a]*SinIntegral[b*x^2])/2","A",3,3,12,0.2500,1,"{3378, 3376, 3375}"
6,1,80,0,0.0445045,"\int \frac{\cos \left(a+b x^2\right)}{x^2} \, dx","Int[Cos[a + b*x^2]/x^2,x]","-\sqrt{2 \pi } \sqrt{b} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\sqrt{2 \pi } \sqrt{b} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{\cos \left(a+b x^2\right)}{x}","-\sqrt{2 \pi } \sqrt{b} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\sqrt{2 \pi } \sqrt{b} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{\cos \left(a+b x^2\right)}{x}",1,"-(Cos[a + b*x^2]/x) - Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]","A",4,4,12,0.3333,1,"{3388, 3353, 3352, 3351}"
7,1,42,0,0.0892469,"\int \frac{\cos \left(a+b x^2\right)}{x^3} \, dx","Int[Cos[a + b*x^2]/x^3,x]","-\frac{1}{2} b \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{2} b \cos (a) \text{Si}\left(b x^2\right)-\frac{\cos \left(a+b x^2\right)}{2 x^2}","-\frac{1}{2} b \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{2} b \cos (a) \text{Si}\left(b x^2\right)-\frac{\cos \left(a+b x^2\right)}{2 x^2}",1,"-Cos[a + b*x^2]/(2*x^2) - (b*CosIntegral[b*x^2]*Sin[a])/2 - (b*Cos[a]*SinIntegral[b*x^2])/2","A",5,5,12,0.4167,1,"{3380, 3297, 3303, 3299, 3302}"
8,1,51,0,0.0519296,"\int x^3 \cos ^2\left(a+b x^2\right) \, dx","Int[x^3*Cos[a + b*x^2]^2,x]","\frac{\cos ^2\left(a+b x^2\right)}{8 b^2}+\frac{x^2 \sin \left(a+b x^2\right) \cos \left(a+b x^2\right)}{4 b}+\frac{x^4}{8}","\frac{\cos ^2\left(a+b x^2\right)}{8 b^2}+\frac{x^2 \sin \left(a+b x^2\right) \cos \left(a+b x^2\right)}{4 b}+\frac{x^4}{8}",1,"x^4/8 + Cos[a + b*x^2]^2/(8*b^2) + (x^2*Cos[a + b*x^2]*Sin[a + b*x^2])/(4*b)","A",3,3,14,0.2143,1,"{3380, 3310, 30}"
9,1,91,0,0.0973785,"\int x^2 \cos ^2\left(a+b x^2\right) \, dx","Int[x^2*Cos[a + b*x^2]^2,x]","-\frac{\sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{16 b^{3/2}}-\frac{\sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{16 b^{3/2}}+\frac{x \sin \left(2 a+2 b x^2\right)}{8 b}+\frac{x^3}{6}","-\frac{\sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{16 b^{3/2}}-\frac{\sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{16 b^{3/2}}+\frac{x \sin \left(2 a+2 b x^2\right)}{8 b}+\frac{x^3}{6}",1,"x^3/6 - (Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]])/(16*b^(3/2)) - (Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])/(16*b^(3/2)) + (x*Sin[2*a + 2*b*x^2])/(8*b)","A",6,5,14,0.3571,1,"{3404, 3386, 3353, 3352, 3351}"
10,1,31,0,0.028877,"\int x \cos ^2\left(a+b x^2\right) \, dx","Int[x*Cos[a + b*x^2]^2,x]","\frac{\sin \left(a+b x^2\right) \cos \left(a+b x^2\right)}{4 b}+\frac{x^2}{4}","\frac{\sin \left(a+b x^2\right) \cos \left(a+b x^2\right)}{4 b}+\frac{x^2}{4}",1,"x^2/4 + (Cos[a + b*x^2]*Sin[a + b*x^2])/(4*b)","A",3,3,12,0.2500,1,"{3380, 2635, 8}"
11,1,70,0,0.0437522,"\int \cos ^2\left(a+b x^2\right) \, dx","Int[Cos[a + b*x^2]^2,x]","\frac{\sqrt{\pi } \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{4 \sqrt{b}}-\frac{\sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{4 \sqrt{b}}+\frac{x}{2}","\frac{\sqrt{\pi } \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{4 \sqrt{b}}-\frac{\sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)}{4 \sqrt{b}}+\frac{x}{2}",1,"x/2 + (Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) - (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])/(4*Sqrt[b])","A",5,4,10,0.4000,1,"{3358, 3354, 3352, 3351}"
12,1,37,0,0.0518501,"\int \frac{\cos ^2\left(a+b x^2\right)}{x} \, dx","Int[Cos[a + b*x^2]^2/x,x]","\frac{1}{4} \cos (2 a) \text{CosIntegral}\left(2 b x^2\right)-\frac{1}{4} \sin (2 a) \text{Si}\left(2 b x^2\right)+\frac{\log (x)}{2}","\frac{1}{4} \cos (2 a) \text{CosIntegral}\left(2 b x^2\right)-\frac{1}{4} \sin (2 a) \text{Si}\left(2 b x^2\right)+\frac{\log (x)}{2}",1,"(Cos[2*a]*CosIntegral[2*b*x^2])/4 + Log[x]/2 - (Sin[2*a]*SinIntegral[2*b*x^2])/4","A",5,4,14,0.2857,1,"{3404, 3378, 3376, 3375}"
13,1,76,0,0.0673088,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^2} \, dx","Int[Cos[a + b*x^2]^2/x^2,x]","-\sqrt{\pi } \sqrt{b} \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-\sqrt{\pi } \sqrt{b} \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-\frac{\cos ^2\left(a+b x^2\right)}{x}","-\sqrt{\pi } \sqrt{b} \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-\sqrt{\pi } \sqrt{b} \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-\frac{\cos ^2\left(a+b x^2\right)}{x}",1,"-(Cos[a + b*x^2]^2/x) - Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]] - Sqrt[b]*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a]","A",6,6,14,0.4286,1,"{3394, 4573, 3373, 3353, 3352, 3351}"
14,1,57,0,0.1175101,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^3} \, dx","Int[Cos[a + b*x^2]^2/x^3,x]","-\frac{1}{2} b \sin (2 a) \text{CosIntegral}\left(2 b x^2\right)-\frac{1}{2} b \cos (2 a) \text{Si}\left(2 b x^2\right)-\frac{\cos \left(2 \left(a+b x^2\right)\right)}{4 x^2}-\frac{1}{4 x^2}","-\frac{1}{2} b \sin (2 a) \text{CosIntegral}\left(2 b x^2\right)-\frac{1}{2} b \cos (2 a) \text{Si}\left(2 b x^2\right)-\frac{\cos \left(2 \left(a+b x^2\right)\right)}{4 x^2}-\frac{1}{4 x^2}",1,"-1/(4*x^2) - Cos[2*(a + b*x^2)]/(4*x^2) - (b*CosIntegral[2*b*x^2]*Sin[2*a])/2 - (b*Cos[2*a]*SinIntegral[2*b*x^2])/2","A",7,6,14,0.4286,1,"{3404, 3380, 3297, 3303, 3299, 3302}"
15,1,79,0,0.0738608,"\int x^3 \cos ^3\left(a+b x^2\right) \, dx","Int[x^3*Cos[a + b*x^2]^3,x]","\frac{\cos ^3\left(a+b x^2\right)}{18 b^2}+\frac{\cos \left(a+b x^2\right)}{3 b^2}+\frac{x^2 \sin \left(a+b x^2\right)}{3 b}+\frac{x^2 \sin \left(a+b x^2\right) \cos ^2\left(a+b x^2\right)}{6 b}","\frac{\cos ^3\left(a+b x^2\right)}{18 b^2}+\frac{\cos \left(a+b x^2\right)}{3 b^2}+\frac{x^2 \sin \left(a+b x^2\right)}{3 b}+\frac{x^2 \sin \left(a+b x^2\right) \cos ^2\left(a+b x^2\right)}{6 b}",1,"Cos[a + b*x^2]/(3*b^2) + Cos[a + b*x^2]^3/(18*b^2) + (x^2*Sin[a + b*x^2])/(3*b) + (x^2*Cos[a + b*x^2]^2*Sin[a + b*x^2])/(6*b)","A",4,4,14,0.2857,1,"{3380, 3310, 3296, 2638}"
16,1,188,0,0.1819995,"\int x^2 \cos ^3\left(a+b x^2\right) \, dx","Int[x^2*Cos[a + b*x^2]^3,x]","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)}{24 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{24 b^{3/2}}+\frac{3 x \sin \left(a+b x^2\right)}{8 b}+\frac{x \sin \left(3 a+3 b x^2\right)}{24 b}","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)}{24 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{24 b^{3/2}}+\frac{3 x \sin \left(a+b x^2\right)}{8 b}+\frac{x \sin \left(3 a+3 b x^2\right)}{24 b}",1,"(-3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(8*b^(3/2)) - (Sqrt[Pi/6]*Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x])/(24*b^(3/2)) - (3*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(8*b^(3/2)) - (Sqrt[Pi/6]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/(24*b^(3/2)) + (3*x*Sin[a + b*x^2])/(8*b) + (x*Sin[3*a + 3*b*x^2])/(24*b)","A",10,5,14,0.3571,1,"{3404, 3386, 3353, 3352, 3351}"
17,1,33,0,0.0283865,"\int x \cos ^3\left(a+b x^2\right) \, dx","Int[x*Cos[a + b*x^2]^3,x]","\frac{\sin \left(a+b x^2\right)}{2 b}-\frac{\sin ^3\left(a+b x^2\right)}{6 b}","\frac{\sin \left(a+b x^2\right)}{2 b}-\frac{\sin ^3\left(a+b x^2\right)}{6 b}",1,"Sin[a + b*x^2]/(2*b) - Sin[a + b*x^2]^3/(6*b)","A",3,2,12,0.1667,1,"{3380, 2633}"
18,1,153,0,0.0890601,"\int \cos ^3\left(a+b x^2\right) \, dx","Int[Cos[a + b*x^2]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}+\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{4 \sqrt{b}}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}+\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{4 \sqrt{b}}",1,"(3*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) + (Sqrt[Pi/6]*Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x])/(4*Sqrt[b]) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt[Pi/6]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/(4*Sqrt[b])","A",8,4,10,0.4000,1,"{3358, 3354, 3352, 3351}"
19,1,55,0,0.0832228,"\int \frac{\cos ^3\left(a+b x^2\right)}{x} \, dx","Int[Cos[a + b*x^2]^3/x,x]","\frac{3}{8} \cos (a) \text{CosIntegral}\left(b x^2\right)+\frac{1}{8} \cos (3 a) \text{CosIntegral}\left(3 b x^2\right)-\frac{3}{8} \sin (a) \text{Si}\left(b x^2\right)-\frac{1}{8} \sin (3 a) \text{Si}\left(3 b x^2\right)","\frac{3}{8} \cos (a) \text{CosIntegral}\left(b x^2\right)+\frac{1}{8} \cos (3 a) \text{CosIntegral}\left(3 b x^2\right)-\frac{3}{8} \sin (a) \text{Si}\left(b x^2\right)-\frac{1}{8} \sin (3 a) \text{Si}\left(3 b x^2\right)",1,"(3*Cos[a]*CosIntegral[b*x^2])/8 + (Cos[3*a]*CosIntegral[3*b*x^2])/8 - (3*Sin[a]*SinIntegral[b*x^2])/8 - (Sin[3*a]*SinIntegral[3*b*x^2])/8","A",8,4,14,0.2857,1,"{3404, 3378, 3376, 3375}"
20,1,168,0,0.1435791,"\int \frac{\cos ^3\left(a+b x^2\right)}{x^2} \, dx","Int[Cos[a + b*x^2]^3/x^2,x]","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-\frac{\cos ^3\left(a+b x^2\right)}{x}","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} x\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-\frac{\cos ^3\left(a+b x^2\right)}{x}",1,"-(Cos[a + b*x^2]^3/x) - (3*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/2 - (Sqrt[b]*Sqrt[(3*Pi)/2]*Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x])/2 - (3*Sqrt[b]*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/2 - (Sqrt[b]*Sqrt[(3*Pi)/2]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/2","A",9,5,14,0.3571,1,"{3394, 4574, 3353, 3352, 3351}"
21,1,91,0,0.2013484,"\int \frac{\cos ^3\left(a+b x^2\right)}{x^3} \, dx","Int[Cos[a + b*x^2]^3/x^3,x]","-\frac{3}{8} b \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{3}{8} b \sin (3 a) \text{CosIntegral}\left(3 b x^2\right)-\frac{3}{8} b \cos (a) \text{Si}\left(b x^2\right)-\frac{3}{8} b \cos (3 a) \text{Si}\left(3 b x^2\right)-\frac{3 \cos \left(a+b x^2\right)}{8 x^2}-\frac{\cos \left(3 \left(a+b x^2\right)\right)}{8 x^2}","-\frac{3}{8} b \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{3}{8} b \sin (3 a) \text{CosIntegral}\left(3 b x^2\right)-\frac{3}{8} b \cos (a) \text{Si}\left(b x^2\right)-\frac{3}{8} b \cos (3 a) \text{Si}\left(3 b x^2\right)-\frac{3 \cos \left(a+b x^2\right)}{8 x^2}-\frac{\cos \left(3 \left(a+b x^2\right)\right)}{8 x^2}",1,"(-3*Cos[a + b*x^2])/(8*x^2) - Cos[3*(a + b*x^2)]/(8*x^2) - (3*b*CosIntegral[b*x^2]*Sin[a])/8 - (3*b*CosIntegral[3*b*x^2]*Sin[3*a])/8 - (3*b*Cos[a]*SinIntegral[b*x^2])/8 - (3*b*Cos[3*a]*SinIntegral[3*b*x^2])/8","A",12,6,14,0.4286,1,"{3404, 3380, 3297, 3303, 3299, 3302}"
22,1,67,0,0.0537244,"\int x \cos ^7\left(a+b x^2\right) \, dx","Int[x*Cos[a + b*x^2]^7,x]","-\frac{\sin ^7\left(a+b x^2\right)}{14 b}+\frac{3 \sin ^5\left(a+b x^2\right)}{10 b}-\frac{\sin ^3\left(a+b x^2\right)}{2 b}+\frac{\sin \left(a+b x^2\right)}{2 b}","-\frac{\sin ^7\left(a+b x^2\right)}{14 b}+\frac{3 \sin ^5\left(a+b x^2\right)}{10 b}-\frac{\sin ^3\left(a+b x^2\right)}{2 b}+\frac{\sin \left(a+b x^2\right)}{2 b}",1,"Sin[a + b*x^2]/(2*b) - Sin[a + b*x^2]^3/(2*b) + (3*Sin[a + b*x^2]^5)/(10*b) - Sin[a + b*x^2]^7/(14*b)","A",3,2,12,0.1667,1,"{3380, 2633}"
23,1,111,0,0.0811548,"\int x^{5/2} \cos \left(a+b x^2\right) \, dx","Int[x^(5/2)*Cos[a + b*x^2],x]","-\frac{3 i e^{i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{16 b \left(-i b x^2\right)^{3/4}}+\frac{3 i e^{-i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{16 b \left(i b x^2\right)^{3/4}}+\frac{x^{3/2} \sin \left(a+b x^2\right)}{2 b}","-\frac{3 i e^{i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{16 b \left(-i b x^2\right)^{3/4}}+\frac{3 i e^{-i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{16 b \left(i b x^2\right)^{3/4}}+\frac{x^{3/2} \sin \left(a+b x^2\right)}{2 b}",1,"(((-3*I)/16)*E^(I*a)*x^(3/2)*Gamma[3/4, (-I)*b*x^2])/(b*((-I)*b*x^2)^(3/4)) + (((3*I)/16)*x^(3/2)*Gamma[3/4, I*b*x^2])/(b*E^(I*a)*(I*b*x^2)^(3/4)) + (x^(3/2)*Sin[a + b*x^2])/(2*b)","A",4,3,14,0.2143,1,"{3386, 3389, 2218}"
24,1,111,0,0.0786466,"\int x^{3/2} \cos \left(a+b x^2\right) \, dx","Int[x^(3/2)*Cos[a + b*x^2],x]","-\frac{i e^{i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{16 b \sqrt[4]{-i b x^2}}+\frac{i e^{-i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{16 b \sqrt[4]{i b x^2}}+\frac{\sqrt{x} \sin \left(a+b x^2\right)}{2 b}","-\frac{i e^{i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{16 b \sqrt[4]{-i b x^2}}+\frac{i e^{-i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{16 b \sqrt[4]{i b x^2}}+\frac{\sqrt{x} \sin \left(a+b x^2\right)}{2 b}",1,"((-I/16)*E^(I*a)*Sqrt[x]*Gamma[1/4, (-I)*b*x^2])/(b*((-I)*b*x^2)^(1/4)) + ((I/16)*Sqrt[x]*Gamma[1/4, I*b*x^2])/(b*E^(I*a)*(I*b*x^2)^(1/4)) + (Sqrt[x]*Sin[a + b*x^2])/(2*b)","A",4,3,14,0.2143,1,"{3386, 3389, 2218}"
25,1,81,0,0.0629466,"\int \sqrt{x} \cos \left(a+b x^2\right) \, dx","Int[Sqrt[x]*Cos[a + b*x^2],x]","-\frac{e^{i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{4 \left(-i b x^2\right)^{3/4}}-\frac{e^{-i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{4 \left(i b x^2\right)^{3/4}}","-\frac{e^{i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{4 \left(-i b x^2\right)^{3/4}}-\frac{e^{-i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{4 \left(i b x^2\right)^{3/4}}",1,"-(E^(I*a)*x^(3/2)*Gamma[3/4, (-I)*b*x^2])/(4*((-I)*b*x^2)^(3/4)) - (x^(3/2)*Gamma[3/4, I*b*x^2])/(4*E^(I*a)*(I*b*x^2)^(3/4))","A",3,2,14,0.1429,1,"{3390, 2218}"
26,1,81,0,0.0653032,"\int \frac{\cos \left(a+b x^2\right)}{\sqrt{x}} \, dx","Int[Cos[a + b*x^2]/Sqrt[x],x]","-\frac{e^{i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{4 \sqrt[4]{-i b x^2}}-\frac{e^{-i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{4 \sqrt[4]{i b x^2}}","-\frac{e^{i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{4 \sqrt[4]{-i b x^2}}-\frac{e^{-i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{4 \sqrt[4]{i b x^2}}",1,"-(E^(I*a)*Sqrt[x]*Gamma[1/4, (-I)*b*x^2])/(4*((-I)*b*x^2)^(1/4)) - (Sqrt[x]*Gamma[1/4, I*b*x^2])/(4*E^(I*a)*(I*b*x^2)^(1/4))","A",3,2,14,0.1429,1,"{3390, 2218}"
27,1,98,0,0.0758502,"\int \frac{\cos \left(a+b x^2\right)}{x^{3/2}} \, dx","Int[Cos[a + b*x^2]/x^(3/2),x]","-\frac{i e^{i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{\left(-i b x^2\right)^{3/4}}+\frac{i e^{-i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{\left(i b x^2\right)^{3/4}}-\frac{2 \cos \left(a+b x^2\right)}{\sqrt{x}}","-\frac{i e^{i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},-i b x^2\right)}{\left(-i b x^2\right)^{3/4}}+\frac{i e^{-i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},i b x^2\right)}{\left(i b x^2\right)^{3/4}}-\frac{2 \cos \left(a+b x^2\right)}{\sqrt{x}}",1,"(-2*Cos[a + b*x^2])/Sqrt[x] - (I*b*E^(I*a)*x^(3/2)*Gamma[3/4, (-I)*b*x^2])/((-I)*b*x^2)^(3/4) + (I*b*x^(3/2)*Gamma[3/4, I*b*x^2])/(E^(I*a)*(I*b*x^2)^(3/4))","A",4,3,14,0.2143,1,"{3388, 3389, 2218}"
28,1,104,0,0.0748721,"\int \frac{\cos \left(a+b x^2\right)}{x^{5/2}} \, dx","Int[Cos[a + b*x^2]/x^(5/2),x]","-\frac{i e^{i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{3 \sqrt[4]{-i b x^2}}+\frac{i e^{-i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{3 \sqrt[4]{i b x^2}}-\frac{2 \cos \left(a+b x^2\right)}{3 x^{3/2}}","-\frac{i e^{i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},-i b x^2\right)}{3 \sqrt[4]{-i b x^2}}+\frac{i e^{-i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},i b x^2\right)}{3 \sqrt[4]{i b x^2}}-\frac{2 \cos \left(a+b x^2\right)}{3 x^{3/2}}",1,"(-2*Cos[a + b*x^2])/(3*x^(3/2)) - ((I/3)*b*E^(I*a)*Sqrt[x]*Gamma[1/4, (-I)*b*x^2])/((-I)*b*x^2)^(1/4) + ((I/3)*b*Sqrt[x]*Gamma[1/4, I*b*x^2])/(E^(I*a)*(I*b*x^2)^(1/4))","A",4,3,14,0.2143,1,"{3388, 3389, 2218}"
29,1,132,0,0.1746583,"\int x^{5/2} \cos ^2\left(a+b x^2\right) \, dx","Int[x^(5/2)*Cos[a + b*x^2]^2,x]","-\frac{3 i e^{2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{64\ 2^{3/4} b \left(-i b x^2\right)^{3/4}}+\frac{3 i e^{-2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{64\ 2^{3/4} b \left(i b x^2\right)^{3/4}}+\frac{x^{3/2} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}+\frac{x^{7/2}}{7}","-\frac{3 i e^{2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{64\ 2^{3/4} b \left(-i b x^2\right)^{3/4}}+\frac{3 i e^{-2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{64\ 2^{3/4} b \left(i b x^2\right)^{3/4}}+\frac{x^{3/2} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}+\frac{x^{7/2}}{7}",1,"x^(7/2)/7 - (((3*I)/64)*E^((2*I)*a)*x^(3/2)*Gamma[3/4, (-2*I)*b*x^2])/(2^(3/4)*b*((-I)*b*x^2)^(3/4)) + (((3*I)/64)*x^(3/2)*Gamma[3/4, (2*I)*b*x^2])/(2^(3/4)*b*E^((2*I)*a)*(I*b*x^2)^(3/4)) + (x^(3/2)*Sin[2*(a + b*x^2)])/(8*b)","A",7,5,16,0.3125,1,"{3402, 3404, 3386, 3389, 2218}"
30,1,132,0,0.1238907,"\int x^{3/2} \cos ^2\left(a+b x^2\right) \, dx","Int[x^(3/2)*Cos[a + b*x^2]^2,x]","-\frac{i e^{2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{64 \sqrt[4]{2} b \sqrt[4]{-i b x^2}}+\frac{i e^{-2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{64 \sqrt[4]{2} b \sqrt[4]{i b x^2}}+\frac{\sqrt{x} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}+\frac{x^{5/2}}{5}","-\frac{i e^{2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{64 \sqrt[4]{2} b \sqrt[4]{-i b x^2}}+\frac{i e^{-2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{64 \sqrt[4]{2} b \sqrt[4]{i b x^2}}+\frac{\sqrt{x} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}+\frac{x^{5/2}}{5}",1,"x^(5/2)/5 - ((I/64)*E^((2*I)*a)*Sqrt[x]*Gamma[1/4, (-2*I)*b*x^2])/(2^(1/4)*b*((-I)*b*x^2)^(1/4)) + ((I/64)*Sqrt[x]*Gamma[1/4, (2*I)*b*x^2])/(2^(1/4)*b*E^((2*I)*a)*(I*b*x^2)^(1/4)) + (Sqrt[x]*Sin[2*(a + b*x^2)])/(8*b)","A",7,5,16,0.3125,1,"{3402, 3404, 3386, 3355, 2208}"
31,1,100,0,0.1303845,"\int \sqrt{x} \cos ^2\left(a+b x^2\right) \, dx","Int[Sqrt[x]*Cos[a + b*x^2]^2,x]","-\frac{e^{2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{8\ 2^{3/4} \left(-i b x^2\right)^{3/4}}-\frac{e^{-2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{8\ 2^{3/4} \left(i b x^2\right)^{3/4}}+\frac{x^{3/2}}{3}","-\frac{e^{2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{8\ 2^{3/4} \left(-i b x^2\right)^{3/4}}-\frac{e^{-2 i a} x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{8\ 2^{3/4} \left(i b x^2\right)^{3/4}}+\frac{x^{3/2}}{3}",1,"x^(3/2)/3 - (E^((2*I)*a)*x^(3/2)*Gamma[3/4, (-2*I)*b*x^2])/(8*2^(3/4)*((-I)*b*x^2)^(3/4)) - (x^(3/2)*Gamma[3/4, (2*I)*b*x^2])/(8*2^(3/4)*E^((2*I)*a)*(I*b*x^2)^(3/4))","A",6,4,16,0.2500,1,"{3402, 3404, 3390, 2218}"
32,1,96,0,0.0681866,"\int \frac{\cos ^2\left(a+b x^2\right)}{\sqrt{x}} \, dx","Int[Cos[a + b*x^2]^2/Sqrt[x],x]","-\frac{e^{2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{8 \sqrt[4]{2} \sqrt[4]{-i b x^2}}-\frac{e^{-2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{8 \sqrt[4]{2} \sqrt[4]{i b x^2}}+\sqrt{x}","-\frac{e^{2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{8 \sqrt[4]{2} \sqrt[4]{-i b x^2}}-\frac{e^{-2 i a} \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{8 \sqrt[4]{2} \sqrt[4]{i b x^2}}+\sqrt{x}",1,"Sqrt[x] - (E^((2*I)*a)*Sqrt[x]*Gamma[1/4, (-2*I)*b*x^2])/(8*2^(1/4)*((-I)*b*x^2)^(1/4)) - (Sqrt[x]*Gamma[1/4, (2*I)*b*x^2])/(8*2^(1/4)*E^((2*I)*a)*(I*b*x^2)^(1/4))","A",6,4,16,0.2500,1,"{3402, 3358, 3356, 2208}"
33,1,117,0,0.1630311,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^{3/2}} \, dx","Int[Cos[a + b*x^2]^2/x^(3/2),x]","-\frac{i e^{2 i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{2^{3/4} \left(-i b x^2\right)^{3/4}}+\frac{i e^{-2 i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{2^{3/4} \left(i b x^2\right)^{3/4}}-\frac{\cos \left(2 \left(a+b x^2\right)\right)}{\sqrt{x}}-\frac{1}{\sqrt{x}}","-\frac{i e^{2 i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},-2 i b x^2\right)}{2^{3/4} \left(-i b x^2\right)^{3/4}}+\frac{i e^{-2 i a} b x^{3/2} \text{Gamma}\left(\frac{3}{4},2 i b x^2\right)}{2^{3/4} \left(i b x^2\right)^{3/4}}-\frac{\cos \left(2 \left(a+b x^2\right)\right)}{\sqrt{x}}-\frac{1}{\sqrt{x}}",1,"-(1/Sqrt[x]) - Cos[2*(a + b*x^2)]/Sqrt[x] - (I*b*E^((2*I)*a)*x^(3/2)*Gamma[3/4, (-2*I)*b*x^2])/(2^(3/4)*((-I)*b*x^2)^(3/4)) + (I*b*x^(3/2)*Gamma[3/4, (2*I)*b*x^2])/(2^(3/4)*E^((2*I)*a)*(I*b*x^2)^(3/4))","A",7,5,16,0.3125,1,"{3402, 3404, 3388, 3389, 2218}"
34,1,116,0,0.0997398,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^{5/2}} \, dx","Int[Cos[a + b*x^2]^2/x^(5/2),x]","-\frac{i e^{2 i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{3 \sqrt[4]{2} \sqrt[4]{-i b x^2}}+\frac{i e^{-2 i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{3 \sqrt[4]{2} \sqrt[4]{i b x^2}}-\frac{2 \cos ^2\left(a+b x^2\right)}{3 x^{3/2}}","-\frac{i e^{2 i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},-2 i b x^2\right)}{3 \sqrt[4]{2} \sqrt[4]{-i b x^2}}+\frac{i e^{-2 i a} b \sqrt{x} \text{Gamma}\left(\frac{1}{4},2 i b x^2\right)}{3 \sqrt[4]{2} \sqrt[4]{i b x^2}}-\frac{2 \cos ^2\left(a+b x^2\right)}{3 x^{3/2}}",1,"(-2*Cos[a + b*x^2]^2)/(3*x^(3/2)) - ((I/3)*b*E^((2*I)*a)*Sqrt[x]*Gamma[1/4, (-2*I)*b*x^2])/(2^(1/4)*((-I)*b*x^2)^(1/4)) + ((I/3)*b*Sqrt[x]*Gamma[1/4, (2*I)*b*x^2])/(2^(1/4)*E^((2*I)*a)*(I*b*x^2)^(1/4))","A",7,6,16,0.3750,1,"{3402, 3394, 4573, 3373, 3355, 2208}"
35,1,31,0,0.0723927,"\int \cos \left(a+\frac{b}{x}\right) \, dx","Int[Cos[a + b/x],x]","b \sin (a) \text{CosIntegral}\left(\frac{b}{x}\right)+b \cos (a) \text{Si}\left(\frac{b}{x}\right)+x \cos \left(a+\frac{b}{x}\right)","b \sin (a) \text{CosIntegral}\left(\frac{b}{x}\right)+b \cos (a) \text{Si}\left(\frac{b}{x}\right)+x \cos \left(a+\frac{b}{x}\right)",1,"x*Cos[a + b/x] + b*CosIntegral[b/x]*Sin[a] + b*Cos[a]*SinIntegral[b/x]","A",5,5,8,0.6250,1,"{3362, 3297, 3303, 3299, 3302}"
36,1,20,0,0.0273317,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x} \, dx","Int[Cos[a + b/x]/x,x]","\sin (a) \text{Si}\left(\frac{b}{x}\right)-\cos (a) \text{CosIntegral}\left(\frac{b}{x}\right)","\sin (a) \text{Si}\left(\frac{b}{x}\right)-\cos (a) \text{CosIntegral}\left(\frac{b}{x}\right)",1,"-(Cos[a]*CosIntegral[b/x]) + Sin[a]*SinIntegral[b/x]","A",3,3,12,0.2500,1,"{3378, 3376, 3375}"
37,1,13,0,0.0144733,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^2} \, dx","Int[Cos[a + b/x]/x^2,x]","-\frac{\sin \left(a+\frac{b}{x}\right)}{b}","-\frac{\sin \left(a+\frac{b}{x}\right)}{b}",1,"-(Sin[a + b/x]/b)","A",2,2,12,0.1667,1,"{3380, 2637}"
38,1,30,0,0.0249832,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^3} \, dx","Int[Cos[a + b/x]/x^3,x]","-\frac{\cos \left(a+\frac{b}{x}\right)}{b^2}-\frac{\sin \left(a+\frac{b}{x}\right)}{b x}","-\frac{\cos \left(a+\frac{b}{x}\right)}{b^2}-\frac{\sin \left(a+\frac{b}{x}\right)}{b x}",1,"-(Cos[a + b/x]/b^2) - Sin[a + b/x]/(b*x)","A",3,3,12,0.2500,1,"{3380, 3296, 2638}"
39,1,46,0,0.0467186,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^4} \, dx","Int[Cos[a + b/x]/x^4,x]","\frac{2 \sin \left(a+\frac{b}{x}\right)}{b^3}-\frac{2 \cos \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{\sin \left(a+\frac{b}{x}\right)}{b x^2}","\frac{2 \sin \left(a+\frac{b}{x}\right)}{b^3}-\frac{2 \cos \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{\sin \left(a+\frac{b}{x}\right)}{b x^2}",1,"(-2*Cos[a + b/x])/(b^2*x) + (2*Sin[a + b/x])/b^3 - Sin[a + b/x]/(b*x^2)","A",4,3,12,0.2500,1,"{3380, 3296, 2637}"
40,1,79,0,0.0495695,"\int \cos \left(a+\frac{b}{x^2}\right) \, dx","Int[Cos[a + b/x^2],x]","\sqrt{2 \pi } \sqrt{b} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)+\sqrt{2 \pi } \sqrt{b} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+x \cos \left(a+\frac{b}{x^2}\right)","\sqrt{2 \pi } \sqrt{b} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)+\sqrt{2 \pi } \sqrt{b} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+x \cos \left(a+\frac{b}{x^2}\right)",1,"x*Cos[a + b/x^2] + Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[b]*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a]","A",5,5,8,0.6250,1,"{3360, 3388, 3353, 3352, 3351}"
41,1,25,0,0.0277989,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x} \, dx","Int[Cos[a + b/x^2]/x,x]","\frac{1}{2} \sin (a) \text{Si}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cos (a) \text{CosIntegral}\left(\frac{b}{x^2}\right)","\frac{1}{2} \sin (a) \text{Si}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cos (a) \text{CosIntegral}\left(\frac{b}{x^2}\right)",1,"-(Cos[a]*CosIntegral[b/x^2])/2 + (Sin[a]*SinIntegral[b/x^2])/2","A",3,3,12,0.2500,1,"{3378, 3376, 3375}"
42,1,74,0,0.0323861,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Int[Cos[a + b/x^2]/x^2,x]","\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)}{\sqrt{b}}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)}{\sqrt{b}}",1,"-((Sqrt[Pi/2]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x])/Sqrt[b]) + (Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a])/Sqrt[b]","A",4,4,12,0.3333,1,"{3384, 3354, 3352, 3351}"
43,1,15,0,0.0150678,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Int[Cos[a + b/x^2]/x^3,x]","-\frac{\sin \left(a+\frac{b}{x^2}\right)}{2 b}","-\frac{\sin \left(a+\frac{b}{x^2}\right)}{2 b}",1,"-Sin[a + b/x^2]/(2*b)","A",2,2,12,0.1667,1,"{3380, 2637}"
44,1,97,0,0.0532183,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Int[Cos[a + b/x^2]/x^4,x]","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)}{2 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{2 b^{3/2}}-\frac{\sin \left(a+\frac{b}{x^2}\right)}{2 b x}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)}{2 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{2 b^{3/2}}-\frac{\sin \left(a+\frac{b}{x^2}\right)}{2 b x}",1,"(Sqrt[Pi/2]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x])/(2*b^(3/2)) + (Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a])/(2*b^(3/2)) - Sin[a + b/x^2]/(2*b*x)","A",5,5,12,0.4167,1,"{3410, 3386, 3353, 3352, 3351}"
45,1,19,0,0.0214578,"\int \frac{\cos ^2\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[Cos[Sqrt[x]]^2/Sqrt[x],x]","\sqrt{x}+\sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)","\sqrt{x}+\sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)",1,"Sqrt[x] + Cos[Sqrt[x]]*Sin[Sqrt[x]]","A",3,3,14,0.2143,1,"{3380, 2635, 8}"
46,1,8,0,0.0088485,"\int \frac{\cos \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[Cos[Sqrt[x]]/Sqrt[x],x]","2 \sin \left(\sqrt{x}\right)","2 \sin \left(\sqrt{x}\right)",1,"2*Sin[Sqrt[x]]","A",2,2,12,0.1667,1,"{3380, 2637}"
47,1,22,0,0.0110084,"\int \cos \left(\sqrt{x}\right) \, dx","Int[Cos[Sqrt[x]],x]","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)","2 \sqrt{x} \sin \left(\sqrt{x}\right)+2 \cos \left(\sqrt{x}\right)",1,"2*Cos[Sqrt[x]] + 2*Sqrt[x]*Sin[Sqrt[x]]","A",3,3,6,0.5000,1,"{3362, 3296, 2638}"
48,1,36,0,0.0213152,"\int \cos ^2\left(\sqrt{x}\right) \, dx","Int[Cos[Sqrt[x]]^2,x]","\frac{x}{2}+\frac{1}{2} \cos ^2\left(\sqrt{x}\right)+\sqrt{x} \sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)","\frac{x}{2}+\frac{1}{2} \cos ^2\left(\sqrt{x}\right)+\sqrt{x} \sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)",1,"x/2 + Cos[Sqrt[x]]^2/2 + Sqrt[x]*Cos[Sqrt[x]]*Sin[Sqrt[x]]","A",3,3,8,0.3750,1,"{3362, 3310, 30}"
49,1,235,0,0.3480015,"\int x^{3/2} \cos \left(a+b \sqrt[3]{x}\right) \, dx","Int[x^(3/2)*Cos[a + b*x^(1/3)],x]","\frac{405405 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{64 b^{15/2}}+\frac{405405 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{64 b^{15/2}}-\frac{429 x^{3/2} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}+\frac{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right)}{16 b^5}+\frac{39 x^{11/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}-\frac{3861 x^{7/6} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}-\frac{405405 \sqrt[6]{x} \sin \left(a+b \sqrt[3]{x}\right)}{64 b^7}+\frac{135135 \sqrt{x} \cos \left(a+b \sqrt[3]{x}\right)}{32 b^6}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}","\frac{405405 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{64 b^{15/2}}+\frac{405405 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{64 b^{15/2}}-\frac{429 x^{3/2} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}+\frac{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right)}{16 b^5}+\frac{39 x^{11/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}-\frac{3861 x^{7/6} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}-\frac{405405 \sqrt[6]{x} \sin \left(a+b \sqrt[3]{x}\right)}{64 b^7}+\frac{135135 \sqrt{x} \cos \left(a+b \sqrt[3]{x}\right)}{32 b^6}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}",1,"(135135*Sqrt[x]*Cos[a + b*x^(1/3)])/(32*b^6) - (3861*x^(7/6)*Cos[a + b*x^(1/3)])/(8*b^4) + (39*x^(11/6)*Cos[a + b*x^(1/3)])/(2*b^2) + (405405*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)])/(64*b^(15/2)) + (405405*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a])/(64*b^(15/2)) - (405405*x^(1/6)*Sin[a + b*x^(1/3)])/(64*b^7) + (27027*x^(5/6)*Sin[a + b*x^(1/3)])/(16*b^5) - (429*x^(3/2)*Sin[a + b*x^(1/3)])/(4*b^3) + (3*x^(13/6)*Sin[a + b*x^(1/3)])/b","A",13,7,16,0.4375,1,"{3416, 3296, 3306, 3305, 3351, 3304, 3352}"
50,1,169,0,0.196254,"\int \sqrt{x} \cos \left(a+b \sqrt[3]{x}\right) \, dx","Int[Sqrt[x]*Cos[a + b*x^(1/3)],x]","\frac{315 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{8 b^{9/2}}-\frac{315 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{8 b^{9/2}}+\frac{21 x^{5/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}-\frac{105 \sqrt{x} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}-\frac{315 \sqrt[6]{x} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}","\frac{315 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{8 b^{9/2}}-\frac{315 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{8 b^{9/2}}+\frac{21 x^{5/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}-\frac{105 \sqrt{x} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}-\frac{315 \sqrt[6]{x} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}",1,"(-315*x^(1/6)*Cos[a + b*x^(1/3)])/(8*b^4) + (21*x^(5/6)*Cos[a + b*x^(1/3)])/(2*b^2) + (315*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)])/(8*b^(9/2)) - (315*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a])/(8*b^(9/2)) - (105*Sqrt[x]*Sin[a + b*x^(1/3)])/(4*b^3) + (3*x^(7/6)*Sin[a + b*x^(1/3)])/b","A",10,7,16,0.4375,1,"{3416, 3296, 3306, 3305, 3351, 3304, 3352}"
51,1,99,0,0.1131559,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{\sqrt{x}} \, dx","Int[Cos[a + b*x^(1/3)]/Sqrt[x],x]","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{b^{3/2}}+\frac{3 \sqrt[6]{x} \sin \left(a+b \sqrt[3]{x}\right)}{b}","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{b^{3/2}}+\frac{3 \sqrt[6]{x} \sin \left(a+b \sqrt[3]{x}\right)}{b}",1,"(-3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)])/b^(3/2) - (3*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a])/b^(3/2) + (3*x^(1/6)*Sin[a + b*x^(1/3)])/b","A",7,7,16,0.4375,1,"{3416, 3296, 3306, 3305, 3351, 3304, 3352}"
52,1,110,0,0.1428773,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{3/2}} \, dx","Int[Cos[a + b*x^(1/3)]/x^(3/2),x]","-4 \sqrt{2 \pi } b^{3/2} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)+4 \sqrt{2 \pi } b^{3/2} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{\sqrt[6]{x}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{\sqrt{x}}","-4 \sqrt{2 \pi } b^{3/2} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)+4 \sqrt{2 \pi } b^{3/2} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{\sqrt[6]{x}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{\sqrt{x}}",1,"(-2*Cos[a + b*x^(1/3)])/Sqrt[x] - 4*b^(3/2)*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] + 4*b^(3/2)*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] + (4*b*Sin[a + b*x^(1/3)])/x^(1/6)","A",8,7,16,0.4375,1,"{3416, 3297, 3306, 3305, 3351, 3304, 3352}"
53,1,184,0,0.2377784,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{5/2}} \, dx","Int[Cos[a + b*x^(1/3)]/x^(5/2),x]","-\frac{32}{315} \sqrt{2 \pi } b^{9/2} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)-\frac{32}{315} \sqrt{2 \pi } b^{9/2} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{315 \sqrt{x}}-\frac{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{315 \sqrt[6]{x}}+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{21 x^{7/6}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{3 x^{3/2}}","-\frac{32}{315} \sqrt{2 \pi } b^{9/2} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)-\frac{32}{315} \sqrt{2 \pi } b^{9/2} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{315 \sqrt{x}}-\frac{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{315 \sqrt[6]{x}}+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{21 x^{7/6}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{3 x^{3/2}}",1,"(-2*Cos[a + b*x^(1/3)])/(3*x^(3/2)) + (8*b^2*Cos[a + b*x^(1/3)])/(105*x^(5/6)) - (32*b^4*Cos[a + b*x^(1/3)])/(315*x^(1/6)) - (32*b^(9/2)*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)])/315 - (32*b^(9/2)*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a])/315 + (4*b*Sin[a + b*x^(1/3)])/(21*x^(7/6)) - (16*b^3*Sin[a + b*x^(1/3)])/(315*Sqrt[x])","A",11,7,16,0.4375,1,"{3416, 3297, 3306, 3305, 3351, 3304, 3352}"
54,1,250,0,0.3369335,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{7/2}} \, dx","Int[Cos[a + b*x^(1/3)]/x^(7/2),x]","\frac{256 \sqrt{2 \pi } b^{15/2} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{675675}-\frac{256 \sqrt{2 \pi } b^{15/2} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{675675}+\frac{64 b^5 \sin \left(a+b \sqrt[3]{x}\right)}{225225 x^{5/6}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{6435 x^{3/2}}-\frac{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}-\frac{256 b^7 \sin \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt[6]{x}}+\frac{128 b^6 \cos \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt{x}}+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{65 x^{13/6}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{5 x^{5/2}}","\frac{256 \sqrt{2 \pi } b^{15/2} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \sqrt[6]{x}\right)}{675675}-\frac{256 \sqrt{2 \pi } b^{15/2} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{675675}+\frac{64 b^5 \sin \left(a+b \sqrt[3]{x}\right)}{225225 x^{5/6}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{6435 x^{3/2}}-\frac{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}-\frac{256 b^7 \sin \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt[6]{x}}+\frac{128 b^6 \cos \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt{x}}+\frac{4 b \sin \left(a+b \sqrt[3]{x}\right)}{65 x^{13/6}}-\frac{2 \cos \left(a+b \sqrt[3]{x}\right)}{5 x^{5/2}}",1,"(-2*Cos[a + b*x^(1/3)])/(5*x^(5/2)) + (8*b^2*Cos[a + b*x^(1/3)])/(715*x^(11/6)) - (32*b^4*Cos[a + b*x^(1/3)])/(45045*x^(7/6)) + (128*b^6*Cos[a + b*x^(1/3)])/(675675*Sqrt[x]) + (256*b^(15/2)*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)])/675675 - (256*b^(15/2)*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a])/675675 + (4*b*Sin[a + b*x^(1/3)])/(65*x^(13/6)) - (16*b^3*Sin[a + b*x^(1/3)])/(6435*x^(3/2)) + (64*b^5*Sin[a + b*x^(1/3)])/(225225*x^(5/6)) - (256*b^7*Sin[a + b*x^(1/3)])/(675675*x^(1/6))","A",14,7,16,0.4375,1,"{3416, 3297, 3306, 3305, 3351, 3304, 3352}"
55,1,310,0,0.3597339,"\int x^{3/2} \cos ^2\left(a+b \sqrt[3]{x}\right) \, dx","Int[x^(3/2)*Cos[a + b*x^(1/3)]^2,x]","\frac{405405 \sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{32768 b^{15/2}}+\frac{405405 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{32768 b^{15/2}}+\frac{39 x^{11/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}-\frac{3861 x^{7/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{128 b^4}-\frac{429 x^{3/2} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{32 b^3}+\frac{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{512 b^5}-\frac{405405 \sqrt[6]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)}{16384 b^7}+\frac{135135 \sqrt{x} \cos ^2\left(a+b \sqrt[3]{x}\right)}{2048 b^6}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}-\frac{39 x^{11/6}}{16 b^2}+\frac{3861 x^{7/6}}{256 b^4}-\frac{135135 \sqrt{x}}{4096 b^6}+\frac{x^{5/2}}{5}","\frac{405405 \sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{32768 b^{15/2}}+\frac{405405 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{32768 b^{15/2}}+\frac{39 x^{11/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}-\frac{3861 x^{7/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{128 b^4}-\frac{429 x^{3/2} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{32 b^3}+\frac{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{512 b^5}-\frac{405405 \sqrt[6]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)}{16384 b^7}+\frac{135135 \sqrt{x} \cos ^2\left(a+b \sqrt[3]{x}\right)}{2048 b^6}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}-\frac{39 x^{11/6}}{16 b^2}+\frac{3861 x^{7/6}}{256 b^4}-\frac{135135 \sqrt{x}}{4096 b^6}+\frac{x^{5/2}}{5}",1,"(-135135*Sqrt[x])/(4096*b^6) + (3861*x^(7/6))/(256*b^4) - (39*x^(11/6))/(16*b^2) + x^(5/2)/5 + (135135*Sqrt[x]*Cos[a + b*x^(1/3)]^2)/(2048*b^6) - (3861*x^(7/6)*Cos[a + b*x^(1/3)]^2)/(128*b^4) + (39*x^(11/6)*Cos[a + b*x^(1/3)]^2)/(8*b^2) + (405405*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]])/(32768*b^(15/2)) + (405405*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a])/(32768*b^(15/2)) + (27027*x^(5/6)*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(512*b^5) - (429*x^(3/2)*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(32*b^3) + (3*x^(13/6)*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(2*b) - (405405*x^(1/6)*Sin[2*(a + b*x^(1/3))])/(16384*b^7)","A",15,10,18,0.5556,1,"{3416, 3311, 30, 3312, 3296, 3306, 3305, 3351, 3304, 3352}"
56,1,218,0,0.2506794,"\int \sqrt{x} \cos ^2\left(a+b \sqrt[3]{x}\right) \, dx","Int[Sqrt[x]*Cos[a + b*x^(1/3)]^2,x]","\frac{315 \sqrt{\pi } \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{512 b^{9/2}}-\frac{315 \sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{512 b^{9/2}}+\frac{21 x^{5/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}-\frac{315 \sqrt[6]{x} \cos ^2\left(a+b \sqrt[3]{x}\right)}{128 b^4}-\frac{105 \sqrt{x} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{32 b^3}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}-\frac{21 x^{5/6}}{16 b^2}+\frac{315 \sqrt[6]{x}}{256 b^4}+\frac{x^{3/2}}{3}","\frac{315 \sqrt{\pi } \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{512 b^{9/2}}-\frac{315 \sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{512 b^{9/2}}+\frac{21 x^{5/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}-\frac{315 \sqrt[6]{x} \cos ^2\left(a+b \sqrt[3]{x}\right)}{128 b^4}-\frac{105 \sqrt{x} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{32 b^3}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}-\frac{21 x^{5/6}}{16 b^2}+\frac{315 \sqrt[6]{x}}{256 b^4}+\frac{x^{3/2}}{3}",1,"(315*x^(1/6))/(256*b^4) - (21*x^(5/6))/(16*b^2) + x^(3/2)/3 - (315*x^(1/6)*Cos[a + b*x^(1/3)]^2)/(128*b^4) + (21*x^(5/6)*Cos[a + b*x^(1/3)]^2)/(8*b^2) + (315*Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]])/(512*b^(9/2)) - (315*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a])/(512*b^(9/2)) - (105*Sqrt[x]*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(32*b^3) + (3*x^(7/6)*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(2*b)","A",12,9,18,0.5000,1,"{3416, 3311, 30, 3312, 3306, 3305, 3351, 3304, 3352}"
57,1,102,0,0.1696365,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{\sqrt{x}} \, dx","Int[Cos[a + b*x^(1/3)]^2/Sqrt[x],x]","-\frac{3 \sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{8 b^{3/2}}-\frac{3 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{8 b^{3/2}}+\frac{3 \sqrt[6]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)}{4 b}+\sqrt{x}","-\frac{3 \sqrt{\pi } \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{8 b^{3/2}}-\frac{3 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{8 b^{3/2}}+\frac{3 \sqrt[6]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)}{4 b}+\sqrt{x}",1,"Sqrt[x] - (3*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]])/(8*b^(3/2)) - (3*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a])/(8*b^(3/2)) + (3*x^(1/6)*Sin[2*(a + b*x^(1/3))])/(4*b)","A",9,8,18,0.4444,1,"{3416, 3312, 3296, 3306, 3305, 3351, 3304, 3352}"
58,1,116,0,0.1869401,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{3/2}} \, dx","Int[Cos[a + b*x^(1/3)]^2/x^(3/2),x]","-8 \sqrt{\pi } b^{3/2} \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+8 \sqrt{\pi } b^{3/2} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{\sqrt{x}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{\sqrt[6]{x}}","-8 \sqrt{\pi } b^{3/2} \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+8 \sqrt{\pi } b^{3/2} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{\sqrt{x}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{\sqrt[6]{x}}",1,"(-2*Cos[a + b*x^(1/3)]^2)/Sqrt[x] - 8*b^(3/2)*Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] + 8*b^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + (8*b*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/x^(1/6)","A",10,9,18,0.5000,1,"{3416, 3314, 30, 3312, 3306, 3305, 3351, 3304, 3352}"
59,1,228,0,0.2501156,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{5/2}} \, dx","Int[Cos[a + b*x^(1/3)]^2/x^(5/2),x]","-\frac{512}{315} \sqrt{\pi } b^{9/2} \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-\frac{512}{315} \sqrt{\pi } b^{9/2} \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+\frac{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}-\frac{512 b^4 \cos ^2\left(a+b \sqrt[3]{x}\right)}{315 \sqrt[6]{x}}-\frac{128 b^3 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{315 \sqrt{x}}-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{3 x^{3/2}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{21 x^{7/6}}-\frac{16 b^2}{105 x^{5/6}}+\frac{256 b^4}{315 \sqrt[6]{x}}","-\frac{512}{315} \sqrt{\pi } b^{9/2} \sin (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-\frac{512}{315} \sqrt{\pi } b^{9/2} \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+\frac{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}-\frac{512 b^4 \cos ^2\left(a+b \sqrt[3]{x}\right)}{315 \sqrt[6]{x}}-\frac{128 b^3 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{315 \sqrt{x}}-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{3 x^{3/2}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{21 x^{7/6}}-\frac{16 b^2}{105 x^{5/6}}+\frac{256 b^4}{315 \sqrt[6]{x}}",1,"(-16*b^2)/(105*x^(5/6)) + (256*b^4)/(315*x^(1/6)) - (2*Cos[a + b*x^(1/3)]^2)/(3*x^(3/2)) + (32*b^2*Cos[a + b*x^(1/3)]^2)/(105*x^(5/6)) - (512*b^4*Cos[a + b*x^(1/3)]^2)/(315*x^(1/6)) - (512*b^(9/2)*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]])/315 - (512*b^(9/2)*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a])/315 + (8*b*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(21*x^(7/6)) - (128*b^3*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(315*Sqrt[x])","A",12,10,18,0.5556,1,"{3416, 3314, 30, 3313, 12, 3306, 3305, 3351, 3304, 3352}"
60,1,328,0,0.3506936,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{7/2}} \, dx","Int[Cos[a + b*x^(1/3)]^2/x^(7/2),x]","\frac{32768 \sqrt{\pi } b^{15/2} \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{675675}-\frac{32768 \sqrt{\pi } b^{15/2} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{675675}-\frac{512 b^4 \cos ^2\left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}+\frac{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}+\frac{2048 b^5 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{225225 x^{5/6}}-\frac{128 b^3 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{6435 x^{3/2}}+\frac{8192 b^6 \cos ^2\left(a+b \sqrt[3]{x}\right)}{675675 \sqrt{x}}-\frac{32768 b^7 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt[6]{x}}-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{5 x^{5/2}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{65 x^{13/6}}+\frac{256 b^4}{45045 x^{7/6}}-\frac{16 b^2}{715 x^{11/6}}-\frac{4096 b^6}{675675 \sqrt{x}}","\frac{32768 \sqrt{\pi } b^{15/2} \cos (2 a) \text{FresnelC}\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{675675}-\frac{32768 \sqrt{\pi } b^{15/2} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{675675}-\frac{512 b^4 \cos ^2\left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}+\frac{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}+\frac{2048 b^5 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{225225 x^{5/6}}-\frac{128 b^3 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{6435 x^{3/2}}+\frac{8192 b^6 \cos ^2\left(a+b \sqrt[3]{x}\right)}{675675 \sqrt{x}}-\frac{32768 b^7 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt[6]{x}}-\frac{2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{5 x^{5/2}}+\frac{8 b \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{65 x^{13/6}}+\frac{256 b^4}{45045 x^{7/6}}-\frac{16 b^2}{715 x^{11/6}}-\frac{4096 b^6}{675675 \sqrt{x}}",1,"(-16*b^2)/(715*x^(11/6)) + (256*b^4)/(45045*x^(7/6)) - (4096*b^6)/(675675*Sqrt[x]) - (2*Cos[a + b*x^(1/3)]^2)/(5*x^(5/2)) + (32*b^2*Cos[a + b*x^(1/3)]^2)/(715*x^(11/6)) - (512*b^4*Cos[a + b*x^(1/3)]^2)/(45045*x^(7/6)) + (8192*b^6*Cos[a + b*x^(1/3)]^2)/(675675*Sqrt[x]) + (32768*b^(15/2)*Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]])/675675 - (32768*b^(15/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a])/675675 + (8*b*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(65*x^(13/6)) - (128*b^3*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(6435*x^(3/2)) + (2048*b^5*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(225225*x^(5/6)) - (32768*b^7*Cos[a + b*x^(1/3)]*Sin[a + b*x^(1/3)])/(675675*x^(1/6))","A",16,9,18,0.5000,1,"{3416, 3314, 30, 3312, 3306, 3305, 3351, 3304, 3352}"
61,1,86,0,0.0682848,"\int \cos ^3\left(\sqrt[3]{x}\right) \, dx","Int[Cos[x^(1/3)]^3,x]","2 x^{2/3} \sin \left(\sqrt[3]{x}\right)+x^{2/3} \sin \left(\sqrt[3]{x}\right) \cos ^2\left(\sqrt[3]{x}\right)+\frac{2}{9} \sin ^3\left(\sqrt[3]{x}\right)-\frac{14}{3} \sin \left(\sqrt[3]{x}\right)+\frac{2}{3} \sqrt[3]{x} \cos ^3\left(\sqrt[3]{x}\right)+4 \sqrt[3]{x} \cos \left(\sqrt[3]{x}\right)","2 x^{2/3} \sin \left(\sqrt[3]{x}\right)+x^{2/3} \sin \left(\sqrt[3]{x}\right) \cos ^2\left(\sqrt[3]{x}\right)+\frac{2}{9} \sin ^3\left(\sqrt[3]{x}\right)-\frac{14}{3} \sin \left(\sqrt[3]{x}\right)+\frac{2}{3} \sqrt[3]{x} \cos ^3\left(\sqrt[3]{x}\right)+4 \sqrt[3]{x} \cos \left(\sqrt[3]{x}\right)",1,"4*x^(1/3)*Cos[x^(1/3)] + (2*x^(1/3)*Cos[x^(1/3)]^3)/3 - (14*Sin[x^(1/3)])/3 + 2*x^(2/3)*Sin[x^(1/3)] + x^(2/3)*Cos[x^(1/3)]^2*Sin[x^(1/3)] + (2*Sin[x^(1/3)]^3)/9","A",7,5,8,0.6250,1,"{3362, 3311, 3296, 2637, 2633}"
62,1,8,0,0.0097518,"\int \frac{\cos \left(\sqrt[6]{x}\right)}{x^{5/6}} \, dx","Int[Cos[x^(1/6)]/x^(5/6),x]","6 \sin \left(\sqrt[6]{x}\right)","6 \sin \left(\sqrt[6]{x}\right)",1,"6*Sin[x^(1/6)]","A",2,2,12,0.1667,1,"{3380, 2637}"
63,0,0,0,0.0196607,"\int (e x)^m \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^m*(b*Cos[c + d*x^n])^p,x]","\int (e x)^m \left(b \cos \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(b \cos \left(c+d x^n\right)\right)^p,x\right)",0,"Defer[Int][(e*x)^m*(b*Cos[c + d*x^n])^p, x]","A",0,0,0,0,-1,"{}"
64,0,0,0,0.0224955,"\int (e x)^m \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^m*(a + b*Cos[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \cos \left(c+d x^n\right)\right)^p,x\right)",0,"Defer[Int][(e*x)^m*(a + b*Cos[c + d*x^n])^p, x]","A",0,0,0,0,-1,"{}"
65,1,93,0,0.1019578,"\int (e x)^{-1+n} \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + n)*(b*Cos[c + d*x^n])^p,x]","-\frac{x^{-n} (e x)^n \sin \left(c+d x^n\right) \left(b \cos \left(c+d x^n\right)\right)^{p+1} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\cos ^2\left(d x^n+c\right)\right)}{b d e n (p+1) \sqrt{\sin ^2\left(c+d x^n\right)}}","-\frac{x^{-n} (e x)^n \sin \left(c+d x^n\right) \left(b \cos \left(c+d x^n\right)\right)^{p+1} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\cos ^2\left(d x^n+c\right)\right)}{b d e n (p+1) \sqrt{\sin ^2\left(c+d x^n\right)}}",1,"-(((e*x)^n*(b*Cos[c + d*x^n])^(1 + p)*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Cos[c + d*x^n]^2]*Sin[c + d*x^n])/(b*d*e*n*(1 + p)*x^n*Sqrt[Sin[c + d*x^n]^2]))","A",3,3,20,0.1500,1,"{3382, 3380, 2643}"
66,0,0,0,0.0486985,"\int (e x)^{-1+2 n} \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + 2*n)*(b*Cos[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(b \cos \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(b \cos \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"((e*x)^(2*n)*Defer[Int][x^(-1 + 2*n)*(b*Cos[c + d*x^n])^p, x])/(e*x^(2*n))","A",0,0,0,0,-1,"{}"
67,1,131,0,0.1665826,"\int (e x)^{-1+n} \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + n)*(a + b*Cos[c + d*x^n])^p,x]","\frac{\sqrt{2} x^{-n} (e x)^n \sin \left(c+d x^n\right) \left(a+b \cos \left(c+d x^n\right)\right)^p \left(\frac{a+b \cos \left(c+d x^n\right)}{a+b}\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};\frac{1}{2} \left(1-\cos \left(d x^n+c\right)\right),\frac{b \left(1-\cos \left(d x^n+c\right)\right)}{a+b}\right)}{d e n \sqrt{\cos \left(c+d x^n\right)+1}}","\frac{\sqrt{2} x^{-n} (e x)^n \sin \left(c+d x^n\right) \left(a+b \cos \left(c+d x^n\right)\right)^p \left(\frac{a+b \cos \left(c+d x^n\right)}{a+b}\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};\frac{1}{2} \left(1-\cos \left(d x^n+c\right)\right),\frac{b \left(1-\cos \left(d x^n+c\right)\right)}{a+b}\right)}{d e n \sqrt{\cos \left(c+d x^n\right)+1}}",1,"(Sqrt[2]*(e*x)^n*AppellF1[1/2, 1/2, -p, 3/2, (1 - Cos[c + d*x^n])/2, (b*(1 - Cos[c + d*x^n]))/(a + b)]*(a + b*Cos[c + d*x^n])^p*Sin[c + d*x^n])/(d*e*n*x^n*Sqrt[1 + Cos[c + d*x^n]]*((a + b*Cos[c + d*x^n])/(a + b))^p)","A",5,5,22,0.2273,1,"{3382, 3380, 2665, 139, 138}"
68,0,0,0,0.054143,"\int (e x)^{-1+2 n} \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + 2*n)*(a + b*Cos[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(a+b \cos \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"((e*x)^(2*n)*Defer[Int][x^(-1 + 2*n)*(a + b*Cos[c + d*x^n])^p, x])/(e*x^(2*n))","A",0,0,0,0,-1,"{}"
69,1,26,0,0.0339921,"\int \frac{\cos \left(a+b x^n\right)}{x} \, dx","Int[Cos[a + b*x^n]/x,x]","\frac{\cos (a) \text{CosIntegral}\left(b x^n\right)}{n}-\frac{\sin (a) \text{Si}\left(b x^n\right)}{n}","\frac{\cos (a) \text{CosIntegral}\left(b x^n\right)}{n}-\frac{\sin (a) \text{Si}\left(b x^n\right)}{n}",1,"(Cos[a]*CosIntegral[b*x^n])/n - (Sin[a]*SinIntegral[b*x^n])/n","A",3,3,12,0.2500,1,"{3378, 3376, 3375}"
70,1,43,0,0.0579186,"\int \frac{\cos ^2\left(a+b x^n\right)}{x} \, dx","Int[Cos[a + b*x^n]^2/x,x]","\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}-\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}+\frac{\log (x)}{2}","\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}-\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}+\frac{\log (x)}{2}",1,"(Cos[2*a]*CosIntegral[2*b*x^n])/(2*n) + Log[x]/2 - (Sin[2*a]*SinIntegral[2*b*x^n])/(2*n)","A",5,4,14,0.2857,1,"{3426, 3378, 3376, 3375}"
71,1,67,0,0.0860536,"\int \frac{\cos ^3\left(a+b x^n\right)}{x} \, dx","Int[Cos[a + b*x^n]^3/x,x]","\frac{3 \cos (a) \text{CosIntegral}\left(b x^n\right)}{4 n}+\frac{\cos (3 a) \text{CosIntegral}\left(3 b x^n\right)}{4 n}-\frac{3 \sin (a) \text{Si}\left(b x^n\right)}{4 n}-\frac{\sin (3 a) \text{Si}\left(3 b x^n\right)}{4 n}","\frac{3 \cos (a) \text{CosIntegral}\left(b x^n\right)}{4 n}+\frac{\cos (3 a) \text{CosIntegral}\left(3 b x^n\right)}{4 n}-\frac{3 \sin (a) \text{Si}\left(b x^n\right)}{4 n}-\frac{\sin (3 a) \text{Si}\left(3 b x^n\right)}{4 n}",1,"(3*Cos[a]*CosIntegral[b*x^n])/(4*n) + (Cos[3*a]*CosIntegral[3*b*x^n])/(4*n) - (3*Sin[a]*SinIntegral[b*x^n])/(4*n) - (Sin[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",8,4,14,0.2857,1,"{3426, 3378, 3376, 3375}"
72,1,79,0,0.0940672,"\int \frac{\cos ^4\left(a+b x^n\right)}{x} \, dx","Int[Cos[a + b*x^n]^4/x,x]","\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{CosIntegral}\left(4 b x^n\right)}{8 n}-\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}-\frac{\sin (4 a) \text{Si}\left(4 b x^n\right)}{8 n}+\frac{3 \log (x)}{8}","\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{CosIntegral}\left(4 b x^n\right)}{8 n}-\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}-\frac{\sin (4 a) \text{Si}\left(4 b x^n\right)}{8 n}+\frac{3 \log (x)}{8}",1,"(Cos[2*a]*CosIntegral[2*b*x^n])/(2*n) + (Cos[4*a]*CosIntegral[4*b*x^n])/(8*n) + (3*Log[x])/8 - (Sin[2*a]*SinIntegral[2*b*x^n])/(2*n) - (Sin[4*a]*SinIntegral[4*b*x^n])/(8*n)","A",8,4,14,0.2857,1,"{3426, 3378, 3376, 3375}"
73,1,83,0,0.0216957,"\int \cos \left(a+b x^n\right) \, dx","Int[Cos[a + b*x^n],x]","-\frac{e^{i a} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-i b x^n\right)}{2 n}-\frac{e^{-i a} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},i b x^n\right)}{2 n}","-\frac{e^{i a} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-i b x^n\right)}{2 n}-\frac{e^{-i a} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},i b x^n\right)}{2 n}",1,"-(E^(I*a)*x*Gamma[n^(-1), (-I)*b*x^n])/(2*n*((-I)*b*x^n)^n^(-1)) - (x*Gamma[n^(-1), I*b*x^n])/(2*E^(I*a)*n*(I*b*x^n)^n^(-1))","A",3,2,8,0.2500,1,"{3366, 2208}"
74,1,102,0,0.0690008,"\int \cos ^2\left(a+b x^n\right) \, dx","Int[Cos[a + b*x^n]^2,x]","-\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-2 i b x^n\right)}{n}-\frac{e^{-2 i a} 2^{-\frac{1}{n}-2} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}","-\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-2 i b x^n\right)}{n}-\frac{e^{-2 i a} 2^{-\frac{1}{n}-2} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}",1,"x/2 - (2^(-2 - n^(-1))*E^((2*I)*a)*x*Gamma[n^(-1), (-2*I)*b*x^n])/(n*((-I)*b*x^n)^n^(-1)) - (2^(-2 - n^(-1))*x*Gamma[n^(-1), (2*I)*b*x^n])/(E^((2*I)*a)*n*(I*b*x^n)^n^(-1))","A",5,3,10,0.3000,1,"{3368, 3366, 2208}"
75,1,179,0,0.0789607,"\int \cos ^3\left(a+b x^n\right) \, dx","Int[Cos[a + b*x^n]^3,x]","-\frac{3 e^{i a} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-i b x^n\right)}{8 n}-\frac{e^{3 i a} 3^{-1/n} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-3 i b x^n\right)}{8 n}-\frac{3 e^{-i a} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},i b x^n\right)}{8 n}-\frac{e^{-3 i a} 3^{-1/n} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},3 i b x^n\right)}{8 n}","-\frac{3 e^{i a} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-i b x^n\right)}{8 n}-\frac{e^{3 i a} 3^{-1/n} x \left(-i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-3 i b x^n\right)}{8 n}-\frac{3 e^{-i a} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},i b x^n\right)}{8 n}-\frac{e^{-3 i a} 3^{-1/n} x \left(i b x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},3 i b x^n\right)}{8 n}",1,"(-3*E^(I*a)*x*Gamma[n^(-1), (-I)*b*x^n])/(8*n*((-I)*b*x^n)^n^(-1)) - (3*x*Gamma[n^(-1), I*b*x^n])/(8*E^(I*a)*n*(I*b*x^n)^n^(-1)) - (E^((3*I)*a)*x*Gamma[n^(-1), (-3*I)*b*x^n])/(8*3^n^(-1)*n*((-I)*b*x^n)^n^(-1)) - (x*Gamma[n^(-1), (3*I)*b*x^n])/(8*3^n^(-1)*E^((3*I)*a)*n*(I*b*x^n)^n^(-1))","A",8,3,10,0.3000,1,"{3368, 3366, 2208}"
76,1,105,0,0.0748536,"\int x^m \cos \left(a+b x^n\right) \, dx","Int[x^m*Cos[a + b*x^n],x]","-\frac{e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-i b x^n\right)}{2 n}-\frac{e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},i b x^n\right)}{2 n}","-\frac{e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-i b x^n\right)}{2 n}-\frac{e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},i b x^n\right)}{2 n}",1,"-(E^(I*a)*x^(1 + m)*Gamma[(1 + m)/n, (-I)*b*x^n])/(2*n*((-I)*b*x^n)^((1 + m)/n)) - (x^(1 + m)*Gamma[(1 + m)/n, I*b*x^n])/(2*E^(I*a)*n*(I*b*x^n)^((1 + m)/n))","A",3,2,12,0.1667,1,"{3424, 2218}"
77,1,141,0,0.1604361,"\int x^m \cos ^2\left(a+b x^n\right) \, dx","Int[x^m*Cos[a + b*x^n]^2,x]","-\frac{e^{2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-2 i b x^n\right)}{n}-\frac{e^{-2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},2 i b x^n\right)}{n}+\frac{x^{m+1}}{2 (m+1)}","-\frac{e^{2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-2 i b x^n\right)}{n}-\frac{e^{-2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},2 i b x^n\right)}{n}+\frac{x^{m+1}}{2 (m+1)}",1,"x^(1 + m)/(2*(1 + m)) - (E^((2*I)*a)*x^(1 + m)*Gamma[(1 + m)/n, (-2*I)*b*x^n])/(2^((1 + m + 2*n)/n)*n*((-I)*b*x^n)^((1 + m)/n)) - (x^(1 + m)*Gamma[(1 + m)/n, (2*I)*b*x^n])/(2^((1 + m + 2*n)/n)*E^((2*I)*a)*n*(I*b*x^n)^((1 + m)/n))","A",5,3,14,0.2143,1,"{3426, 3424, 2218}"
78,1,229,0,0.2117571,"\int x^m \cos ^3\left(a+b x^n\right) \, dx","Int[x^m*Cos[a + b*x^n]^3,x]","-\frac{3 e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-i b x^n\right)}{8 n}-\frac{3 e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},i b x^n\right)}{8 n}-\frac{e^{3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-3 i b x^n\right)}{8 n}-\frac{e^{-3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},3 i b x^n\right)}{8 n}","-\frac{3 e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-i b x^n\right)}{8 n}-\frac{3 e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},i b x^n\right)}{8 n}-\frac{e^{3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-3 i b x^n\right)}{8 n}-\frac{e^{-3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},3 i b x^n\right)}{8 n}",1,"(-3*E^(I*a)*x^(1 + m)*Gamma[(1 + m)/n, (-I)*b*x^n])/(8*n*((-I)*b*x^n)^((1 + m)/n)) - (3*x^(1 + m)*Gamma[(1 + m)/n, I*b*x^n])/(8*E^(I*a)*n*(I*b*x^n)^((1 + m)/n)) - (E^((3*I)*a)*x^(1 + m)*Gamma[(1 + m)/n, (-3*I)*b*x^n])/(8*3^((1 + m)/n)*n*((-I)*b*x^n)^((1 + m)/n)) - (x^(1 + m)*Gamma[(1 + m)/n, (3*I)*b*x^n])/(8*3^((1 + m)/n)*E^((3*I)*a)*n*(I*b*x^n)^((1 + m)/n))","A",8,3,14,0.2143,1,"{3426, 3424, 2218}"
79,1,47,0,0.0864871,"\int x^{-1-n} \cos \left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Cos[a + b*x^n],x]","-\frac{b \sin (a) \text{CosIntegral}\left(b x^n\right)}{n}-\frac{b \cos (a) \text{Si}\left(b x^n\right)}{n}-\frac{x^{-n} \cos \left(a+b x^n\right)}{n}","-\frac{b \sin (a) \text{CosIntegral}\left(b x^n\right)}{n}-\frac{b \cos (a) \text{Si}\left(b x^n\right)}{n}-\frac{x^{-n} \cos \left(a+b x^n\right)}{n}",1,"-(Cos[a + b*x^n]/(n*x^n)) - (b*CosIntegral[b*x^n]*Sin[a])/n - (b*Cos[a]*SinIntegral[b*x^n])/n","A",5,5,16,0.3125,1,"{3380, 3297, 3303, 3299, 3302}"
80,1,69,0,0.1205617,"\int x^{-1-n} \cos ^2\left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Cos[a + b*x^n]^2,x]","-\frac{b \sin (2 a) \text{CosIntegral}\left(2 b x^n\right)}{n}-\frac{b \cos (2 a) \text{Si}\left(2 b x^n\right)}{n}-\frac{x^{-n} \cos \left(2 \left(a+b x^n\right)\right)}{2 n}-\frac{x^{-n}}{2 n}","-\frac{b \sin (2 a) \text{CosIntegral}\left(2 b x^n\right)}{n}-\frac{b \cos (2 a) \text{Si}\left(2 b x^n\right)}{n}-\frac{x^{-n} \cos \left(2 \left(a+b x^n\right)\right)}{2 n}-\frac{x^{-n}}{2 n}",1,"-1/(2*n*x^n) - Cos[2*(a + b*x^n)]/(2*n*x^n) - (b*CosIntegral[2*b*x^n]*Sin[2*a])/n - (b*Cos[2*a]*SinIntegral[2*b*x^n])/n","A",7,6,18,0.3333,1,"{3426, 3380, 3297, 3303, 3299, 3302}"
81,1,113,0,0.1995482,"\int x^{-1-n} \cos ^3\left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Cos[a + b*x^n]^3,x]","-\frac{3 b \sin (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{3 b \sin (3 a) \text{CosIntegral}\left(3 b x^n\right)}{4 n}-\frac{3 b \cos (a) \text{Si}\left(b x^n\right)}{4 n}-\frac{3 b \cos (3 a) \text{Si}\left(3 b x^n\right)}{4 n}-\frac{3 x^{-n} \cos \left(a+b x^n\right)}{4 n}-\frac{x^{-n} \cos \left(3 \left(a+b x^n\right)\right)}{4 n}","-\frac{3 b \sin (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{3 b \sin (3 a) \text{CosIntegral}\left(3 b x^n\right)}{4 n}-\frac{3 b \cos (a) \text{Si}\left(b x^n\right)}{4 n}-\frac{3 b \cos (3 a) \text{Si}\left(3 b x^n\right)}{4 n}-\frac{3 x^{-n} \cos \left(a+b x^n\right)}{4 n}-\frac{x^{-n} \cos \left(3 \left(a+b x^n\right)\right)}{4 n}",1,"(-3*Cos[a + b*x^n])/(4*n*x^n) - Cos[3*(a + b*x^n)]/(4*n*x^n) - (3*b*CosIntegral[b*x^n]*Sin[a])/(4*n) - (3*b*CosIntegral[3*b*x^n]*Sin[3*a])/(4*n) - (3*b*Cos[a]*SinIntegral[b*x^n])/(4*n) - (3*b*Cos[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",12,6,18,0.3333,1,"{3426, 3380, 3297, 3303, 3299, 3302}"
82,1,78,0,0.1110423,"\int x^{-1-2 n} \cos \left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Cos[a + b*x^n],x]","-\frac{b^2 \cos (a) \text{CosIntegral}\left(b x^n\right)}{2 n}+\frac{b^2 \sin (a) \text{Si}\left(b x^n\right)}{2 n}+\frac{b x^{-n} \sin \left(a+b x^n\right)}{2 n}-\frac{x^{-2 n} \cos \left(a+b x^n\right)}{2 n}","-\frac{b^2 \cos (a) \text{CosIntegral}\left(b x^n\right)}{2 n}+\frac{b^2 \sin (a) \text{Si}\left(b x^n\right)}{2 n}+\frac{b x^{-n} \sin \left(a+b x^n\right)}{2 n}-\frac{x^{-2 n} \cos \left(a+b x^n\right)}{2 n}",1,"-Cos[a + b*x^n]/(2*n*x^(2*n)) - (b^2*Cos[a]*CosIntegral[b*x^n])/(2*n) + (b*Sin[a + b*x^n])/(2*n*x^n) + (b^2*Sin[a]*SinIntegral[b*x^n])/(2*n)","A",6,5,16,0.3125,1,"{3380, 3297, 3303, 3299, 3302}"
83,1,95,0,0.1474197,"\int x^{-1-2 n} \cos ^2\left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Cos[a + b*x^n]^2,x]","-\frac{b^2 \cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{n}+\frac{b^2 \sin (2 a) \text{Si}\left(2 b x^n\right)}{n}+\frac{b x^{-n} \sin \left(2 \left(a+b x^n\right)\right)}{2 n}-\frac{x^{-2 n} \cos \left(2 \left(a+b x^n\right)\right)}{4 n}-\frac{x^{-2 n}}{4 n}","-\frac{b^2 \cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{n}+\frac{b^2 \sin (2 a) \text{Si}\left(2 b x^n\right)}{n}+\frac{b x^{-n} \sin \left(2 \left(a+b x^n\right)\right)}{2 n}-\frac{x^{-2 n} \cos \left(2 \left(a+b x^n\right)\right)}{4 n}-\frac{x^{-2 n}}{4 n}",1,"-1/(4*n*x^(2*n)) - Cos[2*(a + b*x^n)]/(4*n*x^(2*n)) - (b^2*Cos[2*a]*CosIntegral[2*b*x^n])/n + (b*Sin[2*(a + b*x^n)])/(2*n*x^n) + (b^2*Sin[2*a]*SinIntegral[2*b*x^n])/n","A",8,6,18,0.3333,1,"{3426, 3380, 3297, 3303, 3299, 3302}"
84,1,165,0,0.2527908,"\int x^{-1-2 n} \cos ^3\left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Cos[a + b*x^n]^3,x]","-\frac{3 b^2 \cos (a) \text{CosIntegral}\left(b x^n\right)}{8 n}-\frac{9 b^2 \cos (3 a) \text{CosIntegral}\left(3 b x^n\right)}{8 n}+\frac{3 b^2 \sin (a) \text{Si}\left(b x^n\right)}{8 n}+\frac{9 b^2 \sin (3 a) \text{Si}\left(3 b x^n\right)}{8 n}+\frac{3 b x^{-n} \sin \left(a+b x^n\right)}{8 n}+\frac{3 b x^{-n} \sin \left(3 \left(a+b x^n\right)\right)}{8 n}-\frac{3 x^{-2 n} \cos \left(a+b x^n\right)}{8 n}-\frac{x^{-2 n} \cos \left(3 \left(a+b x^n\right)\right)}{8 n}","-\frac{3 b^2 \cos (a) \text{CosIntegral}\left(b x^n\right)}{8 n}-\frac{9 b^2 \cos (3 a) \text{CosIntegral}\left(3 b x^n\right)}{8 n}+\frac{3 b^2 \sin (a) \text{Si}\left(b x^n\right)}{8 n}+\frac{9 b^2 \sin (3 a) \text{Si}\left(3 b x^n\right)}{8 n}+\frac{3 b x^{-n} \sin \left(a+b x^n\right)}{8 n}+\frac{3 b x^{-n} \sin \left(3 \left(a+b x^n\right)\right)}{8 n}-\frac{3 x^{-2 n} \cos \left(a+b x^n\right)}{8 n}-\frac{x^{-2 n} \cos \left(3 \left(a+b x^n\right)\right)}{8 n}",1,"(-3*Cos[a + b*x^n])/(8*n*x^(2*n)) - Cos[3*(a + b*x^n)]/(8*n*x^(2*n)) - (3*b^2*Cos[a]*CosIntegral[b*x^n])/(8*n) - (9*b^2*Cos[3*a]*CosIntegral[3*b*x^n])/(8*n) + (3*b*Sin[a + b*x^n])/(8*n*x^n) + (3*b*Sin[3*(a + b*x^n)])/(8*n*x^n) + (3*b^2*Sin[a]*SinIntegral[b*x^n])/(8*n) + (9*b^2*Sin[3*a]*SinIntegral[3*b*x^n])/(8*n)","A",14,6,18,0.3333,1,"{3426, 3380, 3297, 3303, 3299, 3302}"
85,1,99,0,0.0675234,"\int x^2 \cos \left((a+b x)^2\right) \, dx","Int[x^2*Cos[(a + b*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} a^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b^3}-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{2 b^3}-\frac{a \sin \left((a+b x)^2\right)}{b^3}+\frac{(a+b x) \sin \left((a+b x)^2\right)}{2 b^3}","\frac{\sqrt{\frac{\pi }{2}} a^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b^3}-\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{2 b^3}-\frac{a \sin \left((a+b x)^2\right)}{b^3}+\frac{(a+b x) \sin \left((a+b x)^2\right)}{2 b^3}",1,"(a^2*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*(a + b*x)])/b^3 - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*(a + b*x)])/(2*b^3) - (a*Sin[(a + b*x)^2])/b^3 + ((a + b*x)*Sin[(a + b*x)^2])/(2*b^3)","A",7,6,12,0.5000,1,"{3434, 3352, 3380, 2637, 3386, 3351}"
86,1,47,0,0.0322894,"\int x \cos \left((a+b x)^2\right) \, dx","Int[x*Cos[(a + b*x)^2],x]","\frac{\sin \left((a+b x)^2\right)}{2 b^2}-\frac{\sqrt{\frac{\pi }{2}} a \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b^2}","\frac{\sin \left((a+b x)^2\right)}{2 b^2}-\frac{\sqrt{\frac{\pi }{2}} a \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b^2}",1,"-((a*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*(a + b*x)])/b^2) + Sin[(a + b*x)^2]/(2*b^2)","A",5,4,10,0.4000,1,"{3434, 3352, 3380, 2637}"
87,1,29,0,0.0058369,"\int \cos \left((a+b x)^2\right) \, dx","Int[Cos[(a + b*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b}","\frac{\sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b}",1,"(Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*(a + b*x)])/b","A",1,1,8,0.1250,1,"{3352}"
88,0,0,0,0.0084172,"\int \frac{\cos \left((a+b x)^2\right)}{x} \, dx","Int[Cos[(a + b*x)^2]/x,x]","\int \frac{\cos \left((a+b x)^2\right)}{x} \, dx","\text{Int}\left(\frac{\cos \left((a+b x)^2\right)}{x},x\right)",0,"Defer[Int][Cos[(a + b*x)^2]/x, x]","A",0,0,0,0,-1,"{}"
89,0,0,0,0.0085267,"\int \frac{\cos \left((a+b x)^2\right)}{x^2} \, dx","Int[Cos[(a + b*x)^2]/x^2,x]","\int \frac{\cos \left((a+b x)^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\cos \left((a+b x)^2\right)}{x^2},x\right)",0,"Defer[Int][Cos[(a + b*x)^2]/x^2, x]","A",0,0,0,0,-1,"{}"
90,1,346,0,0.3045518,"\int x^2 \cos \left(a+b \sqrt{c+d x}\right) \, dx","Int[x^2*Cos[a + b*Sqrt[c + d*x]],x]","\frac{2 c^2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{40 (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{24 c \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{240 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^5 d^3}+\frac{10 (c+d x)^2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{12 c (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{120 (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{24 c \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{240 \cos \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{2 c^2 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}+\frac{2 (c+d x)^{5/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{4 c (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}","\frac{2 c^2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{40 (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{24 c \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{240 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^5 d^3}+\frac{10 (c+d x)^2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{12 c (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{120 (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{24 c \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{240 \cos \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{2 c^2 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}+\frac{2 (c+d x)^{5/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{4 c (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^3}",1,"(240*Cos[a + b*Sqrt[c + d*x]])/(b^6*d^3) + (24*c*Cos[a + b*Sqrt[c + d*x]])/(b^4*d^3) + (2*c^2*Cos[a + b*Sqrt[c + d*x]])/(b^2*d^3) - (120*(c + d*x)*Cos[a + b*Sqrt[c + d*x]])/(b^4*d^3) - (12*c*(c + d*x)*Cos[a + b*Sqrt[c + d*x]])/(b^2*d^3) + (10*(c + d*x)^2*Cos[a + b*Sqrt[c + d*x]])/(b^2*d^3) + (240*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b^5*d^3) + (24*c*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b^3*d^3) + (2*c^2*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b*d^3) - (40*(c + d*x)^(3/2)*Sin[a + b*Sqrt[c + d*x]])/(b^3*d^3) - (4*c*(c + d*x)^(3/2)*Sin[a + b*Sqrt[c + d*x]])/(b*d^3) + (2*(c + d*x)^(5/2)*Sin[a + b*Sqrt[c + d*x]])/(b*d^3)","A",14,3,18,0.1667,1,"{3432, 3296, 2638}"
91,1,167,0,0.1363398,"\int x \cos \left(a+b \sqrt{c+d x}\right) \, dx","Int[x*Cos[a + b*Sqrt[c + d*x]],x]","-\frac{12 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^2}+\frac{6 (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}-\frac{2 c \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}-\frac{12 \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}+\frac{2 (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^2}-\frac{2 c \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d^2}","-\frac{12 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^3 d^2}+\frac{6 (c+d x) \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}-\frac{2 c \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}-\frac{12 \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}+\frac{2 (c+d x)^{3/2} \sin \left(a+b \sqrt{c+d x}\right)}{b d^2}-\frac{2 c \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d^2}",1,"(-12*Cos[a + b*Sqrt[c + d*x]])/(b^4*d^2) - (2*c*Cos[a + b*Sqrt[c + d*x]])/(b^2*d^2) + (6*(c + d*x)*Cos[a + b*Sqrt[c + d*x]])/(b^2*d^2) - (12*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b^3*d^2) - (2*c*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b*d^2) + (2*(c + d*x)^(3/2)*Sin[a + b*Sqrt[c + d*x]])/(b*d^2)","A",8,3,16,0.1875,1,"{3432, 3296, 2638}"
92,1,54,0,0.0274606,"\int \cos \left(a+b \sqrt{c+d x}\right) \, dx","Int[Cos[a + b*Sqrt[c + d*x]],x]","\frac{2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d}+\frac{2 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d}","\frac{2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d}+\frac{2 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b d}",1,"(2*Cos[a + b*Sqrt[c + d*x]])/(b^2*d) + (2*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]])/(b*d)","A",3,3,14,0.2143,1,"{3362, 3296, 2638}"
93,1,126,0,0.2388691,"\int \frac{\cos \left(a+b \sqrt{c+d x}\right)}{x} \, dx","Int[Cos[a + b*Sqrt[c + d*x]]/x,x]","\cos \left(a-b \sqrt{c}\right) \text{CosIntegral}\left(b \left(\sqrt{c+d x}+\sqrt{c}\right)\right)+\cos \left(a+b \sqrt{c}\right) \text{CosIntegral}\left(b \sqrt{c}-b \sqrt{c+d x}\right)-\sin \left(a-b \sqrt{c}\right) \text{Si}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+\sin \left(a+b \sqrt{c}\right) \text{Si}\left(b \sqrt{c}-b \sqrt{c+d x}\right)","\cos \left(a-b \sqrt{c}\right) \text{CosIntegral}\left(b \left(\sqrt{c+d x}+\sqrt{c}\right)\right)+\cos \left(a+b \sqrt{c}\right) \text{CosIntegral}\left(b \sqrt{c}-b \sqrt{c+d x}\right)-\sin \left(a-b \sqrt{c}\right) \text{Si}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+\sin \left(a+b \sqrt{c}\right) \text{Si}\left(b \sqrt{c}-b \sqrt{c+d x}\right)",1,"Cos[a - b*Sqrt[c]]*CosIntegral[b*(Sqrt[c] + Sqrt[c + d*x])] + Cos[a + b*Sqrt[c]]*CosIntegral[b*Sqrt[c] - b*Sqrt[c + d*x]] - Sin[a - b*Sqrt[c]]*SinIntegral[b*(Sqrt[c] + Sqrt[c + d*x])] + Sin[a + b*Sqrt[c]]*SinIntegral[b*Sqrt[c] - b*Sqrt[c + d*x]]","A",8,4,18,0.2222,1,"{3432, 3303, 3299, 3302}"
94,1,184,0,0.3491143,"\int \frac{\cos \left(a+b \sqrt{c+d x}\right)}{x^2} \, dx","Int[Cos[a + b*Sqrt[c + d*x]]/x^2,x]","\frac{b d \sin \left(a-b \sqrt{c}\right) \text{CosIntegral}\left(b \left(\sqrt{c+d x}+\sqrt{c}\right)\right)}{2 \sqrt{c}}-\frac{b d \sin \left(a+b \sqrt{c}\right) \text{CosIntegral}\left(b \sqrt{c}-b \sqrt{c+d x}\right)}{2 \sqrt{c}}+\frac{b d \cos \left(a-b \sqrt{c}\right) \text{Si}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}+\frac{b d \cos \left(a+b \sqrt{c}\right) \text{Si}\left(b \sqrt{c}-b \sqrt{c+d x}\right)}{2 \sqrt{c}}-\frac{\cos \left(a+b \sqrt{c+d x}\right)}{x}","\frac{b d \sin \left(a-b \sqrt{c}\right) \text{CosIntegral}\left(b \left(\sqrt{c+d x}+\sqrt{c}\right)\right)}{2 \sqrt{c}}-\frac{b d \sin \left(a+b \sqrt{c}\right) \text{CosIntegral}\left(b \sqrt{c}-b \sqrt{c+d x}\right)}{2 \sqrt{c}}+\frac{b d \cos \left(a-b \sqrt{c}\right) \text{Si}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}+\frac{b d \cos \left(a+b \sqrt{c}\right) \text{Si}\left(b \sqrt{c}-b \sqrt{c+d x}\right)}{2 \sqrt{c}}-\frac{\cos \left(a+b \sqrt{c+d x}\right)}{x}",1,"-(Cos[a + b*Sqrt[c + d*x]]/x) + (b*d*CosIntegral[b*(Sqrt[c] + Sqrt[c + d*x])]*Sin[a - b*Sqrt[c]])/(2*Sqrt[c]) - (b*d*CosIntegral[b*Sqrt[c] - b*Sqrt[c + d*x]]*Sin[a + b*Sqrt[c]])/(2*Sqrt[c]) + (b*d*Cos[a - b*Sqrt[c]]*SinIntegral[b*(Sqrt[c] + Sqrt[c + d*x])])/(2*Sqrt[c]) + (b*d*Cos[a + b*Sqrt[c]]*SinIntegral[b*Sqrt[c] - b*Sqrt[c + d*x]])/(2*Sqrt[c])","A",10,6,18,0.3333,1,"{3432, 3342, 3333, 3303, 3299, 3302}"
95,1,537,0,0.5113102,"\int x^2 \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[x^2*Cos[a + b*(c + d*x)^(1/3)],x]","-\frac{6 c^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{6 c^2 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{168 (c+d x)^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{5040 (c+d x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}+\frac{120 c (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{60480 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{720 c \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}+\frac{120960 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}+\frac{24 (c+d x)^{7/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{1008 (c+d x)^{5/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}-\frac{30 c (c+d x)^{4/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{20160 (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{360 c (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}-\frac{120960 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}-\frac{720 c \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{3 c^2 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}+\frac{3 (c+d x)^{8/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{6 c (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}","-\frac{6 c^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{6 c^2 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{168 (c+d x)^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{5040 (c+d x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}+\frac{120 c (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{60480 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{720 c \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}+\frac{120960 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}+\frac{24 (c+d x)^{7/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{1008 (c+d x)^{5/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}-\frac{30 c (c+d x)^{4/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{20160 (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{360 c (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}-\frac{120960 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}-\frac{720 c \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{3 c^2 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}+\frac{3 (c+d x)^{8/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{6 c (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}",1,"(-720*c*Cos[a + b*(c + d*x)^(1/3)])/(b^6*d^3) - (120960*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^8*d^3) + (6*c^2*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d^3) + (360*c*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^4*d^3) + (20160*(c + d*x)*Cos[a + b*(c + d*x)^(1/3)])/(b^6*d^3) - (30*c*(c + d*x)^(4/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d^3) - (1008*(c + d*x)^(5/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^4*d^3) + (24*(c + d*x)^(7/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d^3) + (120960*Sin[a + b*(c + d*x)^(1/3)])/(b^9*d^3) - (6*c^2*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d^3) - (720*c*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^5*d^3) - (60480*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^7*d^3) + (3*c^2*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d^3) + (120*c*(c + d*x)*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d^3) + (5040*(c + d*x)^(4/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^5*d^3) - (6*c*(c + d*x)^(5/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d^3) - (168*(c + d*x)^2*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d^3) + (3*(c + d*x)^(8/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d^3)","A",20,4,18,0.2222,1,"{3432, 3296, 2637, 2638}"
96,1,261,0,0.2310531,"\int x \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[x*Cos[a + b*(c + d*x)^(1/3)],x]","-\frac{60 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{360 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}+\frac{6 c \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{15 (c+d x)^{4/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}-\frac{180 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}-\frac{6 c \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{360 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{3 (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}-\frac{3 c (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}","-\frac{60 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{360 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}+\frac{6 c \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{15 (c+d x)^{4/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}-\frac{180 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}-\frac{6 c \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{360 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{3 (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}-\frac{3 c (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}",1,"(360*Cos[a + b*(c + d*x)^(1/3)])/(b^6*d^2) - (6*c*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d^2) - (180*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^4*d^2) + (15*(c + d*x)^(4/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d^2) + (6*c*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d^2) + (360*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^5*d^2) - (3*c*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d^2) - (60*(c + d*x)*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d^2) + (3*(c + d*x)^(5/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d^2)","A",11,4,16,0.2500,1,"{3432, 3296, 2637, 2638}"
97,1,85,0,0.0551264,"\int \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[Cos[a + b*(c + d*x)^(1/3)],x]","-\frac{6 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{6 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{3 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d}","-\frac{6 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{6 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{3 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(6*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^2*d) - (6*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d) + (3*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b*d)","A",4,3,14,0.2143,1,"{3362, 3296, 2637}"
98,1,234,0,0.4684035,"\int \frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x} \, dx","Int[Cos[a + b*(c + d*x)^(1/3)]/x,x]","\cos \left(a+b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{CosIntegral}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c+d x}+\sqrt[3]{-1} b \sqrt[3]{c}\right)+\sin \left(a+b \sqrt[3]{c}\right) \text{Si}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Si}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)-\sin \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Si}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)","\cos \left(a+b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{CosIntegral}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c+d x}+\sqrt[3]{-1} b \sqrt[3]{c}\right)+\sin \left(a+b \sqrt[3]{c}\right) \text{Si}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Si}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)-\sin \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Si}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)",1,"Cos[a + b*c^(1/3)]*CosIntegral[b*c^(1/3) - b*(c + d*x)^(1/3)] + Cos[a + (-1)^(2/3)*b*c^(1/3)]*CosIntegral[(-1)^(2/3)*b*c^(1/3) - b*(c + d*x)^(1/3)] + Cos[a - (-1)^(1/3)*b*c^(1/3)]*CosIntegral[(-1)^(1/3)*b*c^(1/3) + b*(c + d*x)^(1/3)] + Sin[a + b*c^(1/3)]*SinIntegral[b*c^(1/3) - b*(c + d*x)^(1/3)] + Sin[a + (-1)^(2/3)*b*c^(1/3)]*SinIntegral[(-1)^(2/3)*b*c^(1/3) - b*(c + d*x)^(1/3)] - Sin[a - (-1)^(1/3)*b*c^(1/3)]*SinIntegral[(-1)^(1/3)*b*c^(1/3) + b*(c + d*x)^(1/3)]","A",11,4,18,0.2222,1,"{3432, 3303, 3299, 3302}"
99,1,332,0,0.7410034,"\int \frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x^2} \, dx","Int[Cos[a + b*(c + d*x)^(1/3)]/x^2,x]","-\frac{b d \sin \left(a+b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{\sqrt[3]{-1} b d \sin \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c+d x}+\sqrt[3]{-1} b \sqrt[3]{c}\right)}{3 c^{2/3}}-\frac{(-1)^{2/3} b d \sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{CosIntegral}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{b d \cos \left(a+b \sqrt[3]{c}\right) \text{Si}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{(-1)^{2/3} b d \cos \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Si}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{\sqrt[3]{-1} b d \cos \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Si}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)}{3 c^{2/3}}-\frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x}","-\frac{b d \sin \left(a+b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{\sqrt[3]{-1} b d \sin \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{CosIntegral}\left(b \sqrt[3]{c+d x}+\sqrt[3]{-1} b \sqrt[3]{c}\right)}{3 c^{2/3}}-\frac{(-1)^{2/3} b d \sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{CosIntegral}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{b d \cos \left(a+b \sqrt[3]{c}\right) \text{Si}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{(-1)^{2/3} b d \cos \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Si}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)}{3 c^{2/3}}+\frac{\sqrt[3]{-1} b d \cos \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Si}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)}{3 c^{2/3}}-\frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x}",1,"-(Cos[a + b*(c + d*x)^(1/3)]/x) - (b*d*CosIntegral[b*c^(1/3) - b*(c + d*x)^(1/3)]*Sin[a + b*c^(1/3)])/(3*c^(2/3)) + ((-1)^(1/3)*b*d*CosIntegral[(-1)^(1/3)*b*c^(1/3) + b*(c + d*x)^(1/3)]*Sin[a - (-1)^(1/3)*b*c^(1/3)])/(3*c^(2/3)) - ((-1)^(2/3)*b*d*CosIntegral[(-1)^(2/3)*b*c^(1/3) - b*(c + d*x)^(1/3)]*Sin[a + (-1)^(2/3)*b*c^(1/3)])/(3*c^(2/3)) + (b*d*Cos[a + b*c^(1/3)]*SinIntegral[b*c^(1/3) - b*(c + d*x)^(1/3)])/(3*c^(2/3)) + ((-1)^(2/3)*b*d*Cos[a + (-1)^(2/3)*b*c^(1/3)]*SinIntegral[(-1)^(2/3)*b*c^(1/3) - b*(c + d*x)^(1/3)])/(3*c^(2/3)) + ((-1)^(1/3)*b*d*Cos[a - (-1)^(1/3)*b*c^(1/3)]*SinIntegral[(-1)^(1/3)*b*c^(1/3) + b*(c + d*x)^(1/3)])/(3*c^(2/3))","A",13,6,18,0.3333,1,"{3432, 3342, 3333, 3303, 3299, 3302}"