1,1,126,0,0.3119279,"\int x^3 (a+b x) \sin (c+d x) \, dx","Int[x^3*(a + b*x)*Sin[c + d*x],x]","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}",1,"(-24*b*Cos[c + d*x])/d^5 + (6*a*x*Cos[c + d*x])/d^3 + (12*b*x^2*Cos[c + d*x])/d^3 - (a*x^3*Cos[c + d*x])/d - (b*x^4*Cos[c + d*x])/d - (6*a*Sin[c + d*x])/d^4 - (24*b*x*Sin[c + d*x])/d^4 + (3*a*x^2*Sin[c + d*x])/d^2 + (4*b*x^3*Sin[c + d*x])/d^2","A",11,4,15,0.2667,1,"{6742, 3296, 2637, 2638}"
2,1,96,0,0.2078229,"\int x^2 (a+b x) \sin (c+d x) \, dx","Int[x^2*(a + b*x)*Sin[c + d*x],x]","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}",1,"(2*a*Cos[c + d*x])/d^3 + (6*b*x*Cos[c + d*x])/d^3 - (a*x^2*Cos[c + d*x])/d - (b*x^3*Cos[c + d*x])/d - (6*b*Sin[c + d*x])/d^4 + (2*a*x*Sin[c + d*x])/d^2 + (3*b*x^2*Sin[c + d*x])/d^2","A",9,4,15,0.2667,1,"{6742, 3296, 2638, 2637}"
3,1,65,0,0.1052896,"\int x (a+b x) \sin (c+d x) \, dx","Int[x*(a + b*x)*Sin[c + d*x],x]","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}",1,"(2*b*Cos[c + d*x])/d^3 - (a*x*Cos[c + d*x])/d - (b*x^2*Cos[c + d*x])/d + (a*Sin[c + d*x])/d^2 + (2*b*x*Sin[c + d*x])/d^2","A",7,4,13,0.3077,1,"{6742, 3296, 2637, 2638}"
4,1,28,0,0.0166503,"\int (a+b x) \sin (c+d x) \, dx","Int[(a + b*x)*Sin[c + d*x],x]","\frac{b \sin (c+d x)}{d^2}-\frac{(a+b x) \cos (c+d x)}{d}","\frac{b \sin (c+d x)}{d^2}-\frac{(a+b x) \cos (c+d x)}{d}",1,"-(((a + b*x)*Cos[c + d*x])/d) + (b*Sin[c + d*x])/d^2","A",2,2,12,0.1667,1,"{3296, 2637}"
5,1,29,0,0.1484461,"\int \frac{(a+b x) \sin (c+d x)}{x} \, dx","Int[((a + b*x)*Sin[c + d*x])/x,x]","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)-\frac{b \cos (c+d x)}{d}","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)-\frac{b \cos (c+d x)}{d}",1,"-((b*Cos[c + d*x])/d) + a*CosIntegral[d*x]*Sin[c] + a*Cos[c]*SinIntegral[d*x]","A",6,5,15,0.3333,1,"{6742, 2638, 3303, 3299, 3302}"
6,1,48,0,0.2209581,"\int \frac{(a+b x) \sin (c+d x)}{x^2} \, dx","Int[((a + b*x)*Sin[c + d*x])/x^2,x]","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)",1,"a*d*Cos[c]*CosIntegral[d*x] + b*CosIntegral[d*x]*Sin[c] - (a*Sin[c + d*x])/x + b*Cos[c]*SinIntegral[d*x] - a*d*Sin[c]*SinIntegral[d*x]","A",9,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
7,1,89,0,0.2701962,"\int \frac{(a+b x) \sin (c+d x)}{x^3} \, dx","Int[((a + b*x)*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}+b d \cos (c) \text{CosIntegral}(d x)-b d \sin (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{x}","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}+b d \cos (c) \text{CosIntegral}(d x)-b d \sin (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{x}",1,"-(a*d*Cos[c + d*x])/(2*x) + b*d*Cos[c]*CosIntegral[d*x] - (a*d^2*CosIntegral[d*x]*Sin[c])/2 - (a*Sin[c + d*x])/(2*x^2) - (b*Sin[c + d*x])/x - (a*d^2*Cos[c]*SinIntegral[d*x])/2 - b*d*Sin[c]*SinIntegral[d*x]","A",11,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
8,1,132,0,0.3245512,"\int \frac{(a+b x) \sin (c+d x)}{x^4} \, dx","Int[((a + b*x)*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}-\frac{1}{2} b d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b d^2 \cos (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{2 x^2}-\frac{b d \cos (c+d x)}{2 x}","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}-\frac{1}{2} b d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b d^2 \cos (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{2 x^2}-\frac{b d \cos (c+d x)}{2 x}",1,"-(a*d*Cos[c + d*x])/(6*x^2) - (b*d*Cos[c + d*x])/(2*x) - (a*d^3*Cos[c]*CosIntegral[d*x])/6 - (b*d^2*CosIntegral[d*x]*Sin[c])/2 - (a*Sin[c + d*x])/(3*x^3) - (b*Sin[c + d*x])/(2*x^2) + (a*d^2*Sin[c + d*x])/(6*x) - (b*d^2*Cos[c]*SinIntegral[d*x])/2 + (a*d^3*Sin[c]*SinIntegral[d*x])/6","A",13,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
9,1,166,0,0.3684827,"\int \frac{(a+b x) \sin (c+d x)}{x^5} \, dx","Int[((a + b*x)*Sin[c + d*x])/x^5,x]","\frac{1}{24} a d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a d^4 \cos (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{24 x^2}+\frac{a d^3 \cos (c+d x)}{24 x}-\frac{a \sin (c+d x)}{4 x^4}-\frac{a d \cos (c+d x)}{12 x^3}-\frac{1}{6} b d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} b d^3 \sin (c) \text{Si}(d x)+\frac{b d^2 \sin (c+d x)}{6 x}-\frac{b \sin (c+d x)}{3 x^3}-\frac{b d \cos (c+d x)}{6 x^2}","\frac{1}{24} a d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a d^4 \cos (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{24 x^2}+\frac{a d^3 \cos (c+d x)}{24 x}-\frac{a \sin (c+d x)}{4 x^4}-\frac{a d \cos (c+d x)}{12 x^3}-\frac{1}{6} b d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} b d^3 \sin (c) \text{Si}(d x)+\frac{b d^2 \sin (c+d x)}{6 x}-\frac{b \sin (c+d x)}{3 x^3}-\frac{b d \cos (c+d x)}{6 x^2}",1,"-(a*d*Cos[c + d*x])/(12*x^3) - (b*d*Cos[c + d*x])/(6*x^2) + (a*d^3*Cos[c + d*x])/(24*x) - (b*d^3*Cos[c]*CosIntegral[d*x])/6 + (a*d^4*CosIntegral[d*x]*Sin[c])/24 - (a*Sin[c + d*x])/(4*x^4) - (b*Sin[c + d*x])/(3*x^3) + (a*d^2*Sin[c + d*x])/(24*x^2) + (b*d^2*Sin[c + d*x])/(6*x) + (a*d^4*Cos[c]*SinIntegral[d*x])/24 + (b*d^3*Sin[c]*SinIntegral[d*x])/6","A",15,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
10,1,186,0,0.3200683,"\int x^2 (a+b x)^2 \sin (c+d x) \, dx","Int[x^2*(a + b*x)^2*Sin[c + d*x],x]","\frac{2 a^2 x \sin (c+d x)}{d^2}+\frac{2 a^2 \cos (c+d x)}{d^3}-\frac{a^2 x^2 \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}","\frac{2 a^2 x \sin (c+d x)}{d^2}+\frac{2 a^2 \cos (c+d x)}{d^3}-\frac{a^2 x^2 \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}",1,"(-24*b^2*Cos[c + d*x])/d^5 + (2*a^2*Cos[c + d*x])/d^3 + (12*a*b*x*Cos[c + d*x])/d^3 + (12*b^2*x^2*Cos[c + d*x])/d^3 - (a^2*x^2*Cos[c + d*x])/d - (2*a*b*x^3*Cos[c + d*x])/d - (b^2*x^4*Cos[c + d*x])/d - (12*a*b*Sin[c + d*x])/d^4 - (24*b^2*x*Sin[c + d*x])/d^4 + (2*a^2*x*Sin[c + d*x])/d^2 + (6*a*b*x^2*Sin[c + d*x])/d^2 + (4*b^2*x^3*Sin[c + d*x])/d^2","A",14,4,17,0.2353,1,"{6742, 3296, 2638, 2637}"
11,1,135,0,0.186066,"\int x (a+b x)^2 \sin (c+d x) \, dx","Int[x*(a + b*x)^2*Sin[c + d*x],x]","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}",1,"(4*a*b*Cos[c + d*x])/d^3 + (6*b^2*x*Cos[c + d*x])/d^3 - (a^2*x*Cos[c + d*x])/d - (2*a*b*x^2*Cos[c + d*x])/d - (b^2*x^3*Cos[c + d*x])/d - (6*b^2*Sin[c + d*x])/d^4 + (a^2*Sin[c + d*x])/d^2 + (4*a*b*x*Sin[c + d*x])/d^2 + (3*b^2*x^2*Sin[c + d*x])/d^2","A",11,4,15,0.2667,1,"{6742, 3296, 2637, 2638}"
12,1,50,0,0.0424857,"\int (a+b x)^2 \sin (c+d x) \, dx","Int[(a + b*x)^2*Sin[c + d*x],x]","\frac{2 b (a+b x) \sin (c+d x)}{d^2}-\frac{(a+b x)^2 \cos (c+d x)}{d}+\frac{2 b^2 \cos (c+d x)}{d^3}","\frac{2 b (a+b x) \sin (c+d x)}{d^2}-\frac{(a+b x)^2 \cos (c+d x)}{d}+\frac{2 b^2 \cos (c+d x)}{d^3}",1,"(2*b^2*Cos[c + d*x])/d^3 - ((a + b*x)^2*Cos[c + d*x])/d + (2*b*(a + b*x)*Sin[c + d*x])/d^2","A",3,2,14,0.1429,1,"{3296, 2638}"
13,1,62,0,0.1826508,"\int \frac{(a+b x)^2 \sin (c+d x)}{x} \, dx","Int[((a + b*x)^2*Sin[c + d*x])/x,x]","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)-\frac{2 a b \cos (c+d x)}{d}+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)-\frac{2 a b \cos (c+d x)}{d}+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}",1,"(-2*a*b*Cos[c + d*x])/d - (b^2*x*Cos[c + d*x])/d + a^2*CosIntegral[d*x]*Sin[c] + (b^2*Sin[c + d*x])/d^2 + a^2*Cos[c]*SinIntegral[d*x]","A",8,7,17,0.4118,1,"{6742, 2638, 3303, 3299, 3302, 3296, 2637}"
14,1,72,0,0.2424287,"\int \frac{(a+b x)^2 \sin (c+d x)}{x^2} \, dx","Int[((a + b*x)^2*Sin[c + d*x])/x^2,x]","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)-\frac{b^2 \cos (c+d x)}{d}","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)-\frac{b^2 \cos (c+d x)}{d}",1,"-((b^2*Cos[c + d*x])/d) + a^2*d*Cos[c]*CosIntegral[d*x] + 2*a*b*CosIntegral[d*x]*Sin[c] - (a^2*Sin[c + d*x])/x + 2*a*b*Cos[c]*SinIntegral[d*x] - a^2*d*Sin[c]*SinIntegral[d*x]","A",10,6,17,0.3529,1,"{6742, 2638, 3297, 3303, 3299, 3302}"
15,1,121,0,0.3398187,"\int \frac{(a+b x)^2 \sin (c+d x)}{x^3} \, dx","Int[((a + b*x)^2*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}+b^2 \sin (c) \text{CosIntegral}(d x)+b^2 \cos (c) \text{Si}(d x)","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}+b^2 \sin (c) \text{CosIntegral}(d x)+b^2 \cos (c) \text{Si}(d x)",1,"-(a^2*d*Cos[c + d*x])/(2*x) + 2*a*b*d*Cos[c]*CosIntegral[d*x] + b^2*CosIntegral[d*x]*Sin[c] - (a^2*d^2*CosIntegral[d*x]*Sin[c])/2 - (a^2*Sin[c + d*x])/(2*x^2) - (2*a*b*Sin[c + d*x])/x + b^2*Cos[c]*SinIntegral[d*x] - (a^2*d^2*Cos[c]*SinIntegral[d*x])/2 - 2*a*b*d*Sin[c]*SinIntegral[d*x]","A",14,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
16,1,175,0,0.410262,"\int \frac{(a+b x)^2 \sin (c+d x)}{x^4} \, dx","Int[((a + b*x)^2*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}-a b d^2 \sin (c) \text{CosIntegral}(d x)-a b d^2 \cos (c) \text{Si}(d x)-\frac{a b \sin (c+d x)}{x^2}-\frac{a b d \cos (c+d x)}{x}+b^2 d \cos (c) \text{CosIntegral}(d x)-b^2 d \sin (c) \text{Si}(d x)-\frac{b^2 \sin (c+d x)}{x}","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}-a b d^2 \sin (c) \text{CosIntegral}(d x)-a b d^2 \cos (c) \text{Si}(d x)-\frac{a b \sin (c+d x)}{x^2}-\frac{a b d \cos (c+d x)}{x}+b^2 d \cos (c) \text{CosIntegral}(d x)-b^2 d \sin (c) \text{Si}(d x)-\frac{b^2 \sin (c+d x)}{x}",1,"-(a^2*d*Cos[c + d*x])/(6*x^2) - (a*b*d*Cos[c + d*x])/x + b^2*d*Cos[c]*CosIntegral[d*x] - (a^2*d^3*Cos[c]*CosIntegral[d*x])/6 - a*b*d^2*CosIntegral[d*x]*Sin[c] - (a^2*Sin[c + d*x])/(3*x^3) - (a*b*Sin[c + d*x])/x^2 - (b^2*Sin[c + d*x])/x + (a^2*d^2*Sin[c + d*x])/(6*x) - a*b*d^2*Cos[c]*SinIntegral[d*x] - b^2*d*Sin[c]*SinIntegral[d*x] + (a^2*d^3*Sin[c]*SinIntegral[d*x])/6","A",17,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
17,1,248,0,0.4802124,"\int \frac{(a+b x)^2 \sin (c+d x)}{x^5} \, dx","Int[((a + b*x)^2*Sin[c + d*x])/x^5,x]","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}-\frac{1}{3} a b d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{3} a b d^3 \sin (c) \text{Si}(d x)+\frac{a b d^2 \sin (c+d x)}{3 x}-\frac{2 a b \sin (c+d x)}{3 x^3}-\frac{a b d \cos (c+d x)}{3 x^2}-\frac{1}{2} b^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b^2 d^2 \cos (c) \text{Si}(d x)-\frac{b^2 \sin (c+d x)}{2 x^2}-\frac{b^2 d \cos (c+d x)}{2 x}","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}-\frac{1}{3} a b d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{3} a b d^3 \sin (c) \text{Si}(d x)+\frac{a b d^2 \sin (c+d x)}{3 x}-\frac{2 a b \sin (c+d x)}{3 x^3}-\frac{a b d \cos (c+d x)}{3 x^2}-\frac{1}{2} b^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b^2 d^2 \cos (c) \text{Si}(d x)-\frac{b^2 \sin (c+d x)}{2 x^2}-\frac{b^2 d \cos (c+d x)}{2 x}",1,"-(a^2*d*Cos[c + d*x])/(12*x^3) - (a*b*d*Cos[c + d*x])/(3*x^2) - (b^2*d*Cos[c + d*x])/(2*x) + (a^2*d^3*Cos[c + d*x])/(24*x) - (a*b*d^3*Cos[c]*CosIntegral[d*x])/3 - (b^2*d^2*CosIntegral[d*x]*Sin[c])/2 + (a^2*d^4*CosIntegral[d*x]*Sin[c])/24 - (a^2*Sin[c + d*x])/(4*x^4) - (2*a*b*Sin[c + d*x])/(3*x^3) - (b^2*Sin[c + d*x])/(2*x^2) + (a^2*d^2*Sin[c + d*x])/(24*x^2) + (a*b*d^2*Sin[c + d*x])/(3*x) - (b^2*d^2*Cos[c]*SinIntegral[d*x])/2 + (a^2*d^4*Cos[c]*SinIntegral[d*x])/24 + (a*b*d^3*Sin[c]*SinIntegral[d*x])/3","A",20,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
18,1,218,0,0.4644471,"\int \frac{x^4 \sin (c+d x)}{a+b x} \, dx","Int[(x^4*Sin[c + d*x])/(a + b*x),x]","\frac{a^4 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^2 \sin (c+d x)}{b^3 d^2}+\frac{a^4 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^3 \cos (c+d x)}{b^4 d}-\frac{a^2 x \cos (c+d x)}{b^3 d}-\frac{2 a x \sin (c+d x)}{b^2 d^2}-\frac{2 a \cos (c+d x)}{b^2 d^3}+\frac{a x^2 \cos (c+d x)}{b^2 d}+\frac{3 x^2 \sin (c+d x)}{b d^2}-\frac{6 \sin (c+d x)}{b d^4}+\frac{6 x \cos (c+d x)}{b d^3}-\frac{x^3 \cos (c+d x)}{b d}","\frac{a^4 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^2 \sin (c+d x)}{b^3 d^2}+\frac{a^4 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^3 \cos (c+d x)}{b^4 d}-\frac{a^2 x \cos (c+d x)}{b^3 d}-\frac{2 a x \sin (c+d x)}{b^2 d^2}-\frac{2 a \cos (c+d x)}{b^2 d^3}+\frac{a x^2 \cos (c+d x)}{b^2 d}+\frac{3 x^2 \sin (c+d x)}{b d^2}-\frac{6 \sin (c+d x)}{b d^4}+\frac{6 x \cos (c+d x)}{b d^3}-\frac{x^3 \cos (c+d x)}{b d}",1,"(-2*a*Cos[c + d*x])/(b^2*d^3) + (a^3*Cos[c + d*x])/(b^4*d) + (6*x*Cos[c + d*x])/(b*d^3) - (a^2*x*Cos[c + d*x])/(b^3*d) + (a*x^2*Cos[c + d*x])/(b^2*d) - (x^3*Cos[c + d*x])/(b*d) + (a^4*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^5 - (6*Sin[c + d*x])/(b*d^4) + (a^2*Sin[c + d*x])/(b^3*d^2) - (2*a*x*Sin[c + d*x])/(b^2*d^2) + (3*x^2*Sin[c + d*x])/(b*d^2) + (a^4*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^5","A",15,7,17,0.4118,1,"{6742, 2638, 3296, 2637, 3303, 3299, 3302}"
19,1,152,0,0.3064503,"\int \frac{x^3 \sin (c+d x)}{a+b x} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x),x]","-\frac{a^3 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^3 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^2 \cos (c+d x)}{b^3 d}-\frac{a \sin (c+d x)}{b^2 d^2}+\frac{a x \cos (c+d x)}{b^2 d}+\frac{2 x \sin (c+d x)}{b d^2}+\frac{2 \cos (c+d x)}{b d^3}-\frac{x^2 \cos (c+d x)}{b d}","-\frac{a^3 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^3 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^2 \cos (c+d x)}{b^3 d}-\frac{a \sin (c+d x)}{b^2 d^2}+\frac{a x \cos (c+d x)}{b^2 d}+\frac{2 x \sin (c+d x)}{b d^2}+\frac{2 \cos (c+d x)}{b d^3}-\frac{x^2 \cos (c+d x)}{b d}",1,"(2*Cos[c + d*x])/(b*d^3) - (a^2*Cos[c + d*x])/(b^3*d) + (a*x*Cos[c + d*x])/(b^2*d) - (x^2*Cos[c + d*x])/(b*d) - (a^3*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^4 - (a*Sin[c + d*x])/(b^2*d^2) + (2*x*Sin[c + d*x])/(b*d^2) - (a^3*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^4","A",11,7,17,0.4118,1,"{6742, 2638, 3296, 2637, 3303, 3299, 3302}"
20,1,99,0,0.2621609,"\int \frac{x^2 \sin (c+d x)}{a+b x} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x),x]","\frac{a^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{a \cos (c+d x)}{b^2 d}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}","\frac{a^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{a \cos (c+d x)}{b^2 d}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}",1,"(a*Cos[c + d*x])/(b^2*d) - (x*Cos[c + d*x])/(b*d) + (a^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^3 + Sin[c + d*x]/(b*d^2) + (a^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^3","A",8,7,17,0.4118,1,"{6742, 2638, 3296, 2637, 3303, 3299, 3302}"
21,1,69,0,0.1657943,"\int \frac{x \sin (c+d x)}{a+b x} \, dx","Int[(x*Sin[c + d*x])/(a + b*x),x]","-\frac{a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{\cos (c+d x)}{b d}","-\frac{a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{\cos (c+d x)}{b d}",1,"-(Cos[c + d*x]/(b*d)) - (a*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^2 - (a*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^2","A",6,5,15,0.3333,1,"{6742, 2638, 3303, 3299, 3302}"
22,1,51,0,0.0782072,"\int \frac{\sin (c+d x)}{a+b x} \, dx","Int[Sin[c + d*x]/(a + b*x),x]","\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b}","\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b}",1,"(CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b + (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b","A",3,3,14,0.2143,1,"{3303, 3299, 3302}"
23,1,73,0,0.2610016,"\int \frac{\sin (c+d x)}{x (a+b x)} \, dx","Int[Sin[c + d*x]/(x*(a + b*x)),x]","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}",1,"(CosIntegral[d*x]*Sin[c])/a - (CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a + (Cos[c]*SinIntegral[d*x])/a - (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a","A",8,4,17,0.2353,1,"{6742, 3303, 3299, 3302}"
24,1,114,0,0.3496865,"\int \frac{\sin (c+d x)}{x^2 (a+b x)} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x)),x]","-\frac{b \sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{b \cos (c) \text{Si}(d x)}{a^2}+\frac{b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}","-\frac{b \sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{b \cos (c) \text{Si}(d x)}{a^2}+\frac{b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}",1,"(d*Cos[c]*CosIntegral[d*x])/a - (b*CosIntegral[d*x]*Sin[c])/a^2 + (b*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^2 - Sin[c + d*x]/(a*x) - (b*Cos[c]*SinIntegral[d*x])/a^2 - (d*Sin[c]*SinIntegral[d*x])/a + (b*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^2","A",12,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
25,1,189,0,0.4907628,"\int \frac{\sin (c+d x)}{x^3 (a+b x)} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x)),x]","\frac{b^2 \sin (c) \text{CosIntegral}(d x)}{a^3}-\frac{b^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}+\frac{b^2 \cos (c) \text{Si}(d x)}{a^3}-\frac{b^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{b d \cos (c) \text{CosIntegral}(d x)}{a^2}+\frac{b d \sin (c) \text{Si}(d x)}{a^2}+\frac{b \sin (c+d x)}{a^2 x}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}","\frac{b^2 \sin (c) \text{CosIntegral}(d x)}{a^3}-\frac{b^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}+\frac{b^2 \cos (c) \text{Si}(d x)}{a^3}-\frac{b^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{b d \cos (c) \text{CosIntegral}(d x)}{a^2}+\frac{b d \sin (c) \text{Si}(d x)}{a^2}+\frac{b \sin (c+d x)}{a^2 x}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}",1,"-(d*Cos[c + d*x])/(2*a*x) - (b*d*Cos[c]*CosIntegral[d*x])/a^2 + (b^2*CosIntegral[d*x]*Sin[c])/a^3 - (d^2*CosIntegral[d*x]*Sin[c])/(2*a) - (b^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^3 - Sin[c + d*x]/(2*a*x^2) + (b*Sin[c + d*x])/(a^2*x) + (b^2*Cos[c]*SinIntegral[d*x])/a^3 - (d^2*Cos[c]*SinIntegral[d*x])/(2*a) + (b*d*Sin[c]*SinIntegral[d*x])/a^2 - (b^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^3","A",17,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
26,1,233,0,0.5089659,"\int \frac{x^4 \sin (c+d x)}{(a+b x)^2} \, dx","Int[(x^4*Sin[c + d*x])/(a + b*x)^2,x]","-\frac{4 a^3 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^4 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^6}-\frac{a^4 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^6}-\frac{4 a^3 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{a^4 \sin (c+d x)}{b^5 (a+b x)}-\frac{3 a^2 \cos (c+d x)}{b^4 d}-\frac{2 a \sin (c+d x)}{b^3 d^2}+\frac{2 a x \cos (c+d x)}{b^3 d}+\frac{2 x \sin (c+d x)}{b^2 d^2}+\frac{2 \cos (c+d x)}{b^2 d^3}-\frac{x^2 \cos (c+d x)}{b^2 d}","-\frac{4 a^3 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^4 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^6}-\frac{a^4 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^6}-\frac{4 a^3 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{a^4 \sin (c+d x)}{b^5 (a+b x)}-\frac{3 a^2 \cos (c+d x)}{b^4 d}-\frac{2 a \sin (c+d x)}{b^3 d^2}+\frac{2 a x \cos (c+d x)}{b^3 d}+\frac{2 x \sin (c+d x)}{b^2 d^2}+\frac{2 \cos (c+d x)}{b^2 d^3}-\frac{x^2 \cos (c+d x)}{b^2 d}",1,"(2*Cos[c + d*x])/(b^2*d^3) - (3*a^2*Cos[c + d*x])/(b^4*d) + (2*a*x*Cos[c + d*x])/(b^3*d) - (x^2*Cos[c + d*x])/(b^2*d) + (a^4*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^6 - (4*a^3*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^5 - (2*a*Sin[c + d*x])/(b^3*d^2) + (2*x*Sin[c + d*x])/(b^2*d^2) - (a^4*Sin[c + d*x])/(b^5*(a + b*x)) - (4*a^3*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^5 - (a^4*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^6","A",15,8,17,0.4706,1,"{6742, 2638, 3296, 2637, 3297, 3303, 3299, 3302}"
27,1,181,0,0.4084686,"\int \frac{x^3 \sin (c+d x)}{(a+b x)^2} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x)^2,x]","\frac{3 a^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^3 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^3 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{3 a^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{a^3 \sin (c+d x)}{b^4 (a+b x)}+\frac{2 a \cos (c+d x)}{b^3 d}+\frac{\sin (c+d x)}{b^2 d^2}-\frac{x \cos (c+d x)}{b^2 d}","\frac{3 a^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^3 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^3 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{3 a^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{a^3 \sin (c+d x)}{b^4 (a+b x)}+\frac{2 a \cos (c+d x)}{b^3 d}+\frac{\sin (c+d x)}{b^2 d^2}-\frac{x \cos (c+d x)}{b^2 d}",1,"(2*a*Cos[c + d*x])/(b^3*d) - (x*Cos[c + d*x])/(b^2*d) - (a^3*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^5 + (3*a^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^4 + Sin[c + d*x]/(b^2*d^2) + (a^3*Sin[c + d*x])/(b^4*(a + b*x)) + (3*a^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^4 + (a^3*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^5","A",12,8,17,0.4706,1,"{6742, 2638, 3296, 2637, 3297, 3303, 3299, 3302}"
28,1,149,0,0.3631685,"\int \frac{x^2 \sin (c+d x)}{(a+b x)^2} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x)^2,x]","\frac{a^2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^2 \sin (c+d x)}{b^3 (a+b x)}-\frac{2 a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}-\frac{2 a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{\cos (c+d x)}{b^2 d}","\frac{a^2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{a^2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^2 \sin (c+d x)}{b^3 (a+b x)}-\frac{2 a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}-\frac{2 a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{\cos (c+d x)}{b^2 d}",1,"-(Cos[c + d*x]/(b^2*d)) + (a^2*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^4 - (2*a*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^3 - (a^2*Sin[c + d*x])/(b^3*(a + b*x)) - (2*a*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^3 - (a^2*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^4","A",10,6,17,0.3529,1,"{6742, 2638, 3297, 3303, 3299, 3302}"
29,1,124,0,0.2849394,"\int \frac{x \sin (c+d x)}{(a+b x)^2} \, dx","Int[(x*Sin[c + d*x])/(a + b*x)^2,x]","\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{a d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{a \sin (c+d x)}{b^2 (a+b x)}","\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{a d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{a \sin (c+d x)}{b^2 (a+b x)}",1,"-((a*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^3) + (CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^2 + (a*Sin[c + d*x])/(b^2*(a + b*x)) + (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^2 + (a*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^3","A",9,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
30,1,72,0,0.0973983,"\int \frac{\sin (c+d x)}{(a+b x)^2} \, dx","Int[Sin[c + d*x]/(a + b*x)^2,x]","\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{\sin (c+d x)}{b (a+b x)}","\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^2}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{\sin (c+d x)}{b (a+b x)}",1,"(d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^2 - Sin[c + d*x]/(b*(a + b*x)) - (d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^2","A",4,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
31,1,149,0,0.4102009,"\int \frac{\sin (c+d x)}{x (a+b x)^2} \, dx","Int[Sin[c + d*x]/(x*(a + b*x)^2),x]","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}-\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a b}+\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a b}+\frac{\sin (c+d x)}{a (a+b x)}","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}-\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a b}+\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a b}+\frac{\sin (c+d x)}{a (a+b x)}",1,"-((d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/(a*b)) + (CosIntegral[d*x]*Sin[c])/a^2 - (CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^2 + Sin[c + d*x]/(a*(a + b*x)) + (Cos[c]*SinIntegral[d*x])/a^2 - (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^2 + (d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(a*b)","A",12,5,17,0.2941,1,"{6742, 3303, 3299, 3302, 3297}"
32,1,188,0,0.5136874,"\int \frac{\sin (c+d x)}{x^2 (a+b x)^2} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x)^2),x]","-\frac{2 b \sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{2 b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}+\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}-\frac{2 b \cos (c) \text{Si}(d x)}{a^3}+\frac{2 b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{b \sin (c+d x)}{a^2 (a+b x)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{a^2 x}","-\frac{2 b \sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{2 b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}+\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2}-\frac{2 b \cos (c) \text{Si}(d x)}{a^3}+\frac{2 b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{b \sin (c+d x)}{a^2 (a+b x)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{a^2 x}",1,"(d*Cos[c]*CosIntegral[d*x])/a^2 + (d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/a^2 - (2*b*CosIntegral[d*x]*Sin[c])/a^3 + (2*b*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^3 - Sin[c + d*x]/(a^2*x) - (b*Sin[c + d*x])/(a^2*(a + b*x)) - (2*b*Cos[c]*SinIntegral[d*x])/a^3 - (d*Sin[c]*SinIntegral[d*x])/a^2 + (2*b*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^3 - (d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^2","A",16,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
33,1,265,0,0.6097461,"\int \frac{x^3 \sin (c+d x)}{(a+b x)^3} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x)^3,x]","\frac{a^3 d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^6}+\frac{3 a^2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^3 d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^6}-\frac{3 a^2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^3 \sin (c+d x)}{2 b^4 (a+b x)^2}-\frac{3 a^2 \sin (c+d x)}{b^4 (a+b x)}+\frac{a^3 d \cos (c+d x)}{2 b^5 (a+b x)}-\frac{3 a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{3 a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{\cos (c+d x)}{b^3 d}","\frac{a^3 d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^6}+\frac{3 a^2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^5}+\frac{a^3 d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^6}-\frac{3 a^2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^3 \sin (c+d x)}{2 b^4 (a+b x)^2}-\frac{3 a^2 \sin (c+d x)}{b^4 (a+b x)}+\frac{a^3 d \cos (c+d x)}{2 b^5 (a+b x)}-\frac{3 a \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}-\frac{3 a \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{\cos (c+d x)}{b^3 d}",1,"-(Cos[c + d*x]/(b^3*d)) + (a^3*d*Cos[c + d*x])/(2*b^5*(a + b*x)) + (3*a^2*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^5 - (3*a*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^4 + (a^3*d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*b^6) + (a^3*Sin[c + d*x])/(2*b^4*(a + b*x)^2) - (3*a^2*Sin[c + d*x])/(b^4*(a + b*x)) - (3*a*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^4 + (a^3*d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*b^6) - (3*a^2*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^5","A",15,6,17,0.3529,1,"{6742, 2638, 3297, 3303, 3299, 3302}"
34,1,241,0,0.5354224,"\int \frac{x^2 \sin (c+d x)}{(a+b x)^3} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x)^3,x]","-\frac{a^2 d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^5}-\frac{a^2 d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^5}-\frac{a^2 \sin (c+d x)}{2 b^3 (a+b x)^2}-\frac{a^2 d \cos (c+d x)}{2 b^4 (a+b x)}+\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}-\frac{2 a d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}+\frac{2 a d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{2 a \sin (c+d x)}{b^3 (a+b x)}","-\frac{a^2 d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^5}-\frac{a^2 d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^5}-\frac{a^2 \sin (c+d x)}{2 b^3 (a+b x)^2}-\frac{a^2 d \cos (c+d x)}{2 b^4 (a+b x)}+\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}-\frac{2 a d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^4}+\frac{2 a d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{2 a \sin (c+d x)}{b^3 (a+b x)}",1,"-(a^2*d*Cos[c + d*x])/(2*b^4*(a + b*x)) - (2*a*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^4 + (CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/b^3 - (a^2*d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*b^5) - (a^2*Sin[c + d*x])/(2*b^3*(a + b*x)^2) + (2*a*Sin[c + d*x])/(b^3*(a + b*x)) + (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^3 - (a^2*d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*b^5) + (2*a*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^4","A",14,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
35,1,179,0,0.349956,"\int \frac{x \sin (c+d x)}{(a+b x)^3} \, dx","Int[(x*Sin[c + d*x])/(a + b*x)^3,x]","\frac{a d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^4}+\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^4}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{\sin (c+d x)}{b^2 (a+b x)}+\frac{a \sin (c+d x)}{2 b^2 (a+b x)^2}+\frac{a d \cos (c+d x)}{2 b^3 (a+b x)}","\frac{a d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^4}+\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{b^3}+\frac{a d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^4}-\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{\sin (c+d x)}{b^2 (a+b x)}+\frac{a \sin (c+d x)}{2 b^2 (a+b x)^2}+\frac{a d \cos (c+d x)}{2 b^3 (a+b x)}",1,"(a*d*Cos[c + d*x])/(2*b^3*(a + b*x)) + (d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/b^3 + (a*d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*b^4) + (a*Sin[c + d*x])/(2*b^2*(a + b*x)^2) - Sin[c + d*x]/(b^2*(a + b*x)) + (a*d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*b^4) - (d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/b^3","A",11,5,15,0.3333,1,"{6742, 3297, 3303, 3299, 3302}"
36,1,104,0,0.1270488,"\int \frac{\sin (c+d x)}{(a+b x)^3} \, dx","Int[Sin[c + d*x]/(a + b*x)^3,x]","-\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^3}-\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^3}-\frac{d \cos (c+d x)}{2 b^2 (a+b x)}-\frac{\sin (c+d x)}{2 b (a+b x)^2}","-\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 b^3}-\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 b^3}-\frac{d \cos (c+d x)}{2 b^2 (a+b x)}-\frac{\sin (c+d x)}{2 b (a+b x)^2}",1,"-(d*Cos[c + d*x])/(2*b^2*(a + b*x)) - (d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*b^3) - Sin[c + d*x]/(2*b*(a + b*x)^2) - (d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*b^3)","A",5,4,14,0.2857,1,"{3297, 3303, 3299, 3302}"
37,1,261,0,0.5422316,"\int \frac{\sin (c+d x)}{x (a+b x)^3} \, dx","Int[Sin[c + d*x]/(x*(a + b*x)^3),x]","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}-\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2 b}+\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2 b}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{\sin (c+d x)}{a^2 (a+b x)}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{\cos (c) \text{Si}(d x)}{a^3}+\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a b^2}+\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a b^2}+\frac{\sin (c+d x)}{2 a (a+b x)^2}+\frac{d \cos (c+d x)}{2 a b (a+b x)}","-\frac{\sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}-\frac{d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^2 b}+\frac{d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^2 b}-\frac{\cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{\sin (c+d x)}{a^2 (a+b x)}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{\cos (c) \text{Si}(d x)}{a^3}+\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a b^2}+\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a b^2}+\frac{\sin (c+d x)}{2 a (a+b x)^2}+\frac{d \cos (c+d x)}{2 a b (a+b x)}",1,"(d*Cos[c + d*x])/(2*a*b*(a + b*x)) - (d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/(a^2*b) + (CosIntegral[d*x]*Sin[c])/a^3 - (CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^3 + (d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*a*b^2) + Sin[c + d*x]/(2*a*(a + b*x)^2) + Sin[c + d*x]/(a^2*(a + b*x)) + (Cos[c]*SinIntegral[d*x])/a^3 - (Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^3 + (d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*a*b^2) + (d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(a^2*b)","A",17,5,17,0.2941,1,"{6742, 3303, 3299, 3302, 3297}"
38,1,299,0,0.6675085,"\int \frac{\sin (c+d x)}{x^2 (a+b x)^3} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x)^3),x]","-\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a^2 b}-\frac{3 b \sin (c) \text{CosIntegral}(d x)}{a^4}+\frac{3 b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^4}+\frac{2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}-\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a^2 b}-\frac{2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{3 b \cos (c) \text{Si}(d x)}{a^4}+\frac{3 b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^4}-\frac{2 b \sin (c+d x)}{a^3 (a+b x)}-\frac{b \sin (c+d x)}{2 a^2 (a+b x)^2}-\frac{d \cos (c+d x)}{2 a^2 (a+b x)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^3}-\frac{d \sin (c) \text{Si}(d x)}{a^3}-\frac{\sin (c+d x)}{a^3 x}","-\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a^2 b}-\frac{3 b \sin (c) \text{CosIntegral}(d x)}{a^4}+\frac{3 b \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^4}+\frac{2 d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^3}-\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a^2 b}-\frac{2 d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{3 b \cos (c) \text{Si}(d x)}{a^4}+\frac{3 b \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^4}-\frac{2 b \sin (c+d x)}{a^3 (a+b x)}-\frac{b \sin (c+d x)}{2 a^2 (a+b x)^2}-\frac{d \cos (c+d x)}{2 a^2 (a+b x)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^3}-\frac{d \sin (c) \text{Si}(d x)}{a^3}-\frac{\sin (c+d x)}{a^3 x}",1,"-(d*Cos[c + d*x])/(2*a^2*(a + b*x)) + (d*Cos[c]*CosIntegral[d*x])/a^3 + (2*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/a^3 - (3*b*CosIntegral[d*x]*Sin[c])/a^4 + (3*b*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^4 - (d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*a^2*b) - Sin[c + d*x]/(a^3*x) - (b*Sin[c + d*x])/(2*a^2*(a + b*x)^2) - (2*b*Sin[c + d*x])/(a^3*(a + b*x)) - (3*b*Cos[c]*SinIntegral[d*x])/a^4 - (d*Sin[c]*SinIntegral[d*x])/a^3 + (3*b*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^4 - (d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*a^2*b) - (2*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^3","A",21,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
39,1,377,0,0.8042046,"\int \frac{\sin (c+d x)}{x^3 (a+b x)^3} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x)^3),x]","\frac{6 b^2 \sin (c) \text{CosIntegral}(d x)}{a^5}-\frac{6 b^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^5}+\frac{6 b^2 \cos (c) \text{Si}(d x)}{a^5}-\frac{6 b^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^5}+\frac{3 b^2 \sin (c+d x)}{a^4 (a+b x)}+\frac{b^2 \sin (c+d x)}{2 a^3 (a+b x)^2}+\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a^3}-\frac{3 b d \cos (c) \text{CosIntegral}(d x)}{a^4}-\frac{3 b d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^4}+\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a^3}+\frac{3 b d \sin (c) \text{Si}(d x)}{a^4}+\frac{3 b d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^4}+\frac{3 b \sin (c+d x)}{a^4 x}+\frac{b d \cos (c+d x)}{2 a^3 (a+b x)}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a^3}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a^3}-\frac{\sin (c+d x)}{2 a^3 x^2}-\frac{d \cos (c+d x)}{2 a^3 x}","\frac{6 b^2 \sin (c) \text{CosIntegral}(d x)}{a^5}-\frac{6 b^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^5}+\frac{6 b^2 \cos (c) \text{Si}(d x)}{a^5}-\frac{6 b^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^5}+\frac{3 b^2 \sin (c+d x)}{a^4 (a+b x)}+\frac{b^2 \sin (c+d x)}{2 a^3 (a+b x)^2}+\frac{d^2 \sin \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{2 a^3}-\frac{3 b d \cos (c) \text{CosIntegral}(d x)}{a^4}-\frac{3 b d \cos \left(c-\frac{a d}{b}\right) \text{CosIntegral}\left(\frac{a d}{b}+d x\right)}{a^4}+\frac{d^2 \cos \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{2 a^3}+\frac{3 b d \sin (c) \text{Si}(d x)}{a^4}+\frac{3 b d \sin \left(c-\frac{a d}{b}\right) \text{Si}\left(x d+\frac{a d}{b}\right)}{a^4}+\frac{3 b \sin (c+d x)}{a^4 x}+\frac{b d \cos (c+d x)}{2 a^3 (a+b x)}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a^3}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a^3}-\frac{\sin (c+d x)}{2 a^3 x^2}-\frac{d \cos (c+d x)}{2 a^3 x}",1,"-(d*Cos[c + d*x])/(2*a^3*x) + (b*d*Cos[c + d*x])/(2*a^3*(a + b*x)) - (3*b*d*Cos[c]*CosIntegral[d*x])/a^4 - (3*b*d*Cos[c - (a*d)/b]*CosIntegral[(a*d)/b + d*x])/a^4 + (6*b^2*CosIntegral[d*x]*Sin[c])/a^5 - (d^2*CosIntegral[d*x]*Sin[c])/(2*a^3) - (6*b^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/a^5 + (d^2*CosIntegral[(a*d)/b + d*x]*Sin[c - (a*d)/b])/(2*a^3) - Sin[c + d*x]/(2*a^3*x^2) + (3*b*Sin[c + d*x])/(a^4*x) + (b^2*Sin[c + d*x])/(2*a^3*(a + b*x)^2) + (3*b^2*Sin[c + d*x])/(a^4*(a + b*x)) + (6*b^2*Cos[c]*SinIntegral[d*x])/a^5 - (d^2*Cos[c]*SinIntegral[d*x])/(2*a^3) + (3*b*d*Sin[c]*SinIntegral[d*x])/a^4 - (6*b^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^5 + (d^2*Cos[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/(2*a^3) + (3*b*d*Sin[c - (a*d)/b]*SinIntegral[(a*d)/b + d*x])/a^4","A",26,5,17,0.2941,1,"{6742, 3297, 3303, 3299, 3302}"
40,1,141,0,0.2076657,"\int x^3 \left(a+b x^2\right) \sin (c+d x) \, dx","Int[x^3*(a + b*x^2)*Sin[c + d*x],x]","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{5 b x^4 \sin (c+d x)}{d^2}-\frac{60 b x^2 \sin (c+d x)}{d^4}+\frac{20 b x^3 \cos (c+d x)}{d^3}+\frac{120 b \sin (c+d x)}{d^6}-\frac{120 b x \cos (c+d x)}{d^5}-\frac{b x^5 \cos (c+d x)}{d}","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{5 b x^4 \sin (c+d x)}{d^2}-\frac{60 b x^2 \sin (c+d x)}{d^4}+\frac{20 b x^3 \cos (c+d x)}{d^3}+\frac{120 b \sin (c+d x)}{d^6}-\frac{120 b x \cos (c+d x)}{d^5}-\frac{b x^5 \cos (c+d x)}{d}",1,"(-120*b*x*Cos[c + d*x])/d^5 + (6*a*x*Cos[c + d*x])/d^3 + (20*b*x^3*Cos[c + d*x])/d^3 - (a*x^3*Cos[c + d*x])/d - (b*x^5*Cos[c + d*x])/d + (120*b*Sin[c + d*x])/d^6 - (6*a*Sin[c + d*x])/d^4 - (60*b*x^2*Sin[c + d*x])/d^4 + (3*a*x^2*Sin[c + d*x])/d^2 + (5*b*x^4*Sin[c + d*x])/d^2","A",12,3,17,0.1765,1,"{3339, 3296, 2637}"
41,1,111,0,0.16329,"\int x^2 \left(a+b x^2\right) \sin (c+d x) \, dx","Int[x^2*(a + b*x^2)*Sin[c + d*x],x]","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}",1,"(-24*b*Cos[c + d*x])/d^5 + (2*a*Cos[c + d*x])/d^3 + (12*b*x^2*Cos[c + d*x])/d^3 - (a*x^2*Cos[c + d*x])/d - (b*x^4*Cos[c + d*x])/d - (24*b*x*Sin[c + d*x])/d^4 + (2*a*x*Sin[c + d*x])/d^2 + (4*b*x^3*Sin[c + d*x])/d^2","A",10,3,17,0.1765,1,"{3339, 3296, 2638}"
42,1,80,0,0.1018414,"\int x \left(a+b x^2\right) \sin (c+d x) \, dx","Int[x*(a + b*x^2)*Sin[c + d*x],x]","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}",1,"(6*b*x*Cos[c + d*x])/d^3 - (a*x*Cos[c + d*x])/d - (b*x^3*Cos[c + d*x])/d - (6*b*Sin[c + d*x])/d^4 + (a*Sin[c + d*x])/d^2 + (3*b*x^2*Sin[c + d*x])/d^2","A",8,3,15,0.2000,1,"{3339, 3296, 2637}"
43,1,53,0,0.0570932,"\int \left(a+b x^2\right) \sin (c+d x) \, dx","Int[(a + b*x^2)*Sin[c + d*x],x]","-\frac{a \cos (c+d x)}{d}+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}","-\frac{a \cos (c+d x)}{d}+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}",1,"(2*b*Cos[c + d*x])/d^3 - (a*Cos[c + d*x])/d - (b*x^2*Cos[c + d*x])/d + (2*b*x*Sin[c + d*x])/d^2","A",6,3,14,0.2143,1,"{3329, 2638, 3296}"
44,1,41,0,0.0908074,"\int \frac{\left(a+b x^2\right) \sin (c+d x)}{x} \, dx","Int[((a + b*x^2)*Sin[c + d*x])/x,x]","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)+\frac{b \sin (c+d x)}{d^2}-\frac{b x \cos (c+d x)}{d}","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)+\frac{b \sin (c+d x)}{d^2}-\frac{b x \cos (c+d x)}{d}",1,"-((b*x*Cos[c + d*x])/d) + a*CosIntegral[d*x]*Sin[c] + (b*Sin[c + d*x])/d^2 + a*Cos[c]*SinIntegral[d*x]","A",7,6,17,0.3529,1,"{3339, 3303, 3299, 3302, 3296, 2637}"
45,1,44,0,0.1074462,"\int \frac{\left(a+b x^2\right) \sin (c+d x)}{x^2} \, dx","Int[((a + b*x^2)*Sin[c + d*x])/x^2,x]","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}-\frac{b \cos (c+d x)}{d}","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}-\frac{b \cos (c+d x)}{d}",1,"-((b*Cos[c + d*x])/d) + a*d*Cos[c]*CosIntegral[d*x] - (a*Sin[c + d*x])/x - a*d*Sin[c]*SinIntegral[d*x]","A",7,6,17,0.3529,1,"{3339, 2638, 3297, 3303, 3299, 3302}"
46,1,74,0,0.1605596,"\int \frac{\left(a+b x^2\right) \sin (c+d x)}{x^3} \, dx","Int[((a + b*x^2)*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)",1,"-(a*d*Cos[c + d*x])/(2*x) + b*CosIntegral[d*x]*Sin[c] - (a*d^2*CosIntegral[d*x]*Sin[c])/2 - (a*Sin[c + d*x])/(2*x^2) + b*Cos[c]*SinIntegral[d*x] - (a*d^2*Cos[c]*SinIntegral[d*x])/2","A",10,5,17,0.2941,1,"{3339, 3297, 3303, 3299, 3302}"
47,1,106,0,0.2069627,"\int \frac{\left(a+b x^2\right) \sin (c+d x)}{x^4} \, dx","Int[((a + b*x^2)*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}+b d \cos (c) \text{CosIntegral}(d x)-b d \sin (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{x}","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}+b d \cos (c) \text{CosIntegral}(d x)-b d \sin (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{x}",1,"-(a*d*Cos[c + d*x])/(6*x^2) + b*d*Cos[c]*CosIntegral[d*x] - (a*d^3*Cos[c]*CosIntegral[d*x])/6 - (a*Sin[c + d*x])/(3*x^3) - (b*Sin[c + d*x])/x + (a*d^2*Sin[c + d*x])/(6*x) - b*d*Sin[c]*SinIntegral[d*x] + (a*d^3*Sin[c]*SinIntegral[d*x])/6","A",12,5,17,0.2941,1,"{3339, 3297, 3303, 3299, 3302}"
48,1,149,0,0.2577032,"\int \frac{\left(a+b x^2\right) \sin (c+d x)}{x^5} \, dx","Int[((a + b*x^2)*Sin[c + d*x])/x^5,x]","\frac{1}{24} a d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a d^4 \cos (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{24 x^2}+\frac{a d^3 \cos (c+d x)}{24 x}-\frac{a \sin (c+d x)}{4 x^4}-\frac{a d \cos (c+d x)}{12 x^3}-\frac{1}{2} b d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b d^2 \cos (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{2 x^2}-\frac{b d \cos (c+d x)}{2 x}","\frac{1}{24} a d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a d^4 \cos (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{24 x^2}+\frac{a d^3 \cos (c+d x)}{24 x}-\frac{a \sin (c+d x)}{4 x^4}-\frac{a d \cos (c+d x)}{12 x^3}-\frac{1}{2} b d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} b d^2 \cos (c) \text{Si}(d x)-\frac{b \sin (c+d x)}{2 x^2}-\frac{b d \cos (c+d x)}{2 x}",1,"-(a*d*Cos[c + d*x])/(12*x^3) - (b*d*Cos[c + d*x])/(2*x) + (a*d^3*Cos[c + d*x])/(24*x) - (b*d^2*CosIntegral[d*x]*Sin[c])/2 + (a*d^4*CosIntegral[d*x]*Sin[c])/24 - (a*Sin[c + d*x])/(4*x^4) - (b*Sin[c + d*x])/(2*x^2) + (a*d^2*Sin[c + d*x])/(24*x^2) - (b*d^2*Cos[c]*SinIntegral[d*x])/2 + (a*d^4*Cos[c]*SinIntegral[d*x])/24","A",14,5,17,0.2941,1,"{3339, 3297, 3303, 3299, 3302}"
49,1,236,0,0.3271054,"\int x^2 \left(a+b x^2\right)^2 \sin (c+d x) \, dx","Int[x^2*(a + b*x^2)^2*Sin[c + d*x],x]","\frac{2 a^2 x \sin (c+d x)}{d^2}+\frac{2 a^2 \cos (c+d x)}{d^3}-\frac{a^2 x^2 \cos (c+d x)}{d}+\frac{8 a b x^3 \sin (c+d x)}{d^2}+\frac{24 a b x^2 \cos (c+d x)}{d^3}-\frac{48 a b x \sin (c+d x)}{d^4}-\frac{48 a b \cos (c+d x)}{d^5}-\frac{2 a b x^4 \cos (c+d x)}{d}+\frac{6 b^2 x^5 \sin (c+d x)}{d^2}-\frac{120 b^2 x^3 \sin (c+d x)}{d^4}+\frac{30 b^2 x^4 \cos (c+d x)}{d^3}-\frac{360 b^2 x^2 \cos (c+d x)}{d^5}+\frac{720 b^2 x \sin (c+d x)}{d^6}+\frac{720 b^2 \cos (c+d x)}{d^7}-\frac{b^2 x^6 \cos (c+d x)}{d}","\frac{2 a^2 x \sin (c+d x)}{d^2}+\frac{2 a^2 \cos (c+d x)}{d^3}-\frac{a^2 x^2 \cos (c+d x)}{d}+\frac{8 a b x^3 \sin (c+d x)}{d^2}+\frac{24 a b x^2 \cos (c+d x)}{d^3}-\frac{48 a b x \sin (c+d x)}{d^4}-\frac{48 a b \cos (c+d x)}{d^5}-\frac{2 a b x^4 \cos (c+d x)}{d}+\frac{6 b^2 x^5 \sin (c+d x)}{d^2}-\frac{120 b^2 x^3 \sin (c+d x)}{d^4}+\frac{30 b^2 x^4 \cos (c+d x)}{d^3}-\frac{360 b^2 x^2 \cos (c+d x)}{d^5}+\frac{720 b^2 x \sin (c+d x)}{d^6}+\frac{720 b^2 \cos (c+d x)}{d^7}-\frac{b^2 x^6 \cos (c+d x)}{d}",1,"(720*b^2*Cos[c + d*x])/d^7 - (48*a*b*Cos[c + d*x])/d^5 + (2*a^2*Cos[c + d*x])/d^3 - (360*b^2*x^2*Cos[c + d*x])/d^5 + (24*a*b*x^2*Cos[c + d*x])/d^3 - (a^2*x^2*Cos[c + d*x])/d + (30*b^2*x^4*Cos[c + d*x])/d^3 - (2*a*b*x^4*Cos[c + d*x])/d - (b^2*x^6*Cos[c + d*x])/d + (720*b^2*x*Sin[c + d*x])/d^6 - (48*a*b*x*Sin[c + d*x])/d^4 + (2*a^2*x*Sin[c + d*x])/d^2 - (120*b^2*x^3*Sin[c + d*x])/d^4 + (8*a*b*x^3*Sin[c + d*x])/d^2 + (6*b^2*x^5*Sin[c + d*x])/d^2","A",17,3,19,0.1579,1,"{3339, 3296, 2638}"
50,1,185,0,0.2351754,"\int x \left(a+b x^2\right)^2 \sin (c+d x) \, dx","Int[x*(a + b*x^2)^2*Sin[c + d*x],x]","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{5 b^2 x^4 \sin (c+d x)}{d^2}-\frac{60 b^2 x^2 \sin (c+d x)}{d^4}+\frac{20 b^2 x^3 \cos (c+d x)}{d^3}+\frac{120 b^2 \sin (c+d x)}{d^6}-\frac{120 b^2 x \cos (c+d x)}{d^5}-\frac{b^2 x^5 \cos (c+d x)}{d}","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{5 b^2 x^4 \sin (c+d x)}{d^2}-\frac{60 b^2 x^2 \sin (c+d x)}{d^4}+\frac{20 b^2 x^3 \cos (c+d x)}{d^3}+\frac{120 b^2 \sin (c+d x)}{d^6}-\frac{120 b^2 x \cos (c+d x)}{d^5}-\frac{b^2 x^5 \cos (c+d x)}{d}",1,"(-120*b^2*x*Cos[c + d*x])/d^5 + (12*a*b*x*Cos[c + d*x])/d^3 - (a^2*x*Cos[c + d*x])/d + (20*b^2*x^3*Cos[c + d*x])/d^3 - (2*a*b*x^3*Cos[c + d*x])/d - (b^2*x^5*Cos[c + d*x])/d + (120*b^2*Sin[c + d*x])/d^6 - (12*a*b*Sin[c + d*x])/d^4 + (a^2*Sin[c + d*x])/d^2 - (60*b^2*x^2*Sin[c + d*x])/d^4 + (6*a*b*x^2*Sin[c + d*x])/d^2 + (5*b^2*x^4*Sin[c + d*x])/d^2","A",14,3,17,0.1765,1,"{3339, 3296, 2637}"
51,1,138,0,0.163132,"\int \left(a+b x^2\right)^2 \sin (c+d x) \, dx","Int[(a + b*x^2)^2*Sin[c + d*x],x]","-\frac{a^2 \cos (c+d x)}{d}+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}","-\frac{a^2 \cos (c+d x)}{d}+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}",1,"(-24*b^2*Cos[c + d*x])/d^5 + (4*a*b*Cos[c + d*x])/d^3 - (a^2*Cos[c + d*x])/d + (12*b^2*x^2*Cos[c + d*x])/d^3 - (2*a*b*x^2*Cos[c + d*x])/d - (b^2*x^4*Cos[c + d*x])/d - (24*b^2*x*Sin[c + d*x])/d^4 + (4*a*b*x*Sin[c + d*x])/d^2 + (4*b^2*x^3*Sin[c + d*x])/d^2","A",11,3,16,0.1875,1,"{3329, 2638, 3296}"
52,1,111,0,0.1724974,"\int \frac{\left(a+b x^2\right)^2 \sin (c+d x)}{x} \, dx","Int[((a + b*x^2)^2*Sin[c + d*x])/x,x]","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)+\frac{2 a b \sin (c+d x)}{d^2}-\frac{2 a b x \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)+\frac{2 a b \sin (c+d x)}{d^2}-\frac{2 a b x \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}",1,"(6*b^2*x*Cos[c + d*x])/d^3 - (2*a*b*x*Cos[c + d*x])/d - (b^2*x^3*Cos[c + d*x])/d + a^2*CosIntegral[d*x]*Sin[c] - (6*b^2*Sin[c + d*x])/d^4 + (2*a*b*Sin[c + d*x])/d^2 + (3*b^2*x^2*Sin[c + d*x])/d^2 + a^2*Cos[c]*SinIntegral[d*x]","A",11,6,19,0.3158,1,"{3339, 3303, 3299, 3302, 3296, 2637}"
53,1,97,0,0.1631027,"\int \frac{\left(a+b x^2\right)^2 \sin (c+d x)}{x^2} \, dx","Int[((a + b*x^2)^2*Sin[c + d*x])/x^2,x]","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}-\frac{2 a b \cos (c+d x)}{d}+\frac{2 b^2 x \sin (c+d x)}{d^2}+\frac{2 b^2 \cos (c+d x)}{d^3}-\frac{b^2 x^2 \cos (c+d x)}{d}","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}-\frac{2 a b \cos (c+d x)}{d}+\frac{2 b^2 x \sin (c+d x)}{d^2}+\frac{2 b^2 \cos (c+d x)}{d^3}-\frac{b^2 x^2 \cos (c+d x)}{d}",1,"(2*b^2*Cos[c + d*x])/d^3 - (2*a*b*Cos[c + d*x])/d - (b^2*x^2*Cos[c + d*x])/d + a^2*d*Cos[c]*CosIntegral[d*x] - (a^2*Sin[c + d*x])/x + (2*b^2*x*Sin[c + d*x])/d^2 - a^2*d*Sin[c]*SinIntegral[d*x]","A",10,7,19,0.3684,1,"{3339, 2638, 3297, 3303, 3299, 3302, 3296}"
54,1,114,0,0.20306,"\int \frac{\left(a+b x^2\right)^2 \sin (c+d x)}{x^3} \, dx","Int[((a + b*x^2)^2*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}",1,"-(a^2*d*Cos[c + d*x])/(2*x) - (b^2*x*Cos[c + d*x])/d + 2*a*b*CosIntegral[d*x]*Sin[c] - (a^2*d^2*CosIntegral[d*x]*Sin[c])/2 + (b^2*Sin[c + d*x])/d^2 - (a^2*Sin[c + d*x])/(2*x^2) + 2*a*b*Cos[c]*SinIntegral[d*x] - (a^2*d^2*Cos[c]*SinIntegral[d*x])/2","A",12,7,19,0.3684,1,"{3339, 3297, 3303, 3299, 3302, 3296, 2637}"
55,1,134,0,0.2378709,"\int \frac{\left(a+b x^2\right)^2 \sin (c+d x)}{x^4} \, dx","Int[((a + b*x^2)^2*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}-\frac{b^2 \cos (c+d x)}{d}","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}-\frac{b^2 \cos (c+d x)}{d}",1,"-((b^2*Cos[c + d*x])/d) - (a^2*d*Cos[c + d*x])/(6*x^2) + 2*a*b*d*Cos[c]*CosIntegral[d*x] - (a^2*d^3*Cos[c]*CosIntegral[d*x])/6 - (a^2*Sin[c + d*x])/(3*x^3) - (2*a*b*Sin[c + d*x])/x + (a^2*d^2*Sin[c + d*x])/(6*x) - 2*a*b*d*Sin[c]*SinIntegral[d*x] + (a^2*d^3*Sin[c]*SinIntegral[d*x])/6","A",13,6,19,0.3158,1,"{3339, 2638, 3297, 3303, 3299, 3302}"
56,1,177,0,0.332833,"\int \frac{\left(a+b x^2\right)^2 \sin (c+d x)}{x^5} \, dx","Int[((a + b*x^2)^2*Sin[c + d*x])/x^5,x]","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}-a b d^2 \sin (c) \text{CosIntegral}(d x)-a b d^2 \cos (c) \text{Si}(d x)-\frac{a b \sin (c+d x)}{x^2}-\frac{a b d \cos (c+d x)}{x}+b^2 \sin (c) \text{CosIntegral}(d x)+b^2 \cos (c) \text{Si}(d x)","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}-a b d^2 \sin (c) \text{CosIntegral}(d x)-a b d^2 \cos (c) \text{Si}(d x)-\frac{a b \sin (c+d x)}{x^2}-\frac{a b d \cos (c+d x)}{x}+b^2 \sin (c) \text{CosIntegral}(d x)+b^2 \cos (c) \text{Si}(d x)",1,"-(a^2*d*Cos[c + d*x])/(12*x^3) - (a*b*d*Cos[c + d*x])/x + (a^2*d^3*Cos[c + d*x])/(24*x) + b^2*CosIntegral[d*x]*Sin[c] - a*b*d^2*CosIntegral[d*x]*Sin[c] + (a^2*d^4*CosIntegral[d*x]*Sin[c])/24 - (a^2*Sin[c + d*x])/(4*x^4) - (a*b*Sin[c + d*x])/x^2 + (a^2*d^2*Sin[c + d*x])/(24*x^2) + b^2*Cos[c]*SinIntegral[d*x] - a*b*d^2*Cos[c]*SinIntegral[d*x] + (a^2*d^4*Cos[c]*SinIntegral[d*x])/24","A",17,5,19,0.2632,1,"{3339, 3297, 3303, 3299, 3302}"
57,1,273,0,0.7299159,"\int \frac{x^4 \sin (c+d x)}{a+b x^2} \, dx","Int[(x^4*Sin[c + d*x])/(a + b*x^2),x]","-\frac{(-a)^{3/2} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^{5/2}}+\frac{(-a)^{3/2} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{5/2}}+\frac{a \cos (c+d x)}{b^2 d}+\frac{2 x \sin (c+d x)}{b d^2}+\frac{2 \cos (c+d x)}{b d^3}-\frac{x^2 \cos (c+d x)}{b d}","-\frac{(-a)^{3/2} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^{5/2}}+\frac{(-a)^{3/2} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{5/2}}+\frac{a \cos (c+d x)}{b^2 d}+\frac{2 x \sin (c+d x)}{b d^2}+\frac{2 \cos (c+d x)}{b d^3}-\frac{x^2 \cos (c+d x)}{b d}",1,"(2*Cos[c + d*x])/(b*d^3) + (a*Cos[c + d*x])/(b^2*d) - (x^2*Cos[c + d*x])/(b*d) - ((-a)^(3/2)*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*b^(5/2)) + ((-a)^(3/2)*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*b^(5/2)) + (2*x*Sin[c + d*x])/(b*d^2) - ((-a)^(3/2)*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*b^(5/2)) - ((-a)^(3/2)*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*b^(5/2))","A",14,7,19,0.3684,1,"{3345, 2638, 3296, 3333, 3303, 3299, 3302}"
58,1,209,0,0.347542,"\int \frac{x^3 \sin (c+d x)}{a+b x^2} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^2),x]","-\frac{a \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^2}-\frac{a \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{a \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}-\frac{a \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}","-\frac{a \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^2}-\frac{a \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{a \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}-\frac{a \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}",1,"-((x*Cos[c + d*x])/(b*d)) - (a*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*b^2) - (a*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*b^2) + Sin[c + d*x]/(b*d^2) + (a*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*b^2) - (a*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*b^2)","A",12,6,19,0.3158,1,"{3345, 3296, 2637, 3303, 3299, 3302}"
59,1,227,0,0.3651649,"\int \frac{x^2 \sin (c+d x)}{a+b x^2} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^2),x]","-\frac{\sqrt{-a} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^{3/2}}+\frac{\sqrt{-a} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{\cos (c+d x)}{b d}","-\frac{\sqrt{-a} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^{3/2}}+\frac{\sqrt{-a} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{\cos (c+d x)}{b d}",1,"-(Cos[c + d*x]/(b*d)) - (Sqrt[-a]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*b^(3/2)) + (Sqrt[-a]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*b^(3/2)) - (Sqrt[-a]*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*b^(3/2)) - (Sqrt[-a]*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*b^(3/2))","A",11,6,19,0.3158,1,"{3345, 2638, 3333, 3303, 3299, 3302}"
60,1,177,0,0.2476841,"\int \frac{x \sin (c+d x)}{a+b x^2} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^2),x]","\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b}","\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b}",1,"(CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*b) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*b) - (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*b) + (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*b)","A",8,4,17,0.2353,1,"{3345, 3303, 3299, 3302}"
61,1,213,0,0.2391828,"\int \frac{\sin (c+d x)}{a+b x^2} \, dx","Int[Sin[c + d*x]/(a + b*x^2),x]","-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 \sqrt{-a} \sqrt{b}}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b}}","-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 \sqrt{-a} \sqrt{b}}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b}}",1,"-(CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*Sqrt[-a]*Sqrt[b]) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*Sqrt[-a]*Sqrt[b]) - (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*Sqrt[-a]*Sqrt[b]) - (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*Sqrt[-a]*Sqrt[b])","A",8,4,16,0.2500,1,"{3333, 3303, 3299, 3302}"
62,1,197,0,0.3823245,"\int \frac{\sin (c+d x)}{x \left(a+b x^2\right)} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^2)),x]","-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}","-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}",1,"(CosIntegral[d*x]*Sin[c])/a - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*a) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*a) + (Cos[c]*SinIntegral[d*x])/a + (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*a) - (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*a)","A",13,4,19,0.2105,1,"{3345, 3303, 3299, 3302}"
63,1,250,0,0.4873278,"\int \frac{\sin (c+d x)}{x^2 \left(a+b x^2\right)} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x^2)),x]","-\frac{\sqrt{b} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 (-a)^{3/2}}+\frac{\sqrt{b} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 (-a)^{3/2}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}","-\frac{\sqrt{b} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 (-a)^{3/2}}+\frac{\sqrt{b} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 (-a)^{3/2}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}",1,"(d*Cos[c]*CosIntegral[d*x])/a - (Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*(-a)^(3/2)) + (Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*(-a)^(3/2)) - Sin[c + d*x]/(a*x) - (d*Sin[c]*SinIntegral[d*x])/a - (Sqrt[b]*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*(-a)^(3/2)) - (Sqrt[b]*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*(-a)^(3/2))","A",14,6,19,0.3158,1,"{3345, 3297, 3303, 3299, 3302, 3333}"
64,1,270,0,0.5077856,"\int \frac{\sin (c+d x)}{x^3 \left(a+b x^2\right)} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x^2)),x]","-\frac{b \sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{b \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^2}+\frac{b \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{b \cos (c) \text{Si}(d x)}{a^2}-\frac{b \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}+\frac{b \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}","-\frac{b \sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{b \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^2}+\frac{b \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{b \cos (c) \text{Si}(d x)}{a^2}-\frac{b \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}+\frac{b \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}",1,"-(d*Cos[c + d*x])/(2*a*x) - (b*CosIntegral[d*x]*Sin[c])/a^2 - (d^2*CosIntegral[d*x]*Sin[c])/(2*a) + (b*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*a^2) + (b*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*a^2) - Sin[c + d*x]/(2*a*x^2) - (b*Cos[c]*SinIntegral[d*x])/a^2 - (d^2*Cos[c]*SinIntegral[d*x])/(2*a) - (b*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*a^2) + (b*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*a^2)","A",18,5,19,0.2632,1,"{3345, 3297, 3303, 3299, 3302}"
65,1,450,0,0.7828613,"\int \frac{x^4 \sin (c+d x)}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*Sin[c + d*x])/(a + b*x^2)^2,x]","-\frac{3 \sqrt{-a} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^{5/2}}+\frac{3 \sqrt{-a} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{a d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}-\frac{a d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^3}-\frac{a d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}+\frac{a d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^3}-\frac{3 \sqrt{-a} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{3 \sqrt{-a} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{x^3 \sin (c+d x)}{2 b \left(a+b x^2\right)}+\frac{x \sin (c+d x)}{2 b^2}-\frac{\cos (c+d x)}{b^2 d}","-\frac{3 \sqrt{-a} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^{5/2}}+\frac{3 \sqrt{-a} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{a d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}-\frac{a d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^3}-\frac{a d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}+\frac{a d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^3}-\frac{3 \sqrt{-a} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{3 \sqrt{-a} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{x^3 \sin (c+d x)}{2 b \left(a+b x^2\right)}+\frac{x \sin (c+d x)}{2 b^2}-\frac{\cos (c+d x)}{b^2 d}",1,"-(Cos[c + d*x]/(b^2*d)) - (a*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^3) - (a*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^3) - (3*Sqrt[-a]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(4*b^(5/2)) + (3*Sqrt[-a]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(4*b^(5/2)) + (x*Sin[c + d*x])/(2*b^2) - (x^3*Sin[c + d*x])/(2*b*(a + b*x^2)) - (3*Sqrt[-a]*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^(5/2)) - (a*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^3) - (3*Sqrt[-a]*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^(5/2)) + (a*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^3)","A",24,9,19,0.4737,1,"{3343, 3345, 2638, 3333, 3303, 3299, 3302, 3346, 3296}"
66,1,431,0,0.6613481,"\int \frac{x^3 \sin (c+d x)}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^2)^2,x]","\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^2}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\sqrt{-a} d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{\sqrt{-a} d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^{5/2}}+\frac{\sqrt{-a} d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}+\frac{\sqrt{-a} d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}-\frac{x^2 \sin (c+d x)}{2 b \left(a+b x^2\right)}+\frac{\sin (c+d x)}{2 b^2}","\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 b^2}+\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\sqrt{-a} d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{\sqrt{-a} d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^{5/2}}+\frac{\sqrt{-a} d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}+\frac{\sqrt{-a} d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}-\frac{x^2 \sin (c+d x)}{2 b \left(a+b x^2\right)}+\frac{\sin (c+d x)}{2 b^2}",1,"(Sqrt[-a]*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^(5/2)) - (Sqrt[-a]*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^(5/2)) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*b^2) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*b^2) + Sin[c + d*x]/(2*b^2) - (x^2*Sin[c + d*x])/(2*b*(a + b*x^2)) - (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*b^2) + (Sqrt[-a]*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^(5/2)) + (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*b^2) + (Sqrt[-a]*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^(5/2))","A",20,8,19,0.4211,1,"{3343, 3345, 3303, 3299, 3302, 3346, 2637, 3334}"
67,1,416,0,0.572871,"\int \frac{x^2 \sin (c+d x)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^2)^2,x]","\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^2}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^2}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{x \sin (c+d x)}{2 b \left(a+b x^2\right)}","\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 b^2}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^2}-\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{x \sin (c+d x)}{2 b \left(a+b x^2\right)}",1,"(d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^2) + (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^2) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(4*Sqrt[-a]*b^(3/2)) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(4*Sqrt[-a]*b^(3/2)) - (x*Sin[c + d*x])/(2*b*(a + b*x^2)) - (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*Sqrt[-a]*b^(3/2)) + (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*b^2) - (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*Sqrt[-a]*b^(3/2)) - (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*b^2)","A",17,6,19,0.3158,1,"{3343, 3333, 3303, 3299, 3302, 3346}"
68,1,239,0,0.314809,"\int \frac{x \sin (c+d x)}{\left(a+b x^2\right)^2} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^2)^2,x]","\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sin (c+d x)}{2 b \left(a+b x^2\right)}","\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sin (c+d x)}{2 b \left(a+b x^2\right)}",1,"(d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*Sqrt[-a]*b^(3/2)) - (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*Sqrt[-a]*b^(3/2)) - Sin[c + d*x]/(2*b*(a + b*x^2)) + (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*Sqrt[-a]*b^(3/2)) + (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*Sqrt[-a]*b^(3/2))","A",9,5,17,0.2941,1,"{3341, 3334, 3303, 3299, 3302}"
69,1,476,0,0.806036,"\int \frac{\sin (c+d x)}{\left(a+b x^2\right)^2} \, dx","Int[Sin[c + d*x]/(a + b*x^2)^2,x]","-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 a b}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a b}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{\sin (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sin (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}","-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 a b}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a b}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{\sin (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sin (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}",1,"-(d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*a*b) - (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*a*b) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(4*(-a)^(3/2)*Sqrt[b]) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(4*(-a)^(3/2)*Sqrt[b]) - Sin[c + d*x]/(4*a*Sqrt[b]*(Sqrt[-a] - Sqrt[b]*x)) + Sin[c + d*x]/(4*a*Sqrt[b]*(Sqrt[-a] + Sqrt[b]*x)) + (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*(-a)^(3/2)*Sqrt[b]) - (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*a*b) + (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*(-a)^(3/2)*Sqrt[b]) + (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*a*b)","A",18,5,16,0.3125,1,"{3333, 3297, 3303, 3299, 3302}"
70,1,435,0,0.8316229,"\int \frac{\sin (c+d x)}{x \left(a+b x^2\right)^2} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^2)^2),x]","-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^2}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}+\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sin (c+d x)}{2 a \left(a+b x^2\right)}","-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^2}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}+\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sin (c+d x)}{2 a \left(a+b x^2\right)}",1,"(d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*(-a)^(3/2)*Sqrt[b]) - (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*(-a)^(3/2)*Sqrt[b]) + (CosIntegral[d*x]*Sin[c])/a^2 - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*a^2) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*a^2) + Sin[c + d*x]/(2*a*(a + b*x^2)) + (Cos[c]*SinIntegral[d*x])/a^2 + (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*a^2) + (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*(-a)^(3/2)*Sqrt[b]) - (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*a^2) + (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*(-a)^(3/2)*Sqrt[b])","A",22,6,19,0.3158,1,"{3345, 3303, 3299, 3302, 3341, 3334}"
71,1,501,0,1.3129017,"\int \frac{\sin (c+d x)}{x^2 \left(a+b x^2\right)^2} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x^2)^2),x]","\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 a^2}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a^2}+\frac{\sqrt{b} \sin (c+d x)}{4 a^2 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{\sqrt{b} \sin (c+d x)}{4 a^2 \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{a^2 x}+\frac{3 \sqrt{b} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{5/2}}-\frac{3 \sqrt{b} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{5/2}}","\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 a^2}+\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a^2}+\frac{\sqrt{b} \sin (c+d x)}{4 a^2 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{\sqrt{b} \sin (c+d x)}{4 a^2 \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{a^2 x}+\frac{3 \sqrt{b} \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{4 (-a)^{5/2}}-\frac{3 \sqrt{b} \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{5/2}}",1,"(d*Cos[c]*CosIntegral[d*x])/a^2 + (d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*a^2) + (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*a^2) + (3*Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(4*(-a)^(5/2)) - (3*Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(4*(-a)^(5/2)) - Sin[c + d*x]/(a^2*x) + (Sqrt[b]*Sin[c + d*x])/(4*a^2*(Sqrt[-a] - Sqrt[b]*x)) - (Sqrt[b]*Sin[c + d*x])/(4*a^2*(Sqrt[-a] + Sqrt[b]*x)) - (d*Sin[c]*SinIntegral[d*x])/a^2 + (3*Sqrt[b]*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*(-a)^(5/2)) + (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(4*a^2) + (3*Sqrt[b]*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*(-a)^(5/2)) - (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(4*a^2)","A",32,6,19,0.3158,1,"{3345, 3297, 3303, 3299, 3302, 3333}"
72,1,476,0,1.0075962,"\int \frac{x^3 \sin (c+d x)}{\left(a+b x^2\right)^3} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^2)^3,x]","-\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 b^3}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}+\frac{3 d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{3 d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}-\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 b^3}+\frac{3 d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{3 d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}-\frac{\sin (c+d x)}{4 b^2 \left(a+b x^2\right)}-\frac{d x \cos (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{x^2 \sin (c+d x)}{4 b \left(a+b x^2\right)^2}","-\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 b^3}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}+\frac{3 d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{3 d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}-\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 b^3}+\frac{3 d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{3 d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}-\frac{\sin (c+d x)}{4 b^2 \left(a+b x^2\right)}-\frac{d x \cos (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{x^2 \sin (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"-(d*x*Cos[c + d*x])/(8*b^2*(a + b*x^2)) + (3*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*Sqrt[-a]*b^(5/2)) - (3*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*Sqrt[-a]*b^(5/2)) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*b^3) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*b^3) - (x^2*Sin[c + d*x])/(4*b*(a + b*x^2)^2) - Sin[c + d*x]/(4*b^2*(a + b*x^2)) + (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*b^3) + (3*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*Sqrt[-a]*b^(5/2)) - (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*b^3) + (3*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*Sqrt[-a]*b^(5/2))","A",27,8,19,0.4211,1,"{3343, 3341, 3334, 3303, 3299, 3302, 3344, 3345}"
73,1,746,0,1.1353859,"\int \frac{x^2 \sin (c+d x)}{\left(a+b x^2\right)^3} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^2)^3,x]","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a b^2}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{\sin (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sin (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{x \sin (c+d x)}{4 b \left(a+b x^2\right)^2}","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a b^2}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}+\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{\sin (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sin (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{x \sin (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"-(d*Cos[c + d*x])/(8*b^2*(a + b*x^2)) - (d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a*b^2) - (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a*b^2) + (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(3/2)*b^(3/2)) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*Sqrt[-a]*b^(5/2)) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(3/2)*b^(3/2)) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*Sqrt[-a]*b^(5/2)) - Sin[c + d*x]/(16*a*b^(3/2)*(Sqrt[-a] - Sqrt[b]*x)) + Sin[c + d*x]/(16*a*b^(3/2)*(Sqrt[-a] + Sqrt[b]*x)) - (x*Sin[c + d*x])/(4*b*(a + b*x^2)^2) + (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(3/2)*b^(3/2)) + (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*Sqrt[-a]*b^(5/2)) - (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a*b^2) + (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(3/2)*b^(3/2)) + (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*Sqrt[-a]*b^(5/2)) + (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a*b^2)","A",28,7,19,0.3684,1,"{3343, 3333, 3297, 3303, 3299, 3302, 3342}"
74,1,512,0,0.7693188,"\int \frac{x \sin (c+d x)}{\left(a+b x^2\right)^3} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^2)^3,x]","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a b^2}+\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{d \cos (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{\sin (c+d x)}{4 b \left(a+b x^2\right)^2}","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a b^2}+\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}-\frac{d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \cos (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{d \cos (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{\sin (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"-(d*Cos[c + d*x])/(16*a*b^(3/2)*(Sqrt[-a] - Sqrt[b]*x)) + (d*Cos[c + d*x])/(16*a*b^(3/2)*(Sqrt[-a] + Sqrt[b]*x)) - (d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(3/2)*b^(3/2)) + (d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(3/2)*b^(3/2)) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*a*b^2) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*a*b^2) - Sin[c + d*x]/(4*b*(a + b*x^2)^2) - (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a*b^2) - (d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(3/2)*b^(3/2)) + (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a*b^2) - (d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(3/2)*b^(3/2))","A",19,6,17,0.3529,1,"{3341, 3334, 3297, 3303, 3299, 3302}"
75,1,856,0,1.181254,"\int \frac{\sin (c+d x)}{\left(a+b x^2\right)^3} \, dx","Int[Sin[c + d*x]/(a + b*x^2)^3,x]","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{\text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cos (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{3 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^2 b}-\frac{3 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^2 b}+\frac{3 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{3 \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \sin (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{3 \sin (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\sin (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\sin (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)^2}-\frac{3 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{\text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}+\frac{\cos (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cos (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{3 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^2 b}-\frac{3 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^2 b}+\frac{3 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{3 \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \sin (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{3 \sin (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\sin (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\sin (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)^2}-\frac{3 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}",1,"(d*Cos[c + d*x])/(16*(-a)^(3/2)*b*(Sqrt[-a] - Sqrt[b]*x)) + (d*Cos[c + d*x])/(16*(-a)^(3/2)*b*(Sqrt[-a] + Sqrt[b]*x)) - (3*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^2*b) - (3*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^2*b) - (3*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(5/2)*Sqrt[b]) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(3/2)*b^(3/2)) + (3*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(5/2)*Sqrt[b]) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(3/2)*b^(3/2)) - Sin[c + d*x]/(16*(-a)^(3/2)*Sqrt[b]*(Sqrt[-a] - Sqrt[b]*x)^2) - (3*Sin[c + d*x])/(16*a^2*Sqrt[b]*(Sqrt[-a] - Sqrt[b]*x)) + Sin[c + d*x]/(16*(-a)^(3/2)*Sqrt[b]*(Sqrt[-a] + Sqrt[b]*x)^2) + (3*Sin[c + d*x])/(16*a^2*Sqrt[b]*(Sqrt[-a] + Sqrt[b]*x)) - (3*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(5/2)*Sqrt[b]) + (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(3/2)*b^(3/2)) - (3*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^2*b) - (3*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(5/2)*Sqrt[b]) + (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(3/2)*b^(3/2)) + (3*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^2*b)","A",28,5,16,0.3125,1,"{3333, 3297, 3303, 3299, 3302}"
76,1,730,0,1.8302437,"\int \frac{\sin (c+d x)}{x \left(a+b x^2\right)^3} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^2)^3),x]","-\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a^2 b}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^3}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}-\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^2 b}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^3}+\frac{\sin (c+d x)}{2 a^2 \left(a+b x^2\right)}+\frac{d \cos (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{d \cos (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{\cos (c) \text{Si}(d x)}{a^3}-\frac{5 d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{5 d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{5 d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{5 d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{\sin (c+d x)}{4 a \left(a+b x^2\right)^2}","-\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a^2 b}-\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}-\frac{\sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^3}-\frac{\sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}+\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}-\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^2 b}+\frac{\cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}-\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^3}+\frac{\sin (c+d x)}{2 a^2 \left(a+b x^2\right)}+\frac{d \cos (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{d \cos (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^3}+\frac{\cos (c) \text{Si}(d x)}{a^3}-\frac{5 d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{5 d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{5 d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{5 d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{\sin (c+d x)}{4 a \left(a+b x^2\right)^2}",1,"(d*Cos[c + d*x])/(16*a^2*Sqrt[b]*(Sqrt[-a] - Sqrt[b]*x)) - (d*Cos[c + d*x])/(16*a^2*Sqrt[b]*(Sqrt[-a] + Sqrt[b]*x)) - (5*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(5/2)*Sqrt[b]) + (5*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(5/2)*Sqrt[b]) + (CosIntegral[d*x]*Sin[c])/a^3 - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*a^3) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*a^2*b) - (CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*a^3) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*a^2*b) + Sin[c + d*x]/(4*a*(a + b*x^2)^2) + Sin[c + d*x]/(2*a^2*(a + b*x^2)) + (Cos[c]*SinIntegral[d*x])/a^3 + (Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*a^3) + (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^2*b) - (5*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(5/2)*Sqrt[b]) - (Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*a^3) - (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^2*b) - (5*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(5/2)*Sqrt[b])","A",41,7,19,0.3684,1,"{3345, 3303, 3299, 3302, 3341, 3334, 3297}"
77,1,875,0,2.846198,"\int \frac{\sin (c+d x)}{x^2 \left(a+b x^2\right)^3} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x^2)^3),x]","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}-\frac{\text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cos (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)}+\frac{\cos (c) \text{CosIntegral}(d x) d}{a^3}+\frac{7 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^3}+\frac{7 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}-\frac{\sin (c) \text{Si}(d x) d}{a^3}+\frac{7 \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^3}-\frac{7 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}-\frac{15 \sqrt{b} \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}+\frac{15 \sqrt{b} \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}-\frac{\sin (c+d x)}{a^3 x}+\frac{7 \sqrt{b} \sin (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{7 \sqrt{b} \sin (c+d x)}{16 a^3 \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\sqrt{b} \sin (c+d x)}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\sqrt{b} \sin (c+d x)}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)^2}-\frac{15 \sqrt{b} \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{15 \sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}-\frac{\text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cos (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cos (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)}+\frac{\cos (c) \text{CosIntegral}(d x) d}{a^3}+\frac{7 \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^3}+\frac{7 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}-\frac{\sin (c) \text{Si}(d x) d}{a^3}+\frac{7 \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^3}-\frac{7 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}-\frac{15 \sqrt{b} \text{CosIntegral}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}+\frac{15 \sqrt{b} \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sin \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}-\frac{\sin (c+d x)}{a^3 x}+\frac{7 \sqrt{b} \sin (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{7 \sqrt{b} \sin (c+d x)}{16 a^3 \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\sqrt{b} \sin (c+d x)}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\sqrt{b} \sin (c+d x)}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)^2}-\frac{15 \sqrt{b} \cos \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{15 \sqrt{b} \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}",1,"(d*Cos[c + d*x])/(16*(-a)^(5/2)*(Sqrt[-a] - Sqrt[b]*x)) + (d*Cos[c + d*x])/(16*(-a)^(5/2)*(Sqrt[-a] + Sqrt[b]*x)) + (d*Cos[c]*CosIntegral[d*x])/a^3 + (7*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^3) + (7*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^3) - (15*Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(7/2)) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(5/2)*Sqrt[b]) + (15*Sqrt[b]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(7/2)) - (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*(-a)^(5/2)*Sqrt[b]) - Sin[c + d*x]/(a^3*x) - (Sqrt[b]*Sin[c + d*x])/(16*(-a)^(5/2)*(Sqrt[-a] - Sqrt[b]*x)^2) + (7*Sqrt[b]*Sin[c + d*x])/(16*a^3*(Sqrt[-a] - Sqrt[b]*x)) + (Sqrt[b]*Sin[c + d*x])/(16*(-a)^(5/2)*(Sqrt[-a] + Sqrt[b]*x)^2) - (7*Sqrt[b]*Sin[c + d*x])/(16*a^3*(Sqrt[-a] + Sqrt[b]*x)) - (d*Sin[c]*SinIntegral[d*x])/a^3 - (15*Sqrt[b]*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(7/2)) + (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(5/2)*Sqrt[b]) + (7*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^3) - (15*Sqrt[b]*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(7/2)) + (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(5/2)*Sqrt[b]) - (7*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^3)","A",60,6,19,0.3158,1,"{3345, 3297, 3303, 3299, 3302, 3333}"
78,1,791,0,1.8767775,"\int \frac{\sin (c+d x)}{x^3 \left(a+b x^2\right)^3} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x^2)^3),x]","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a^3}+\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}-\frac{3 b \sin (c) \text{CosIntegral}(d x)}{a^4}+\frac{3 b \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^4}+\frac{3 b \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}-\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^3}-\frac{3 b \cos (c) \text{Si}(d x)}{a^4}-\frac{3 b \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}+\frac{3 b \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^4}-\frac{b \sin (c+d x)}{a^3 \left(a+b x^2\right)}-\frac{b \sin (c+d x)}{4 a^2 \left(a+b x^2\right)^2}-\frac{\sqrt{b} d \cos (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sqrt{b} d \cos (c+d x)}{16 a^3 \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a^3}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a^3}-\frac{\sin (c+d x)}{2 a^3 x^2}-\frac{d \cos (c+d x)}{2 a^3 x}-\frac{9 \sqrt{b} d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}+\frac{9 \sqrt{b} d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{7/2}}-\frac{9 \sqrt{b} d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{9 \sqrt{b} d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}","\frac{d^2 \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 a^3}+\frac{d^2 \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}-\frac{3 b \sin (c) \text{CosIntegral}(d x)}{a^4}+\frac{3 b \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{2 a^4}+\frac{3 b \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}-\frac{d^2 \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}+\frac{d^2 \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^3}-\frac{3 b \cos (c) \text{Si}(d x)}{a^4}-\frac{3 b \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}+\frac{3 b \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^4}-\frac{b \sin (c+d x)}{a^3 \left(a+b x^2\right)}-\frac{b \sin (c+d x)}{4 a^2 \left(a+b x^2\right)^2}-\frac{\sqrt{b} d \cos (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sqrt{b} d \cos (c+d x)}{16 a^3 \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a^3}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a^3}-\frac{\sin (c+d x)}{2 a^3 x^2}-\frac{d \cos (c+d x)}{2 a^3 x}-\frac{9 \sqrt{b} d \cos \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}+\frac{9 \sqrt{b} d \cos \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{CosIntegral}\left(\frac{\sqrt{-a} d}{\sqrt{b}}+d x\right)}{16 (-a)^{7/2}}-\frac{9 \sqrt{b} d \sin \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Si}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{9 \sqrt{b} d \sin \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Si}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}",1,"-(d*Cos[c + d*x])/(2*a^3*x) - (Sqrt[b]*d*Cos[c + d*x])/(16*a^3*(Sqrt[-a] - Sqrt[b]*x)) + (Sqrt[b]*d*Cos[c + d*x])/(16*a^3*(Sqrt[-a] + Sqrt[b]*x)) - (9*Sqrt[b]*d*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(7/2)) + (9*Sqrt[b]*d*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(7/2)) - (3*b*CosIntegral[d*x]*Sin[c])/a^4 - (d^2*CosIntegral[d*x]*Sin[c])/(2*a^3) + (3*b*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(2*a^4) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x]*Sin[c - (Sqrt[-a]*d)/Sqrt[b]])/(16*a^3) + (3*b*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(2*a^4) + (d^2*CosIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x]*Sin[c + (Sqrt[-a]*d)/Sqrt[b]])/(16*a^3) - Sin[c + d*x]/(2*a^3*x^2) - (b*Sin[c + d*x])/(4*a^2*(a + b*x^2)^2) - (b*Sin[c + d*x])/(a^3*(a + b*x^2)) - (3*b*Cos[c]*SinIntegral[d*x])/a^4 - (d^2*Cos[c]*SinIntegral[d*x])/(2*a^3) - (3*b*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(2*a^4) - (d^2*Cos[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*a^3) - (9*Sqrt[b]*d*Sin[c + (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] - d*x])/(16*(-a)^(7/2)) + (3*b*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(2*a^4) + (d^2*Cos[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*a^3) - (9*Sqrt[b]*d*Sin[c - (Sqrt[-a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[-a]*d)/Sqrt[b] + d*x])/(16*(-a)^(7/2))","A",46,7,19,0.3684,1,"{3345, 3297, 3303, 3299, 3302, 3341, 3334}"
79,1,156,0,0.2488646,"\int x^3 \left(a+b x^3\right) \sin (c+d x) \, dx","Int[x^3*(a + b*x^3)*Sin[c + d*x],x]","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{6 b x^5 \sin (c+d x)}{d^2}-\frac{120 b x^3 \sin (c+d x)}{d^4}+\frac{30 b x^4 \cos (c+d x)}{d^3}-\frac{360 b x^2 \cos (c+d x)}{d^5}+\frac{720 b x \sin (c+d x)}{d^6}+\frac{720 b \cos (c+d x)}{d^7}-\frac{b x^6 \cos (c+d x)}{d}","\frac{3 a x^2 \sin (c+d x)}{d^2}-\frac{6 a \sin (c+d x)}{d^4}+\frac{6 a x \cos (c+d x)}{d^3}-\frac{a x^3 \cos (c+d x)}{d}+\frac{6 b x^5 \sin (c+d x)}{d^2}-\frac{120 b x^3 \sin (c+d x)}{d^4}+\frac{30 b x^4 \cos (c+d x)}{d^3}-\frac{360 b x^2 \cos (c+d x)}{d^5}+\frac{720 b x \sin (c+d x)}{d^6}+\frac{720 b \cos (c+d x)}{d^7}-\frac{b x^6 \cos (c+d x)}{d}",1,"(720*b*Cos[c + d*x])/d^7 + (6*a*x*Cos[c + d*x])/d^3 - (360*b*x^2*Cos[c + d*x])/d^5 - (a*x^3*Cos[c + d*x])/d + (30*b*x^4*Cos[c + d*x])/d^3 - (b*x^6*Cos[c + d*x])/d - (6*a*Sin[c + d*x])/d^4 + (720*b*x*Sin[c + d*x])/d^6 + (3*a*x^2*Sin[c + d*x])/d^2 - (120*b*x^3*Sin[c + d*x])/d^4 + (6*b*x^5*Sin[c + d*x])/d^2","A",13,4,17,0.2353,1,"{3339, 3296, 2637, 2638}"
80,1,126,0,0.1908897,"\int x^2 \left(a+b x^3\right) \sin (c+d x) \, dx","Int[x^2*(a + b*x^3)*Sin[c + d*x],x]","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{5 b x^4 \sin (c+d x)}{d^2}-\frac{60 b x^2 \sin (c+d x)}{d^4}+\frac{20 b x^3 \cos (c+d x)}{d^3}+\frac{120 b \sin (c+d x)}{d^6}-\frac{120 b x \cos (c+d x)}{d^5}-\frac{b x^5 \cos (c+d x)}{d}","\frac{2 a x \sin (c+d x)}{d^2}+\frac{2 a \cos (c+d x)}{d^3}-\frac{a x^2 \cos (c+d x)}{d}+\frac{5 b x^4 \sin (c+d x)}{d^2}-\frac{60 b x^2 \sin (c+d x)}{d^4}+\frac{20 b x^3 \cos (c+d x)}{d^3}+\frac{120 b \sin (c+d x)}{d^6}-\frac{120 b x \cos (c+d x)}{d^5}-\frac{b x^5 \cos (c+d x)}{d}",1,"(2*a*Cos[c + d*x])/d^3 - (120*b*x*Cos[c + d*x])/d^5 - (a*x^2*Cos[c + d*x])/d + (20*b*x^3*Cos[c + d*x])/d^3 - (b*x^5*Cos[c + d*x])/d + (120*b*Sin[c + d*x])/d^6 + (2*a*x*Sin[c + d*x])/d^2 - (60*b*x^2*Sin[c + d*x])/d^4 + (5*b*x^4*Sin[c + d*x])/d^2","A",11,4,17,0.2353,1,"{3339, 3296, 2638, 2637}"
81,1,95,0,0.1319771,"\int x \left(a+b x^3\right) \sin (c+d x) \, dx","Int[x*(a + b*x^3)*Sin[c + d*x],x]","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}","\frac{a \sin (c+d x)}{d^2}-\frac{a x \cos (c+d x)}{d}+\frac{4 b x^3 \sin (c+d x)}{d^2}+\frac{12 b x^2 \cos (c+d x)}{d^3}-\frac{24 b x \sin (c+d x)}{d^4}-\frac{24 b \cos (c+d x)}{d^5}-\frac{b x^4 \cos (c+d x)}{d}",1,"(-24*b*Cos[c + d*x])/d^5 - (a*x*Cos[c + d*x])/d + (12*b*x^2*Cos[c + d*x])/d^3 - (b*x^4*Cos[c + d*x])/d + (a*Sin[c + d*x])/d^2 - (24*b*x*Sin[c + d*x])/d^4 + (4*b*x^3*Sin[c + d*x])/d^2","A",9,4,15,0.2667,1,"{3339, 3296, 2637, 2638}"
82,1,68,0,0.0871561,"\int \left(a+b x^3\right) \sin (c+d x) \, dx","Int[(a + b*x^3)*Sin[c + d*x],x]","-\frac{a \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}","-\frac{a \cos (c+d x)}{d}+\frac{3 b x^2 \sin (c+d x)}{d^2}-\frac{6 b \sin (c+d x)}{d^4}+\frac{6 b x \cos (c+d x)}{d^3}-\frac{b x^3 \cos (c+d x)}{d}",1,"-((a*Cos[c + d*x])/d) + (6*b*x*Cos[c + d*x])/d^3 - (b*x^3*Cos[c + d*x])/d - (6*b*Sin[c + d*x])/d^4 + (3*b*x^2*Sin[c + d*x])/d^2","A",7,4,14,0.2857,1,"{3329, 2638, 3296, 2637}"
83,1,57,0,0.1149276,"\int \frac{\left(a+b x^3\right) \sin (c+d x)}{x} \, dx","Int[((a + b*x^3)*Sin[c + d*x])/x,x]","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}","a \sin (c) \text{CosIntegral}(d x)+a \cos (c) \text{Si}(d x)+\frac{2 b x \sin (c+d x)}{d^2}+\frac{2 b \cos (c+d x)}{d^3}-\frac{b x^2 \cos (c+d x)}{d}",1,"(2*b*Cos[c + d*x])/d^3 - (b*x^2*Cos[c + d*x])/d + a*CosIntegral[d*x]*Sin[c] + (2*b*x*Sin[c + d*x])/d^2 + a*Cos[c]*SinIntegral[d*x]","A",8,6,17,0.3529,1,"{3339, 3303, 3299, 3302, 3296, 2638}"
84,1,56,0,0.1167174,"\int \frac{\left(a+b x^3\right) \sin (c+d x)}{x^2} \, dx","Int[((a + b*x^3)*Sin[c + d*x])/x^2,x]","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}+\frac{b \sin (c+d x)}{d^2}-\frac{b x \cos (c+d x)}{d}","a d \cos (c) \text{CosIntegral}(d x)-a d \sin (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{x}+\frac{b \sin (c+d x)}{d^2}-\frac{b x \cos (c+d x)}{d}",1,"-((b*x*Cos[c + d*x])/d) + a*d*Cos[c]*CosIntegral[d*x] + (b*Sin[c + d*x])/d^2 - (a*Sin[c + d*x])/x - a*d*Sin[c]*SinIntegral[d*x]","A",8,7,17,0.4118,1,"{3339, 3297, 3303, 3299, 3302, 3296, 2637}"
85,1,70,0,0.1268116,"\int \frac{\left(a+b x^3\right) \sin (c+d x)}{x^3} \, dx","Int[((a + b*x^3)*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}-\frac{b \cos (c+d x)}{d}","-\frac{1}{2} a d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a d^2 \cos (c) \text{Si}(d x)-\frac{a \sin (c+d x)}{2 x^2}-\frac{a d \cos (c+d x)}{2 x}-\frac{b \cos (c+d x)}{d}",1,"-((b*Cos[c + d*x])/d) - (a*d*Cos[c + d*x])/(2*x) - (a*d^2*CosIntegral[d*x]*Sin[c])/2 - (a*Sin[c + d*x])/(2*x^2) - (a*d^2*Cos[c]*SinIntegral[d*x])/2","A",8,6,17,0.3529,1,"{3339, 2638, 3297, 3303, 3299, 3302}"
86,1,91,0,0.1956946,"\int \frac{\left(a+b x^3\right) \sin (c+d x)}{x^4} \, dx","Int[((a + b*x^3)*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)","-\frac{1}{6} a d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a d^3 \sin (c) \text{Si}(d x)+\frac{a d^2 \sin (c+d x)}{6 x}-\frac{a \sin (c+d x)}{3 x^3}-\frac{a d \cos (c+d x)}{6 x^2}+b \sin (c) \text{CosIntegral}(d x)+b \cos (c) \text{Si}(d x)",1,"-(a*d*Cos[c + d*x])/(6*x^2) - (a*d^3*Cos[c]*CosIntegral[d*x])/6 + b*CosIntegral[d*x]*Sin[c] - (a*Sin[c + d*x])/(3*x^3) + (a*d^2*Sin[c + d*x])/(6*x) + b*Cos[c]*SinIntegral[d*x] + (a*d^3*Sin[c]*SinIntegral[d*x])/6","A",11,5,17,0.2941,1,"{3339, 3297, 3303, 3299, 3302}"
87,1,235,0,0.3260373,"\int x \left(a+b x^3\right)^2 \sin (c+d x) \, dx","Int[x*(a + b*x^3)^2*Sin[c + d*x],x]","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{8 a b x^3 \sin (c+d x)}{d^2}+\frac{24 a b x^2 \cos (c+d x)}{d^3}-\frac{48 a b x \sin (c+d x)}{d^4}-\frac{48 a b \cos (c+d x)}{d^5}-\frac{2 a b x^4 \cos (c+d x)}{d}+\frac{7 b^2 x^6 \sin (c+d x)}{d^2}-\frac{210 b^2 x^4 \sin (c+d x)}{d^4}+\frac{2520 b^2 x^2 \sin (c+d x)}{d^6}+\frac{42 b^2 x^5 \cos (c+d x)}{d^3}-\frac{840 b^2 x^3 \cos (c+d x)}{d^5}-\frac{5040 b^2 \sin (c+d x)}{d^8}+\frac{5040 b^2 x \cos (c+d x)}{d^7}-\frac{b^2 x^7 \cos (c+d x)}{d}","\frac{a^2 \sin (c+d x)}{d^2}-\frac{a^2 x \cos (c+d x)}{d}+\frac{8 a b x^3 \sin (c+d x)}{d^2}+\frac{24 a b x^2 \cos (c+d x)}{d^3}-\frac{48 a b x \sin (c+d x)}{d^4}-\frac{48 a b \cos (c+d x)}{d^5}-\frac{2 a b x^4 \cos (c+d x)}{d}+\frac{7 b^2 x^6 \sin (c+d x)}{d^2}-\frac{210 b^2 x^4 \sin (c+d x)}{d^4}+\frac{2520 b^2 x^2 \sin (c+d x)}{d^6}+\frac{42 b^2 x^5 \cos (c+d x)}{d^3}-\frac{840 b^2 x^3 \cos (c+d x)}{d^5}-\frac{5040 b^2 \sin (c+d x)}{d^8}+\frac{5040 b^2 x \cos (c+d x)}{d^7}-\frac{b^2 x^7 \cos (c+d x)}{d}",1,"(-48*a*b*Cos[c + d*x])/d^5 + (5040*b^2*x*Cos[c + d*x])/d^7 - (a^2*x*Cos[c + d*x])/d + (24*a*b*x^2*Cos[c + d*x])/d^3 - (840*b^2*x^3*Cos[c + d*x])/d^5 - (2*a*b*x^4*Cos[c + d*x])/d + (42*b^2*x^5*Cos[c + d*x])/d^3 - (b^2*x^7*Cos[c + d*x])/d - (5040*b^2*Sin[c + d*x])/d^8 + (a^2*Sin[c + d*x])/d^2 - (48*a*b*x*Sin[c + d*x])/d^4 + (2520*b^2*x^2*Sin[c + d*x])/d^6 + (8*a*b*x^3*Sin[c + d*x])/d^2 - (210*b^2*x^4*Sin[c + d*x])/d^4 + (7*b^2*x^6*Sin[c + d*x])/d^2","A",17,4,17,0.2353,1,"{3339, 3296, 2637, 2638}"
88,1,188,0,0.2423728,"\int \left(a+b x^3\right)^2 \sin (c+d x) \, dx","Int[(a + b*x^3)^2*Sin[c + d*x],x]","-\frac{a^2 \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{6 b^2 x^5 \sin (c+d x)}{d^2}-\frac{120 b^2 x^3 \sin (c+d x)}{d^4}+\frac{30 b^2 x^4 \cos (c+d x)}{d^3}-\frac{360 b^2 x^2 \cos (c+d x)}{d^5}+\frac{720 b^2 x \sin (c+d x)}{d^6}+\frac{720 b^2 \cos (c+d x)}{d^7}-\frac{b^2 x^6 \cos (c+d x)}{d}","-\frac{a^2 \cos (c+d x)}{d}+\frac{6 a b x^2 \sin (c+d x)}{d^2}-\frac{12 a b \sin (c+d x)}{d^4}+\frac{12 a b x \cos (c+d x)}{d^3}-\frac{2 a b x^3 \cos (c+d x)}{d}+\frac{6 b^2 x^5 \sin (c+d x)}{d^2}-\frac{120 b^2 x^3 \sin (c+d x)}{d^4}+\frac{30 b^2 x^4 \cos (c+d x)}{d^3}-\frac{360 b^2 x^2 \cos (c+d x)}{d^5}+\frac{720 b^2 x \sin (c+d x)}{d^6}+\frac{720 b^2 \cos (c+d x)}{d^7}-\frac{b^2 x^6 \cos (c+d x)}{d}",1,"(720*b^2*Cos[c + d*x])/d^7 - (a^2*Cos[c + d*x])/d + (12*a*b*x*Cos[c + d*x])/d^3 - (360*b^2*x^2*Cos[c + d*x])/d^5 - (2*a*b*x^3*Cos[c + d*x])/d + (30*b^2*x^4*Cos[c + d*x])/d^3 - (b^2*x^6*Cos[c + d*x])/d - (12*a*b*Sin[c + d*x])/d^4 + (720*b^2*x*Sin[c + d*x])/d^6 + (6*a*b*x^2*Sin[c + d*x])/d^2 - (120*b^2*x^3*Sin[c + d*x])/d^4 + (6*b^2*x^5*Sin[c + d*x])/d^2","A",14,4,16,0.2500,1,"{3329, 2638, 3296, 2637}"
89,1,161,0,0.2564655,"\int \frac{\left(a+b x^3\right)^2 \sin (c+d x)}{x} \, dx","Int[((a + b*x^3)^2*Sin[c + d*x])/x,x]","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{5 b^2 x^4 \sin (c+d x)}{d^2}-\frac{60 b^2 x^2 \sin (c+d x)}{d^4}+\frac{20 b^2 x^3 \cos (c+d x)}{d^3}+\frac{120 b^2 \sin (c+d x)}{d^6}-\frac{120 b^2 x \cos (c+d x)}{d^5}-\frac{b^2 x^5 \cos (c+d x)}{d}","a^2 \sin (c) \text{CosIntegral}(d x)+a^2 \cos (c) \text{Si}(d x)+\frac{4 a b x \sin (c+d x)}{d^2}+\frac{4 a b \cos (c+d x)}{d^3}-\frac{2 a b x^2 \cos (c+d x)}{d}+\frac{5 b^2 x^4 \sin (c+d x)}{d^2}-\frac{60 b^2 x^2 \sin (c+d x)}{d^4}+\frac{20 b^2 x^3 \cos (c+d x)}{d^3}+\frac{120 b^2 \sin (c+d x)}{d^6}-\frac{120 b^2 x \cos (c+d x)}{d^5}-\frac{b^2 x^5 \cos (c+d x)}{d}",1,"(4*a*b*Cos[c + d*x])/d^3 - (120*b^2*x*Cos[c + d*x])/d^5 - (2*a*b*x^2*Cos[c + d*x])/d + (20*b^2*x^3*Cos[c + d*x])/d^3 - (b^2*x^5*Cos[c + d*x])/d + a^2*CosIntegral[d*x]*Sin[c] + (120*b^2*Sin[c + d*x])/d^6 + (4*a*b*x*Sin[c + d*x])/d^2 - (60*b^2*x^2*Sin[c + d*x])/d^4 + (5*b^2*x^4*Sin[c + d*x])/d^2 + a^2*Cos[c]*SinIntegral[d*x]","A",14,7,19,0.3684,1,"{3339, 3303, 3299, 3302, 3296, 2638, 2637}"
90,1,145,0,0.233297,"\int \frac{\left(a+b x^3\right)^2 \sin (c+d x)}{x^2} \, dx","Int[((a + b*x^3)^2*Sin[c + d*x])/x^2,x]","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}+\frac{2 a b \sin (c+d x)}{d^2}-\frac{2 a b x \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}","a^2 d \cos (c) \text{CosIntegral}(d x)-a^2 d \sin (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{x}+\frac{2 a b \sin (c+d x)}{d^2}-\frac{2 a b x \cos (c+d x)}{d}+\frac{4 b^2 x^3 \sin (c+d x)}{d^2}+\frac{12 b^2 x^2 \cos (c+d x)}{d^3}-\frac{24 b^2 x \sin (c+d x)}{d^4}-\frac{24 b^2 \cos (c+d x)}{d^5}-\frac{b^2 x^4 \cos (c+d x)}{d}",1,"(-24*b^2*Cos[c + d*x])/d^5 - (2*a*b*x*Cos[c + d*x])/d + (12*b^2*x^2*Cos[c + d*x])/d^3 - (b^2*x^4*Cos[c + d*x])/d + a^2*d*Cos[c]*CosIntegral[d*x] + (2*a*b*Sin[c + d*x])/d^2 - (a^2*Sin[c + d*x])/x - (24*b^2*x*Sin[c + d*x])/d^4 + (4*b^2*x^3*Sin[c + d*x])/d^2 - a^2*d*Sin[c]*SinIntegral[d*x]","A",13,8,19,0.4211,1,"{3339, 3297, 3303, 3299, 3302, 3296, 2637, 2638}"
91,1,142,0,0.2185879,"\int \frac{\left(a+b x^3\right)^2 \sin (c+d x)}{x^3} \, dx","Int[((a + b*x^3)^2*Sin[c + d*x])/x^3,x]","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}-\frac{2 a b \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}","-\frac{1}{2} a^2 d^2 \sin (c) \text{CosIntegral}(d x)-\frac{1}{2} a^2 d^2 \cos (c) \text{Si}(d x)-\frac{a^2 \sin (c+d x)}{2 x^2}-\frac{a^2 d \cos (c+d x)}{2 x}-\frac{2 a b \cos (c+d x)}{d}+\frac{3 b^2 x^2 \sin (c+d x)}{d^2}-\frac{6 b^2 \sin (c+d x)}{d^4}+\frac{6 b^2 x \cos (c+d x)}{d^3}-\frac{b^2 x^3 \cos (c+d x)}{d}",1,"(-2*a*b*Cos[c + d*x])/d - (a^2*d*Cos[c + d*x])/(2*x) + (6*b^2*x*Cos[c + d*x])/d^3 - (b^2*x^3*Cos[c + d*x])/d - (a^2*d^2*CosIntegral[d*x]*Sin[c])/2 - (6*b^2*Sin[c + d*x])/d^4 - (a^2*Sin[c + d*x])/(2*x^2) + (3*b^2*x^2*Sin[c + d*x])/d^2 - (a^2*d^2*Cos[c]*SinIntegral[d*x])/2","A",12,8,19,0.4211,1,"{3339, 2638, 3297, 3303, 3299, 3302, 3296, 2637}"
92,1,151,0,0.2516887,"\int \frac{\left(a+b x^3\right)^2 \sin (c+d x)}{x^4} \, dx","Int[((a + b*x^3)^2*Sin[c + d*x])/x^4,x]","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)+\frac{2 b^2 x \sin (c+d x)}{d^2}+\frac{2 b^2 \cos (c+d x)}{d^3}-\frac{b^2 x^2 \cos (c+d x)}{d}","-\frac{1}{6} a^2 d^3 \cos (c) \text{CosIntegral}(d x)+\frac{1}{6} a^2 d^3 \sin (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{6 x}-\frac{a^2 \sin (c+d x)}{3 x^3}-\frac{a^2 d \cos (c+d x)}{6 x^2}+2 a b \sin (c) \text{CosIntegral}(d x)+2 a b \cos (c) \text{Si}(d x)+\frac{2 b^2 x \sin (c+d x)}{d^2}+\frac{2 b^2 \cos (c+d x)}{d^3}-\frac{b^2 x^2 \cos (c+d x)}{d}",1,"(2*b^2*Cos[c + d*x])/d^3 - (a^2*d*Cos[c + d*x])/(6*x^2) - (b^2*x^2*Cos[c + d*x])/d - (a^2*d^3*Cos[c]*CosIntegral[d*x])/6 + 2*a*b*CosIntegral[d*x]*Sin[c] - (a^2*Sin[c + d*x])/(3*x^3) + (a^2*d^2*Sin[c + d*x])/(6*x) + (2*b^2*x*Sin[c + d*x])/d^2 + 2*a*b*Cos[c]*SinIntegral[d*x] + (a^2*d^3*Sin[c]*SinIntegral[d*x])/6","A",14,7,19,0.3684,1,"{3339, 3297, 3303, 3299, 3302, 3296, 2638}"
93,1,167,0,0.2827666,"\int \frac{\left(a+b x^3\right)^2 \sin (c+d x)}{x^5} \, dx","Int[((a + b*x^3)^2*Sin[c + d*x])/x^5,x]","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}","\frac{1}{24} a^2 d^4 \sin (c) \text{CosIntegral}(d x)+\frac{1}{24} a^2 d^4 \cos (c) \text{Si}(d x)+\frac{a^2 d^2 \sin (c+d x)}{24 x^2}+\frac{a^2 d^3 \cos (c+d x)}{24 x}-\frac{a^2 \sin (c+d x)}{4 x^4}-\frac{a^2 d \cos (c+d x)}{12 x^3}+2 a b d \cos (c) \text{CosIntegral}(d x)-2 a b d \sin (c) \text{Si}(d x)-\frac{2 a b \sin (c+d x)}{x}+\frac{b^2 \sin (c+d x)}{d^2}-\frac{b^2 x \cos (c+d x)}{d}",1,"-(a^2*d*Cos[c + d*x])/(12*x^3) + (a^2*d^3*Cos[c + d*x])/(24*x) - (b^2*x*Cos[c + d*x])/d + 2*a*b*d*Cos[c]*CosIntegral[d*x] + (a^2*d^4*CosIntegral[d*x]*Sin[c])/24 + (b^2*Sin[c + d*x])/d^2 - (a^2*Sin[c + d*x])/(4*x^4) + (a^2*d^2*Sin[c + d*x])/(24*x^2) - (2*a*b*Sin[c + d*x])/x + (a^2*d^4*Cos[c]*SinIntegral[d*x])/24 - 2*a*b*d*Sin[c]*SinIntegral[d*x]","A",15,7,19,0.3684,1,"{3339, 3297, 3303, 3299, 3302, 3296, 2637}"
94,1,371,0,0.9150901,"\int \frac{x^4 \sin (c+d x)}{a+b x^3} \, dx","Int[(x^4*Sin[c + d*x])/(a + b*x^3),x]","\frac{a^{2/3} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{5/3}}-\frac{(-1)^{2/3} a^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}+\frac{a^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}","\frac{a^{2/3} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{5/3}}+\frac{(-1)^{2/3} a^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{5/3}}-\frac{(-1)^{2/3} a^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}+\frac{a^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}+\frac{\sin (c+d x)}{b d^2}-\frac{x \cos (c+d x)}{b d}",1,"-((x*Cos[c + d*x])/(b*d)) + (a^(2/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*b^(5/3)) + ((-1)^(2/3)*a^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*b^(5/3)) - ((-1)^(1/3)*a^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*b^(5/3)) + Sin[c + d*x]/(b*d^2) - ((-1)^(2/3)*a^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*b^(5/3)) + (a^(2/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*b^(5/3)) - ((-1)^(1/3)*a^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*b^(5/3))","A",15,6,19,0.3158,1,"{3345, 3296, 2637, 3303, 3299, 3302}"
95,1,357,0,0.6757492,"\int \frac{x^3 \sin (c+d x)}{a+b x^3} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^3),x]","-\frac{\sqrt[3]{a} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{a} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{\cos (c+d x)}{b d}","-\frac{\sqrt[3]{a} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{a} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{a} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{\cos (c+d x)}{b d}",1,"-(Cos[c + d*x]/(b*d)) - (a^(1/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*b^(4/3)) + ((-1)^(1/3)*a^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*b^(4/3)) - ((-1)^(2/3)*a^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*b^(4/3)) - ((-1)^(1/3)*a^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*b^(4/3)) - (a^(1/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*b^(4/3)) - ((-1)^(2/3)*a^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*b^(4/3))","A",14,6,19,0.3158,1,"{3345, 2638, 3333, 3303, 3299, 3302}"
96,1,281,0,0.452726,"\int \frac{x^2 \sin (c+d x)}{a+b x^3} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^3),x]","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b}+\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b}-\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}+\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b}+\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 b}-\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}+\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}",1,"(CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*b) + (CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*b) + (CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*b) - (Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*b) + (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*b) + (Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*b)","A",11,4,19,0.2105,1,"{3345, 3303, 3299, 3302}"
97,1,343,0,0.4131914,"\int \frac{x \sin (c+d x)}{a+b x^3} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^3),x]","-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{(-1)^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}","-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{(-1)^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{(-1)^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}",1,"-(CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^(1/3)*b^(2/3)) - (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(1/3)*b^(2/3))","A",11,4,17,0.2353,1,"{3345, 3303, 3299, 3302}"
98,1,343,0,0.4292603,"\int \frac{\sin (c+d x)}{a+b x^3} \, dx","Int[Sin[c + d*x]/(a + b*x^3),x]","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{2/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}",1,"(CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^(2/3)*b^(1/3)) - ((-1)^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(2/3)*b^(1/3)) + ((-1)^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(2/3)*b^(1/3)) + ((-1)^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^(2/3)*b^(1/3)) + (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(2/3)*b^(1/3)) + ((-1)^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(2/3)*b^(1/3))","A",11,4,16,0.2500,1,"{3333, 3303, 3299, 3302}"
99,1,301,0,0.5271773,"\int \frac{\sin (c+d x)}{x \left(a+b x^3\right)} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^3)),x]","-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a}-\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a}+\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}","-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a}-\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a}+\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}+\frac{\sin (c) \text{CosIntegral}(d x)}{a}+\frac{\cos (c) \text{Si}(d x)}{a}",1,"(CosIntegral[d*x]*Sin[c])/a - (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a) - (CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a) - (CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a) + (Cos[c]*SinIntegral[d*x])/a + (Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a) - (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a) - (Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a)","A",16,4,19,0.2105,1,"{3345, 3303, 3299, 3302}"
100,1,380,0,0.6086594,"\int \frac{\sin (c+d x)}{x^2 \left(a+b x^3\right)} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x^3)),x]","\frac{\sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{b} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}","\frac{\sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{4/3}}+\frac{(-1)^{2/3} \sqrt[3]{b} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{b} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a}-\frac{d \sin (c) \text{Si}(d x)}{a}-\frac{\sin (c+d x)}{a x}",1,"(d*Cos[c]*CosIntegral[d*x])/a + (b^(1/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^(4/3)) + ((-1)^(2/3)*b^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(4/3)) - ((-1)^(1/3)*b^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(4/3)) - Sin[c + d*x]/(a*x) - (d*Sin[c]*SinIntegral[d*x])/a - ((-1)^(2/3)*b^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^(4/3)) + (b^(1/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(4/3)) - ((-1)^(1/3)*b^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(4/3))","A",17,5,19,0.2632,1,"{3345, 3297, 3303, 3299, 3302}"
101,1,408,0,0.6806669,"\int \frac{\sin (c+d x)}{x^3 \left(a+b x^3\right)} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x^3)),x]","-\frac{b^{2/3} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{5/3}}-\frac{\sqrt[3]{-1} b^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{b^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}","-\frac{b^{2/3} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{5/3}}+\frac{\sqrt[3]{-1} b^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^{5/3}}-\frac{\sqrt[3]{-1} b^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{b^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{d^2 \sin (c) \text{CosIntegral}(d x)}{2 a}-\frac{d^2 \cos (c) \text{Si}(d x)}{2 a}-\frac{\sin (c+d x)}{2 a x^2}-\frac{d \cos (c+d x)}{2 a x}",1,"-(d*Cos[c + d*x])/(2*a*x) - (d^2*CosIntegral[d*x]*Sin[c])/(2*a) - (b^(2/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^(5/3)) - Sin[c + d*x]/(2*a*x^2) - (d^2*Cos[c]*SinIntegral[d*x])/(2*a) - ((-1)^(1/3)*b^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^(5/3)) - (b^(2/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^(5/3))","A",18,6,19,0.3158,1,"{3345, 3297, 3303, 3299, 3302, 3333}"
102,1,714,0,1.0728186,"\int \frac{x^3 \sin (c+d x)}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^3)^2,x]","-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{(-1)^{2/3} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{\sqrt[3]{-1} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{(-1)^{2/3} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{\sqrt[3]{-1} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{x \sin (c+d x)}{3 b \left(a+b x^3\right)}","-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{(-1)^{2/3} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{\sqrt[3]{-1} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{(-1)^{2/3} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{\sqrt[3]{-1} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{x \sin (c+d x)}{3 b \left(a+b x^3\right)}",1,"-((-1)^(2/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(1/3)*b^(5/3)) - (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(1/3)*b^(5/3)) + ((-1)^(1/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(1/3)*b^(5/3)) + (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(9*a^(2/3)*b^(4/3)) - ((-1)^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(2/3)*b^(4/3)) + ((-1)^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(2/3)*b^(4/3)) - (x*Sin[c + d*x])/(3*b*(a + b*x^3)) + ((-1)^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(2/3)*b^(4/3)) - ((-1)^(2/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(1/3)*b^(5/3)) + (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3)) + (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(1/3)*b^(5/3)) + ((-1)^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3)) - ((-1)^(1/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(1/3)*b^(5/3))","A",23,6,19,0.3158,1,"{3343, 3333, 3303, 3299, 3302, 3346}"
103,1,371,0,0.6192095,"\int \frac{x^2 \sin (c+d x)}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^3)^2,x]","-\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}-\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{\sin (c+d x)}{3 b \left(a+b x^3\right)}","-\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{2/3} b^{4/3}}-\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{\sin (c+d x)}{3 b \left(a+b x^3\right)}",1,"-((-1)^(1/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(2/3)*b^(4/3)) + (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3)) + ((-1)^(2/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3)) - Sin[c + d*x]/(3*b*(a + b*x^3)) - ((-1)^(1/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(2/3)*b^(4/3)) - (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3)) - ((-1)^(2/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(2/3)*b^(4/3))","A",12,5,19,0.2632,1,"{3341, 3334, 3303, 3299, 3302}"
104,1,691,0,1.2973633,"\int \frac{x \sin (c+d x)}{\left(a+b x^3\right)^2} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^3)^2,x]","-\frac{(-1)^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a b}-\frac{d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a b}-\frac{d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}+\frac{d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}-\frac{\sin (c+d x)}{3 b x \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x}","-\frac{(-1)^{2/3} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a b}-\frac{d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a b}-\frac{d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}+\frac{d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}-\frac{\sin (c+d x)}{3 b x \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x}",1,"-(d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a*b) - (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a*b) - (d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a*b) - (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(9*a^(4/3)*b^(2/3)) - ((-1)^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(4/3)*b^(2/3)) + ((-1)^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(4/3)*b^(2/3)) + Sin[c + d*x]/(3*a*b*x) - Sin[c + d*x]/(3*b*x*(a + b*x^3)) + ((-1)^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(4/3)*b^(2/3)) - (d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a*b) - (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3)) + (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a*b) + ((-1)^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3)) + (d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a*b)","A",34,7,17,0.4118,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3346}"
105,1,735,0,1.3406473,"\int \frac{\sin (c+d x)}{\left(a+b x^3\right)^2} \, dx","Int[Sin[c + d*x]/(a + b*x^3)^2,x]","\frac{(-1)^{2/3} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sqrt[3]{-1} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{2 \sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\sin (c+d x)}{3 b x^2 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^2}","\frac{(-1)^{2/3} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sqrt[3]{-1} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{2 \sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\sin (c+d x)}{3 b x^2 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^2}",1,"((-1)^(2/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(4/3)*b^(2/3)) + (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3)) - ((-1)^(1/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3)) + (2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(9*a^(5/3)*b^(1/3)) - (2*(-1)^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(5/3)*b^(1/3)) + (2*(-1)^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(5/3)*b^(1/3)) + Sin[c + d*x]/(3*a*b*x^2) - Sin[c + d*x]/(3*b*x^2*(a + b*x^3)) + (2*(-1)^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(5/3)*b^(1/3)) + ((-1)^(2/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(4/3)*b^(2/3)) + (2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3)) - (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3)) + (2*(-1)^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3)) + ((-1)^(1/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(4/3)*b^(2/3))","A",36,8,16,0.5000,1,"{3331, 3345, 3297, 3303, 3299, 3302, 3333, 3346}"
106,1,693,0,1.4849667,"\int \frac{\sin (c+d x)}{x \left(a+b x^3\right)^2} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^3)^2),x]","-\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^2}-\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^2}+\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{3 b x^3 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^3}","-\frac{\sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^2}-\frac{\sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{3 a^2}+\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}+\frac{\sin (c) \text{CosIntegral}(d x)}{a^2}+\frac{\cos (c) \text{Si}(d x)}{a^2}-\frac{\sin (c+d x)}{3 b x^3 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^3}",1,"((-1)^(1/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(5/3)*b^(1/3)) - (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3)) - ((-1)^(2/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3)) + (CosIntegral[d*x]*Sin[c])/a^2 - (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^2) - (CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^2) - (CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^2) + Sin[c + d*x]/(3*a*b*x^3) - Sin[c + d*x]/(3*b*x^3*(a + b*x^3)) + (Cos[c]*SinIntegral[d*x])/a^2 + (Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^2) + ((-1)^(1/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(5/3)*b^(1/3)) - (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^2) + (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3)) - (Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^2) + ((-1)^(2/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(5/3)*b^(1/3))","A",41,8,19,0.4211,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3346, 3334}"
107,1,712,0,1.6017682,"\int \frac{\sin (c+d x)}{x^2 \left(a+b x^3\right)^2} \, dx","Int[Sin[c + d*x]/(x^2*(a + b*x^3)^2),x]","\frac{4 \sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{7/3}}+\frac{4 (-1)^{2/3} \sqrt[3]{b} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{7/3}}+\frac{d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^2}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^2}+\frac{d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^2}+\frac{d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^2}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^2}-\frac{d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^2}-\frac{4 (-1)^{2/3} \sqrt[3]{b} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{7/3}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{4 \sin (c+d x)}{3 a^2 x}-\frac{\sin (c+d x)}{3 b x^4 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^4}","\frac{4 \sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{7/3}}+\frac{4 (-1)^{2/3} \sqrt[3]{b} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^{7/3}}+\frac{d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^2}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^2}+\frac{d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{9 a^2}+\frac{d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^2}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^2}-\frac{d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^2}-\frac{4 (-1)^{2/3} \sqrt[3]{b} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{7/3}}+\frac{4 \sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{7/3}}-\frac{4 \sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{7/3}}+\frac{d \cos (c) \text{CosIntegral}(d x)}{a^2}-\frac{d \sin (c) \text{Si}(d x)}{a^2}-\frac{4 \sin (c+d x)}{3 a^2 x}-\frac{\sin (c+d x)}{3 b x^4 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{3 a b x^4}",1,"(d*Cos[c]*CosIntegral[d*x])/a^2 + (d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^2) + (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^2) + (d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^2) + (4*b^(1/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(9*a^(7/3)) + (4*(-1)^(2/3)*b^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(7/3)) - (4*(-1)^(1/3)*b^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(7/3)) + Sin[c + d*x]/(3*a*b*x^4) - (4*Sin[c + d*x])/(3*a^2*x) - Sin[c + d*x]/(3*b*x^4*(a + b*x^3)) - (d*Sin[c]*SinIntegral[d*x])/a^2 - (4*(-1)^(2/3)*b^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(7/3)) + (d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^2) + (4*b^(1/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)) - (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^2) - (4*(-1)^(1/3)*b^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)) - (d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^2)","A",47,7,19,0.3684,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3346}"
108,1,800,0,1.7880313,"\int \frac{\sin (c+d x)}{x^3 \left(a+b x^3\right)^2} \, dx","Int[Sin[c + d*x]/(x^3*(a + b*x^3)^2),x]","-\frac{\text{CosIntegral}(d x) \sin (c) d^2}{2 a^2}-\frac{\cos (c) \text{Si}(d x) d^2}{2 a^2}-\frac{\cos (c+d x) d}{2 a^2 x}-\frac{(-1)^{2/3} \sqrt[3]{b} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3}}-\frac{\sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{(-1)^{2/3} \sqrt[3]{b} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3}}+\frac{\sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{5 b^{2/3} \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}+\frac{5 \sqrt[3]{-1} b^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{5 (-1)^{2/3} b^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{\sin (c+d x)}{3 b x^5 \left(b x^3+a\right)}-\frac{5 \sin (c+d x)}{6 a^2 x^2}+\frac{\sin (c+d x)}{3 a b x^5}-\frac{5 \sqrt[3]{-1} b^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{8/3}}-\frac{5 b^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{5 (-1)^{2/3} b^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}","-\frac{\text{CosIntegral}(d x) \sin (c) d^2}{2 a^2}-\frac{\cos (c) \text{Si}(d x) d^2}{2 a^2}-\frac{\cos (c+d x) d}{2 a^2 x}-\frac{(-1)^{2/3} \sqrt[3]{b} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3}}-\frac{\sqrt[3]{b} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{b} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{(-1)^{2/3} \sqrt[3]{b} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3}}+\frac{\sqrt[3]{b} \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3}}-\frac{5 b^{2/3} \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}+\frac{5 \sqrt[3]{-1} b^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{5 (-1)^{2/3} b^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{\sin (c+d x)}{3 b x^5 \left(b x^3+a\right)}-\frac{5 \sin (c+d x)}{6 a^2 x^2}+\frac{\sin (c+d x)}{3 a b x^5}-\frac{5 \sqrt[3]{-1} b^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{8/3}}-\frac{5 b^{2/3} \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}-\frac{5 (-1)^{2/3} b^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{8/3}}",1,"-(d*Cos[c + d*x])/(2*a^2*x) - ((-1)^(2/3)*b^(1/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(7/3)) - (b^(1/3)*d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)) + ((-1)^(1/3)*b^(1/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)) - (d^2*CosIntegral[d*x]*Sin[c])/(2*a^2) - (5*b^(2/3)*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(9*a^(8/3)) + (5*(-1)^(1/3)*b^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(8/3)) - (5*(-1)^(2/3)*b^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(9*a^(8/3)) + Sin[c + d*x]/(3*a*b*x^5) - (5*Sin[c + d*x])/(6*a^2*x^2) - Sin[c + d*x]/(3*b*x^5*(a + b*x^3)) - (d^2*Cos[c]*SinIntegral[d*x])/(2*a^2) - (5*(-1)^(1/3)*b^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(8/3)) - ((-1)^(2/3)*b^(1/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(7/3)) - (5*b^(2/3)*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(8/3)) + (b^(1/3)*d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)) - (5*(-1)^(2/3)*b^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(8/3)) - ((-1)^(1/3)*b^(1/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3))","A",51,8,19,0.4211,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3333, 3346}"
109,1,772,0,2.7661392,"\int \frac{x^3 \sin (c+d x)}{\left(a+b x^3\right)^3} \, dx","Int[(x^3*Sin[c + d*x])/(a + b*x^3)^3,x]","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{d^2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a b^2}+\frac{d^2 \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}+\frac{d^2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a b^2}-\frac{d^2 \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}+\frac{d^2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}+\frac{d^2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}-\frac{\sin (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{18 a b^2 x^2}-\frac{d \cos (c+d x)}{18 b^2 x \left(a+b x^3\right)}+\frac{d \cos (c+d x)}{18 a b^2 x}-\frac{x \sin (c+d x)}{6 b \left(a+b x^3\right)^2}","\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{d^2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a b^2}+\frac{d^2 \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}+\frac{d^2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a b^2}-\frac{d^2 \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}+\frac{d^2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}+\frac{d^2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}-\frac{\sin (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}+\frac{\sin (c+d x)}{18 a b^2 x^2}-\frac{d \cos (c+d x)}{18 b^2 x \left(a+b x^3\right)}+\frac{d \cos (c+d x)}{18 a b^2 x}-\frac{x \sin (c+d x)}{6 b \left(a+b x^3\right)^2}",1,"(d*Cos[c + d*x])/(18*a*b^2*x) - (d*Cos[c + d*x])/(18*b^2*x*(a + b*x^3)) + (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(27*a^(5/3)*b^(4/3)) + (d^2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(54*a*b^2) - ((-1)^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(5/3)*b^(4/3)) + (d^2*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(54*a*b^2) + ((-1)^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(5/3)*b^(4/3)) + (d^2*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(54*a*b^2) + Sin[c + d*x]/(18*a*b^2*x^2) - (x*Sin[c + d*x])/(6*b*(a + b*x^3)^2) - Sin[c + d*x]/(18*b^2*x^2*(a + b*x^3)) + ((-1)^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(5/3)*b^(4/3)) - (d^2*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(54*a*b^2) + (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3)) + (d^2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(54*a*b^2) + ((-1)^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3)) + (d^2*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(54*a*b^2)","A",71,10,19,0.5263,1,"{3343, 3331, 3345, 3297, 3303, 3299, 3302, 3333, 3346, 3344}"
110,1,777,0,1.5280251,"\int \frac{x^2 \sin (c+d x)}{\left(a+b x^3\right)^3} \, dx","Int[(x^2*Sin[c + d*x])/(a + b*x^3)^3,x]","-\frac{d^2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a^{4/3} b^{5/3}}-\frac{(-1)^{2/3} d^2 \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} d^2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d^2 \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}-\frac{d^2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} d^2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{d \cos (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}+\frac{d \cos (c+d x)}{18 a b^2 x^2}-\frac{\sin (c+d x)}{6 b \left(a+b x^3\right)^2}","-\frac{d^2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a^{4/3} b^{5/3}}-\frac{(-1)^{2/3} d^2 \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} d^2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{d \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}+d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d^2 \cos \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}-\frac{d^2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} d^2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d \sin \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}-\frac{d \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{(-1)^{2/3} d \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{d \cos (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}+\frac{d \cos (c+d x)}{18 a b^2 x^2}-\frac{\sin (c+d x)}{6 b \left(a+b x^3\right)^2}",1,"(d*Cos[c + d*x])/(18*a*b^2*x^2) - (d*Cos[c + d*x])/(18*b^2*x^2*(a + b*x^3)) - ((-1)^(1/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(5/3)*b^(4/3)) + (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3)) + ((-1)^(2/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3)) - (d^2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(54*a^(4/3)*b^(5/3)) - ((-1)^(2/3)*d^2*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(4/3)*b^(5/3)) + ((-1)^(1/3)*d^2*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(4/3)*b^(5/3)) - Sin[c + d*x]/(6*b*(a + b*x^3)^2) + ((-1)^(2/3)*d^2*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(54*a^(4/3)*b^(5/3)) - ((-1)^(1/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(5/3)*b^(4/3)) - (d^2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(4/3)*b^(5/3)) - (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3)) + ((-1)^(1/3)*d^2*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(4/3)*b^(5/3)) - ((-1)^(2/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(5/3)*b^(4/3))","A",37,9,19,0.4737,1,"{3341, 3332, 3346, 3297, 3303, 3299, 3302, 3334, 3345}"
111,1,1141,0,3.1159017,"\int \frac{x \sin (c+d x)}{\left(a+b x^3\right)^3} \, dx","Int[(x*Sin[c + d*x])/(a + b*x^3)^3,x]","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\cos (c+d x) d}{18 b^2 x^3 \left(b x^3+a\right)}+\frac{\cos (c+d x) d}{18 a b^2 x^3}-\frac{2 \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^2 b}-\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^2 b}+\frac{2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}+\frac{2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}-\frac{2 (-1)^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sin (c+d x)}{9 a^2 b x}+\frac{\sin (c+d x)}{18 b^2 x^4 \left(b x^3+a\right)}-\frac{\sin (c+d x)}{6 b x \left(b x^3+a\right)^2}-\frac{\sin (c+d x)}{18 a b^2 x^4}+\frac{2 (-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{\sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\cos (c+d x) d}{18 b^2 x^3 \left(b x^3+a\right)}+\frac{\cos (c+d x) d}{18 a b^2 x^3}-\frac{2 \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^2 b}-\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^2 b}+\frac{2 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}+\frac{2 \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}-\frac{2 (-1)^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sin (c+d x)}{9 a^2 b x}+\frac{\sin (c+d x)}{18 b^2 x^4 \left(b x^3+a\right)}-\frac{\sin (c+d x)}{6 b x \left(b x^3+a\right)^2}-\frac{\sin (c+d x)}{18 a b^2 x^4}+\frac{2 (-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}",1,"(d*Cos[c + d*x])/(18*a*b^2*x^3) - (d*Cos[c + d*x])/(18*b^2*x^3*(a + b*x^3)) - (2*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^2*b) - (2*d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^2*b) - (2*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^2*b) - (2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(27*a^(7/3)*b^(2/3)) + (d^2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(54*a^(5/3)*b^(4/3)) - (2*(-1)^(2/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(7/3)*b^(2/3)) - ((-1)^(1/3)*d^2*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(5/3)*b^(4/3)) + (2*(-1)^(1/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(7/3)*b^(2/3)) + ((-1)^(2/3)*d^2*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(5/3)*b^(4/3)) - Sin[c + d*x]/(18*a*b^2*x^4) + (2*Sin[c + d*x])/(9*a^2*b*x) - Sin[c + d*x]/(6*b*x*(a + b*x^3)^2) + Sin[c + d*x]/(18*b^2*x^4*(a + b*x^3)) + (2*(-1)^(2/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(7/3)*b^(2/3)) + ((-1)^(1/3)*d^2*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(54*a^(5/3)*b^(4/3)) - (2*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^2*b) - (2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(7/3)*b^(2/3)) + (d^2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(5/3)*b^(4/3)) + (2*d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^2*b) + (2*(-1)^(1/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(7/3)*b^(2/3)) + ((-1)^(2/3)*d^2*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(5/3)*b^(4/3)) + (2*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^2*b)","A",89,9,17,0.5294,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3346, 3344, 3333}"
112,1,1161,0,3.367894,"\int \frac{\sin (c+d x)}{\left(a+b x^3\right)^3} \, dx","Int[Sin[c + d*x]/(a + b*x^3)^3,x]","-\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}+\frac{\cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^2 b}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\cos (c+d x) d}{18 a^2 b x}-\frac{\cos (c+d x) d}{18 b^2 x^4 \left(b x^3+a\right)}+\frac{\cos (c+d x) d}{18 a b^2 x^4}+\frac{(-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3} b^{2/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{(-1)^{2/3} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3} b^{2/3}}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{5 \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 \sqrt[3]{-1} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 (-1)^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{\sin (c+d x)}{9 b^2 x^5 \left(b x^3+a\right)}+\frac{5 \sin (c+d x)}{18 a^2 b x^2}-\frac{\sin (c+d x)}{6 b x^2 \left(b x^3+a\right)^2}-\frac{\sin (c+d x)}{9 a b^2 x^5}+\frac{5 \sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}","-\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}+\frac{\cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^2 b}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^2 b}-\frac{\cos (c+d x) d}{18 a^2 b x}-\frac{\cos (c+d x) d}{18 b^2 x^4 \left(b x^3+a\right)}+\frac{\cos (c+d x) d}{18 a b^2 x^4}+\frac{(-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3} b^{2/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{(-1)^{2/3} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{9 a^{7/3} b^{2/3}}-\frac{\sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{\sqrt[3]{-1} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{9 a^{7/3} b^{2/3}}+\frac{5 \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}-\frac{5 \sqrt[3]{-1} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 (-1)^{2/3} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{\sin (c+d x)}{9 b^2 x^5 \left(b x^3+a\right)}+\frac{5 \sin (c+d x)}{18 a^2 b x^2}-\frac{\sin (c+d x)}{6 b x^2 \left(b x^3+a\right)^2}-\frac{\sin (c+d x)}{9 a b^2 x^5}+\frac{5 \sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}+\frac{5 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{8/3} \sqrt[3]{b}}",1,"(d*Cos[c + d*x])/(18*a*b^2*x^4) - (d*Cos[c + d*x])/(18*a^2*b*x) - (d*Cos[c + d*x])/(18*b^2*x^4*(a + b*x^3)) + ((-1)^(2/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(7/3)*b^(2/3)) + (d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)*b^(2/3)) - ((-1)^(1/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)*b^(2/3)) + (5*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(27*a^(8/3)*b^(1/3)) - (d^2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(54*a^2*b) - (5*(-1)^(1/3)*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(8/3)*b^(1/3)) - (d^2*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(54*a^2*b) + (5*(-1)^(2/3)*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(27*a^(8/3)*b^(1/3)) - (d^2*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(54*a^2*b) - Sin[c + d*x]/(9*a*b^2*x^5) + (5*Sin[c + d*x])/(18*a^2*b*x^2) - Sin[c + d*x]/(6*b*x^2*(a + b*x^3)^2) + Sin[c + d*x]/(9*b^2*x^5*(a + b*x^3)) + (5*(-1)^(1/3)*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(8/3)*b^(1/3)) + (d^2*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(54*a^2*b) + ((-1)^(2/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(9*a^(7/3)*b^(2/3)) + (5*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3)) - (d^2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(54*a^2*b) - (d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)*b^(2/3)) + (5*(-1)^(2/3)*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3)) - (d^2*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(54*a^2*b) + ((-1)^(1/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(9*a^(7/3)*b^(2/3))","A",99,10,16,0.6250,1,"{3331, 3343, 3345, 3297, 3303, 3299, 3302, 3333, 3346, 3344}"
113,1,1163,0,3.8930931,"\int \frac{\sin (c+d x)}{x \left(a+b x^3\right)^3} \, dx","Int[Sin[c + d*x]/(x*(a + b*x^3)^3),x]","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}+\frac{(-1)^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{(-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{7/3} b^{2/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\cos (c+d x) d}{18 b^2 x^5 \left(b x^3+a\right)}-\frac{\cos (c+d x) d}{18 a^2 b x^2}+\frac{\cos (c+d x) d}{18 a b^2 x^5}+\frac{4 \sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^{8/3} \sqrt[3]{b}}-\frac{4 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}-\frac{4 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 \sqrt[3]{-1} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 (-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{\text{CosIntegral}(d x) \sin (c)}{a^3}-\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}+\frac{\sin (c+d x)}{6 b^2 x^6 \left(b x^3+a\right)}-\frac{\sin (c+d x)}{6 b x^3 \left(b x^3+a\right)^2}+\frac{\sin (c+d x)}{3 a^2 b x^3}-\frac{\sin (c+d x)}{6 a b^2 x^6}+\frac{\cos (c) \text{Si}(d x)}{a^3}+\frac{\cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^3}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}","\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}+\frac{(-1)^{2/3} \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{(-1)^{2/3} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{7/3} b^{2/3}}+\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\sqrt[3]{-1} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{7/3} b^{2/3}}-\frac{\cos (c+d x) d}{18 b^2 x^5 \left(b x^3+a\right)}-\frac{\cos (c+d x) d}{18 a^2 b x^2}+\frac{\cos (c+d x) d}{18 a b^2 x^5}+\frac{4 \sqrt[3]{-1} \cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^{8/3} \sqrt[3]{b}}-\frac{4 \cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}-\frac{4 (-1)^{2/3} \cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 \sqrt[3]{-1} \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{4 (-1)^{2/3} \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^{8/3} \sqrt[3]{b}}+\frac{\text{CosIntegral}(d x) \sin (c)}{a^3}-\frac{\text{CosIntegral}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\text{CosIntegral}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sin \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\text{CosIntegral}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sin \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}+\frac{\sin (c+d x)}{6 b^2 x^6 \left(b x^3+a\right)}-\frac{\sin (c+d x)}{6 b x^3 \left(b x^3+a\right)^2}+\frac{\sin (c+d x)}{3 a^2 b x^3}-\frac{\sin (c+d x)}{6 a b^2 x^6}+\frac{\cos (c) \text{Si}(d x)}{a^3}+\frac{\cos \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^3}-\frac{\cos \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}-\frac{\cos \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Si}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^3}",1,"(d*Cos[c + d*x])/(18*a*b^2*x^5) - (d*Cos[c + d*x])/(18*a^2*b*x^2) - (d*Cos[c + d*x])/(18*b^2*x^5*(a + b*x^3)) + (4*(-1)^(1/3)*d*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(8/3)*b^(1/3)) - (4*d*Cos[c - (a^(1/3)*d)/b^(1/3)]*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3)) - (4*(-1)^(2/3)*d*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3)) + (CosIntegral[d*x]*Sin[c])/a^3 - (CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(3*a^3) + (d^2*CosIntegral[(a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - (a^(1/3)*d)/b^(1/3)])/(54*a^(7/3)*b^(2/3)) - (CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(3*a^3) + ((-1)^(2/3)*d^2*CosIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x]*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(7/3)*b^(2/3)) - (CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(3*a^3) - ((-1)^(1/3)*d^2*CosIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x]*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)])/(54*a^(7/3)*b^(2/3)) - Sin[c + d*x]/(6*a*b^2*x^6) + Sin[c + d*x]/(3*a^2*b*x^3) - Sin[c + d*x]/(6*b*x^3*(a + b*x^3)^2) + Sin[c + d*x]/(6*b^2*x^6*(a + b*x^3)) + (Cos[c]*SinIntegral[d*x])/a^3 + (Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(3*a^3) - ((-1)^(2/3)*d^2*Cos[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(54*a^(7/3)*b^(2/3)) + (4*(-1)^(1/3)*d*Sin[c + ((-1)^(1/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(1/3)*a^(1/3)*d)/b^(1/3) - d*x])/(27*a^(8/3)*b^(1/3)) - (Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(3*a^3) + (d^2*Cos[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(7/3)*b^(2/3)) + (4*d*Sin[c - (a^(1/3)*d)/b^(1/3)]*SinIntegral[(a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3)) - (Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(3*a^3) - ((-1)^(1/3)*d^2*Cos[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(54*a^(7/3)*b^(2/3)) + (4*(-1)^(2/3)*d*Sin[c - ((-1)^(2/3)*a^(1/3)*d)/b^(1/3)]*SinIntegral[((-1)^(2/3)*a^(1/3)*d)/b^(1/3) + d*x])/(27*a^(8/3)*b^(1/3))","A",110,9,19,0.4737,1,"{3343, 3345, 3297, 3303, 3299, 3302, 3346, 3334, 3344}"