1,1,29,34,0.0487482,"\int x^3 \cos \left(a+b x^2\right) \, dx","Integrate[x^3*Cos[a + b*x^2],x]","\frac{b x^2 \sin \left(a+b x^2\right)+\cos \left(a+b x^2\right)}{2 b^2}","\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] + b*x^2*Sin[a + b*x^2])/(2*b^2)","A",1
2,1,82,91,0.148928,"\int x^2 \cos \left(a+b x^2\right) \, dx","Integrate[x^2*Cos[a + b*x^2],x]","\frac{-\sqrt{2 \pi } \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{2 \pi } \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+2 \sqrt{b} x \sin \left(a+b x^2\right)}{4 b^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} 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[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]) - Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + 2*Sqrt[b]*x*Sin[a + b*x^2])/(4*b^(3/2))","A",1
3,1,15,15,0.0027173,"\int x \cos \left(a+b x^2\right) \, dx","Integrate[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",1
4,1,57,70,0.0914048,"\int \cos \left(a+b x^2\right) \, dx","Integrate[Cos[a + b*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)\right)}{\sqrt{b}}","\frac{\sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} 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] - FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]))/Sqrt[b]","A",1
5,1,24,25,0.0500259,"\int \frac{\cos \left(a+b x^2\right)}{x} \, dx","Integrate[Cos[a + b*x^2]/x,x]","\frac{1}{2} \left(\cos (a) \text{Ci}\left(b x^2\right)-\sin (a) \text{Si}\left(b x^2\right)\right)","\frac{1}{2} \cos (a) \text{Ci}\left(b x^2\right)-\frac{1}{2} \sin (a) \text{Si}\left(b x^2\right)",1,"(Cos[a]*CosIntegral[b*x^2] - Sin[a]*SinIntegral[b*x^2])/2","A",1
6,1,81,80,0.1807356,"\int \frac{\cos \left(a+b x^2\right)}{x^2} \, dx","Integrate[Cos[a + b*x^2]/x^2,x]","-\sqrt{2 \pi } \sqrt{b} \left(\sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)\right)+\frac{\sin (a) \sin \left(b x^2\right)}{x}-\frac{\cos (a) \cos \left(b x^2\right)}{x}","-\sqrt{2 \pi } \sqrt{b} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} 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]*Cos[b*x^2])/x) - Sqrt[b]*Sqrt[2*Pi]*(Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] + FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]) + (Sin[a]*Sin[b*x^2])/x","A",1
7,1,42,42,0.0710818,"\int \frac{\cos \left(a+b x^2\right)}{x^3} \, dx","Integrate[Cos[a + b*x^2]/x^3,x]","-\frac{b x^2 \sin (a) \text{Ci}\left(b x^2\right)+b x^2 \cos (a) \text{Si}\left(b x^2\right)+\cos \left(a+b x^2\right)}{2 x^2}","-\frac{1}{2} b \sin (a) \text{Ci}\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,"-1/2*(Cos[a + b*x^2] + b*x^2*CosIntegral[b*x^2]*Sin[a] + b*x^2*Cos[a]*SinIntegral[b*x^2])/x^2","A",1
8,1,40,51,0.1142849,"\int x^3 \cos ^2\left(a+b x^2\right) \, dx","Integrate[x^3*Cos[a + b*x^2]^2,x]","\frac{2 b x^2 \left(\sin \left(2 \left(a+b x^2\right)\right)+b x^2\right)+\cos \left(2 \left(a+b x^2\right)\right)}{16 b^2}","\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,"(Cos[2*(a + b*x^2)] + 2*b*x^2*(b*x^2 + Sin[2*(a + b*x^2)]))/(16*b^2)","A",1
9,1,87,91,0.1708541,"\int x^2 \cos ^2\left(a+b x^2\right) \, dx","Integrate[x^2*Cos[a + b*x^2]^2,x]","\frac{-3 \sqrt{\pi } \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-3 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+2 \sqrt{b} x \left(3 \sin \left(2 \left(a+b x^2\right)\right)+4 b x^2\right)}{48 b^{3/2}}","-\frac{\sqrt{\pi } \sin (2 a) C\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,"(-3*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]] - 3*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a] + 2*Sqrt[b]*x*(4*b*x^2 + 3*Sin[2*(a + b*x^2)]))/(48*b^(3/2))","A",1
10,1,27,31,0.0434869,"\int x \cos ^2\left(a+b x^2\right) \, dx","Integrate[x*Cos[a + b*x^2]^2,x]","\frac{2 \left(a+b x^2\right)+\sin \left(2 \left(a+b x^2\right)\right)}{8 b}","\frac{\sin \left(a+b x^2\right) \cos \left(a+b x^2\right)}{4 b}+\frac{x^2}{4}",1,"(2*(a + b*x^2) + Sin[2*(a + b*x^2)])/(8*b)","A",1
11,1,67,70,0.0540415,"\int \cos ^2\left(a+b x^2\right) \, dx","Integrate[Cos[a + b*x^2]^2,x]","\frac{\sqrt{\pi } \cos (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)-\sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+2 \sqrt{b} x}{4 \sqrt{b}}","\frac{\sqrt{\pi } \cos (2 a) C\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,"(2*Sqrt[b]*x + Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]] - Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])/(4*Sqrt[b])","A",1
12,1,34,37,0.0618129,"\int \frac{\cos ^2\left(a+b x^2\right)}{x} \, dx","Integrate[Cos[a + b*x^2]^2/x,x]","\frac{1}{4} \left(\cos (2 a) \text{Ci}\left(2 b x^2\right)-\sin (2 a) \text{Si}\left(2 b x^2\right)+2 \log (x)\right)","\frac{1}{4} \cos (2 a) \text{Ci}\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] + 2*Log[x] - Sin[2*a]*SinIntegral[2*b*x^2])/4","A",1
13,1,76,76,0.1609967,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^2} \, dx","Integrate[Cos[a + b*x^2]^2/x^2,x]","-\frac{\sqrt{\pi } \sqrt{b} x \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+\sqrt{\pi } \sqrt{b} x \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+\cos ^2\left(a+b x^2\right)}{x}","-\sqrt{\pi } \sqrt{b} \sin (2 a) C\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 + Sqrt[b]*Sqrt[Pi]*x*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]] + Sqrt[b]*Sqrt[Pi]*x*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])/x)","A",1
14,1,50,57,0.1185121,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^3} \, dx","Integrate[Cos[a + b*x^2]^2/x^3,x]","-\frac{b x^2 \sin (2 a) \text{Ci}\left(2 b x^2\right)+b x^2 \cos (2 a) \text{Si}\left(2 b x^2\right)+\cos ^2\left(a+b x^2\right)}{2 x^2}","-\frac{1}{2} b \sin (2 a) \text{Ci}\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,"-1/2*(Cos[a + b*x^2]^2 + b*x^2*CosIntegral[2*b*x^2]*Sin[2*a] + b*x^2*Cos[2*a]*SinIntegral[2*b*x^2])/x^2","A",1
15,1,55,79,0.1379814,"\int x^3 \cos ^3\left(a+b x^2\right) \, dx","Integrate[x^3*Cos[a + b*x^2]^3,x]","\frac{3 b x^2 \left(9 \sin \left(a+b x^2\right)+\sin \left(3 \left(a+b x^2\right)\right)\right)+27 \cos \left(a+b x^2\right)+\cos \left(3 \left(a+b x^2\right)\right)}{72 b^2}","\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,"(27*Cos[a + b*x^2] + Cos[3*(a + b*x^2)] + 3*b*x^2*(9*Sin[a + b*x^2] + Sin[3*(a + b*x^2)]))/(72*b^2)","A",1
16,1,160,188,0.4251793,"\int x^2 \cos ^3\left(a+b x^2\right) \, dx","Integrate[x^2*Cos[a + b*x^2]^3,x]","\frac{-27 \sqrt{2 \pi } \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{6 \pi } \sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-27 \sqrt{2 \pi } \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{6 \pi } \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)+54 \sqrt{b} x \sin \left(a+b x^2\right)+6 \sqrt{b} x \sin \left(3 \left(a+b x^2\right)\right)}{144 b^{3/2}}","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} 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,"(-27*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[6*Pi]*Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x] - 27*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] - Sqrt[6*Pi]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a] + 54*Sqrt[b]*x*Sin[a + b*x^2] + 6*Sqrt[b]*x*Sin[3*(a + b*x^2)])/(144*b^(3/2))","A",1
17,1,33,33,0.0155046,"\int x \cos ^3\left(a+b x^2\right) \, dx","Integrate[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",1
18,1,116,153,0.2309337,"\int \cos ^3\left(a+b x^2\right) \, dx","Integrate[Cos[a + b*x^2]^3,x]","\frac{\sqrt{\frac{\pi }{6}} \left(3 \sqrt{3} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-3 \sqrt{3} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)\right)}{4 \sqrt{b}}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{4 \sqrt{b}}+\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} 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,"(Sqrt[Pi/6]*(3*Sqrt[3]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] + Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x] - 3*Sqrt[3]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] - FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a]))/(4*Sqrt[b])","A",1
19,1,50,55,0.0937651,"\int \frac{\cos ^3\left(a+b x^2\right)}{x} \, dx","Integrate[Cos[a + b*x^2]^3/x,x]","\frac{1}{8} \left(3 \cos (a) \text{Ci}\left(b x^2\right)+\cos (3 a) \text{Ci}\left(3 b x^2\right)-3 \sin (a) \text{Si}\left(b x^2\right)-\sin (3 a) \text{Si}\left(3 b x^2\right)\right)","\frac{3}{8} \cos (a) \text{Ci}\left(b x^2\right)+\frac{1}{8} \cos (3 a) \text{Ci}\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] + Cos[3*a]*CosIntegral[3*b*x^2] - 3*Sin[a]*SinIntegral[b*x^2] - Sin[3*a]*SinIntegral[3*b*x^2])/8","A",1
20,1,166,168,0.6395714,"\int \frac{\cos ^3\left(a+b x^2\right)}{x^2} \, dx","Integrate[Cos[a + b*x^2]^3/x^2,x]","-\frac{3 \sqrt{2 \pi } \sqrt{b} x \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\sqrt{6 \pi } \sqrt{b} x \sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)+3 \sqrt{2 \pi } \sqrt{b} x \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\sqrt{6 \pi } \sqrt{b} x \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)+3 \cos \left(a+b x^2\right)+\cos \left(3 \left(a+b x^2\right)\right)}{4 x}","-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} 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,"-1/4*(3*Cos[a + b*x^2] + Cos[3*(a + b*x^2)] + 3*Sqrt[b]*Sqrt[2*Pi]*x*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] + Sqrt[b]*Sqrt[6*Pi]*x*Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x] + 3*Sqrt[b]*Sqrt[2*Pi]*x*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + Sqrt[b]*Sqrt[6*Pi]*x*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/x","A",1
21,1,90,91,0.1751633,"\int \frac{\cos ^3\left(a+b x^2\right)}{x^3} \, dx","Integrate[Cos[a + b*x^2]^3/x^3,x]","-\frac{3 b x^2 \sin (a) \text{Ci}\left(b x^2\right)+3 b x^2 \sin (3 a) \text{Ci}\left(3 b x^2\right)+3 b x^2 \cos (a) \text{Si}\left(b x^2\right)+3 b x^2 \cos (3 a) \text{Si}\left(3 b x^2\right)+3 \cos \left(a+b x^2\right)+\cos \left(3 \left(a+b x^2\right)\right)}{8 x^2}","-\frac{3}{8} b \sin (a) \text{Ci}\left(b x^2\right)-\frac{3}{8} b \sin (3 a) \text{Ci}\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,"-1/8*(3*Cos[a + b*x^2] + Cos[3*(a + b*x^2)] + 3*b*x^2*CosIntegral[b*x^2]*Sin[a] + 3*b*x^2*CosIntegral[3*b*x^2]*Sin[3*a] + 3*b*x^2*Cos[a]*SinIntegral[b*x^2] + 3*b*x^2*Cos[3*a]*SinIntegral[3*b*x^2])/x^2","A",1
22,1,54,67,0.0858631,"\int x \cos ^7\left(a+b x^2\right) \, dx","Integrate[x*Cos[a + b*x^2]^7,x]","\frac{-5 \sin ^7\left(a+b x^2\right)+21 \sin ^5\left(a+b x^2\right)-35 \sin ^3\left(a+b x^2\right)+35 \sin \left(a+b x^2\right)}{70 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,"(35*Sin[a + b*x^2] - 35*Sin[a + b*x^2]^3 + 21*Sin[a + b*x^2]^5 - 5*Sin[a + b*x^2]^7)/(70*b)","A",1
23,1,113,111,0.1950435,"\int x^{5/2} \cos \left(a+b x^2\right) \, dx","Integrate[x^(5/2)*Cos[a + b*x^2],x]","\frac{b x^{11/2} \left(8 \left(b^2 x^4\right)^{3/4} \sin \left(a+b x^2\right)+3 \left(i b x^2\right)^{3/4} (\sin (a)-i \cos (a)) \Gamma \left(\frac{3}{4},-i b x^2\right)+3 \left(-i b x^2\right)^{3/4} (\sin (a)+i \cos (a)) \Gamma \left(\frac{3}{4},i b x^2\right)\right)}{16 \left(b^2 x^4\right)^{7/4}}","\frac{x^{3/2} \sin \left(a+b x^2\right)}{2 b}-\frac{3 i e^{i a} x^{3/2} \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} \Gamma \left(\frac{3}{4},i b x^2\right)}{16 b \left(i b x^2\right)^{3/4}}",1,"(b*x^(11/2)*(3*(I*b*x^2)^(3/4)*Gamma[3/4, (-I)*b*x^2]*((-I)*Cos[a] + Sin[a]) + 3*((-I)*b*x^2)^(3/4)*Gamma[3/4, I*b*x^2]*(I*Cos[a] + Sin[a]) + 8*(b^2*x^4)^(3/4)*Sin[a + b*x^2]))/(16*(b^2*x^4)^(7/4))","A",1
24,1,111,111,0.1524958,"\int x^{3/2} \cos \left(a+b x^2\right) \, dx","Integrate[x^(3/2)*Cos[a + b*x^2],x]","\frac{b x^{9/2} \left(8 \sqrt[4]{b^2 x^4} \sin \left(a+b x^2\right)+\sqrt[4]{i b x^2} (\sin (a)-i \cos (a)) \Gamma \left(\frac{1}{4},-i b x^2\right)+\sqrt[4]{-i b x^2} (\sin (a)+i \cos (a)) \Gamma \left(\frac{1}{4},i b x^2\right)\right)}{16 \left(b^2 x^4\right)^{5/4}}","\frac{\sqrt{x} \sin \left(a+b x^2\right)}{2 b}-\frac{i e^{i a} \sqrt{x} \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} \Gamma \left(\frac{1}{4},i b x^2\right)}{16 b \sqrt[4]{i b x^2}}",1,"(b*x^(9/2)*((I*b*x^2)^(1/4)*Gamma[1/4, (-I)*b*x^2]*((-I)*Cos[a] + Sin[a]) + ((-I)*b*x^2)^(1/4)*Gamma[1/4, I*b*x^2]*(I*Cos[a] + Sin[a]) + 8*(b^2*x^4)^(1/4)*Sin[a + b*x^2]))/(16*(b^2*x^4)^(5/4))","A",1
25,1,89,81,0.0838132,"\int \sqrt{x} \cos \left(a+b x^2\right) \, dx","Integrate[Sqrt[x]*Cos[a + b*x^2],x]","-\frac{x^{3/2} \left(\left(-i b x^2\right)^{3/4} (\cos (a)-i \sin (a)) \Gamma \left(\frac{3}{4},i b x^2\right)+\left(i b x^2\right)^{3/4} (\cos (a)+i \sin (a)) \Gamma \left(\frac{3}{4},-i b x^2\right)\right)}{4 \left(b^2 x^4\right)^{3/4}}","-\frac{e^{i a} x^{3/2} \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} \Gamma \left(\frac{3}{4},i b x^2\right)}{4 \left(i b x^2\right)^{3/4}}",1,"-1/4*(x^(3/2)*(((-I)*b*x^2)^(3/4)*Gamma[3/4, I*b*x^2]*(Cos[a] - I*Sin[a]) + (I*b*x^2)^(3/4)*Gamma[3/4, (-I)*b*x^2]*(Cos[a] + I*Sin[a])))/(b^2*x^4)^(3/4)","A",1
26,1,89,81,0.0660173,"\int \frac{\cos \left(a+b x^2\right)}{\sqrt{x}} \, dx","Integrate[Cos[a + b*x^2]/Sqrt[x],x]","-\frac{\sqrt{x} \left(\sqrt[4]{-i b x^2} (\cos (a)-i \sin (a)) \Gamma \left(\frac{1}{4},i b x^2\right)+\sqrt[4]{i b x^2} (\cos (a)+i \sin (a)) \Gamma \left(\frac{1}{4},-i b x^2\right)\right)}{4 \sqrt[4]{b^2 x^4}}","-\frac{e^{i a} \sqrt{x} \Gamma \left(\frac{1}{4},-i b x^2\right)}{4 \sqrt[4]{-i b x^2}}-\frac{e^{-i a} \sqrt{x} \Gamma \left(\frac{1}{4},i b x^2\right)}{4 \sqrt[4]{i b x^2}}",1,"-1/4*(Sqrt[x]*(((-I)*b*x^2)^(1/4)*Gamma[1/4, I*b*x^2]*(Cos[a] - I*Sin[a]) + (I*b*x^2)^(1/4)*Gamma[1/4, (-I)*b*x^2]*(Cos[a] + I*Sin[a])))/(b^2*x^4)^(1/4)","A",1
27,1,114,98,0.172989,"\int \frac{\cos \left(a+b x^2\right)}{x^{3/2}} \, dx","Integrate[Cos[a + b*x^2]/x^(3/2),x]","\frac{-2 \left(b^2 x^4\right)^{3/4} \cos \left(a+b x^2\right)+b x^2 \left(i b x^2\right)^{3/4} (\sin (a)-i \cos (a)) \Gamma \left(\frac{3}{4},-i b x^2\right)+i \left(-i b x^2\right)^{7/4} (\sin (a)+i \cos (a)) \Gamma \left(\frac{3}{4},i b x^2\right)}{\sqrt{x} \left(b^2 x^4\right)^{3/4}}","-\frac{2 \cos \left(a+b x^2\right)}{\sqrt{x}}-\frac{i e^{i a} b x^{3/2} \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} \Gamma \left(\frac{3}{4},i b x^2\right)}{\left(i b x^2\right)^{3/4}}",1,"(-2*(b^2*x^4)^(3/4)*Cos[a + b*x^2] + b*x^2*(I*b*x^2)^(3/4)*Gamma[3/4, (-I)*b*x^2]*((-I)*Cos[a] + Sin[a]) + I*((-I)*b*x^2)^(7/4)*Gamma[3/4, I*b*x^2]*(I*Cos[a] + Sin[a]))/(Sqrt[x]*(b^2*x^4)^(3/4))","A",1
28,1,117,104,0.153898,"\int \frac{\cos \left(a+b x^2\right)}{x^{5/2}} \, dx","Integrate[Cos[a + b*x^2]/x^(5/2),x]","\frac{-2 \sqrt[4]{b^2 x^4} \cos \left(a+b x^2\right)+b x^2 \sqrt[4]{i b x^2} (\sin (a)-i \cos (a)) \Gamma \left(\frac{1}{4},-i b x^2\right)+i \left(-i b x^2\right)^{5/4} (\sin (a)+i \cos (a)) \Gamma \left(\frac{1}{4},i b x^2\right)}{3 x^{3/2} \sqrt[4]{b^2 x^4}}","-\frac{i e^{i a} b \sqrt{x} \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} \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*(b^2*x^4)^(1/4)*Cos[a + b*x^2] + b*x^2*(I*b*x^2)^(1/4)*Gamma[1/4, (-I)*b*x^2]*((-I)*Cos[a] + Sin[a]) + I*((-I)*b*x^2)^(5/4)*Gamma[1/4, I*b*x^2]*(I*Cos[a] + Sin[a]))/(3*x^(3/2)*(b^2*x^4)^(1/4))","A",1
29,1,142,132,0.4044418,"\int x^{5/2} \cos ^2\left(a+b x^2\right) \, dx","Integrate[x^(5/2)*Cos[a + b*x^2]^2,x]","\frac{b x^{11/2} \left(16 \left(b^2 x^4\right)^{3/4} \left(7 \sin \left(2 \left(a+b x^2\right)\right)+8 b x^2\right)+21 \sqrt[4]{2} \left(i b x^2\right)^{3/4} (\sin (2 a)-i \cos (2 a)) \Gamma \left(\frac{3}{4},-2 i b x^2\right)+21 \sqrt[4]{2} \left(-i b x^2\right)^{3/4} (\sin (2 a)+i \cos (2 a)) \Gamma \left(\frac{3}{4},2 i b x^2\right)\right)}{896 \left(b^2 x^4\right)^{7/4}}","\frac{x^{3/2} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}-\frac{3 i e^{2 i a} x^{3/2} \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} \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^{7/2}}{7}",1,"(b*x^(11/2)*(21*2^(1/4)*(I*b*x^2)^(3/4)*Gamma[3/4, (-2*I)*b*x^2]*((-I)*Cos[2*a] + Sin[2*a]) + 21*2^(1/4)*((-I)*b*x^2)^(3/4)*Gamma[3/4, (2*I)*b*x^2]*(I*Cos[2*a] + Sin[2*a]) + 16*(b^2*x^4)^(3/4)*(8*b*x^2 + 7*Sin[2*(a + b*x^2)])))/(896*(b^2*x^4)^(7/4))","A",1
30,1,142,132,0.3279379,"\int x^{3/2} \cos ^2\left(a+b x^2\right) \, dx","Integrate[x^(3/2)*Cos[a + b*x^2]^2,x]","\frac{b x^{9/2} \left(16 \sqrt[4]{b^2 x^4} \left(5 \sin \left(2 \left(a+b x^2\right)\right)+8 b x^2\right)+5\ 2^{3/4} \sqrt[4]{i b x^2} (\sin (2 a)-i \cos (2 a)) \Gamma \left(\frac{1}{4},-2 i b x^2\right)+5\ 2^{3/4} \sqrt[4]{-i b x^2} (\sin (2 a)+i \cos (2 a)) \Gamma \left(\frac{1}{4},2 i b x^2\right)\right)}{640 \left(b^2 x^4\right)^{5/4}}","\frac{\sqrt{x} \sin \left(2 \left(a+b x^2\right)\right)}{8 b}-\frac{i e^{2 i a} \sqrt{x} \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} \Gamma \left(\frac{1}{4},2 i b x^2\right)}{64 \sqrt[4]{2} b \sqrt[4]{i b x^2}}+\frac{x^{5/2}}{5}",1,"(b*x^(9/2)*(5*2^(3/4)*(I*b*x^2)^(1/4)*Gamma[1/4, (-2*I)*b*x^2]*((-I)*Cos[2*a] + Sin[2*a]) + 5*2^(3/4)*((-I)*b*x^2)^(1/4)*Gamma[1/4, (2*I)*b*x^2]*(I*Cos[2*a] + Sin[2*a]) + 16*(b^2*x^4)^(1/4)*(8*b*x^2 + 5*Sin[2*(a + b*x^2)])))/(640*(b^2*x^4)^(5/4))","A",1
31,1,122,100,0.2175247,"\int \sqrt{x} \cos ^2\left(a+b x^2\right) \, dx","Integrate[Sqrt[x]*Cos[a + b*x^2]^2,x]","\frac{x^{3/2} \left(-3 \sqrt[4]{2} \left(-i b x^2\right)^{3/4} (\cos (2 a)-i \sin (2 a)) \Gamma \left(\frac{3}{4},2 i b x^2\right)-3 \sqrt[4]{2} \left(i b x^2\right)^{3/4} (\cos (2 a)+i \sin (2 a)) \Gamma \left(\frac{3}{4},-2 i b x^2\right)+16 \left(b^2 x^4\right)^{3/4}\right)}{48 \left(b^2 x^4\right)^{3/4}}","-\frac{e^{2 i a} x^{3/2} \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} \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)*(16*(b^2*x^4)^(3/4) - 3*2^(1/4)*((-I)*b*x^2)^(3/4)*Gamma[3/4, (2*I)*b*x^2]*(Cos[2*a] - I*Sin[2*a]) - 3*2^(1/4)*(I*b*x^2)^(3/4)*Gamma[3/4, (-2*I)*b*x^2]*(Cos[2*a] + I*Sin[2*a])))/(48*(b^2*x^4)^(3/4))","A",1
32,1,120,96,0.2206071,"\int \frac{\cos ^2\left(a+b x^2\right)}{\sqrt{x}} \, dx","Integrate[Cos[a + b*x^2]^2/Sqrt[x],x]","-\frac{\sqrt{x} \left(2^{3/4} \sqrt[4]{-i b x^2} (\cos (2 a)-i \sin (2 a)) \Gamma \left(\frac{1}{4},2 i b x^2\right)+2^{3/4} \sqrt[4]{i b x^2} (\cos (2 a)+i \sin (2 a)) \Gamma \left(\frac{1}{4},-2 i b x^2\right)-16 \sqrt[4]{b^2 x^4}\right)}{16 \sqrt[4]{b^2 x^4}}","-\frac{e^{2 i a} \sqrt{x} \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} \Gamma \left(\frac{1}{4},2 i b x^2\right)}{8 \sqrt[4]{2} \sqrt[4]{i b x^2}}+\sqrt{x}",1,"-1/16*(Sqrt[x]*(-16*(b^2*x^4)^(1/4) + 2^(3/4)*((-I)*b*x^2)^(1/4)*Gamma[1/4, (2*I)*b*x^2]*(Cos[2*a] - I*Sin[2*a]) + 2^(3/4)*(I*b*x^2)^(1/4)*Gamma[1/4, (-2*I)*b*x^2]*(Cos[2*a] + I*Sin[2*a])))/(b^2*x^4)^(1/4)","A",1
33,1,137,117,0.337342,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^{3/2}} \, dx","Integrate[Cos[a + b*x^2]^2/x^(3/2),x]","\frac{-4 \left(b^2 x^4\right)^{3/4} \cos ^2\left(a+b x^2\right)+\sqrt[4]{2} b x^2 \left(i b x^2\right)^{3/4} (\sin (2 a)-i \cos (2 a)) \Gamma \left(\frac{3}{4},-2 i b x^2\right)+i \sqrt[4]{2} \left(-i b x^2\right)^{7/4} (\sin (2 a)+i \cos (2 a)) \Gamma \left(\frac{3}{4},2 i b x^2\right)}{2 \sqrt{x} \left(b^2 x^4\right)^{3/4}}","-\frac{\cos \left(2 \left(a+b x^2\right)\right)}{\sqrt{x}}-\frac{i e^{2 i a} b x^{3/2} \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} \Gamma \left(\frac{3}{4},2 i b x^2\right)}{2^{3/4} \left(i b x^2\right)^{3/4}}-\frac{1}{\sqrt{x}}",1,"(-4*(b^2*x^4)^(3/4)*Cos[a + b*x^2]^2 + 2^(1/4)*b*x^2*(I*b*x^2)^(3/4)*Gamma[3/4, (-2*I)*b*x^2]*((-I)*Cos[2*a] + Sin[2*a]) + I*2^(1/4)*((-I)*b*x^2)^(7/4)*Gamma[3/4, (2*I)*b*x^2]*(I*Cos[2*a] + Sin[2*a]))/(2*Sqrt[x]*(b^2*x^4)^(3/4))","A",1
34,1,137,116,0.3429431,"\int \frac{\cos ^2\left(a+b x^2\right)}{x^{5/2}} \, dx","Integrate[Cos[a + b*x^2]^2/x^(5/2),x]","\frac{-4 \sqrt[4]{b^2 x^4} \cos ^2\left(a+b x^2\right)+2^{3/4} b x^2 \sqrt[4]{i b x^2} (\sin (2 a)-i \cos (2 a)) \Gamma \left(\frac{1}{4},-2 i b x^2\right)+i 2^{3/4} \left(-i b x^2\right)^{5/4} (\sin (2 a)+i \cos (2 a)) \Gamma \left(\frac{1}{4},2 i b x^2\right)}{6 x^{3/2} \sqrt[4]{b^2 x^4}}","-\frac{i e^{2 i a} b \sqrt{x} \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} \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,"(-4*(b^2*x^4)^(1/4)*Cos[a + b*x^2]^2 + 2^(3/4)*b*x^2*(I*b*x^2)^(1/4)*Gamma[1/4, (-2*I)*b*x^2]*((-I)*Cos[2*a] + Sin[2*a]) + I*2^(3/4)*((-I)*b*x^2)^(5/4)*Gamma[1/4, (2*I)*b*x^2]*(I*Cos[2*a] + Sin[2*a]))/(6*x^(3/2)*(b^2*x^4)^(1/4))","A",1
35,1,31,31,0.0315195,"\int \cos \left(a+\frac{b}{x}\right) \, dx","Integrate[Cos[a + b/x],x]","b \sin (a) \text{Ci}\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{Ci}\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",1
36,1,20,20,0.0416882,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x} \, dx","Integrate[Cos[a + b/x]/x,x]","\sin (a) \text{Si}\left(\frac{b}{x}\right)-\cos (a) \text{Ci}\left(\frac{b}{x}\right)","\sin (a) \text{Si}\left(\frac{b}{x}\right)-\cos (a) \text{Ci}\left(\frac{b}{x}\right)",1,"-(Cos[a]*CosIntegral[b/x]) + Sin[a]*SinIntegral[b/x]","A",1
37,1,13,13,0.0029403,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^2} \, dx","Integrate[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",1
38,1,29,30,0.0510224,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^3} \, dx","Integrate[Cos[a + b/x]/x^3,x]","-\frac{b \sin \left(a+\frac{b}{x}\right)+x \cos \left(a+\frac{b}{x}\right)}{b^2 x}","-\frac{\cos \left(a+\frac{b}{x}\right)}{b^2}-\frac{\sin \left(a+\frac{b}{x}\right)}{b x}",1,"-((x*Cos[a + b/x] + b*Sin[a + b/x])/(b^2*x))","A",1
39,1,46,46,0.0046233,"\int \frac{\cos \left(a+\frac{b}{x}\right)}{x^4} \, dx","Integrate[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",1
40,1,80,79,0.1330151,"\int \cos \left(a+\frac{b}{x^2}\right) \, dx","Integrate[Cos[a + b/x^2],x]","\sqrt{2 \pi } \sqrt{b} \left(\sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+\cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)\right)-x \sin (a) \sin \left(\frac{b}{x^2}\right)+x \cos (a) \cos \left(\frac{b}{x^2}\right)","\sqrt{2 \pi } \sqrt{b} \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{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]*Cos[b/x^2] + Sqrt[b]*Sqrt[2*Pi]*(Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x] + FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a]) - x*Sin[a]*Sin[b/x^2]","A",1
41,1,24,25,0.0417374,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x} \, dx","Integrate[Cos[a + b/x^2]/x,x]","\frac{1}{2} \left(\sin (a) \text{Si}\left(\frac{b}{x^2}\right)-\cos (a) \text{Ci}\left(\frac{b}{x^2}\right)\right)","\frac{1}{2} \sin (a) \text{Si}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cos (a) \text{Ci}\left(\frac{b}{x^2}\right)",1,"(-(Cos[a]*CosIntegral[b/x^2]) + Sin[a]*SinIntegral[b/x^2])/2","A",1
42,1,62,74,0.1066561,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Integrate[Cos[a + b/x^2]/x^2,x]","-\frac{\sqrt{\frac{\pi }{2}} \left(\cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)-\sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)\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) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}",1,"-((Sqrt[Pi/2]*(Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] - FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a]))/Sqrt[b])","A",1
43,1,15,15,0.0028085,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Integrate[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,"-1/2*Sin[a + b/x^2]/b","A",1
44,1,88,97,0.1569905,"\int \frac{\cos \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Integrate[Cos[a + b/x^2]/x^4,x]","\frac{\sqrt{2 \pi } x \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+\sqrt{2 \pi } x \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)-2 \sqrt{b} \sin \left(a+\frac{b}{x^2}\right)}{4 b^{3/2} x}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{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[2*Pi]*x*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[2*Pi]*x*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a] - 2*Sqrt[b]*Sin[a + b/x^2])/(4*b^(3/2)*x)","A",1
45,1,18,19,0.0291671,"\int \frac{\cos ^2\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Cos[Sqrt[x]]^2/Sqrt[x],x]","\sqrt{x}+\frac{1}{2} \sin \left(2 \sqrt{x}\right)","\sqrt{x}+\sin \left(\sqrt{x}\right) \cos \left(\sqrt{x}\right)",1,"Sqrt[x] + Sin[2*Sqrt[x]]/2","A",1
46,1,8,8,0.0020599,"\int \frac{\cos \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Cos[Sqrt[x]]/Sqrt[x],x]","2 \sin \left(\sqrt{x}\right)","2 \sin \left(\sqrt{x}\right)",1,"2*Sin[Sqrt[x]]","A",1
47,1,22,22,0.0149318,"\int \cos \left(\sqrt{x}\right) \, dx","Integrate[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",1
48,1,31,36,0.0241578,"\int \cos ^2\left(\sqrt{x}\right) \, dx","Integrate[Cos[Sqrt[x]]^2,x]","\frac{1}{4} \left(2 \left(x+\sqrt{x} \sin \left(2 \sqrt{x}\right)\right)+\cos \left(2 \sqrt{x}\right)\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,"(Cos[2*Sqrt[x]] + 2*(x + Sqrt[x]*Sin[2*Sqrt[x]]))/4","A",1
49,1,165,235,0.577663,"\int x^{3/2} \cos \left(a+b \sqrt[3]{x}\right) \, dx","Integrate[x^(3/2)*Cos[a + b*x^(1/3)],x]","\frac{6 \sqrt{b} \sqrt[6]{x} \left(26 \left(16 b^5 x^{5/3}-396 b^3 x+3465 b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)+\left(64 b^6 x^2-2288 b^4 x^{4/3}+36036 b^2 x^{2/3}-135135\right) \sin \left(a+b \sqrt[3]{x}\right)\right)+405405 \sqrt{2 \pi } \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+405405 \sqrt{2 \pi } \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{128 b^{15/2}}","\frac{405405 \sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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{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{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right)}{16 b^5}-\frac{3861 x^{7/6} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}-\frac{429 x^{3/2} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}+\frac{39 x^{11/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}",1,"(405405*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] + 405405*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] + 6*Sqrt[b]*x^(1/6)*(26*(3465*b*x^(1/3) - 396*b^3*x + 16*b^5*x^(5/3))*Cos[a + b*x^(1/3)] + (-135135 + 36036*b^2*x^(2/3) - 2288*b^4*x^(4/3) + 64*b^6*x^2)*Sin[a + b*x^(1/3)]))/(128*b^(15/2))","A",1
50,1,141,169,0.3544883,"\int \sqrt{x} \cos \left(a+b \sqrt[3]{x}\right) \, dx","Integrate[Sqrt[x]*Cos[a + b*x^(1/3)],x]","\frac{6 \sqrt{b} \sqrt[6]{x} \left(2 b \sqrt[3]{x} \left(4 b^2 x^{2/3}-35\right) \sin \left(a+b \sqrt[3]{x}\right)+7 \left(4 b^2 x^{2/3}-15\right) \cos \left(a+b \sqrt[3]{x}\right)\right)+315 \sqrt{2 \pi } \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)-315 \sqrt{2 \pi } \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)}{16 b^{9/2}}","\frac{315 \sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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{315 \sqrt[6]{x} \cos \left(a+b \sqrt[3]{x}\right)}{8 b^4}-\frac{105 \sqrt{x} \sin \left(a+b \sqrt[3]{x}\right)}{4 b^3}+\frac{21 x^{5/6} \cos \left(a+b \sqrt[3]{x}\right)}{2 b^2}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right)}{b}",1,"(315*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] - 315*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] + 6*Sqrt[b]*x^(1/6)*(7*(-15 + 4*b^2*x^(2/3))*Cos[a + b*x^(1/3)] + 2*b*(-35 + 4*b^2*x^(2/3))*x^(1/3)*Sin[a + b*x^(1/3)]))/(16*b^(9/2))","A",1
51,1,94,99,0.1537551,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{\sqrt{x}} \, dx","Integrate[Cos[a + b*x^(1/3)]/Sqrt[x],x]","-\frac{3 \left(\sqrt{2 \pi } \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+\sqrt{2 \pi } \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)-2 \sqrt{b} \sqrt[6]{x} \sin \left(a+b \sqrt[3]{x}\right)\right)}{2 b^{3/2}}","-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] + Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] - 2*Sqrt[b]*x^(1/6)*Sin[a + b*x^(1/3)]))/(2*b^(3/2))","A",1
52,1,110,110,0.252895,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{3/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]/x^(3/2),x]","-4 \sqrt{2 \pi } b^{3/2} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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",1
53,1,180,184,0.2486625,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{5/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]/x^(5/2),x]","-\frac{2 \left(16 \sqrt{2 \pi } b^{9/2} x^{3/2} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+16 \sqrt{2 \pi } b^{9/2} x^{3/2} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)+16 b^4 x^{4/3} \cos \left(a+b \sqrt[3]{x}\right)+8 b^3 x \sin \left(a+b \sqrt[3]{x}\right)-12 b^2 x^{2/3} \cos \left(a+b \sqrt[3]{x}\right)-30 b \sqrt[3]{x} \sin \left(a+b \sqrt[3]{x}\right)+105 \cos \left(a+b \sqrt[3]{x}\right)\right)}{315 x^{3/2}}","-\frac{32}{315} \sqrt{2 \pi } b^{9/2} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{315 \sqrt[6]{x}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{315 \sqrt{x}}+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}+\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*(105*Cos[a + b*x^(1/3)] - 12*b^2*x^(2/3)*Cos[a + b*x^(1/3)] + 16*b^4*x^(4/3)*Cos[a + b*x^(1/3)] + 16*b^(9/2)*Sqrt[2*Pi]*x^(3/2)*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] + 16*b^(9/2)*Sqrt[2*Pi]*x^(3/2)*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] - 30*b*x^(1/3)*Sin[a + b*x^(1/3)] + 8*b^3*x*Sin[a + b*x^(1/3)]))/(315*x^(3/2))","A",1
54,1,238,250,0.3357448,"\int \frac{\cos \left(a+b \sqrt[3]{x}\right)}{x^{7/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]/x^(7/2),x]","\frac{2 \left(128 \sqrt{2 \pi } b^{15/2} x^{5/2} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)-128 \sqrt{2 \pi } b^{15/2} x^{5/2} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[6]{x}\right)-128 b^7 x^{7/3} \sin \left(a+b \sqrt[3]{x}\right)+64 b^6 x^2 \cos \left(a+b \sqrt[3]{x}\right)+96 b^5 x^{5/3} \sin \left(a+b \sqrt[3]{x}\right)-240 b^4 x^{4/3} \cos \left(a+b \sqrt[3]{x}\right)-840 b^3 x \sin \left(a+b \sqrt[3]{x}\right)+3780 b^2 x^{2/3} \cos \left(a+b \sqrt[3]{x}\right)+20790 b \sqrt[3]{x} \sin \left(a+b \sqrt[3]{x}\right)-135135 \cos \left(a+b \sqrt[3]{x}\right)\right)}{675675 x^{5/2}}","\frac{256 \sqrt{2 \pi } b^{15/2} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \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{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{64 b^5 \sin \left(a+b \sqrt[3]{x}\right)}{225225 x^{5/6}}-\frac{32 b^4 \cos \left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}-\frac{16 b^3 \sin \left(a+b \sqrt[3]{x}\right)}{6435 x^{3/2}}+\frac{8 b^2 \cos \left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}+\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*(-135135*Cos[a + b*x^(1/3)] + 3780*b^2*x^(2/3)*Cos[a + b*x^(1/3)] - 240*b^4*x^(4/3)*Cos[a + b*x^(1/3)] + 64*b^6*x^2*Cos[a + b*x^(1/3)] + 128*b^(15/2)*Sqrt[2*Pi]*x^(5/2)*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)] - 128*b^(15/2)*Sqrt[2*Pi]*x^(5/2)*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x^(1/6)]*Sin[a] + 20790*b*x^(1/3)*Sin[a + b*x^(1/3)] - 840*b^3*x*Sin[a + b*x^(1/3)] + 96*b^5*x^(5/3)*Sin[a + b*x^(1/3)] - 128*b^7*x^(7/3)*Sin[a + b*x^(1/3)]))/(675675*x^(5/2))","A",1
55,1,174,310,0.6448313,"\int x^{3/2} \cos ^2\left(a+b \sqrt[3]{x}\right) \, dx","Integrate[x^(3/2)*Cos[a + b*x^(1/3)]^2,x]","\frac{2 \sqrt{b} \sqrt[6]{x} \left(780 \left(256 b^5 x^{5/3}-1584 b^3 x+3465 b \sqrt[3]{x}\right) \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)+15 \left(4096 b^6 x^2-36608 b^4 x^{4/3}+144144 b^2 x^{2/3}-135135\right) \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+16384 b^7 x^{7/3}\right)+2027025 \sqrt{\pi } \sin (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+2027025 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{163840 b^{15/2}}","\frac{405405 \sqrt{\pi } \sin (2 a) C\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{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{27027 x^{5/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{512 b^5}-\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{39 x^{11/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}+\frac{3 x^{13/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}-\frac{135135 \sqrt{x}}{4096 b^6}+\frac{3861 x^{7/6}}{256 b^4}-\frac{39 x^{11/6}}{16 b^2}+\frac{x^{5/2}}{5}",1,"(2027025*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] + 2027025*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 2*Sqrt[b]*x^(1/6)*(16384*b^7*x^(7/3) + 780*(3465*b*x^(1/3) - 1584*b^3*x + 256*b^5*x^(5/3))*Cos[2*(a + b*x^(1/3))] + 15*(-135135 + 144144*b^2*x^(2/3) - 36608*b^4*x^(4/3) + 4096*b^6*x^2)*Sin[2*(a + b*x^(1/3))]))/(163840*b^(15/2))","A",1
56,1,148,218,0.4379218,"\int \sqrt{x} \cos ^2\left(a+b \sqrt[3]{x}\right) \, dx","Integrate[Sqrt[x]*Cos[a + b*x^(1/3)]^2,x]","\frac{2 \sqrt{b} \sqrt[6]{x} \left(63 \left(16 b^2 x^{2/3}-15\right) \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)+4 b \sqrt[3]{x} \left(9 \left(16 b^2 x^{2/3}-35\right) \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+64 b^3 x\right)\right)+945 \sqrt{\pi } \cos (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-945 \sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)}{1536 b^{9/2}}","\frac{315 \sqrt{\pi } \cos (2 a) C\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{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{21 x^{5/6} \cos ^2\left(a+b \sqrt[3]{x}\right)}{8 b^2}+\frac{3 x^{7/6} \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{2 b}+\frac{315 \sqrt[6]{x}}{256 b^4}-\frac{21 x^{5/6}}{16 b^2}+\frac{x^{3/2}}{3}",1,"(945*Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] - 945*Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 2*Sqrt[b]*x^(1/6)*(63*(-15 + 16*b^2*x^(2/3))*Cos[2*(a + b*x^(1/3))] + 4*b*x^(1/3)*(64*b^3*x + 9*(-35 + 16*b^2*x^(2/3))*Sin[2*(a + b*x^(1/3))])))/(1536*b^(9/2))","A",1
57,1,103,102,0.1842697,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{\sqrt{x}} \, dx","Integrate[Cos[a + b*x^(1/3)]^2/Sqrt[x],x]","\frac{-3 \sqrt{\pi } \sin (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-3 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+2 \sqrt{b} \sqrt[6]{x} \left(3 \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+4 b \sqrt[3]{x}\right)}{8 b^{3/2}}","-\frac{3 \sqrt{\pi } \sin (2 a) C\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,"(-3*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] - 3*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 2*Sqrt[b]*x^(1/6)*(4*b*x^(1/3) + 3*Sin[2*(a + b*x^(1/3))]))/(8*b^(3/2))","A",1
58,1,116,116,0.2463348,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{3/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]^2/x^(3/2),x]","\frac{8 \sqrt{\pi } b^{3/2} \sqrt{x} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)+4 b \sqrt[3]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)-\cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)-1}{\sqrt{x}}-8 \sqrt{\pi } b^{3/2} \cos (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)","-8 \sqrt{\pi } b^{3/2} \cos (2 a) C\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,"-8*b^(3/2)*Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] + (-1 - Cos[2*(a + b*x^(1/3))] + 8*b^(3/2)*Sqrt[Pi]*Sqrt[x]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 4*b*x^(1/3)*Sin[2*(a + b*x^(1/3))])/Sqrt[x]","A",1
59,1,185,228,0.2737051,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{5/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]^2/x^(5/2),x]","\frac{-512 \sqrt{\pi } b^{9/2} x^{3/2} \sin (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-512 \sqrt{\pi } b^{9/2} x^{3/2} \cos (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-256 b^4 x^{4/3} \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)-64 b^3 x \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+48 b^2 x^{2/3} \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)+60 b \sqrt[3]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)-105 \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)-105}{315 x^{3/2}}","-\frac{512}{315} \sqrt{\pi } b^{9/2} \sin (2 a) C\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{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{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{105 x^{5/6}}-\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{256 b^4}{315 \sqrt[6]{x}}-\frac{16 b^2}{105 x^{5/6}}",1,"(-105 - 105*Cos[2*(a + b*x^(1/3))] + 48*b^2*x^(2/3)*Cos[2*(a + b*x^(1/3))] - 256*b^4*x^(4/3)*Cos[2*(a + b*x^(1/3))] - 512*b^(9/2)*Sqrt[Pi]*x^(3/2)*Cos[2*a]*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] - 512*b^(9/2)*Sqrt[Pi]*x^(3/2)*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 60*b*x^(1/3)*Sin[2*(a + b*x^(1/3))] - 64*b^3*x*Sin[2*(a + b*x^(1/3))])/(315*x^(3/2))","A",1
60,1,249,328,0.3844639,"\int \frac{\cos ^2\left(a+b \sqrt[3]{x}\right)}{x^{7/2}} \, dx","Integrate[Cos[a + b*x^(1/3)]^2/x^(7/2),x]","\frac{32768 \sqrt{\pi } b^{15/2} x^{5/2} \cos (2 a) C\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-32768 \sqrt{\pi } b^{15/2} x^{5/2} \sin (2 a) S\left(\frac{2 \sqrt{b} \sqrt[6]{x}}{\sqrt{\pi }}\right)-16384 b^7 x^{7/3} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+4096 b^6 x^2 \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)+3072 b^5 x^{5/3} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)-3840 b^4 x^{4/3} \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)-6720 b^3 x \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)+15120 b^2 x^{2/3} \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)+41580 b \sqrt[3]{x} \sin \left(2 \left(a+b \sqrt[3]{x}\right)\right)-135135 \cos \left(2 \left(a+b \sqrt[3]{x}\right)\right)-135135}{675675 x^{5/2}}","\frac{32768 \sqrt{\pi } b^{15/2} \cos (2 a) C\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{32768 b^7 \sin \left(a+b \sqrt[3]{x}\right) \cos \left(a+b \sqrt[3]{x}\right)}{675675 \sqrt[6]{x}}+\frac{8192 b^6 \cos ^2\left(a+b \sqrt[3]{x}\right)}{675675 \sqrt{x}}+\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{512 b^4 \cos ^2\left(a+b \sqrt[3]{x}\right)}{45045 x^{7/6}}-\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{32 b^2 \cos ^2\left(a+b \sqrt[3]{x}\right)}{715 x^{11/6}}-\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{4096 b^6}{675675 \sqrt{x}}+\frac{256 b^4}{45045 x^{7/6}}-\frac{16 b^2}{715 x^{11/6}}",1,"(-135135 - 135135*Cos[2*(a + b*x^(1/3))] + 15120*b^2*x^(2/3)*Cos[2*(a + b*x^(1/3))] - 3840*b^4*x^(4/3)*Cos[2*(a + b*x^(1/3))] + 4096*b^6*x^2*Cos[2*(a + b*x^(1/3))] + 32768*b^(15/2)*Sqrt[Pi]*x^(5/2)*Cos[2*a]*FresnelC[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]] - 32768*b^(15/2)*Sqrt[Pi]*x^(5/2)*FresnelS[(2*Sqrt[b]*x^(1/6))/Sqrt[Pi]]*Sin[2*a] + 41580*b*x^(1/3)*Sin[2*(a + b*x^(1/3))] - 6720*b^3*x*Sin[2*(a + b*x^(1/3))] + 3072*b^5*x^(5/3)*Sin[2*(a + b*x^(1/3))] - 16384*b^7*x^(7/3)*Sin[2*(a + b*x^(1/3))])/(675675*x^(5/2))","A",1
61,1,66,86,0.0979871,"\int \cos ^3\left(\sqrt[3]{x}\right) \, dx","Integrate[Cos[x^(1/3)]^3,x]","\frac{1}{36} \left(81 \left(x^{2/3}-2\right) \sin \left(\sqrt[3]{x}\right)+\left(9 x^{2/3}-2\right) \sin \left(3 \sqrt[3]{x}\right)+162 \sqrt[3]{x} \cos \left(\sqrt[3]{x}\right)+6 \sqrt[3]{x} \cos \left(3 \sqrt[3]{x}\right)\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,"(162*x^(1/3)*Cos[x^(1/3)] + 6*x^(1/3)*Cos[3*x^(1/3)] + 81*(-2 + x^(2/3))*Sin[x^(1/3)] + (-2 + 9*x^(2/3))*Sin[3*x^(1/3)])/36","A",1
62,1,8,8,0.0022144,"\int \frac{\cos \left(\sqrt[6]{x}\right)}{x^{5/6}} \, dx","Integrate[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",1
63,0,0,21,1.0097657,"\int (e x)^m \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(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,"Integrate[(e*x)^m*(b*Cos[c + d*x^n])^p, x]","A",-1
64,0,0,23,1.2863857,"\int (e x)^m \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(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,"Integrate[(e*x)^m*(a + b*Cos[c + d*x^n])^p, x]","A",-1
65,1,89,93,0.1743758,"\int (e x)^{-1+n} \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(b*Cos[c + d*x^n])^p,x]","-\frac{x^{1-n} (e x)^{n-1} \sqrt{\sin ^2\left(c+d x^n\right)} \cot \left(c+d x^n\right) \left(b \cos \left(c+d x^n\right)\right)^p \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\cos ^2\left(d x^n+c\right)\right)}{d n (p+1)}","-\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,"-((x^(1 - n)*(e*x)^(-1 + n)*(b*Cos[c + d*x^n])^p*Cot[c + d*x^n]*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Cos[c + d*x^n]^2]*Sqrt[Sin[c + d*x^n]^2])/(d*n*(1 + p)))","A",1
66,0,0,39,0.9333192,"\int (e x)^{-1+2 n} \left(b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(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,"Integrate[(e*x)^(-1 + 2*n)*(b*Cos[c + d*x^n])^p, x]","A",-1
67,1,149,131,0.4278242,"\int (e x)^{-1+n} \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Cos[c + d*x^n])^p,x]","-\frac{x^{-n} (e x)^n \csc \left(c+d x^n\right) \sqrt{-\frac{b \left(\cos \left(c+d x^n\right)-1\right)}{a+b}} \sqrt{\frac{b \left(\cos \left(c+d x^n\right)+1\right)}{b-a}} \left(a+b \cos \left(c+d x^n\right)\right)^{p+1} F_1\left(p+1;\frac{1}{2},\frac{1}{2};p+2;\frac{a+b \cos \left(d x^n+c\right)}{a-b},\frac{a+b \cos \left(d x^n+c\right)}{a+b}\right)}{b d e n (p+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,"-(((e*x)^n*AppellF1[1 + p, 1/2, 1/2, 2 + p, (a + b*Cos[c + d*x^n])/(a - b), (a + b*Cos[c + d*x^n])/(a + b)]*Sqrt[-((b*(-1 + Cos[c + d*x^n]))/(a + b))]*Sqrt[(b*(1 + Cos[c + d*x^n]))/(-a + b)]*(a + b*Cos[c + d*x^n])^(1 + p)*Csc[c + d*x^n])/(b*d*e*n*(1 + p)*x^n))","A",0
68,0,0,41,1.1419078,"\int (e x)^{-1+2 n} \left(a+b \cos \left(c+d x^n\right)\right)^p \, dx","Integrate[(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,"Integrate[(e*x)^(-1 + 2*n)*(a + b*Cos[c + d*x^n])^p, x]","A",-1
69,1,24,26,0.0659858,"\int \frac{\cos \left(a+b x^n\right)}{x} \, dx","Integrate[Cos[a + b*x^n]/x,x]","\frac{\cos (a) \text{Ci}\left(b x^n\right)-\sin (a) \text{Si}\left(b x^n\right)}{n}","\frac{\cos (a) \text{Ci}\left(b x^n\right)}{n}-\frac{\sin (a) \text{Si}\left(b x^n\right)}{n}",1,"(Cos[a]*CosIntegral[b*x^n] - Sin[a]*SinIntegral[b*x^n])/n","A",1
70,1,37,43,0.0935037,"\int \frac{\cos ^2\left(a+b x^n\right)}{x} \, dx","Integrate[Cos[a + b*x^n]^2/x,x]","\frac{\cos (2 a) \text{Ci}\left(2 b x^n\right)-\sin (2 a) \text{Si}\left(2 b x^n\right)+n \log (x)}{2 n}","\frac{\cos (2 a) \text{Ci}\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] + n*Log[x] - Sin[2*a]*SinIntegral[2*b*x^n])/(2*n)","A",1
71,1,53,67,0.1265137,"\int \frac{\cos ^3\left(a+b x^n\right)}{x} \, dx","Integrate[Cos[a + b*x^n]^3/x,x]","\frac{3 \cos (a) \text{Ci}\left(b x^n\right)+\cos (3 a) \text{Ci}\left(3 b x^n\right)-3 \sin (a) \text{Si}\left(b x^n\right)-\sin (3 a) \text{Si}\left(3 b x^n\right)}{4 n}","\frac{3 \cos (a) \text{Ci}\left(b x^n\right)}{4 n}+\frac{\cos (3 a) \text{Ci}\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] + Cos[3*a]*CosIntegral[3*b*x^n] - 3*Sin[a]*SinIntegral[b*x^n] - Sin[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",1
72,1,66,79,0.1365709,"\int \frac{\cos ^4\left(a+b x^n\right)}{x} \, dx","Integrate[Cos[a + b*x^n]^4/x,x]","\frac{4 \cos (2 a) \text{Ci}\left(2 b x^n\right)+\cos (4 a) \text{Ci}\left(4 b x^n\right)-4 \sin (2 a) \text{Si}\left(2 b x^n\right)-\sin (4 a) \text{Si}\left(4 b x^n\right)}{8 n}+\frac{3 \log (x)}{8}","\frac{\cos (2 a) \text{Ci}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{Ci}\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,"(3*Log[x])/8 + (4*Cos[2*a]*CosIntegral[2*b*x^n] + Cos[4*a]*CosIntegral[4*b*x^n] - 4*Sin[2*a]*SinIntegral[2*b*x^n] - Sin[4*a]*SinIntegral[4*b*x^n])/(8*n)","A",1
73,1,92,83,0.0820896,"\int \cos \left(a+b x^n\right) \, dx","Integrate[Cos[a + b*x^n],x]","-\frac{x \left(b^2 x^{2 n}\right)^{-1/n} \left((\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b x^n\right)+(\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b x^n\right)\right)}{2 n}","-\frac{e^{i a} x \left(-i b x^n\right)^{-1/n} \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} \Gamma \left(\frac{1}{n},i b x^n\right)}{2 n}",1,"-1/2*(x*(((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), I*b*x^n]*(Cos[a] - I*Sin[a]) + (I*b*x^n)^n^(-1)*Gamma[n^(-1), (-I)*b*x^n]*(Cos[a] + I*Sin[a])))/(n*(b^2*x^(2*n))^n^(-1))","A",1
74,1,94,102,0.245632,"\int \cos ^2\left(a+b x^n\right) \, dx","Integrate[Cos[a + b*x^n]^2,x]","-\frac{x \left(e^{2 i a} 2^{-1/n} \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i b x^n\right)+e^{-2 i a} 2^{-1/n} \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i b x^n\right)-2 n\right)}{4 n}","-\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \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} \Gamma \left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}",1,"-1/4*(x*(-2*n + (E^((2*I)*a)*Gamma[n^(-1), (-2*I)*b*x^n])/(2^n^(-1)*((-I)*b*x^n)^n^(-1)) + Gamma[n^(-1), (2*I)*b*x^n]/(2^n^(-1)*E^((2*I)*a)*(I*b*x^n)^n^(-1))))/n","A",1
75,1,173,179,0.2418767,"\int \cos ^3\left(a+b x^n\right) \, dx","Integrate[Cos[a + b*x^n]^3,x]","-\frac{e^{-3 i a} 3^{-1/n} x \left(b^2 x^{2 n}\right)^{-1/n} \left(e^{2 i a} 3^{\frac{1}{n}+1} \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b x^n\right)+e^{4 i a} 3^{\frac{1}{n}+1} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b x^n\right)+e^{6 i a} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-3 i b x^n\right)+\left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},3 i b x^n\right)\right)}{8 n}","-\frac{3 e^{i a} x \left(-i b x^n\right)^{-1/n} \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} \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} \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} \Gamma \left(\frac{1}{n},3 i b x^n\right)}{8 n}",1,"-1/8*(x*(3^(1 + n^(-1))*E^((4*I)*a)*(I*b*x^n)^n^(-1)*Gamma[n^(-1), (-I)*b*x^n] + 3^(1 + n^(-1))*E^((2*I)*a)*((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), I*b*x^n] + E^((6*I)*a)*(I*b*x^n)^n^(-1)*Gamma[n^(-1), (-3*I)*b*x^n] + ((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), (3*I)*b*x^n]))/(3^n^(-1)*E^((3*I)*a)*n*(b^2*x^(2*n))^n^(-1))","A",1
76,1,115,105,0.2045849,"\int x^m \cos \left(a+b x^n\right) \, dx","Integrate[x^m*Cos[a + b*x^n],x]","-\frac{x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left((\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)+(\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)\right)}{2 n}","-\frac{e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \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}} \Gamma \left(\frac{m+1}{n},i b x^n\right)}{2 n}",1,"-1/2*(x^(1 + m)*(((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, I*b*x^n]*(Cos[a] - I*Sin[a]) + (I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a])))/(n*(b^2*x^(2*n))^((1 + m)/n))","A",1
77,1,129,141,0.5196903,"\int x^m \cos ^2\left(a+b x^n\right) \, dx","Integrate[x^m*Cos[a + b*x^n]^2,x]","-\frac{x^{m+1} \left(e^{2 i a} (m+1) 2^{-\frac{m+1}{n}} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 i b x^n\right)+e^{-2 i a} (m+1) 2^{-\frac{m+1}{n}} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 i b x^n\right)-2 n\right)}{4 (m+1) 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}} \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}} \Gamma \left(\frac{m+1}{n},2 i b x^n\right)}{n}+\frac{x^{m+1}}{2 (m+1)}",1,"-1/4*(x^(1 + m)*(-2*n + (E^((2*I)*a)*(1 + m)*Gamma[(1 + m)/n, (-2*I)*b*x^n])/(2^((1 + m)/n)*((-I)*b*x^n)^((1 + m)/n)) + ((1 + m)*Gamma[(1 + m)/n, (2*I)*b*x^n])/(2^((1 + m)/n)*E^((2*I)*a)*(I*b*x^n)^((1 + m)/n))))/((1 + m)*n)","A",1
78,1,221,229,0.5591979,"\int x^m \cos ^3\left(a+b x^n\right) \, dx","Integrate[x^m*Cos[a + b*x^n]^3,x]","-\frac{e^{-3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left(e^{2 i a} 3^{\frac{m+n+1}{n}} \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)+e^{4 i a} 3^{\frac{m+n+1}{n}} \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)+e^{6 i a} \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 i b x^n\right)+\left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},3 i b x^n\right)\right)}{8 n}","-\frac{3 e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \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}} \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}} \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}} \Gamma \left(\frac{m+1}{n},3 i b x^n\right)}{8 n}",1,"-1/8*(x^(1 + m)*(3^((1 + m + n)/n)*E^((4*I)*a)*(I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-I)*b*x^n] + 3^((1 + m + n)/n)*E^((2*I)*a)*((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, I*b*x^n] + E^((6*I)*a)*(I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-3*I)*b*x^n] + ((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (3*I)*b*x^n]))/(3^((1 + m)/n)*E^((3*I)*a)*n*(b^2*x^(2*n))^((1 + m)/n))","A",1
79,1,45,47,0.0961118,"\int x^{-1-n} \cos \left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cos[a + b*x^n],x]","-\frac{x^{-n} \left(b \sin (a) x^n \text{Ci}\left(b x^n\right)+b \cos (a) x^n \text{Si}\left(b x^n\right)+\cos \left(a+b x^n\right)\right)}{n}","-\frac{b \sin (a) \text{Ci}\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] + b*x^n*CosIntegral[b*x^n]*Sin[a] + b*x^n*Cos[a]*SinIntegral[b*x^n])/(n*x^n))","A",1
80,1,53,69,0.1917615,"\int x^{-1-n} \cos ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cos[a + b*x^n]^2,x]","-\frac{x^{-n} \left(b \sin (2 a) x^n \text{Ci}\left(2 b x^n\right)+b \cos (2 a) x^n \text{Si}\left(2 b x^n\right)+\cos ^2\left(a+b x^n\right)\right)}{n}","-\frac{b \sin (2 a) \text{Ci}\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,"-((Cos[a + b*x^n]^2 + b*x^n*CosIntegral[2*b*x^n]*Sin[2*a] + b*x^n*Cos[2*a]*SinIntegral[2*b*x^n])/(n*x^n))","A",1
81,1,95,113,0.2383948,"\int x^{-1-n} \cos ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cos[a + b*x^n]^3,x]","-\frac{x^{-n} \left(3 b \sin (a) x^n \text{Ci}\left(b x^n\right)+3 b \sin (3 a) x^n \text{Ci}\left(3 b x^n\right)+3 b \cos (a) x^n \text{Si}\left(b x^n\right)+3 b \cos (3 a) x^n \text{Si}\left(3 b x^n\right)+3 \cos \left(a+b x^n\right)+\cos \left(3 \left(a+b x^n\right)\right)\right)}{4 n}","-\frac{3 b \sin (a) \text{Ci}\left(b x^n\right)}{4 n}-\frac{3 b \sin (3 a) \text{Ci}\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,"-1/4*(3*Cos[a + b*x^n] + Cos[3*(a + b*x^n)] + 3*b*x^n*CosIntegral[b*x^n]*Sin[a] + 3*b*x^n*CosIntegral[3*b*x^n]*Sin[3*a] + 3*b*x^n*Cos[a]*SinIntegral[b*x^n] + 3*b*x^n*Cos[3*a]*SinIntegral[3*b*x^n])/(n*x^n)","A",1
82,1,70,78,0.137163,"\int x^{-1-2 n} \cos \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Cos[a + b*x^n],x]","-\frac{x^{-2 n} \left(b^2 \cos (a) x^{2 n} \text{Ci}\left(b x^n\right)-b^2 \sin (a) x^{2 n} \text{Si}\left(b x^n\right)-b x^n \sin \left(a+b x^n\right)+\cos \left(a+b x^n\right)\right)}{2 n}","-\frac{b^2 \cos (a) \text{Ci}\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,"-1/2*(Cos[a + b*x^n] + b^2*x^(2*n)*Cos[a]*CosIntegral[b*x^n] - b*x^n*Sin[a + b*x^n] - b^2*x^(2*n)*Sin[a]*SinIntegral[b*x^n])/(n*x^(2*n))","A",1
83,1,82,95,0.2244307,"\int x^{-1-2 n} \cos ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Cos[a + b*x^n]^2,x]","-\frac{x^{-2 n} \left(4 b^2 \cos (2 a) x^{2 n} \text{Ci}\left(2 b x^n\right)-4 b^2 \sin (2 a) x^{2 n} \text{Si}\left(2 b x^n\right)-2 b x^n \sin \left(2 \left(a+b x^n\right)\right)+\cos \left(2 \left(a+b x^n\right)\right)+1\right)}{4 n}","-\frac{b^2 \cos (2 a) \text{Ci}\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*(1 + Cos[2*(a + b*x^n)] + 4*b^2*x^(2*n)*Cos[2*a]*CosIntegral[2*b*x^n] - 2*b*x^n*Sin[2*(a + b*x^n)] - 4*b^2*x^(2*n)*Sin[2*a]*SinIntegral[2*b*x^n])/(n*x^(2*n))","A",1
84,1,141,165,0.3603699,"\int x^{-1-2 n} \cos ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Cos[a + b*x^n]^3,x]","-\frac{x^{-2 n} \left(3 b^2 \cos (a) x^{2 n} \text{Ci}\left(b x^n\right)+9 b^2 \cos (3 a) x^{2 n} \text{Ci}\left(3 b x^n\right)-3 b^2 \sin (a) x^{2 n} \text{Si}\left(b x^n\right)-9 b^2 \sin (3 a) x^{2 n} \text{Si}\left(3 b x^n\right)-3 b x^n \sin \left(a+b x^n\right)-3 b x^n \sin \left(3 \left(a+b x^n\right)\right)+3 \cos \left(a+b x^n\right)+\cos \left(3 \left(a+b x^n\right)\right)\right)}{8 n}","-\frac{3 b^2 \cos (a) \text{Ci}\left(b x^n\right)}{8 n}-\frac{9 b^2 \cos (3 a) \text{Ci}\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,"-1/8*(3*Cos[a + b*x^n] + Cos[3*(a + b*x^n)] + 3*b^2*x^(2*n)*Cos[a]*CosIntegral[b*x^n] + 9*b^2*x^(2*n)*Cos[3*a]*CosIntegral[3*b*x^n] - 3*b*x^n*Sin[a + b*x^n] - 3*b*x^n*Sin[3*(a + b*x^n)] - 3*b^2*x^(2*n)*Sin[a]*SinIntegral[b*x^n] - 9*b^2*x^(2*n)*Sin[3*a]*SinIntegral[3*b*x^n])/(n*x^(2*n))","A",1
85,1,76,99,0.2847029,"\int x^2 \cos \left((a+b x)^2\right) \, dx","Integrate[x^2*Cos[(a + b*x)^2],x]","-\frac{-2 \sqrt{2 \pi } a^2 C\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)+\sqrt{2 \pi } S\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)+2 (a-b x) \sin \left((a+b x)^2\right)}{4 b^3}","\frac{\sqrt{\frac{\pi }{2}} a^2 C\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,"-1/4*(-2*a^2*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*(a + b*x)] + Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*(a + b*x)] + 2*(a - b*x)*Sin[(a + b*x)^2])/b^3","A",1
86,1,42,47,0.0490113,"\int x \cos \left((a+b x)^2\right) \, dx","Integrate[x*Cos[(a + b*x)^2],x]","\frac{\sin \left((a+b x)^2\right)-\sqrt{2 \pi } a C\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{2 b^2}","\frac{\sin \left((a+b x)^2\right)}{2 b^2}-\frac{\sqrt{\frac{\pi }{2}} a C\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b^2}",1,"(-(a*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*(a + b*x)]) + Sin[(a + b*x)^2])/(2*b^2)","A",1
87,1,29,29,0.0080751,"\int \cos \left((a+b x)^2\right) \, dx","Integrate[Cos[(a + b*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b}","\frac{\sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} (a+b x)\right)}{b}",1,"(Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*(a + b*x)])/b","A",1
88,0,0,15,2.6468755,"\int \frac{\cos \left((a+b x)^2\right)}{x} \, dx","Integrate[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,"Integrate[Cos[(a + b*x)^2]/x, x]","A",-1
89,0,0,15,5.2188138,"\int \frac{\cos \left((a+b x)^2\right)}{x^2} \, dx","Integrate[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,"Integrate[Cos[(a + b*x)^2]/x^2, x]","A",-1
90,1,224,346,0.8306786,"\int x^2 \cos \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x^2*Cos[a + b*Sqrt[c + d*x]],x]","\frac{e^{-i \left(a+b \sqrt{c+d x}\right)} \left(\left(-i b^5 d^2 x^2 \sqrt{c+d x}+b^4 d x (4 c+5 d x)+4 i b^3 \sqrt{c+d x} (2 c+5 d x)-12 b^2 (4 c+5 d x)-120 i b \sqrt{c+d x}+120\right) e^{2 i \left(a+b \sqrt{c+d x}\right)}+i b^5 d^2 x^2 \sqrt{c+d x}+b^4 d x (4 c+5 d x)-4 i b^3 \sqrt{c+d x} (2 c+5 d x)-12 b^2 (4 c+5 d x)+120 i b \sqrt{c+d x}+120\right)}{b^6 d^3}","\frac{240 \cos \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{240 \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)}{b^5 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{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{2 c^2 \cos \left(a+b \sqrt{c+d x}\right)}{b^2 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{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,"(120 + (120*I)*b*Sqrt[c + d*x] + I*b^5*d^2*x^2*Sqrt[c + d*x] - (4*I)*b^3*Sqrt[c + d*x]*(2*c + 5*d*x) - 12*b^2*(4*c + 5*d*x) + b^4*d*x*(4*c + 5*d*x) + E^((2*I)*(a + b*Sqrt[c + d*x]))*(120 - (120*I)*b*Sqrt[c + d*x] - I*b^5*d^2*x^2*Sqrt[c + d*x] + (4*I)*b^3*Sqrt[c + d*x]*(2*c + 5*d*x) - 12*b^2*(4*c + 5*d*x) + b^4*d*x*(4*c + 5*d*x)))/(b^6*d^3*E^(I*(a + b*Sqrt[c + d*x])))","C",1
91,1,71,167,0.283049,"\int x \cos \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x*Cos[a + b*Sqrt[c + d*x]],x]","\frac{2 \left(b \left(b^2 d x-6\right) \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)+\left(b^2 (2 c+3 d x)-6\right) \cos \left(a+b \sqrt{c+d x}\right)\right)}{b^4 d^2}","-\frac{12 \cos \left(a+b \sqrt{c+d x}\right)}{b^4 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{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,"(2*((-6 + b^2*(2*c + 3*d*x))*Cos[a + b*Sqrt[c + d*x]] + b*Sqrt[c + d*x]*(-6 + b^2*d*x)*Sin[a + b*Sqrt[c + d*x]]))/(b^4*d^2)","A",1
92,1,48,54,0.0744355,"\int \cos \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[Cos[a + b*Sqrt[c + d*x]],x]","\frac{2 \left(b \sqrt{c+d x} \sin \left(a+b \sqrt{c+d x}\right)+\cos \left(a+b \sqrt{c+d x}\right)\right)}{b^2 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*Sqrt[c + d*x]*Sin[a + b*Sqrt[c + d*x]]))/(b^2*d)","A",1
93,1,145,126,0.6709392,"\int \frac{\cos \left(a+b \sqrt{c+d x}\right)}{x} \, dx","Integrate[Cos[a + b*Sqrt[c + d*x]]/x,x]","\frac{1}{2} e^{-i \left(a+b \sqrt{c}\right)} \left(e^{2 i \left(a+b \sqrt{c}\right)} \text{Ei}\left(i b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)+e^{2 i a} \text{Ei}\left(i b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+\text{Ei}\left(-i b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)+e^{2 i b \sqrt{c}} \text{Ei}\left(-i b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)\right)","\cos \left(a-b \sqrt{c}\right) \text{Ci}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+\cos \left(a+b \sqrt{c}\right) \text{Ci}\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,"(ExpIntegralEi[(-I)*b*(-Sqrt[c] + Sqrt[c + d*x])] + E^((2*I)*(a + b*Sqrt[c]))*ExpIntegralEi[I*b*(-Sqrt[c] + Sqrt[c + d*x])] + E^((2*I)*b*Sqrt[c])*ExpIntegralEi[(-I)*b*(Sqrt[c] + Sqrt[c + d*x])] + E^((2*I)*a)*ExpIntegralEi[I*b*(Sqrt[c] + Sqrt[c + d*x])])/(2*E^(I*(a + b*Sqrt[c])))","C",1
94,1,240,184,1.2048841,"\int \frac{\cos \left(a+b \sqrt{c+d x}\right)}{x^2} \, dx","Integrate[Cos[a + b*Sqrt[c + d*x]]/x^2,x]","\frac{i \left(e^{-i a} \left(-b d x e^{-i b \sqrt{c}} \text{Ei}\left(-i b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)+b d x e^{i b \sqrt{c}} \text{Ei}\left(-i b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+2 i \sqrt{c} e^{-i b \sqrt{c+d x}}\right)+e^{i \left(a-b \sqrt{c}\right)} \left(b d x e^{2 i b \sqrt{c}} \text{Ei}\left(i b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)-b d x \text{Ei}\left(i b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+2 i \sqrt{c} e^{i b \left(\sqrt{c+d x}+\sqrt{c}\right)}\right)\right)}{4 \sqrt{c} x}","\frac{b d \sin \left(a-b \sqrt{c}\right) \text{Ci}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{b d \sin \left(a+b \sqrt{c}\right) \text{Ci}\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,"((I/4)*((((2*I)*Sqrt[c])/E^(I*b*Sqrt[c + d*x]) - (b*d*x*ExpIntegralEi[(-I)*b*(-Sqrt[c] + Sqrt[c + d*x])])/E^(I*b*Sqrt[c]) + b*d*E^(I*b*Sqrt[c])*x*ExpIntegralEi[(-I)*b*(Sqrt[c] + Sqrt[c + d*x])])/E^(I*a) + E^(I*(a - b*Sqrt[c]))*((2*I)*Sqrt[c]*E^(I*b*(Sqrt[c] + Sqrt[c + d*x])) + b*d*E^((2*I)*b*Sqrt[c])*x*ExpIntegralEi[I*b*(-Sqrt[c] + Sqrt[c + d*x])] - b*d*x*ExpIntegralEi[I*b*(Sqrt[c] + Sqrt[c + d*x])])))/(Sqrt[c]*x)","C",1
95,1,382,537,1.0975158,"\int x^2 \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x^2*Cos[a + b*(c + d*x)^(1/3)],x]","\frac{3 e^{-i \left(a+b \sqrt[3]{c+d x}\right)} \left(-i b^8 d^2 x^2 (c+d x)^{2/3} \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)+2 b^7 d x \sqrt[3]{c+d x} (3 c+4 d x) \left(1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)+2 i b^6 \left(9 c^2+36 c d x+28 d^2 x^2\right) \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)-24 b^5 (c+d x)^{2/3} (9 c+14 d x) \left(1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)-240 i b^4 \sqrt[3]{c+d x} (6 c+7 d x) \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)+240 b^3 (27 c+28 d x) \left(1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)+20160 i b^2 (c+d x)^{2/3} \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)-40320 b \sqrt[3]{c+d x} \left(1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)-40320 i \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)\right)}{2 b^9 d^3}","\frac{120960 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}-\frac{120960 \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}-\frac{60480 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}+\frac{20160 (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}-\frac{720 c \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{5040 (c+d x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 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{1008 (c+d x)^{5/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 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{6 c^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{168 (c+d x)^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{120 c (c+d x) \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{24 (c+d x)^{7/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 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{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,"(3*((-40320*I)*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3)))) - 40320*b*(1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(c + d*x)^(1/3) + (20160*I)*b^2*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(c + d*x)^(2/3) - I*b^8*d^2*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*x^2*(c + d*x)^(2/3) + 2*b^7*d*(1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*x*(c + d*x)^(1/3)*(3*c + 4*d*x) - (240*I)*b^4*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(c + d*x)^(1/3)*(6*c + 7*d*x) - 24*b^5*(1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(c + d*x)^(2/3)*(9*c + 14*d*x) + 240*b^3*(1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(27*c + 28*d*x) + (2*I)*b^6*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*(9*c^2 + 36*c*d*x + 28*d^2*x^2)))/(2*b^9*d^3*E^(I*(a + b*(c + d*x)^(1/3))))","C",1
96,1,117,261,0.4249158,"\int x \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x*Cos[a + b*(c + d*x)^(1/3)],x]","\frac{3 \left(b \left(b^4 d x (c+d x)^{2/3}-2 b^2 (9 c+10 d x)+120 \sqrt[3]{c+d x}\right) \sin \left(a+b \sqrt[3]{c+d x}\right)+\left(b^4 \sqrt[3]{c+d x} (3 c+5 d x)-60 b^2 (c+d x)^{2/3}+120\right) \cos \left(a+b \sqrt[3]{c+d x}\right)\right)}{b^6 d^2}","\frac{360 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{360 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}-\frac{180 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}-\frac{60 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{6 c \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 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,"(3*((120 - 60*b^2*(c + d*x)^(2/3) + b^4*(c + d*x)^(1/3)*(3*c + 5*d*x))*Cos[a + b*(c + d*x)^(1/3)] + b*(120*(c + d*x)^(1/3) + b^4*d*x*(c + d*x)^(2/3) - 2*b^2*(9*c + 10*d*x))*Sin[a + b*(c + d*x)^(1/3)]))/(b^6*d^2)","A",1
97,1,65,85,0.1131667,"\int \cos \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[Cos[a + b*(c + d*x)^(1/3)],x]","\frac{3 \left(b^2 (c+d x)^{2/3}-2\right) \sin \left(a+b \sqrt[3]{c+d x}\right)+6 b \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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*b*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)] + 3*(-2 + b^2*(c + d*x)^(2/3))*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d)","A",1
98,1,243,234,0.4282632,"\int \frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x} \, dx","Integrate[Cos[a + b*(c + d*x)^(1/3)]/x,x]","\frac{1}{2} \left(\text{RootSum}\left[c-\text{$\#$1}^3\&,-i \sin (\text{$\#$1} b+a) \text{Ci}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cos (\text{$\#$1} b+a) \text{Ci}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\sin (\text{$\#$1} b+a) \text{Si}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-i \cos (\text{$\#$1} b+a) \text{Si}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]+\text{RootSum}\left[c-\text{$\#$1}^3\&,i \sin (\text{$\#$1} b+a) \text{Ci}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cos (\text{$\#$1} b+a) \text{Ci}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\sin (\text{$\#$1} b+a) \text{Si}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+i \cos (\text{$\#$1} b+a) \text{Si}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]\right)","\cos \left(a+b \sqrt[3]{c}\right) \text{Ci}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Ci}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\cos \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Ci}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)+\sin \left(a+b \sqrt[3]{c}\right) \text{Si}\left(b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)+\sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Si}\left((-1)^{2/3} b \sqrt[3]{c}-b \sqrt[3]{c+d x}\right)-\sin \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Si}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)",1,"(RootSum[c - #1^3 & , Cos[a + b*#1]*CosIntegral[b*((c + d*x)^(1/3) - #1)] - I*CosIntegral[b*((c + d*x)^(1/3) - #1)]*Sin[a + b*#1] - I*Cos[a + b*#1]*SinIntegral[b*((c + d*x)^(1/3) - #1)] - Sin[a + b*#1]*SinIntegral[b*((c + d*x)^(1/3) - #1)] & ] + RootSum[c - #1^3 & , Cos[a + b*#1]*CosIntegral[b*((c + d*x)^(1/3) - #1)] + I*CosIntegral[b*((c + d*x)^(1/3) - #1)]*Sin[a + b*#1] + I*Cos[a + b*#1]*SinIntegral[b*((c + d*x)^(1/3) - #1)] - Sin[a + b*#1]*SinIntegral[b*((c + d*x)^(1/3) - #1)] & ])/2","C",0
99,1,138,332,0.6019139,"\int \frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x^2} \, dx","Integrate[Cos[a + b*(c + d*x)^(1/3)]/x^2,x]","-\frac{1}{6} i b d \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{e^{-i \text{$\#$1} b-i a} \text{Ei}\left(-i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]+\frac{1}{6} i b d \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{e^{i \text{$\#$1} b+i a} \text{Ei}\left(i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]-\frac{\cos \left(a+b \sqrt[3]{c+d x}\right)}{x}","-\frac{b d \sin \left(a+b \sqrt[3]{c}\right) \text{Ci}\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{Ci}\left(\sqrt[3]{-1} \sqrt[3]{c} b+\sqrt[3]{c+d x} b\right)}{3 c^{2/3}}-\frac{(-1)^{2/3} b d \sin \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Ci}\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) - (I/6)*b*d*RootSum[c - #1^3 & , (E^((-I)*a - I*b*#1)*ExpIntegralEi[(-I)*b*((c + d*x)^(1/3) - #1)])/#1^2 & ] + (I/6)*b*d*RootSum[c - #1^3 & , (E^(I*a + I*b*#1)*ExpIntegralEi[I*b*((c + d*x)^(1/3) - #1)])/#1^2 & ]","C",1