1,1,359,126,0.023000," ","int(x^3*(b*x+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}+a \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{4 b c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-3 a c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+\frac{6 b \,c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}+3 a \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{4 b \,c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}+a \,c^{3} \cos \left(d x +c \right)-\frac{b \,c^{4} \cos \left(d x +c \right)}{d}}{d^{4}}"," ",0,"1/d^4*(b/d*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+a*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-4*b*c/d*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3*a*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6/d*b*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3*a*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d*b*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c^3*cos(d*x+c)-1/d*b*c^4*cos(d*x+c))","B"
2,1,225,96,0.024000," ","int(x^2*(b*x+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d}+a \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)-\frac{3 b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}-2 a c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{3 b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-a \,c^{2} \cos \left(d x +c \right)+\frac{b \,c^{3} \cos \left(d x +c \right)}{d}}{d^{3}}"," ",0,"1/d^3*(b/d*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-3*b*c/d*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*a*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+3/d*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*c^2*cos(d*x+c)+1/d*b*c^3*cos(d*x+c))","B"
3,1,121,65,0.021000," ","int(x*(b*x+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}+a \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{2 b c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}+a c \cos \left(d x +c \right)-\frac{b \,c^{2} \cos \left(d x +c \right)}{d}}{d^{2}}"," ",0,"1/d^2*(b/d*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-2*b*c/d*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c*cos(d*x+c)-1/d*b*c^2*cos(d*x+c))","A"
4,1,52,28,0.023000," ","int((b*x+a)*sin(d*x+c),x)","\frac{\frac{b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-a \cos \left(d x +c \right)+\frac{b c \cos \left(d x +c \right)}{d}}{d}"," ",0,"1/d*(b/d*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*cos(d*x+c)+b*c/d*cos(d*x+c))","A"
5,1,31,29,0.027000," ","int((b*x+a)*sin(d*x+c)/x,x)","-\frac{b \cos \left(d x +c \right)}{d}+a \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"-b*cos(d*x+c)/d+a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
6,1,56,48,0.033000," ","int((b*x+a)*sin(d*x+c)/x^2,x)","d \left(\frac{b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d}+a \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)\right)"," ",0,"d*(b/d*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+a*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","A"
7,1,88,81,0.039000," ","int((b*x+a)*sin(d*x+c)/x^3,x)","d^{2} \left(\frac{b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d}+a \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)\right)"," ",0,"d^2*(b/d*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+a*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c)))","A"
8,1,117,114,0.035000," ","int((b*x+a)*sin(d*x+c)/x^4,x)","d^{3} \left(\frac{b \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)}{d}+a \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)\right)"," ",0,"d^3*(b/d*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+a*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c)))","A"
9,1,145,144,0.033000," ","int((b*x+a)*sin(d*x+c)/x^5,x)","d^{4} \left(\frac{b \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)}{d}+a \left(-\frac{\sin \left(d x +c \right)}{4 x^{4} d^{4}}-\frac{\cos \left(d x +c \right)}{12 x^{3} d^{3}}+\frac{\sin \left(d x +c \right)}{24 x^{2} d^{2}}+\frac{\cos \left(d x +c \right)}{24 x d}+\frac{\Si \left(d x \right) \cos \left(c \right)}{24}+\frac{\Ci \left(d x \right) \sin \left(c \right)}{24}\right)\right)"," ",0,"d^4*(b/d*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c))+a*(-1/4*sin(d*x+c)/x^4/d^4-1/12*cos(d*x+c)/x^3/d^3+1/24*sin(d*x+c)/x^2/d^2+1/24*cos(d*x+c)/x/d+1/24*Si(d*x)*cos(c)+1/24*Ci(d*x)*sin(c)))","A"
10,1,468,186,0.025000," ","int(x^2*(b*x+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+\frac{2 a b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-\frac{4 b^{2} c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+a^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)-\frac{6 a b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}+\frac{6 b^{2} c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}-2 a^{2} c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{6 a b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-\frac{4 b^{2} c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-a^{2} c^{2} \cos \left(d x +c \right)+\frac{2 a b \,c^{3} \cos \left(d x +c \right)}{d}-\frac{b^{2} c^{4} \cos \left(d x +c \right)}{d^{2}}}{d^{3}}"," ",0,"1/d^3*(1/d^2*b^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+2/d*a*b*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-4/d^2*b^2*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-6/d*a*b*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6/d^2*b^2*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*a^2*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+6/d*a*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d^2*b^2*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a^2*c^2*cos(d*x+c)+2/d*a*b*c^3*cos(d*x+c)-1/d^2*b^2*c^4*cos(d*x+c))","B"
11,1,281,135,0.026000," ","int(x*(b*x+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+\frac{2 a b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d}-\frac{3 b^{2} c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+a^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{4 a b c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}+\frac{3 b^{2} c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+a^{2} c \cos \left(d x +c \right)-\frac{2 a b \,c^{2} \cos \left(d x +c \right)}{d}+\frac{b^{2} c^{3} \cos \left(d x +c \right)}{d^{2}}}{d^{2}}"," ",0,"1/d^2*(1/d^2*b^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+2/d*a*b*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-3/d^2*b^2*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d*a*b*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+3/d^2*b^2*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a^2*c*cos(d*x+c)-2/d*a*b*c^2*cos(d*x+c)+1/d^2*b^2*c^3*cos(d*x+c))","B"
12,1,148,50,0.024000," ","int((b*x+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+\frac{2 a b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d}-\frac{2 b^{2} c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-a^{2} \cos \left(d x +c \right)+\frac{2 a b c \cos \left(d x +c \right)}{d}-\frac{b^{2} c^{2} \cos \left(d x +c \right)}{d^{2}}}{d}"," ",0,"1/d*(1/d^2*b^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+2/d*a*b*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-2/d^2*b^2*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a^2*cos(d*x+c)+2/d*a*b*c*cos(d*x+c)-1/d^2*b^2*c^2*cos(d*x+c))","B"
13,1,79,62,0.030000," ","int((b*x+a)^2*sin(d*x+c)/x,x)","\frac{\left(1+c \right) b^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{2 c \,b^{2} \cos \left(d x +c \right)}{d^{2}}+a^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"(1+c)/d^2*b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-2*a*b*cos(d*x+c)/d+2*c/d^2*b^2*cos(d*x+c)+a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
14,1,74,72,0.038000," ","int((b*x+a)^2*sin(d*x+c)/x^2,x)","d \left(-\frac{b^{2} \cos \left(d x +c \right)}{d^{2}}+\frac{2 a b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)\right)"," ",0,"d*(-1/d^2*b^2*cos(d*x+c)+2/d*a*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+a^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","A"
15,1,114,113,0.037000," ","int((b*x+a)^2*sin(d*x+c)/x^3,x)","d^{2} \left(\frac{b^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{2}}+\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)\right)"," ",0,"d^2*(1/d^2*b^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+2/d*a*b*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+a^2*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c)))","A"
16,1,158,165,0.042000," ","int((b*x+a)^2*sin(d*x+c)/x^4,x)","d^{3} \left(\frac{b^{2} \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d^{2}}+\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)}{d}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)\right)"," ",0,"d^3*(1/d^2*b^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+2/d*a*b*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+a^2*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c)))","A"
17,1,201,218,0.039000," ","int((b*x+a)^2*sin(d*x+c)/x^5,x)","d^{4} \left(\frac{b^{2} \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)}{d^{2}}+\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)}{d}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{4 x^{4} d^{4}}-\frac{\cos \left(d x +c \right)}{12 x^{3} d^{3}}+\frac{\sin \left(d x +c \right)}{24 x^{2} d^{2}}+\frac{\cos \left(d x +c \right)}{24 x d}+\frac{\Si \left(d x \right) \cos \left(c \right)}{24}+\frac{\Ci \left(d x \right) \sin \left(c \right)}{24}\right)\right)"," ",0,"d^4*(1/d^2*b^2*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+2/d*a*b*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c))+a^2*(-1/4*sin(d*x+c)/x^4/d^4-1/12*cos(d*x+c)/x^3/d^3+1/24*sin(d*x+c)/x^2/d^2+1/24*cos(d*x+c)/x/d+1/24*Si(d*x)*cos(c)+1/24*Ci(d*x)*sin(c)))","A"
18,1,777,221,0.033000," ","int(x^4*sin(d*x+c)/(b*x+a),x)","\frac{\frac{\left(a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right) d \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{4}}+\frac{\left(-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,b^{2} c^{2} d +b^{3} c^{3}+a^{2} b \,d^{2}-2 a \,b^{2} c d +b^{3} c^{2}-a \,b^{2} d +b^{3} c +b^{3}\right) d \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{4}}+\frac{4 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{3}}-\frac{4 d c \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}-a b d +b^{2} c +b^{2}\right) \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{b^{3}}+\frac{6 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d \,c^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}+\frac{6 \left(-d a +c b +b \right) d \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{2}}+\frac{4 \left(d a -c b \right) d \,c^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}+\frac{4 d \,c^{3} \cos \left(d x +c \right)}{b}+d \,c^{4} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{5}}"," ",0,"1/d^5*((a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*d/b^4*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+(-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3+a^2*b*d^2-2*a*b^2*c*d+b^3*c^2-a*b^2*d+b^3*c+b^3)*d/b^4*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+4*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d*c/b^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-4*d*c*(a^2*d^2-2*a*b*c*d+b^2*c^2-a*b*d+b^2*c+b^2)/b^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d*c^2/b^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+6*(-a*d+b*c+b)*d*c^2/b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+4*(a*d-b*c)*d*c^3/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+4*d*c^3/b*cos(d*x+c)+d*c^4*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b))","B"
19,1,514,153,0.028000," ","int(x^3*sin(d*x+c)/(b*x+a),x)","\frac{-\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{3}}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}-a b d +b^{2} c +b^{2}\right) d \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{b^{3}}-\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}-\frac{3 d c \left(-d a +c b +b \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{2}}-\frac{3 \left(d a -c b \right) d \,c^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}-\frac{3 d \,c^{2} \cos \left(d x +c \right)}{b}-d \,c^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{4}}"," ",0,"1/d^4*(-(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d/b^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+(a^2*d^2-2*a*b*c*d+b^2*c^2-a*b*d+b^2*c+b^2)*d/b^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d*c/b^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-3*d*c*(-a*d+b*c+b)/b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-3*(a*d-b*c)*d*c^2/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-3*d*c^2/b*cos(d*x+c)-d*c^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b))","B"
20,1,315,102,0.026000," ","int(x^2*sin(d*x+c)/(b*x+a),x)","\frac{\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}+\frac{\left(-d a +c b +b \right) d \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{2}}+\frac{2 \left(d a -c b \right) d c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}+\frac{2 d c \cos \left(d x +c \right)}{b}+d \,c^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{3}}"," ",0,"1/d^3*((a^2*d^2-2*a*b*c*d+b^2*c^2)*d/b^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+(-a*d+b*c+b)*d/b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+2*(a*d-b*c)*d*c/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+2*d*c/b*cos(d*x+c)+d*c^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b))","B"
21,1,180,70,0.025000," ","int(x*sin(d*x+c)/(b*x+a),x)","\frac{-\frac{\left(d a -c b \right) d \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}-\frac{d \cos \left(d x +c \right)}{b}-d c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{2}}"," ",0,"1/d^2*(-(a*d-b*c)*d/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-d/b*cos(d*x+c)-d*c*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b))","B"
22,1,73,54,0.023000," ","int(sin(d*x+c)/(b*x+a),x)","\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}"," ",0,"Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b","A"
23,1,99,74,0.031000," ","int(sin(d*x+c)/x/(b*x+a),x)","-\frac{b \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{a}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a}"," ",0,"-b/a*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+1/a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
24,1,144,117,0.030000," ","int(sin(d*x+c)/x^2/(b*x+a),x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a}+\frac{b^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{a^{2} d}-\frac{b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{a^{2} d}\right)"," ",0,"d*(1/a*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+b^2/a^2/d*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-1/a^2*b/d*(Si(d*x)*cos(c)+Ci(d*x)*sin(c)))","A"
25,1,202,182,0.029000," ","int(sin(d*x+c)/x^3/(b*x+a),x)","d^{2} \left(-\frac{b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{a^{2} d}-\frac{b^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{2} a^{3}}+\frac{-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}}{a}+\frac{b^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{a^{3} d^{2}}\right)"," ",0,"d^2*(-1/a^2*b/d*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-1/d^2*b^3/a^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+1/a*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+1/a^3*b^2/d^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c)))","A"
26,1,1214,236,0.038000," ","int(x^4*sin(d*x+c)/(b*x+a)^2,x)","\frac{-\frac{4 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{4}}+\frac{\left(a^{4} d^{4}-4 a^{3} b c \,d^{3}+6 a^{2} b^{2} c^{2} d^{2}-4 a \,b^{3} c^{3} d +b^{4} c^{4}\right) d^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{4}}+\frac{\left(3 a^{2} d^{2}-6 a b c d +3 b^{2} c^{2}-2 a b d +2 b^{2} c +b^{2}\right) d^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{b^{4}}-\frac{12 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{2} c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{3}}+\frac{4 \left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d^{2} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{3}}-\frac{4 d^{2} c \left(-2 d a +2 c b +b \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{3}}-\frac{12 \left(d a -c b \right) d^{2} c^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}+\frac{6 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{2} c^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{2}}-\frac{6 d^{2} c^{2} \cos \left(d x +c \right)}{b^{2}}-\frac{4 d^{2} c^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}+\frac{4 d^{2} \left(d a -c b \right) c^{3} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}+d^{2} c^{4} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{d^{5}}"," ",0,"1/d^5*(-4/b^4*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+(a^4*d^4-4*a^3*b*c*d^3+6*a^2*b^2*c^2*d^2-4*a*b^3*c^3*d+b^4*c^4)*d^2/b^4*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+(3*a^2*d^2-6*a*b*c*d+3*b^2*c^2-2*a*b*d+2*b^2*c+b^2)*d^2/b^4*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-12/b^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^2*c*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+4*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d^2*c/b^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-4*d^2*c*(-2*a*d+2*b*c+b)/b^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-12/b^2*(a*d-b*c)*d^2*c^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+6*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^2*c^2/b^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-6*d^2*c^2/b^2*cos(d*x+c)-4*d^2*c^3/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+4*d^2*(a*d-b*c)/b*c^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+d^2*c^4*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","B"
27,1,848,186,0.036000," ","int(x^3*sin(d*x+c)/(b*x+a)^2,x)","\frac{\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{3}}-\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{3}}+\frac{\left(-2 d a +2 c b +b \right) d^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{b^{3}}+\frac{6 \left(d a -c b \right) d^{2} c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}-\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{2} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{2}}+\frac{3 d^{2} c \cos \left(d x +c \right)}{b^{2}}+\frac{3 d^{2} c^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}-\frac{3 d^{2} \left(d a -c b \right) c^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}-d^{2} c^{3} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{d^{4}}"," ",0,"1/d^4*(3/b^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d^2/b^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+(-2*a*d+2*b*c+b)*d^2/b^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+6/b^2*(a*d-b*c)*d^2*c*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^2*c/b^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+3*d^2*c/b^2*cos(d*x+c)+3*d^2*c^2/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-3*d^2*(a*d-b*c)/b*c^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^2*c^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","B"
28,1,553,152,0.033000," ","int(x^2*sin(d*x+c)/(b*x+a)^2,x)","\frac{-\frac{2 \left(d a -c b \right) d^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{2}}-\frac{d^{2} \cos \left(d x +c \right)}{b^{2}}-\frac{2 d^{2} c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}+\frac{2 \left(d a -c b \right) d^{2} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}+d^{2} c^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{d^{3}}"," ",0,"1/d^3*(-2/b^2*(a*d-b*c)*d^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^2/b^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^2/b^2*cos(d*x+c)-2*d^2*c/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+2/b*(a*d-b*c)*d^2*c*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+d^2*c^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","B"
29,1,315,130,0.031000," ","int(x*sin(d*x+c)/(b*x+a)^2,x)","\frac{\frac{d^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b}-\frac{d^{2} \left(d a -c b \right) \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}-d^{2} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{d^{2}}"," ",0,"1/d^2*(d^2/b*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-d^2*(a*d-b*c)/b*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^2*c*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","B"
30,1,107,73,0.026000," ","int(sin(d*x+c)/(b*x+a)^2,x)","d \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)"," ",0,"d*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)","A"
31,1,210,153,0.032000," ","int(sin(d*x+c)/x/(b*x+a)^2,x)","-\frac{b \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{a^{2}}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{2}}-\frac{d b \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{a}"," ",0,"-b/a^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+1/a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-d*b/a*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)","A"
32,1,256,191,0.031000," ","int(sin(d*x+c)/x^2/(b*x+a)^2,x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a^{2}}+\frac{2 b^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d \,a^{3}}-\frac{2 b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d \,a^{3}}+\frac{b^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{a^{2}}\right)"," ",0,"d*(1/a^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+2/d*b^2/a^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-2/d/a^3*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+b^2/a^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","A"
33,1,1208,263,0.037000," ","int(x^3*sin(d*x+c)/(b*x+a)^3,x)","\frac{-\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) d^{3} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b^{3}}-\frac{3 \left(d a -c b \right) d^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{3}}+\frac{3 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) d^{3} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{3}}-\frac{d^{3} \cos \left(d x +c \right)}{b^{3}}-\frac{3 d^{3} \left(d a -c b \right)^{2} c \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b^{2}}-\frac{3 d^{3} c \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}+\frac{6 \left(d a -c b \right) d^{3} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{2}}-\frac{3 \left(d a -c b \right) d^{3} c^{2} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b}+\frac{3 d^{3} c^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}-d^{3} c^{3} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{d^{4}}"," ",0,"1/d^4*(-(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)*d^3/b^3*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)-3/b^3*(a*d-b*c)*d^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+3/b^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)*d^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^3/b^3*cos(d*x+c)-3*d^3*(a*d-b*c)^2/b^2*c*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)-3*d^3*c/b^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+6/b^2*(a*d-b*c)*d^3*c*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-3/b*(a*d-b*c)*d^3*c^2*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)+3*d^3*c^2/b*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^3*c^3*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b))","B"
34,1,779,240,0.033000," ","int(x^2*sin(d*x+c)/(b*x+a)^3,x)","\frac{\frac{d^{3} \left(d a -c b \right)^{2} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b^{2}}+\frac{d^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{b^{2}}-\frac{2 d^{3} \left(d a -c b \right) \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b^{2}}+\frac{2 d^{3} \left(d a -c b \right) c \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b}-\frac{2 d^{3} c \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}+d^{3} c^{2} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{d^{3}}"," ",0,"1/d^3*(d^3*(a*d-b*c)^2/b^2*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)+d^3/b^2*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-2*d^3*(a*d-b*c)/b^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+2*d^3*(a*d-b*c)/b*c*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)-2*d^3*c/b*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)+d^3*c^2*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b))","B"
35,1,419,174,0.029000," ","int(x*sin(d*x+c)/(b*x+a)^3,x)","\frac{-\frac{d^{3} \left(d a -c b \right) \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{b}+\frac{d^{3} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{b}-d^{3} c \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{d^{2}}"," ",0,"1/d^2*(-d^3*(a*d-b*c)/b*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)+d^3/b*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)-d^3*c*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b))","B"
36,1,145,98,0.027000," ","int(sin(d*x+c)/(b*x+a)^3,x)","d^{2} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)"," ",0,"d^2*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)","A"
37,1,359,259,0.030000," ","int(sin(d*x+c)/x/(b*x+a)^3,x)","-\frac{d^{2} b \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{a}-\frac{b \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{a^{3}}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{3}}-\frac{d b \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{a^{2}}"," ",0,"-d^2*b/a*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)-b/a^3*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+1/a^3*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-d*b/a^2*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b)","A"
38,1,405,297,0.032000," ","int(sin(d*x+c)/x^2/(b*x+a)^3,x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a^{3}}+\frac{d \,b^{2} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{a^{2}}+\frac{3 b^{2} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d \,a^{4}}-\frac{3 b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d \,a^{4}}+\frac{2 b^{2} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{a^{3}}\right)"," ",0,"d*(1/a^3*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+d*b^2/a^2*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)+3/d*b^2/a^4*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)-3/d/a^4*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+2*b^2/a^3*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","A"
39,1,466,367,0.031000," ","int(sin(d*x+c)/x^3/(b*x+a)^3,x)","d^{2} \left(-\frac{3 b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d \,a^{4}}-\frac{b^{3} \left(-\frac{\sin \left(d x +c \right)}{2 \left(\left(d x +c \right) b +d a -c b \right)^{2} b}+\frac{-\frac{\cos \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}-\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}}{b}}{2 b}\right)}{a^{3}}-\frac{6 b^{3} \left(\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}-\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}\right)}{d^{2} a^{5}}+\frac{-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}}{a^{3}}+\frac{6 b^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{2} a^{5}}-\frac{3 b^{3} \left(-\frac{\sin \left(d x +c \right)}{\left(\left(d x +c \right) b +d a -c b \right) b}+\frac{\frac{\Si \left(d x +c +\frac{d a -c b}{b}\right) \sin \left(\frac{d a -c b}{b}\right)}{b}+\frac{\Ci \left(d x +c +\frac{d a -c b}{b}\right) \cos \left(\frac{d a -c b}{b}\right)}{b}}{b}\right)}{d \,a^{4}}\right)"," ",0,"d^2*(-3/d/a^4*b*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-b^3/a^3*(-1/2*sin(d*x+c)/((d*x+c)*b+d*a-c*b)^2/b+1/2*(-cos(d*x+c)/((d*x+c)*b+d*a-c*b)/b-(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)/b)/b)-6/d^2*b^3/a^5*(Si(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b-Ci(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b)+1/a^3*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+6/d^2/a^5*b^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-3/d*b^3/a^4*(-sin(d*x+c)/((d*x+c)*b+d*a-c*b)/b+(Si(d*x+c+(a*d-b*c)/b)*sin((a*d-b*c)/b)/b+Ci(d*x+c+(a*d-b*c)/b)*cos((a*d-b*c)/b)/b)/b))","A"
40,1,449,141,0.023000," ","int(x^3*(b*x^2+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{5 b c \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+a \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{10 b \,c^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-3 a c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)-\frac{10 b \,c^{3} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+3 a \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{5 b \,c^{4} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+a \,c^{3} \cos \left(d x +c \right)+\frac{b \,c^{5} \cos \left(d x +c \right)}{d^{2}}}{d^{4}}"," ",0,"1/d^4*(1/d^2*b*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))-5/d^2*b*c*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+a*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+10/d^2*b*c^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3*a*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-10/d^2*b*c^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3*a*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+5/d^2*b*c^4*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c^3*cos(d*x+c)+1/d^2*b*c^5*cos(d*x+c))","B"
41,1,302,111,0.022000," ","int(x^2*(b*x^2+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}-\frac{4 b c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+a \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+\frac{6 b \,c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}-2 a c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{4 b \,c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-a \,c^{2} \cos \left(d x +c \right)-\frac{b \,c^{4} \cos \left(d x +c \right)}{d^{2}}}{d^{3}}"," ",0,"1/d^3*(1/d^2*b*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-4/d^2*b*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6/d^2*b*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*a*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d^2*b*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*c^2*cos(d*x+c)-1/d^2*b*c^4*cos(d*x+c))","B"
42,1,181,80,0.023000," ","int(x*(b*x^2+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{3 b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+a \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{3 b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+a c \cos \left(d x +c \right)+\frac{b \,c^{3} \cos \left(d x +c \right)}{d^{2}}}{d^{2}}"," ",0,"1/d^2*(1/d^2*b*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3/d^2*b*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+3/d^2*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c*cos(d*x+c)+1/d^2*b*c^3*cos(d*x+c))","B"
43,1,99,53,0.023000," ","int((b*x^2+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}-\frac{2 b c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-a \cos \left(d x +c \right)-\frac{b \,c^{2} \cos \left(d x +c \right)}{d^{2}}}{d}"," ",0,"1/d*(1/d^2*b*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2/d^2*b*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*cos(d*x+c)-1/d^2*b*c^2*cos(d*x+c))","A"
44,1,60,41,0.026000," ","int((b*x^2+a)*sin(d*x+c)/x,x)","\frac{\left(1+c \right) b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+\frac{2 c b \cos \left(d x +c \right)}{d^{2}}+a \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"(1+c)/d^2*b*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+2*c/d^2*b*cos(d*x+c)+a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
45,1,48,44,0.033000," ","int((b*x^2+a)*sin(d*x+c)/x^2,x)","d \left(-\frac{b \cos \left(d x +c \right)}{d^{2}}+a \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)\right)"," ",0,"d*(-1/d^2*b*cos(d*x+c)+a*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","A"
46,1,73,66,0.034000," ","int((b*x^2+a)*sin(d*x+c)/x^3,x)","d^{2} \left(\frac{b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{2}}+a \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)\right)"," ",0,"d^2*(1/d^2*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+a*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c)))","A"
47,1,102,96,0.033000," ","int((b*x^2+a)*sin(d*x+c)/x^4,x)","d^{3} \left(\frac{b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d^{2}}+a \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)\right)"," ",0,"d^3*(1/d^2*b*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+a*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c)))","A"
48,1,131,129,0.033000," ","int((b*x^2+a)*sin(d*x+c)/x^5,x)","d^{4} \left(\frac{b \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)}{d^{2}}+a \left(-\frac{\sin \left(d x +c \right)}{4 x^{4} d^{4}}-\frac{\cos \left(d x +c \right)}{12 x^{3} d^{3}}+\frac{\sin \left(d x +c \right)}{24 x^{2} d^{2}}+\frac{\cos \left(d x +c \right)}{24 x d}+\frac{\Si \left(d x \right) \cos \left(c \right)}{24}+\frac{\Ci \left(d x \right) \sin \left(c \right)}{24}\right)\right)"," ",0,"d^4*(1/d^2*b*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+a*(-1/4*sin(d*x+c)/x^4/d^4-1/12*cos(d*x+c)/x^3/d^3+1/24*sin(d*x+c)/x^2/d^2+1/24*cos(d*x+c)/x/d+1/24*Si(d*x)*cos(c)+1/24*Ci(d*x)*sin(c)))","A"
49,1,746,236,0.023000," ","int(x^2*(b*x^2+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{6} \cos \left(d x +c \right)+6 \left(d x +c \right)^{5} \sin \left(d x +c \right)+30 \left(d x +c \right)^{4} \cos \left(d x +c \right)-120 \left(d x +c \right)^{3} \sin \left(d x +c \right)-360 \left(d x +c \right)^{2} \cos \left(d x +c \right)+720 \cos \left(d x +c \right)+720 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-\frac{6 b^{2} c \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+\frac{2 a b \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+\frac{15 b^{2} c^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-\frac{8 a b c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{20 b^{2} c^{3} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+a^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+\frac{12 a b \,c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+\frac{15 b^{2} c^{4} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-2 a^{2} c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{8 a b \,c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{6 b^{2} c^{5} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-a^{2} c^{2} \cos \left(d x +c \right)-\frac{2 a b \,c^{4} \cos \left(d x +c \right)}{d^{2}}-\frac{b^{2} c^{6} \cos \left(d x +c \right)}{d^{4}}}{d^{3}}"," ",0,"1/d^3*(1/d^4*b^2*(-(d*x+c)^6*cos(d*x+c)+6*(d*x+c)^5*sin(d*x+c)+30*(d*x+c)^4*cos(d*x+c)-120*(d*x+c)^3*sin(d*x+c)-360*(d*x+c)^2*cos(d*x+c)+720*cos(d*x+c)+720*(d*x+c)*sin(d*x+c))-6/d^4*b^2*c*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))+2/d^2*a*b*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+15/d^4*b^2*c^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-8/d^2*a*b*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-20/d^4*b^2*c^3*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+12/d^2*a*b*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+15/d^4*b^2*c^4*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*a^2*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-8/d^2*a*b*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6/d^4*b^2*c^5*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a^2*c^2*cos(d*x+c)-2/d^2*a*b*c^4*cos(d*x+c)-1/d^4*b^2*c^6*cos(d*x+c))","B"
50,1,514,185,0.024000," ","int(x*(b*x^2+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-\frac{5 b^{2} c \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}+\frac{2 a b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+\frac{10 b^{2} c^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-\frac{6 a b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}-\frac{10 b^{2} c^{3} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}+a^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{6 a b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+\frac{5 b^{2} c^{4} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+a^{2} c \cos \left(d x +c \right)+\frac{2 a b \,c^{3} \cos \left(d x +c \right)}{d^{2}}+\frac{b^{2} c^{5} \cos \left(d x +c \right)}{d^{4}}}{d^{2}}"," ",0,"1/d^2*(1/d^4*b^2*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))-5/d^4*b^2*c*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+2/d^2*a*b*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+10/d^4*b^2*c^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-6/d^2*a*b*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-10/d^4*b^2*c^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+6/d^2*a*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+5/d^4*b^2*c^4*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a^2*c*cos(d*x+c)+2/d^2*a*b*c^3*cos(d*x+c)+1/d^4*b^2*c^5*cos(d*x+c))","B"
51,1,336,138,0.023000," ","int((b*x^2+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-\frac{4 b^{2} c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+\frac{2 a b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{2}}+\frac{6 b^{2} c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-\frac{4 a b c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}-\frac{4 b^{2} c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-a^{2} \cos \left(d x +c \right)-\frac{2 a b \,c^{2} \cos \left(d x +c \right)}{d^{2}}-\frac{b^{2} c^{4} \cos \left(d x +c \right)}{d^{4}}}{d}"," ",0,"1/d*(1/d^4*b^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-4/d^4*b^2*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+2/d^2*a*b*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6/d^4*b^2*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-4/d^2*a*b*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d^4*b^2*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a^2*cos(d*x+c)-2/d^2*a*b*c^2*cos(d*x+c)-1/d^4*b^2*c^4*cos(d*x+c))","B"
52,1,236,111,0.031000," ","int((b*x^2+a)^2*sin(d*x+c)/x,x)","\frac{\left(c^{3}+c^{2}+c +1\right) b^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-\frac{4 b^{2} c \left(c^{2}+c +1\right) \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}+\frac{2 \left(1+c \right) a b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{2}}+\frac{6 \left(1+c \right) b^{2} c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+\frac{4 c a b \cos \left(d x +c \right)}{d^{2}}+\frac{4 c^{3} b^{2} \cos \left(d x +c \right)}{d^{4}}+a^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"(c^3+c^2+c+1)/d^4*b^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-4*b^2*c*(c^2+c+1)/d^4*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+2*(1+c)/d^2*a*b*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+6*(1+c)/d^4*b^2*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+4*c/d^2*a*b*cos(d*x+c)+4*c^3/d^4*b^2*cos(d*x+c)+a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","B"
53,1,156,97,0.047000," ","int((b*x^2+a)^2*sin(d*x+c)/x^2,x)","d \left(\frac{\left(3 c^{2}+2 c +1\right) b^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{4}}-\frac{4 b^{2} c \left(1+2 c \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}-\frac{2 a b \cos \left(d x +c \right)}{d^{2}}-\frac{6 c^{2} b^{2} \cos \left(d x +c \right)}{d^{4}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)\right)"," ",0,"d*((3*c^2+2*c+1)/d^4*b^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-4*b^2*c*(1+2*c)/d^4*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-2/d^2*a*b*cos(d*x+c)-6*c^2/d^4*b^2*cos(d*x+c)+a^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","A"
54,1,124,106,0.043000," ","int((b*x^2+a)^2*sin(d*x+c)/x^3,x)","d^{2} \left(\frac{\left(1+3 c \right) b^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{4}}+\frac{4 c \,b^{2} \cos \left(d x +c \right)}{d^{4}}+\frac{2 a b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{2}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)\right)"," ",0,"d^2*((1+3*c)/d^4*b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+4*c/d^4*b^2*cos(d*x+c)+2/d^2*a*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+a^2*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c)))","A"
55,1,120,124,0.046000," ","int((b*x^2+a)^2*sin(d*x+c)/x^4,x)","d^{3} \left(-\frac{b^{2} \cos \left(d x +c \right)}{d^{4}}+\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d^{2}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)\right)"," ",0,"d^3*(-1/d^4*b^2*cos(d*x+c)+2/d^2*a*b*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+a^2*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c)))","A"
56,1,157,165,0.045000," ","int((b*x^2+a)^2*sin(d*x+c)/x^5,x)","d^{4} \left(\frac{b^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{4}}+\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)}{d^{2}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{4 x^{4} d^{4}}-\frac{\cos \left(d x +c \right)}{12 x^{3} d^{3}}+\frac{\sin \left(d x +c \right)}{24 x^{2} d^{2}}+\frac{\cos \left(d x +c \right)}{24 x d}+\frac{\Si \left(d x \right) \cos \left(c \right)}{24}+\frac{\Ci \left(d x \right) \sin \left(c \right)}{24}\right)\right)"," ",0,"d^4*(1/d^4*b^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+2/d^2*a*b*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+a^2*(-1/4*sin(d*x+c)/x^4/d^4-1/12*cos(d*x+c)/x^3/d^3+1/24*sin(d*x+c)/x^2/d^2+1/24*cos(d*x+c)/x/d+1/24*Si(d*x)*cos(c)+1/24*Ci(d*x)*sin(c)))","A"
57,1,1656,217,0.075000," ","int(x^4*sin(d*x+c)/(b*x^2+a),x)","\frac{\frac{b \,d^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+2 c b \,d^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+a \,d^{4} \cos \left(d x +c \right)-3 b \,c^{2} d^{2} \cos \left(d x +c \right)}{b^{2}}-\frac{d^{2} \left(4 \left(d \sqrt{-a b}+c b \right) a c \,d^{2}-4 \left(d \sqrt{-a b}+c b \right) b \,c^{3}-a^{2} d^{4}+2 a b \,c^{2} d^{2}+3 b^{2} c^{4}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b^{3}}-\frac{d^{2} \left(-4 \left(d \sqrt{-a b}-c b \right) a c \,d^{2}+4 \left(d \sqrt{-a b}-c b \right) b \,c^{3}-a^{2} d^{4}+2 a b \,c^{2} d^{2}+3 b^{2} c^{4}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b^{3}}+\frac{-4 c \,d^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+8 c^{2} d^{2} \cos \left(d x +c \right)}{b}+\frac{2 c \,d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}-3 \left(d \sqrt{-a b}+c b \right) c^{2}+2 a c \,d^{2}+2 b \,c^{3}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{\left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b^{2}}+\frac{2 c \,d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+3 \left(d \sqrt{-a b}-c b \right) c^{2}+2 a c \,d^{2}+2 b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{\left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b^{2}}-\frac{6 c^{2} d^{2} \cos \left(d x +c \right)}{b}+\frac{3 c^{2} d^{2} \left(2 \left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{\left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b^{2}}+\frac{3 c^{2} d^{2} \left(-2 \left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{\left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b^{2}}-\frac{2 c^{3} d^{2} \left(d \sqrt{-a b}+c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{2 c^{3} d^{2} \left(d \sqrt{-a b}-c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+c^{4} d^{2} \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{d^{5}}"," ",0,"1/d^5*((b*d^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+2*c*b*d^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*d^4*cos(d*x+c)-3*b*c^2*d^2*cos(d*x+c))/b^2-1/2*d^2*(4*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-4*(d*(-a*b)^(1/2)+c*b)*b*c^3-a^2*d^4+2*a*b*c^2*d^2+3*b^2*c^4)/((d*(-a*b)^(1/2)+c*b)/b-c)/b^3*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2*d^2*(-4*(d*(-a*b)^(1/2)-c*b)*a*c*d^2+4*(d*(-a*b)^(1/2)-c*b)*b*c^3-a^2*d^4+2*a*b*c^2*d^2+3*b^2*c^4)/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b^3*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+(-4*c*d^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+8*c^2*d^2*cos(d*x+c))/b+2*c*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2-3*(d*(-a*b)^(1/2)+c*b)*c^2+2*a*c*d^2+2*b*c^3)/((d*(-a*b)^(1/2)+c*b)/b-c)/b^2*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+2*c*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+3*(d*(-a*b)^(1/2)-c*b)*c^2+2*a*c*d^2+2*b*c^3)/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-6*c^2*d^2/b*cos(d*x+c)+3*c^2*d^2*(2*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/((d*(-a*b)^(1/2)+c*b)/b-c)/b^2*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+3*c^2*d^2*(-2*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-2*c^3*d^2*(d*(-a*b)^(1/2)+c*b)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+2*c^3*d^2*(d*(-a*b)^(1/2)-c*b)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+c^4*d^2*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","B"
58,1,1184,169,0.056000," ","int(x^3*sin(d*x+c)/(b*x^2+a),x)","\frac{\frac{d^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-2 c \,d^{2} \cos \left(d x +c \right)}{b}-\frac{d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}-3 \left(d \sqrt{-a b}+c b \right) c^{2}+2 a c \,d^{2}+2 b \,c^{3}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+3 \left(d \sqrt{-a b}-c b \right) c^{2}+2 a c \,d^{2}+2 b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{3 c \,d^{2} \cos \left(d x +c \right)}{b}-\frac{3 c \,d^{2} \left(2 \left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{3 c \,d^{2} \left(-2 \left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{3 c^{2} d^{2} \left(d \sqrt{-a b}+c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{3 c^{2} d^{2} \left(d \sqrt{-a b}-c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-c^{3} d^{2} \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{d^{4}}"," ",0,"1/d^4*((d^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-2*c*d^2*cos(d*x+c))/b-1/2*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2-3*(d*(-a*b)^(1/2)+c*b)*c^2+2*a*c*d^2+2*b*c^3)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+3*(d*(-a*b)^(1/2)-c*b)*c^2+2*a*c*d^2+2*b*c^3)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+3*c*d^2/b*cos(d*x+c)-3/2*c*d^2*(2*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-3/2*c*d^2*(-2*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+3/2*c^2*d^2*(d*(-a*b)^(1/2)+c*b)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-3/2*c^2*d^2*(d*(-a*b)^(1/2)-c*b)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-c^3*d^2*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","B"
59,1,798,171,0.048000," ","int(x^2*sin(d*x+c)/(b*x^2+a),x)","\frac{-\frac{d^{2} \cos \left(d x +c \right)}{b}+\frac{d^{2} \left(2 \left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-2 \left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{c \,d^{2} \left(d \sqrt{-a b}+c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{c \,d^{2} \left(d \sqrt{-a b}-c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+c^{2} d^{2} \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{d^{3}}"," ",0,"1/d^3*(-d^2/b*cos(d*x+c)+1/2*d^2*(2*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2*d^2*(-2*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-c*d^2*(d*(-a*b)^(1/2)+c*b)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+c*d^2*(d*(-a*b)^(1/2)-c*b)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+c^2*d^2*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","B"
60,1,494,137,0.038000," ","int(x*sin(d*x+c)/(b*x^2+a),x)","\frac{\frac{d^{2} \left(d \sqrt{-a b}+c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(d \sqrt{-a b}-c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-d^{2} c \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{d^{2}}"," ",0,"1/d^2*(1/2*d^2*(d*(-a*b)^(1/2)+c*b)/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2*d^2*(d*(-a*b)^(1/2)-c*b)/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-d^2*c*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","B"
61,1,229,157,0.032000," ","int(sin(d*x+c)/(b*x^2+a),x)","d \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)"," ",0,"d*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)))","A"
62,1,200,157,0.040000," ","int(sin(d*x+c)/x/(b*x^2+a),x)","-\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 a}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 a}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a}"," ",0,"-1/2/a*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2/a*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
63,1,270,194,0.037000," ","int(sin(d*x+c)/x^2/(b*x^2+a),x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a}-\frac{b \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{a}\right)"," ",0,"d*(1/a*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-b/a*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","A"
64,1,259,222,0.056000," ","int(sin(d*x+c)/x^3/(b*x^2+a),x)","d^{2} \left(-\frac{\sin \left(d x +c \right)}{2 a \,x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 a x d}+\frac{b \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 d^{2} a^{2}}+\frac{b \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 d^{2} a^{2}}-\frac{\left(a \,d^{2}+2 b \right) \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{2 a^{2} d^{2}}\right)"," ",0,"d^2*(-1/2*sin(d*x+c)/a/x^2/d^2-1/2*cos(d*x+c)/a/x/d+1/2*b/d^2/a^2*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2*b/d^2/a^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/2/a^2*(a*d^2+2*b)/d^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c)))","A"
65,1,3453,350,0.141000," ","int(x^4*sin(d*x+c)/(b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"1/d^5*(-d^4/b^2*cos(d*x+c)+sin(d*x+c)*(1/2*d^2*(a^2*d^4-6*a*b*c^2*d^2+b^2*c^4)/a*(d*x+c)+1/2*c*d^2*(3*a^2*d^4+2*a*b*c^2*d^2-b^2*c^4)/a)/b^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4*d^2*(8*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-3*a^2*d^4-2*a*b*c^2*d^2+b^2*c^4)/a/((d*(-a*b)^(1/2)+c*b)/b-c)/b^3*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4*d^2*(-8*(d*(-a*b)^(1/2)-c*b)*a*c*d^2-3*a^2*d^4-2*a*b*c^2*d^2+b^2*c^4)/a/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b^3*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4*d^2*((d*(-a*b)^(1/2)+c*b)/b*a^2*d^4-6*(d*(-a*b)^(1/2)+c*b)*a*c^2*d^2+(d*(-a*b)^(1/2)+c*b)*b*c^4+3*a^2*c*d^4+2*a*b*c^3*d^2-b^2*c^5)/a/((d*(-a*b)^(1/2)+c*b)/b-c)/b^3*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a^2*d^4+6*(d*(-a*b)^(1/2)-c*b)*a*c^2*d^2-(d*(-a*b)^(1/2)-c*b)*b*c^4+3*a^2*c*d^4+2*a*b*c^3*d^2-b^2*c^5)/a/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b^3*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(2*c^2*d^2*(3*a*d^2-b*c^2)/a/b*(d*x+c)-2*c*d^2*(a^2*d^4-b^2*c^4)/a/b^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-c*d^2*(2*(d*(-a*b)^(1/2)+c*b)/b*a*d^2+a*c*d^2+b*c^3)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-c*d^2*(-2*(d*(-a*b)^(1/2)-c*b)/b*a*d^2+a*c*d^2+b*c^3)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-c*d^2*(3*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-(d*(-a*b)^(1/2)+c*b)*b*c^3-a^2*d^4+b^2*c^4)/a/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-c*d^2*(-3*(d*(-a*b)^(1/2)-c*b)*a*c*d^2+(d*(-a*b)^(1/2)-c*b)*b*c^3-a^2*d^4+b^2*c^4)/a/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(-3*c^2*d^2*(a*d^2-b*c^2)/a/b*(d*x+c)-3*c^3*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+3/2*c^2*d^2*(a*d^2+b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+3/2*c^2*d^2*(a*d^2+b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+3/2*c^2*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2-(d*(-a*b)^(1/2)+c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+3/2*c^2*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+(d*(-a*b)^(1/2)-c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(-2*c^4*d^2/a*(d*x+c)+2*c^3*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-c^4*d^2/a/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-c^4*d^2/a/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+c^3*d^2*((d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+c^3*d^2*(-(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+c^4*d^4*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
66,1,2563,331,0.108000," ","int(x^3*sin(d*x+c)/(b*x^2+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(-\frac{c \,d^{2} \left(3 a \,d^{2}-b \,c^{2}\right) \left(d x +c \right)}{2 a b}+\frac{d^{2} \left(a^{2} d^{4}-b^{2} c^{4}\right)}{2 a \,b^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{d^{2} \left(\frac{2 \left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}+a c \,d^{2}+b \,c^{3}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-\frac{2 \left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+a c \,d^{2}+b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{d^{2} \left(3 \left(d \sqrt{-a b}+c b \right) a c \,d^{2}-\left(d \sqrt{-a b}+c b \right) b \,c^{3}-a^{2} d^{4}+b^{2} c^{4}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{3} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-3 \left(d \sqrt{-a b}-c b \right) a c \,d^{2}+\left(d \sqrt{-a b}-c b \right) b \,c^{3}-a^{2} d^{4}+b^{2} c^{4}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{3} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{\sin \left(d x +c \right) \left(\frac{3 c \,d^{2} \left(a \,d^{2}-b \,c^{2}\right) \left(d x +c \right)}{2 a b}+\frac{3 c^{2} d^{2} \left(a \,d^{2}+b \,c^{2}\right)}{2 a b}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}-\frac{3 c \,d^{2} \left(a \,d^{2}+b \,c^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{3 c \,d^{2} \left(a \,d^{2}+b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 c \,d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}-\left(d \sqrt{-a b}+c b \right) c^{2}+a c \,d^{2}+b \,c^{3}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{3 c \,d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+\left(d \sqrt{-a b}-c b \right) c^{2}+a c \,d^{2}+b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{\sin \left(d x +c \right) \left(\frac{3 c^{3} d^{2} \left(d x +c \right)}{2 a}-\frac{3 c^{2} d^{2} \left(a \,d^{2}+b \,c^{2}\right)}{2 a b}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{3 c^{3} d^{2} \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a b \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{3 c^{3} d^{2} \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a b \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 c^{2} d^{2} \left(\left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{3 c^{2} d^{2} \left(-\left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-c^{3} d^{4} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)}{d^{4}}"," ",0,"1/d^4*(sin(d*x+c)*(-1/2*c*d^2*(3*a*d^2-b*c^2)/a/b*(d*x+c)+1/2*d^2*(a^2*d^4-b^2*c^4)/a/b^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4*d^2*(2*(d*(-a*b)^(1/2)+c*b)/b*a*d^2+a*c*d^2+b*c^3)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4*d^2*(-2*(d*(-a*b)^(1/2)-c*b)/b*a*d^2+a*c*d^2+b*c^3)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/4*d^2*(3*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-(d*(-a*b)^(1/2)+c*b)*b*c^3-a^2*d^4+b^2*c^4)/a/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+1/4*d^2*(-3*(d*(-a*b)^(1/2)-c*b)*a*c*d^2+(d*(-a*b)^(1/2)-c*b)*b*c^3-a^2*d^4+b^2*c^4)/a/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(3/2*c*d^2*(a*d^2-b*c^2)/a/b*(d*x+c)+3/2*c^2*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-3/4*c*d^2*(a*d^2+b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-3/4*c*d^2*(a*d^2+b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/4*c*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2-(d*(-a*b)^(1/2)+c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/4*c*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+(d*(-a*b)^(1/2)-c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(3/2*c^3*d^2/a*(d*x+c)-3/2*c^2*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+3/4*c^3*d^2/a/b/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+3/4*c^3*d^2/a/b/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/4*c^2*d^2*((d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/4*c^2*d^2*(-(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-c^3*d^4*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
67,1,1804,318,0.088000," ","int(x^2*sin(d*x+c)/(b*x^2+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(-\frac{d^{2} \left(a \,d^{2}-b \,c^{2}\right) \left(d x +c \right)}{2 a b}-\frac{c \,d^{2} \left(a \,d^{2}+b \,c^{2}\right)}{2 a b}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{d^{2} \left(a \,d^{2}+b \,c^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(a \,d^{2}+b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}-\left(d \sqrt{-a b}+c b \right) c^{2}+a c \,d^{2}+b \,c^{3}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+\left(d \sqrt{-a b}-c b \right) c^{2}+a c \,d^{2}+b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{\sin \left(d x +c \right) \left(-\frac{c^{2} d^{2} \left(d x +c \right)}{a}+\frac{c \,d^{2} \left(a \,d^{2}+b \,c^{2}\right)}{a b}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}-\frac{c^{2} d^{2} \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 a b \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{c^{2} d^{2} \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 a b \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{c \,d^{2} \left(\left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{2 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{c \,d^{2} \left(-\left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{2 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+c^{2} d^{4} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)}{d^{3}}"," ",0,"1/d^3*(sin(d*x+c)*(-1/2*d^2*(a*d^2-b*c^2)/a/b*(d*x+c)-1/2*c*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4*d^2*(a*d^2+b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4*d^2*(a*d^2+b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/4*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2-(d*(-a*b)^(1/2)+c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+1/4*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+(d*(-a*b)^(1/2)-c*b)*c^2+a*c*d^2+b*c^3)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+sin(d*x+c)*(-c^2*d^2/a*(d*x+c)+c*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-1/2*c^2*d^2/a/b/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2*c^2*d^2/a/b/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/2*c*d^2*((d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+1/2*c*d^2*(-(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+c^2*d^4*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
68,1,1109,181,0.066000," ","int(x*sin(d*x+c)/(b*x^2+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(\frac{c \,d^{2} \left(d x +c \right)}{2 a}-\frac{d^{2} \left(a \,d^{2}+b \,c^{2}\right)}{2 a b}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{c \,d^{2} \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a b \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{c \,d^{2} \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a b \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{d^{2} \left(\left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a \,b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(-\left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a \,b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-c \,d^{4} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)}{d^{2}}"," ",0,"1/d^2*(sin(d*x+c)*(1/2*c*d^2/a*(d*x+c)-1/2*d^2*(a*d^2+b*c^2)/a/b)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4*c*d^2/a/b/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4*c*d^2/a/b/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4*d^2*((d*(-a*b)^(1/2)+c*b)*c-a*d^2-b*c^2)/a/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4*d^2*(-(d*(-a*b)^(1/2)-c*b)*c-a*d^2-b*c^2)/a/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-c*d^4*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
69,1,495,364,0.049000," ","int(sin(d*x+c)/(b*x^2+a)^2,x)","d^{3} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)"," ",0,"d^3*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))","A"
70,1,482,337,0.057000," ","int(sin(d*x+c)/x/(b*x^2+a)^2,x)","\frac{\sin \left(d x +c \right) d^{2}}{2 a \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}-\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 a^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 a^{2}}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{2}}-\frac{d^{2} \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{4 a b \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{4 a b \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}"," ",0,"1/2*sin(d*x+c)*d^2/a/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-1/2/a^2*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/2/a^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-1/4*d^2/a/b/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4*d^2/a/b/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))","A"
71,1,769,389,0.053000," ","int(sin(d*x+c)/x^2/(b*x^2+a)^2,x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a^{2}}-\frac{b \,d^{2} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)}{a}-\frac{b \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{a^{2}}\right)"," ",0,"d*(1/a^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-1/a*b*d^2*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))-1/a^2*b*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","A"
72,1,3391,374,0.153000," ","int(x^3*sin(d*x+c)/(b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"1/d^4*(1/8*sin(d*x+c)*d^2*(3*(d*x+c)^3*a*b^2*c*d^2+3*(d*x+c)^3*b^3*c^3-4*(d*x+c)^2*a^2*b*d^4-9*(d*x+c)^2*a*b^2*c^2*d^2-9*(d*x+c)^2*b^3*c^4+5*(d*x+c)*a^2*b*c*d^4+14*(d*x+c)*a*b^2*c^3*d^2+9*(d*x+c)*b^3*c^5-2*a^3*d^6-7*a^2*b*c^2*d^4-8*a*b^2*c^4*d^2-3*b^3*c^6)/a^2/b^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2-1/8*cos(d*x+c)*d^4*((d*x+c)*a*d^2-3*(d*x+c)*b*c^2+2*a*c*d^2+2*b*c^3)/a/b^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-1/16*d^2*((d*(-a*b)^(1/2)+c*b)/b*a^2*d^4-3*(d*(-a*b)^(1/2)+c*b)*a*c^2*d^2+2*a^2*c*d^4+2*a*b*c^3*d^2-3*a*b*c*d^2-3*b^2*c^3)/a^2/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/16*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a^2*d^4+3*(d*(-a*b)^(1/2)-c*b)*a*c^2*d^2+2*a^2*c*d^4+2*a*b*c^3*d^2-3*a*b*c*d^2-3*b^2*c^3)/a^2/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16*d^2*((d*(-a*b)^(1/2)+c*b)*a*c*d^2+(d*(-a*b)^(1/2)+c*b)*b*c^3-a^2*d^4-2*a*b*c^2*d^2-b^2*c^4)/a^2/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16*d^2*(-(d*(-a*b)^(1/2)-c*b)*a*c*d^2-(d*(-a*b)^(1/2)-c*b)*b*c^3-a^2*d^4-2*a*b*c^2*d^2-b^2*c^4)/a^2/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-3/8*sin(d*x+c)*c*d^2*((d*x+c)^3*a*b*d^2+3*(d*x+c)^3*b^2*c^2-3*(d*x+c)^2*a*b*c*d^2-9*(d*x+c)^2*b^2*c^3-(d*x+c)*a^2*d^4+8*(d*x+c)*a*b*c^2*d^2+9*(d*x+c)*b^2*c^4-3*a^2*c*d^4-6*a*b*c^3*d^2-3*b^2*c^5)/a^2/b/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2-3/8*cos(d*x+c)*c*d^4*(2*(d*x+c)*b*c-a*d^2-b*c^2)/a/b^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-3/16*c*d^2*(2*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-a^2*d^4-a*b*c^2*d^2+a*b*d^2+3*c^2*b^2)/a^2/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-3/16*c*d^2*(-2*(d*(-a*b)^(1/2)-c*b)*a*c*d^2-a^2*d^4-a*b*c^2*d^2+a*b*d^2+3*c^2*b^2)/a^2/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+3/16*c*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2+3*(d*(-a*b)^(1/2)+c*b)*c^2-3*a*c*d^2-3*b*c^3)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+3/16*c*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2-3*(d*(-a*b)^(1/2)-c*b)*c^2-3*a*c*d^2-3*b*c^3)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+3/8*sin(d*x+c)*c^2*d^2*(3*c*(d*x+c)^3*b^2-9*b^2*c^2*(d*x+c)^2+5*(d*x+c)*a*b*c*d^2+9*(d*x+c)*b^2*c^3-2*a^2*d^4-5*a*b*c^2*d^2-3*b^2*c^4)/a^2/b/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+3/8*cos(d*x+c)*c^2*d^4/a/b*(d*x+c)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+3/16*c^2*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2+3*c*b)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+3/16*c^2*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+3*c*b)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16*c^2*d^2*(3*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16*c^2*d^2*(-3*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-d^6*c^3*(1/8*sin(d*x+c)*(3*(d*x+c)^3*b-9*c*(d*x+c)^2*b+5*(d*x+c)*a*d^2+9*(d*x+c)*b*c^2-5*a*c*d^2-3*b*c^3)/a^2/d^4/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)/a/b/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+3*b)/a^2/b^2/d^4/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+3*b)/a^2/b^2/d^4/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16/a^2/b/d^4*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16/a^2/b/d^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
73,1,2310,574,0.123000," ","int(x^2*sin(d*x+c)/(b*x^2+a)^3,x)","\frac{\frac{\sin \left(d x +c \right) d^{2} \left(\left(d x +c \right)^{3} a b \,d^{2}+3 \left(d x +c \right)^{3} b^{2} c^{2}-3 \left(d x +c \right)^{2} a b c \,d^{2}-9 \left(d x +c \right)^{2} b^{2} c^{3}-\left(d x +c \right) a^{2} d^{4}+8 \left(d x +c \right) a b \,c^{2} d^{2}+9 \left(d x +c \right) b^{2} c^{4}-3 a^{2} c \,d^{4}-6 a b \,c^{3} d^{2}-3 b^{2} c^{5}\right)}{8 a^{2} b \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right) d^{4} \left(2 \left(d x +c \right) b c -a \,d^{2}-b \,c^{2}\right)}{8 a \,b^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{d^{2} \left(2 \left(d \sqrt{-a b}+c b \right) a c \,d^{2}-a^{2} d^{4}-a b \,c^{2} d^{2}+a b \,d^{2}+3 c^{2} b^{2}\right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{3} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-2 \left(d \sqrt{-a b}-c b \right) a c \,d^{2}-a^{2} d^{4}-a b \,c^{2} d^{2}+a b \,d^{2}+3 c^{2} b^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{3} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}+3 \left(d \sqrt{-a b}+c b \right) c^{2}-3 a c \,d^{2}-3 b \,c^{3}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}-3 \left(d \sqrt{-a b}-c b \right) c^{2}-3 a c \,d^{2}-3 b \,c^{3}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{\sin \left(d x +c \right) c \,d^{2} \left(3 c \left(d x +c \right)^{3} b^{2}-9 b^{2} c^{2} \left(d x +c \right)^{2}+5 \left(d x +c \right) a b c \,d^{2}+9 \left(d x +c \right) b^{2} c^{3}-2 a^{2} d^{4}-5 a b \,c^{2} d^{2}-3 b^{2} c^{4}\right)}{4 a^{2} b \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}-\frac{\cos \left(d x +c \right) c \,d^{4} \left(d x +c \right)}{4 a b \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}-\frac{c \,d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}+3 c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{8 a^{2} b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{c \,d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+3 c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{8 a^{2} b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+\frac{c \,d^{2} \left(3 \left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-3 b \,c^{2}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{8 a^{2} b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{c \,d^{2} \left(-3 \left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-3 b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{8 a^{2} b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}+c^{2} d^{6} \left(\frac{\sin \left(d x +c \right) \left(3 \left(d x +c \right)^{3} b -9 c \left(d x +c \right)^{2} b +5 \left(d x +c \right) a \,d^{2}+9 \left(d x +c \right) b \,c^{2}-5 a c \,d^{2}-3 b \,c^{3}\right)}{8 a^{2} d^{4} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right)}{8 a b \,d^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}-\frac{3 \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}\right)}{d^{3}}"," ",0,"1/d^3*(1/8*sin(d*x+c)*d^2*((d*x+c)^3*a*b*d^2+3*(d*x+c)^3*b^2*c^2-3*(d*x+c)^2*a*b*c*d^2-9*(d*x+c)^2*b^2*c^3-(d*x+c)*a^2*d^4+8*(d*x+c)*a*b*c^2*d^2+9*(d*x+c)*b^2*c^4-3*a^2*c*d^4-6*a*b*c^3*d^2-3*b^2*c^5)/a^2/b/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)*d^4*(2*(d*x+c)*b*c-a*d^2-b*c^2)/a/b^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*d^2*(2*(d*(-a*b)^(1/2)+c*b)*a*c*d^2-a^2*d^4-a*b*c^2*d^2+a*b*d^2+3*c^2*b^2)/a^2/b^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*d^2*(-2*(d*(-a*b)^(1/2)-c*b)*a*c*d^2-a^2*d^4-a*b*c^2*d^2+a*b*d^2+3*c^2*b^2)/a^2/b^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/16*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2+3*(d*(-a*b)^(1/2)+c*b)*c^2-3*a*c*d^2-3*b*c^3)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/16*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2-3*(d*(-a*b)^(1/2)-c*b)*c^2-3*a*c*d^2-3*b*c^3)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-1/4*sin(d*x+c)*c*d^2*(3*c*(d*x+c)^3*b^2-9*b^2*c^2*(d*x+c)^2+5*(d*x+c)*a*b*c*d^2+9*(d*x+c)*b^2*c^3-2*a^2*d^4-5*a*b*c^2*d^2-3*b^2*c^4)/a^2/b/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2-1/4*cos(d*x+c)*c*d^4/a/b*(d*x+c)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-1/8*c*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2+3*c*b)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/8*c*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+3*c*b)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/8*c*d^2*(3*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+1/8*c*d^2*(-3*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))+c^2*d^6*(1/8*sin(d*x+c)*(3*(d*x+c)^3*b-9*c*(d*x+c)^2*b+5*(d*x+c)*a*d^2+9*(d*x+c)*b*c^2-5*a*c*d^2-3*b*c^3)/a^2/d^4/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)/a/b/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+3*b)/a^2/b^2/d^4/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+3*b)/a^2/b^2/d^4/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16/a^2/b/d^4*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16/a^2/b/d^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
74,1,1374,398,0.081000," ","int(x*sin(d*x+c)/(b*x^2+a)^3,x)","\frac{\frac{\sin \left(d x +c \right) d^{2} \left(3 c \left(d x +c \right)^{3} b^{2}-9 b^{2} c^{2} \left(d x +c \right)^{2}+5 \left(d x +c \right) a b c \,d^{2}+9 \left(d x +c \right) b^{2} c^{3}-2 a^{2} d^{4}-5 a b \,c^{2} d^{2}-3 b^{2} c^{4}\right)}{8 a^{2} b \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right) d^{4} \left(d x +c \right)}{8 a b \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{d^{2} \left(\frac{\left(d \sqrt{-a b}+c b \right) a \,d^{2}}{b}+3 c b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{d^{2} \left(-\frac{\left(d \sqrt{-a b}-c b \right) a \,d^{2}}{b}+3 c b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{d^{2} \left(3 \left(d \sqrt{-a b}+c b \right) c -a \,d^{2}-3 b \,c^{2}\right) \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{d^{2} \left(-3 \left(d \sqrt{-a b}-c b \right) c -a \,d^{2}-3 b \,c^{2}\right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-c \,d^{6} \left(\frac{\sin \left(d x +c \right) \left(3 \left(d x +c \right)^{3} b -9 c \left(d x +c \right)^{2} b +5 \left(d x +c \right) a \,d^{2}+9 \left(d x +c \right) b \,c^{2}-5 a c \,d^{2}-3 b \,c^{3}\right)}{8 a^{2} d^{4} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right)}{8 a b \,d^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}-\frac{3 \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}\right)}{d^{2}}"," ",0,"1/d^2*(1/8*sin(d*x+c)*d^2*(3*c*(d*x+c)^3*b^2-9*b^2*c^2*(d*x+c)^2+5*(d*x+c)*a*b*c*d^2+9*(d*x+c)*b^2*c^3-2*a^2*d^4-5*a*b*c^2*d^2-3*b^2*c^4)/a^2/b/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)*d^4/a/b*(d*x+c)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*d^2*((d*(-a*b)^(1/2)+c*b)/b*a*d^2+3*c*b)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*d^2*(-(d*(-a*b)^(1/2)-c*b)/b*a*d^2+3*c*b)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/16*d^2*(3*(d*(-a*b)^(1/2)+c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/16*d^2*(-3*(d*(-a*b)^(1/2)-c*b)*c-a*d^2-3*b*c^2)/a^2/b^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))-c*d^6*(1/8*sin(d*x+c)*(3*(d*x+c)^3*b-9*c*(d*x+c)^2*b+5*(d*x+c)*a*d^2+9*(d*x+c)*b*c^2-5*a*c*d^2-3*b*c^3)/a^2/d^4/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)/a/b/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+3*b)/a^2/b^2/d^4/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+3*b)/a^2/b^2/d^4/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16/a^2/b/d^4*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16/a^2/b/d^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))))","B"
75,1,602,652,0.060000," ","int(sin(d*x+c)/(b*x^2+a)^3,x)","d^{5} \left(\frac{\sin \left(d x +c \right) \left(3 \left(d x +c \right)^{3} b -9 c \left(d x +c \right)^{2} b +5 \left(d x +c \right) a \,d^{2}+9 \left(d x +c \right) b \,c^{2}-5 a c \,d^{2}-3 b \,c^{3}\right)}{8 a^{2} d^{4} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right)}{8 a b \,d^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}-\frac{3 \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}\right)"," ",0,"d^5*(1/8*sin(d*x+c)*(3*(d*x+c)^3*b-9*c*(d*x+c)^2*b+5*(d*x+c)*a*d^2+9*(d*x+c)*b*c^2-5*a*c*d^2-3*b*c^3)/a^2/d^4/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)/a/b/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+3*b)/a^2/b^2/d^4/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+3*b)/a^2/b^2/d^4/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16/a^2/b/d^4*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16/a^2/b/d^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))","A"
76,1,584,574,0.066000," ","int(sin(d*x+c)/x/(b*x^2+a)^3,x)","\frac{\sin \left(d x +c \right) d^{2} \left(2 \left(d x +c \right)^{2} b -4 \left(d x +c \right) b c +3 a \,d^{2}+2 b \,c^{2}\right)}{4 a^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}-\frac{\cos \left(d x +c \right) d^{3} x}{8 a^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}-\frac{\left(a \,d^{2}+8 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 b \,a^{3}}-\frac{\left(a \,d^{2}+8 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 b \,a^{3}}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{3}}-\frac{5 d^{2} \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}-\frac{5 d^{2} \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}"," ",0,"1/4*sin(d*x+c)*d^2*(2*(d*x+c)^2*b-4*(d*x+c)*b*c+3*a*d^2+2*b*c^2)/a^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2-1/8*cos(d*x+c)*d^3*x/a^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)-1/16*(a*d^2+8*b)/b/a^3*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))-1/16*(a*d^2+8*b)/b/a^3*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))+1/a^3*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-5/16*d^2/a^2/b/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-5/16*d^2/a^2/b/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b))","A"
77,1,1375,671,0.078000," ","int(sin(d*x+c)/x^2/(b*x^2+a)^3,x)","d \left(\frac{-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a^{3}}-\frac{b \,d^{4} \left(\frac{\sin \left(d x +c \right) \left(3 \left(d x +c \right)^{3} b -9 c \left(d x +c \right)^{2} b +5 \left(d x +c \right) a \,d^{2}+9 \left(d x +c \right) b \,c^{2}-5 a c \,d^{2}-3 b \,c^{3}\right)}{8 a^{2} d^{4} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}+\frac{\cos \left(d x +c \right)}{8 a b \,d^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{\left(a \,d^{2}+3 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b^{2} d^{4} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}-\frac{3 \left(-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}-\frac{3 \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 a^{2} b \,d^{4}}\right)}{a}-\frac{b \,d^{2} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{2 a \,d^{2}}-\frac{c}{2 a \,d^{2}}\right)}{\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}}+\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a \,d^{2} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a \,d^{2} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}-\frac{-\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{4 a b \,d^{2}}-\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)+\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{4 a b \,d^{2}}\right)}{a^{2}}-\frac{b \left(\frac{\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{2 \left(\frac{d \sqrt{-a b}+c b}{b}-c \right) b}+\frac{\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{2 \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right) b}\right)}{a^{3}}\right)"," ",0,"d*(1/a^3*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-1/a*b*d^4*(1/8*sin(d*x+c)*(3*(d*x+c)^3*b-9*c*(d*x+c)^2*b+5*(d*x+c)*a*d^2+9*(d*x+c)*b*c^2-5*a*c*d^2-3*b*c^3)/a^2/d^4/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2+1/8*cos(d*x+c)/a/b/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+3*b)/a^2/b^2/d^4/((d*(-a*b)^(1/2)+c*b)/b-c)*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+3*b)/a^2/b^2/d^4/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-3/16/a^2/b/d^4*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-3/16/a^2/b/d^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))-b*d^2/a^2*(sin(d*x+c)*(1/2/a/d^2*(d*x+c)-1/2*c/a/d^2)/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/4/a/d^2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/4/a/d^2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/4/a/b/d^2*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))-1/4/a/b/d^2*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))-1/a^3*b*(1/2/((d*(-a*b)^(1/2)+c*b)/b-c)/b*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/2/(-(d*(-a*b)^(1/2)-c*b)/b-c)/b*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))))","B"
78,1,701,629,0.080000," ","int(sin(d*x+c)/x^3/(b*x^2+a)^3,x)","d^{2} \left(-\frac{\sin \left(d x +c \right) \left(6 b^{2} \left(d x +c \right)^{4}-24 c \left(d x +c \right)^{3} b^{2}+9 \left(d x +c \right)^{2} a b \,d^{2}+36 b^{2} c^{2} \left(d x +c \right)^{2}-18 \left(d x +c \right) a b c \,d^{2}-24 \left(d x +c \right) b^{2} c^{3}+2 a^{2} d^{4}+9 a b \,c^{2} d^{2}+6 b^{2} c^{4}\right)}{4 a^{3} x^{2} d^{2} \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)^{2}}-\frac{\cos \left(d x +c \right) \left(3 \left(d x +c \right)^{2} b -6 \left(d x +c \right) b c +4 a \,d^{2}+3 b \,c^{2}\right)}{8 a^{3} x d \left(\left(d x +c \right)^{2} b -2 \left(d x +c \right) b c +a \,d^{2}+b \,c^{2}\right)}+\frac{\left(a \,d^{2}+24 b \right) \left(\Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)+\Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)\right)}{16 d^{2} a^{4}}+\frac{\left(a \,d^{2}+24 b \right) \left(\Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)-\Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)\right)}{16 d^{2} a^{4}}-\frac{\left(a \,d^{2}+6 b \right) \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{2 a^{4} d^{2}}+\frac{-\frac{9 \Si \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{16}+\frac{9 \Ci \left(d x +c -\frac{d \sqrt{-a b}+c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}+c b}{b}\right)}{16}}{a^{3} \left(\frac{d \sqrt{-a b}+c b}{b}-c \right)}+\frac{\frac{9 \Si \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \sin \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{16}+\frac{9 \Ci \left(d x +c +\frac{d \sqrt{-a b}-c b}{b}\right) \cos \left(\frac{d \sqrt{-a b}-c b}{b}\right)}{16}}{a^{3} \left(-\frac{d \sqrt{-a b}-c b}{b}-c \right)}\right)"," ",0,"d^2*(-1/4*sin(d*x+c)*(6*b^2*(d*x+c)^4-24*c*(d*x+c)^3*b^2+9*(d*x+c)^2*a*b*d^2+36*b^2*c^2*(d*x+c)^2-18*(d*x+c)*a*b*c*d^2-24*(d*x+c)*b^2*c^3+2*a^2*d^4+9*a*b*c^2*d^2+6*b^2*c^4)/a^3/x^2/d^2/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)^2-1/8*cos(d*x+c)*(3*(d*x+c)^2*b-6*(d*x+c)*b*c+4*a*d^2+3*b*c^2)/a^3/x/d/((d*x+c)^2*b-2*(d*x+c)*b*c+a*d^2+b*c^2)+1/16*(a*d^2+24*b)/d^2/a^4*(Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b))+1/16*(a*d^2+24*b)/d^2/a^4*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)-Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b))-1/2/a^4*(a*d^2+6*b)/d^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+9/16/a^3/((d*(-a*b)^(1/2)+c*b)/b-c)*(-Si(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*sin((d*(-a*b)^(1/2)+c*b)/b)+Ci(d*x+c-(d*(-a*b)^(1/2)+c*b)/b)*cos((d*(-a*b)^(1/2)+c*b)/b))+9/16/a^3/(-(d*(-a*b)^(1/2)-c*b)/b-c)*(Si(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*sin((d*(-a*b)^(1/2)-c*b)/b)+Ci(d*x+c+(d*(-a*b)^(1/2)-c*b)/b)*cos((d*(-a*b)^(1/2)-c*b)/b)))","A"
79,1,556,156,0.023000," ","int(x^3*(b*x^3+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{6} \cos \left(d x +c \right)+6 \left(d x +c \right)^{5} \sin \left(d x +c \right)+30 \left(d x +c \right)^{4} \cos \left(d x +c \right)-120 \left(d x +c \right)^{3} \sin \left(d x +c \right)-360 \left(d x +c \right)^{2} \cos \left(d x +c \right)+720 \cos \left(d x +c \right)+720 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{6 b c \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{15 b \,c^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+a \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{20 b \,c^{3} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-3 a c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)+\frac{15 b \,c^{4} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+3 a \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{6 b \,c^{5} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+a \,c^{3} \cos \left(d x +c \right)-\frac{b \,c^{6} \cos \left(d x +c \right)}{d^{3}}}{d^{4}}"," ",0,"1/d^4*(1/d^3*b*(-(d*x+c)^6*cos(d*x+c)+6*(d*x+c)^5*sin(d*x+c)+30*(d*x+c)^4*cos(d*x+c)-120*(d*x+c)^3*sin(d*x+c)-360*(d*x+c)^2*cos(d*x+c)+720*cos(d*x+c)+720*(d*x+c)*sin(d*x+c))-6/d^3*b*c*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))+15/d^3*b*c^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+a*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-20/d^3*b*c^3*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3*a*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+15/d^3*b*c^4*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3*a*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6/d^3*b*c^5*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c^3*cos(d*x+c)-1/d^3*b*c^6*cos(d*x+c))","B"
80,1,392,126,0.023000," ","int(x^2*(b*x^3+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{5 b c \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+\frac{10 b \,c^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+a \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)-\frac{10 b \,c^{3} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-2 a c \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)+\frac{5 b \,c^{4} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-a \,c^{2} \cos \left(d x +c \right)+\frac{b \,c^{5} \cos \left(d x +c \right)}{d^{3}}}{d^{3}}"," ",0,"1/d^3*(1/d^3*b*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))-5/d^3*b*c*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+10/d^3*b*c^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-10/d^3*b*c^3*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-2*a*c*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+5/d^3*b*c^4*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*c^2*cos(d*x+c)+1/d^3*b*c^5*cos(d*x+c))","B"
81,1,258,95,0.022000," ","int(x*(b*x^3+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{4 b c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{6 b \,c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+a \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{4 b \,c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+a c \cos \left(d x +c \right)-\frac{b \,c^{4} \cos \left(d x +c \right)}{d^{3}}}{d^{2}}"," ",0,"1/d^2*(1/d^3*b*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-4/d^3*b*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+6/d^3*b*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-4/d^3*b*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a*c*cos(d*x+c)-1/d^3*b*c^4*cos(d*x+c))","B"
82,1,159,68,0.023000," ","int((b*x^3+a)*sin(d*x+c),x)","\frac{\frac{b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{3 b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+\frac{3 b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-a \cos \left(d x +c \right)+\frac{b \,c^{3} \cos \left(d x +c \right)}{d^{3}}}{d}"," ",0,"1/d*(1/d^3*b*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-3/d^3*b*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+3/d^3*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a*cos(d*x+c)+1/d^3*b*c^3*cos(d*x+c))","B"
83,1,112,57,0.029000," ","int((b*x^3+a)*sin(d*x+c)/x,x)","\frac{\left(c^{2}+c +1\right) b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{3 c b \left(1+c \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{3 c^{2} b \cos \left(d x +c \right)}{d^{3}}+a \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"(c^2+c+1)/d^3*b*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-3*c*b*(1+c)/d^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-3*c^2/d^3*b*cos(d*x+c)+a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","A"
84,1,79,56,0.037000," ","int((b*x^3+a)*sin(d*x+c)/x^2,x)","d \left(\frac{\left(1+2 c \right) b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{3 c b \cos \left(d x +c \right)}{d^{3}}+a \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)\right)"," ",0,"d*((1+2*c)/d^3*b*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+3*c/d^3*b*cos(d*x+c)+a*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","A"
85,1,65,62,0.039000," ","int((b*x^3+a)*sin(d*x+c)/x^3,x)","d^{2} \left(-\frac{b \cos \left(d x +c \right)}{d^{3}}+a \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)\right)"," ",0,"d^2*(-b*cos(d*x+c)/d^3+a*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c)))","A"
86,1,87,81,0.036000," ","int((b*x^3+a)*sin(d*x+c)/x^4,x)","d^{3} \left(\frac{b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{3}}+a \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)\right)"," ",0,"d^3*(1/d^3*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))+a*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c)))","A"
87,1,822,235,0.025000," ","int(x*(b*x^3+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{7} \cos \left(d x +c \right)+7 \left(d x +c \right)^{6} \sin \left(d x +c \right)+42 \left(d x +c \right)^{5} \cos \left(d x +c \right)-210 \left(d x +c \right)^{4} \sin \left(d x +c \right)-840 \left(d x +c \right)^{3} \cos \left(d x +c \right)+2520 \left(d x +c \right)^{2} \sin \left(d x +c \right)-5040 \sin \left(d x +c \right)+5040 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-\frac{7 b^{2} c \left(-\left(d x +c \right)^{6} \cos \left(d x +c \right)+6 \left(d x +c \right)^{5} \sin \left(d x +c \right)+30 \left(d x +c \right)^{4} \cos \left(d x +c \right)-120 \left(d x +c \right)^{3} \sin \left(d x +c \right)-360 \left(d x +c \right)^{2} \cos \left(d x +c \right)+720 \cos \left(d x +c \right)+720 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+\frac{21 b^{2} c^{2} \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{2 a b \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{35 b^{2} c^{3} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}-\frac{8 a b c \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{35 b^{2} c^{4} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{12 a b \,c^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{21 b^{2} c^{5} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+a^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-\frac{8 a b \,c^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{7 b^{2} c^{6} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+a^{2} c \cos \left(d x +c \right)-\frac{2 a b \,c^{4} \cos \left(d x +c \right)}{d^{3}}+\frac{b^{2} c^{7} \cos \left(d x +c \right)}{d^{6}}}{d^{2}}"," ",0,"1/d^2*(1/d^6*b^2*(-(d*x+c)^7*cos(d*x+c)+7*(d*x+c)^6*sin(d*x+c)+42*(d*x+c)^5*cos(d*x+c)-210*(d*x+c)^4*sin(d*x+c)-840*(d*x+c)^3*cos(d*x+c)+2520*(d*x+c)^2*sin(d*x+c)-5040*sin(d*x+c)+5040*(d*x+c)*cos(d*x+c))-7/d^6*b^2*c*(-(d*x+c)^6*cos(d*x+c)+6*(d*x+c)^5*sin(d*x+c)+30*(d*x+c)^4*cos(d*x+c)-120*(d*x+c)^3*sin(d*x+c)-360*(d*x+c)^2*cos(d*x+c)+720*cos(d*x+c)+720*(d*x+c)*sin(d*x+c))+21/d^6*b^2*c^2*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))+2/d^3*a*b*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-35/d^6*b^2*c^3*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))-8/d^3*a*b*c*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+35/d^6*b^2*c^4*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+12/d^3*a*b*c^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-21/d^6*b^2*c^5*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-8/d^3*a*b*c^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+7/d^6*b^2*c^6*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a^2*c*cos(d*x+c)-2/d^3*a*b*c^4*cos(d*x+c)+1/d^6*b^2*c^7*cos(d*x+c))","B"
88,1,599,188,0.024000," ","int((b*x^3+a)^2*sin(d*x+c),x)","\frac{\frac{b^{2} \left(-\left(d x +c \right)^{6} \cos \left(d x +c \right)+6 \left(d x +c \right)^{5} \sin \left(d x +c \right)+30 \left(d x +c \right)^{4} \cos \left(d x +c \right)-120 \left(d x +c \right)^{3} \sin \left(d x +c \right)-360 \left(d x +c \right)^{2} \cos \left(d x +c \right)+720 \cos \left(d x +c \right)+720 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}-\frac{6 b^{2} c \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{15 b^{2} c^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+\frac{2 a b \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{20 b^{2} c^{3} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-\frac{6 a b c \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}+\frac{15 b^{2} c^{4} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+\frac{6 a b \,c^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{6 b^{2} c^{5} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-a^{2} \cos \left(d x +c \right)+\frac{2 a b \,c^{3} \cos \left(d x +c \right)}{d^{3}}-\frac{b^{2} c^{6} \cos \left(d x +c \right)}{d^{6}}}{d}"," ",0,"1/d*(1/d^6*b^2*(-(d*x+c)^6*cos(d*x+c)+6*(d*x+c)^5*sin(d*x+c)+30*(d*x+c)^4*cos(d*x+c)-120*(d*x+c)^3*sin(d*x+c)-360*(d*x+c)^2*cos(d*x+c)+720*cos(d*x+c)+720*(d*x+c)*sin(d*x+c))-6/d^6*b^2*c*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))+15/d^6*b^2*c^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+2/d^3*a*b*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-20/d^6*b^2*c^3*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))-6/d^3*a*b*c*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+15/d^6*b^2*c^4*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+6/d^3*a*b*c^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6/d^6*b^2*c^5*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-a^2*cos(d*x+c)+2/d^3*a*b*c^3*cos(d*x+c)-1/d^6*b^2*c^6*cos(d*x+c))","B"
89,1,487,161,0.036000," ","int((b*x^3+a)^2*sin(d*x+c)/x,x)","\frac{\left(c^{5}+c^{4}+c^{3}+c^{2}+c +1\right) b^{2} \left(-\left(d x +c \right)^{5} \cos \left(d x +c \right)+5 \left(d x +c \right)^{4} \sin \left(d x +c \right)+20 \left(d x +c \right)^{3} \cos \left(d x +c \right)-60 \left(d x +c \right)^{2} \sin \left(d x +c \right)+120 \sin \left(d x +c \right)-120 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-\frac{6 b^{2} c \left(c^{4}+c^{3}+c^{2}+c +1\right) \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+\frac{15 \left(c^{3}+c^{2}+c +1\right) c^{2} b^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{2 \left(c^{2}+c +1\right) a b \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{3}}-\frac{20 b^{2} c^{3} \left(c^{2}+c +1\right) \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}-\frac{6 c a b \left(1+c \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}+\frac{15 \left(1+c \right) b^{2} c^{4} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-\frac{6 c^{2} a b \cos \left(d x +c \right)}{d^{3}}+\frac{6 c^{5} b^{2} \cos \left(d x +c \right)}{d^{6}}+a^{2} \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)"," ",0,"(c^5+c^4+c^3+c^2+c+1)/d^6*b^2*(-(d*x+c)^5*cos(d*x+c)+5*(d*x+c)^4*sin(d*x+c)+20*(d*x+c)^3*cos(d*x+c)-60*(d*x+c)^2*sin(d*x+c)+120*sin(d*x+c)-120*(d*x+c)*cos(d*x+c))-6*b^2*c*(c^4+c^3+c^2+c+1)/d^6*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+15*(c^3+c^2+c+1)/d^6*c^2*b^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+2*(c^2+c+1)/d^3*a*b*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-20*b^2*c^3*(c^2+c+1)/d^6*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))-6*c*a*b*(1+c)/d^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+15*(1+c)/d^6*b^2*c^4*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6*c^2/d^3*a*b*cos(d*x+c)+6*c^5/d^6*b^2*cos(d*x+c)+a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))","B"
90,1,365,145,0.056000," ","int((b*x^3+a)^2*sin(d*x+c)/x^2,x)","d \left(\frac{\left(5 c^{4}+4 c^{3}+3 c^{2}+2 c +1\right) b^{2} \left(-\left(d x +c \right)^{4} \cos \left(d x +c \right)+4 \left(d x +c \right)^{3} \sin \left(d x +c \right)+12 \left(d x +c \right)^{2} \cos \left(d x +c \right)-24 \cos \left(d x +c \right)-24 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)-\frac{20 b^{2} c^{3} \left(1+2 c \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{2 \left(1+2 c \right) a b \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{3}}-\frac{6 b^{2} c \left(4 c^{3}+3 c^{2}+2 c +1\right) \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+\frac{6 c a b \cos \left(d x +c \right)}{d^{3}}-\frac{15 c^{4} b^{2} \cos \left(d x +c \right)}{d^{6}}+\frac{15 \left(3 c^{2}+2 c +1\right) c^{2} b^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}\right)"," ",0,"d*((5*c^4+4*c^3+3*c^2+2*c+1)/d^6*b^2*(-(d*x+c)^4*cos(d*x+c)+4*(d*x+c)^3*sin(d*x+c)+12*(d*x+c)^2*cos(d*x+c)-24*cos(d*x+c)-24*(d*x+c)*sin(d*x+c))+a^2*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))-20*b^2*c^3*(1+2*c)/d^6*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+2*(1+2*c)/d^3*a*b*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6*b^2*c*(4*c^3+3*c^2+2*c+1)/d^6*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+6*c/d^3*a*b*cos(d*x+c)-15*c^4/d^6*b^2*cos(d*x+c)+15*(3*c^2+2*c+1)/d^6*c^2*b^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c)))","B"
91,1,251,134,0.053000," ","int((b*x^3+a)^2*sin(d*x+c)/x^3,x)","d^{2} \left(\frac{20 c^{3} b^{2} \cos \left(d x +c \right)}{d^{6}}-\frac{2 a b \cos \left(d x +c \right)}{d^{3}}+\frac{\left(10 c^{3}+6 c^{2}+3 c +1\right) b^{2} \left(-\left(d x +c \right)^{3} \cos \left(d x +c \right)+3 \left(d x +c \right)^{2} \sin \left(d x +c \right)-6 \sin \left(d x +c \right)+6 \left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}\right)+\frac{15 \left(1+3 c \right) c^{2} b^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}-\frac{6 b^{2} c \left(6 c^{2}+3 c +1\right) \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}\right)"," ",0,"d^2*(20*c^3/d^6*b^2*cos(d*x+c)-2*a*b*cos(d*x+c)/d^3+(10*c^3+6*c^2+3*c+1)/d^6*b^2*(-(d*x+c)^3*cos(d*x+c)+3*(d*x+c)^2*sin(d*x+c)-6*sin(d*x+c)+6*(d*x+c)*cos(d*x+c))+a^2*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))+15*(1+3*c)/d^6*c^2*b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-6*b^2*c*(6*c^2+3*c+1)/d^6*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c)))","A"
92,1,196,141,0.057000," ","int((b*x^3+a)^2*sin(d*x+c)/x^4,x)","d^{3} \left(\frac{2 a b \left(\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)\right)}{d^{3}}-\frac{15 c^{2} b^{2} \cos \left(d x +c \right)}{d^{6}}+\frac{\left(10 c^{2}+4 c +1\right) b^{2} \left(-\left(d x +c \right)^{2} \cos \left(d x +c \right)+2 \cos \left(d x +c \right)+2 \left(d x +c \right) \sin \left(d x +c \right)\right)}{d^{6}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{3 x^{3} d^{3}}-\frac{\cos \left(d x +c \right)}{6 x^{2} d^{2}}+\frac{\sin \left(d x +c \right)}{6 x d}+\frac{\Si \left(d x \right) \sin \left(c \right)}{6}-\frac{\Ci \left(d x \right) \cos \left(c \right)}{6}\right)-\frac{6 b^{2} c \left(1+4 c \right) \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}\right)"," ",0,"d^3*(2/d^3*a*b*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-15*c^2/d^6*b^2*cos(d*x+c)+(10*c^2+4*c+1)/d^6*b^2*(-(d*x+c)^2*cos(d*x+c)+2*cos(d*x+c)+2*(d*x+c)*sin(d*x+c))+a^2*(-1/3*sin(d*x+c)/x^3/d^3-1/6*cos(d*x+c)/x^2/d^2+1/6*sin(d*x+c)/x/d+1/6*Si(d*x)*sin(c)-1/6*Ci(d*x)*cos(c))-6*b^2*c*(1+4*c)/d^6*(sin(d*x+c)-(d*x+c)*cos(d*x+c)))","A"
93,1,167,155,0.052000," ","int((b*x^3+a)^2*sin(d*x+c)/x^5,x)","d^{4} \left(\frac{2 a b \left(-\frac{\sin \left(d x +c \right)}{x d}-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)\right)}{d^{3}}+\frac{6 c \,b^{2} \cos \left(d x +c \right)}{d^{6}}+\frac{\left(1+5 c \right) b^{2} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)}{d^{6}}+a^{2} \left(-\frac{\sin \left(d x +c \right)}{4 x^{4} d^{4}}-\frac{\cos \left(d x +c \right)}{12 x^{3} d^{3}}+\frac{\sin \left(d x +c \right)}{24 x^{2} d^{2}}+\frac{\cos \left(d x +c \right)}{24 x d}+\frac{\Si \left(d x \right) \cos \left(c \right)}{24}+\frac{\Ci \left(d x \right) \sin \left(c \right)}{24}\right)\right)"," ",0,"d^4*(2/d^3*a*b*(-sin(d*x+c)/x/d-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+6*c/d^6*b^2*cos(d*x+c)+(1+5*c)/d^6*b^2*(sin(d*x+c)-(d*x+c)*cos(d*x+c))+a^2*(-1/4*sin(d*x+c)/x^4/d^4-1/12*cos(d*x+c)/x^3/d^3+1/24*sin(d*x+c)/x^2/d^2+1/24*cos(d*x+c)/x/d+1/24*Si(d*x)*cos(c)+1/24*Ci(d*x)*sin(c)))","A"
94,1,559,263,0.061000," ","int(x^4*sin(d*x+c)/(b*x^3+a),x)","\frac{\frac{d^{3} \left(\sin \left(d x +c \right)-\left(d x +c \right) \cos \left(d x +c \right)\right)-3 c \,d^{3} \cos \left(d x +c \right)}{b}+\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(6 \textit{\_R1}^{2} b \,c^{2}-\textit{\_R1} a \,d^{3}-8 \textit{\_R1} b \,c^{3}-3 a c \,d^{3}+3 b \,c^{4}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b^{2}}+\frac{4 c \,d^{3} \cos \left(d x +c \right)}{b}-\frac{4 c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(3 \textit{\_R1}^{2} b c -3 \textit{\_R1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b^{2}}+\frac{2 c^{2} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1}^{2} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{b}-\frac{4 c^{3} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}+\frac{c^{4} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}}{d^{5}}"," ",0,"1/d^5*((d^3*(sin(d*x+c)-(d*x+c)*cos(d*x+c))-3*c*d^3*cos(d*x+c))/b+1/3/b^2*d^3*sum((6*_R1^2*b*c^2-_R1*a*d^3-8*_R1*b*c^3-3*a*c*d^3+3*b*c^4)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+4*c*d^3/b*cos(d*x+c)-4/3/b^2*c*d^3*sum((3*_R1^2*b*c-3*_R1*b*c^2-a*d^3+b*c^3)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+2*c^2*d^3/b*sum(_R1^2/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-4/3*c^3*d^3/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/3*c^4*d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
95,1,392,249,0.052000," ","int(x^3*sin(d*x+c)/(b*x^3+a),x)","\frac{-\frac{d^{3} \cos \left(d x +c \right)}{b}+\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(3 \textit{\_R1}^{2} b c -3 \textit{\_R1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b^{2}}-\frac{c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1}^{2} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{b}+\frac{c^{2} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{b}-\frac{c^{3} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}}{d^{4}}"," ",0,"1/d^4*(-d^3/b*cos(d*x+c)+1/3/b^2*d^3*sum((3*_R1^2*b*c-3*_R1*b*c^2-a*d^3+b*c^3)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-c*d^3/b*sum(_R1^2/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+c^2*d^3/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/3*c^3*d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
96,1,266,205,0.041000," ","int(x^2*sin(d*x+c)/(b*x^3+a),x)","\frac{\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1}^{2} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}-\frac{2 d^{3} c \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}+\frac{d^{3} c^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}}{d^{3}}"," ",0,"1/d^3*(1/3*d^3/b*sum(_R1^2/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-2/3*d^3*c/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/3*d^3*c^2/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
97,1,176,235,0.040000," ","int(x*sin(d*x+c)/(b*x^3+a),x)","\frac{\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}-\frac{c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}}{d^{2}}"," ",0,"1/d^2*(1/3*d^3/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/3*c*d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
98,1,85,235,0.038000," ","int(sin(d*x+c)/(b*x^3+a),x)","\frac{d^{2} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 b}"," ",0,"1/3*d^2/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))","C"
99,1,88,225,0.048000," ","int(sin(d*x+c)/x/(b*x^3+a),x)","\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{3 a}"," ",0,"1/a*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-1/3/a*sum(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))","C"
100,1,116,272,0.055000," ","int(sin(d*x+c)/x^2/(b*x^3+a),x)","d \left(-\frac{\sin \left(d x +c \right)}{a x d}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1} -c}}{3 a}+\frac{-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a}\right)"," ",0,"d*(-sin(d*x+c)/a/x/d-1/3/a*sum(1/(_R1-c)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/a*(-Si(d*x)*sin(c)+Ci(d*x)*cos(c)))","C"
101,1,136,292,0.041000," ","int(sin(d*x+c)/x^3/(b*x^3+a),x)","d^{2} \left(\frac{-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}}{a}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{3 a}\right)"," ",0,"d^2*(1/a*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))-1/3/a*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
102,1,1185,496,0.110000," ","int(x^3*sin(d*x+c)/(b*x^3+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(\frac{c^{2} d^{3} \left(d x +c \right)^{2}}{a}-\frac{d^{3} \left(a \,d^{3}+5 b \,c^{3}\right) \left(d x +c \right)}{3 a b}-\frac{2 c \,d^{3} \left(a \,d^{3}-b \,c^{3}\right)}{3 a b}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(3 \textit{\_R1} b \,c^{2}+a \,d^{3}-b \,c^{3}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,b^{2}}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(3 \textit{\_RR1}^{2} b \,c^{2}-\textit{\_RR1} a \,d^{3}-5 \textit{\_RR1} b \,c^{3}-2 a c \,d^{3}+2 b \,c^{4}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{9 a \,b^{2}}+\frac{\sin \left(d x +c \right) \left(-\frac{2 c^{2} d^{3} \left(d x +c \right)^{2}}{a}+\frac{3 c^{3} d^{3} \left(d x +c \right)}{a}+\frac{c \,d^{3} \left(a \,d^{3}-b \,c^{3}\right)}{a b}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}-\frac{2 c^{2} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 a b}+\frac{c \,d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1}^{2} b c -3 \textit{\_RR1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{3 a \,b^{2}}+\frac{\sin \left(d x +c \right) \left(\frac{c^{2} d^{3} \left(d x +c \right)^{2}}{a}-\frac{c^{3} d^{3} \left(d x +c \right)}{a}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{c^{2} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1} +c \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{3 a b}-\frac{c^{2} d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_RR1} \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{3 a b}-c^{3} d^{6} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{3 a \,d^{3}}-\frac{c}{3 a \,d^{3}}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,d^{3} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a \,d^{3} b}\right)}{d^{4}}"," ",0,"1/d^4*(sin(d*x+c)*(c^2*d^3/a*(d*x+c)^2-1/3*d^3*(a*d^3+5*b*c^3)/a/b*(d*x+c)-2/3*c*d^3*(a*d^3-b*c^3)/a/b)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/9*d^3/a/b^2*sum((3*_R1*b*c^2+a*d^3-b*c^3)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*d^3/a/b^2*sum((3*_RR1^2*b*c^2-_RR1*a*d^3-5*_RR1*b*c^3-2*a*c*d^3+2*b*c^4)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+sin(d*x+c)*(-2*c^2*d^3/a*(d*x+c)^2+3*c^3*d^3/a*(d*x+c)+c*d^3*(a*d^3-b*c^3)/a/b)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-2/3*c^2*d^3/a/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/3*c*d^3/a/b^2*sum((2*_RR1^2*b*c-3*_RR1*b*c^2-a*d^3+b*c^3)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+sin(d*x+c)*(c^2*d^3/a*(d*x+c)^2-c^3*d^3/a*(d*x+c))/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/3*c^2*d^3/a/b*sum((_R1+c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/3*c^2*d^3/a/b*sum(_RR1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-c^3*d^6*(sin(d*x+c)*(1/3/a/d^3*(d*x+c)-1/3*c/a/d^3)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9/a/d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a/d^3/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
103,1,823,261,0.087000," ","int(x^2*sin(d*x+c)/(b*x^3+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(\frac{2 c \,d^{3} \left(d x +c \right)^{2}}{3 a}-\frac{c^{2} d^{3} \left(d x +c \right)}{a}-\frac{d^{3} \left(a \,d^{3}-b \,c^{3}\right)}{3 a b}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_R1} \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a b}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1}^{2} b c -3 \textit{\_RR1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{9 a \,b^{2}}+\frac{\sin \left(d x +c \right) \left(-\frac{2 c \,d^{3} \left(d x +c \right)^{2}}{3 a}+\frac{2 c^{2} d^{3} \left(d x +c \right)}{3 a}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}-\frac{2 c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1} +c \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a b}+\frac{2 c \,d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_RR1} \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{9 a b}+c^{2} d^{6} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{3 a \,d^{3}}-\frac{c}{3 a \,d^{3}}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,d^{3} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a \,d^{3} b}\right)}{d^{3}}"," ",0,"1/d^3*(sin(d*x+c)*(2/3*c*d^3/a*(d*x+c)^2-c^2*d^3/a*(d*x+c)-1/3*d^3*(a*d^3-b*c^3)/a/b)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9*c*d^3/a/b*sum(_R1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*d^3/a/b^2*sum((2*_RR1^2*b*c-3*_RR1*b*c^2-a*d^3+b*c^3)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+sin(d*x+c)*(-2/3*c*d^3/a*(d*x+c)^2+2/3*c^2*d^3/a*(d*x+c))/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-2/9*c*d^3/a/b*sum((_R1+c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+2/9*c*d^3/a/b*sum(_RR1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+c^2*d^6*(sin(d*x+c)*(1/3/a/d^3*(d*x+c)-1/3*c/a/d^3)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9/a/d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a/d^3/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
104,1,508,503,0.069000," ","int(x*sin(d*x+c)/(b*x^3+a)^2,x)","\frac{\frac{\sin \left(d x +c \right) \left(\frac{d^{3} \left(d x +c \right)^{2}}{3 a}-\frac{c \,d^{3} \left(d x +c \right)}{3 a}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1} +c \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a b}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\textit{\_RR1} \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{9 a b}-c \,d^{6} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{3 a \,d^{3}}-\frac{c}{3 a \,d^{3}}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,d^{3} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a \,d^{3} b}\right)}{d^{2}}"," ",0,"1/d^2*(sin(d*x+c)*(1/3*d^3/a*(d*x+c)^2-1/3*c*d^3/a*(d*x+c))/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/9*d^3/a/b*sum((_R1+c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*d^3/a/b*sum(_RR1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-c*d^6*(sin(d*x+c)*(1/3/a/d^3*(d*x+c)-1/3*c/a/d^3)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9/a/d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a/d^3/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
105,1,248,515,0.053000," ","int(sin(d*x+c)/(b*x^3+a)^2,x)","d^{5} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{3 a \,d^{3}}-\frac{c}{3 a \,d^{3}}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,d^{3} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a \,d^{3} b}\right)"," ",0,"d^5*(sin(d*x+c)*(1/3/a/d^3*(d*x+c)-1/3*c/a/d^3)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9/a/d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a/d^3/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
106,1,233,505,0.064000," ","int(sin(d*x+c)/x/(b*x^3+a)^2,x)","\frac{\sin \left(d x +c \right) d^{3}}{3 a \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{2}}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{3 a^{2}}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{9 a b}"," ",0,"1/3*sin(d*x+c)*d^3/a/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/a^2*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-1/3/a^2*sum(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*d^3/a/b*sum(1/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))","C"
107,1,283,522,0.068000," ","int(sin(d*x+c)/x^2/(b*x^3+a)^2,x)","d \left(\frac{\sin \left(d x +c \right) \left(-\frac{4 b \left(d x +c \right)^{3}}{3 a^{2}}+\frac{4 c b \left(d x +c \right)^{2}}{a^{2}}-\frac{4 c^{2} b \left(d x +c \right)}{a^{2}}-\frac{3 a \,d^{3}-4 b \,c^{3}}{3 a^{2}}\right)}{x d \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{4 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1} -c}\right)}{9 a^{2}}+\frac{-\Si \left(d x \right) \sin \left(c \right)+\Ci \left(d x \right) \cos \left(c \right)}{a^{2}}+\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{9 a^{2}}\right)"," ",0,"d*(sin(d*x+c)*(-4/3/a^2*b*(d*x+c)^3+4*c/a^2*b*(d*x+c)^2-4*c^2/a^2*b*(d*x+c)-1/3*(3*a*d^3-4*b*c^3)/a^2)/x/d/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-4/9/a^2*sum(1/(_R1-c)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/a^2*(-Si(d*x)*sin(c)+Ci(d*x)*cos(c))+1/9/a^2*sum(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
108,1,388,572,0.058000," ","int(sin(d*x+c)/x^3/(b*x^3+a)^2,x)","d^{2} \left(\frac{-\frac{\sin \left(d x +c \right)}{2 x^{2} d^{2}}-\frac{\cos \left(d x +c \right)}{2 x d}-\frac{\Si \left(d x \right) \cos \left(c \right)}{2}-\frac{\Ci \left(d x \right) \sin \left(c \right)}{2}}{a^{2}}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{3 a^{2}}-\frac{b \,d^{3} \left(\frac{\sin \left(d x +c \right) \left(\frac{d x +c}{3 a \,d^{3}}-\frac{c}{3 a \,d^{3}}\right)}{\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}}+\frac{2 \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{9 a \,d^{3} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a \,d^{3} b}\right)}{a}\right)"," ",0,"d^2*(1/a^2*(-1/2*sin(d*x+c)/x^2/d^2-1/2*cos(d*x+c)/x/d-1/2*Si(d*x)*cos(c)-1/2*Ci(d*x)*sin(c))-1/3/a^2*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/a*b*d^3*(sin(d*x+c)*(1/3/a/d^3*(d*x+c)-1/3*c/a/d^3)/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+2/9/a/d^3/b*sum(1/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a/d^3/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
109,1,2032,578,0.189000," ","int(x^3*sin(d*x+c)/(b*x^3+a)^3,x)","\frac{\frac{\sin \left(d x +c \right) d^{3} \left(12 b^{2} c^{2} \left(d x +c \right)^{5}+\left(d x +c \right)^{4} a b \,d^{3}-55 \left(d x +c \right)^{4} b^{2} c^{3}-4 \left(d x +c \right)^{3} a b c \,d^{3}+100 \left(d x +c \right)^{3} b^{2} c^{4}+27 \left(d x +c \right)^{2} a b \,c^{2} d^{3}-90 \left(d x +c \right)^{2} b^{2} c^{5}-2 \left(d x +c \right) a^{2} d^{6}-38 \left(d x +c \right) a b \,c^{3} d^{3}+40 \left(d x +c \right) b^{2} c^{6}-7 a^{2} c \,d^{6}+14 a b \,c^{4} d^{3}-7 b^{2} c^{7}\right)}{18 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}+\frac{\cos \left(d x +c \right) d^{3} \left(\left(d x +c \right)^{2} a \,d^{3}-\left(d x +c \right)^{2} b \,c^{3}+\left(d x +c \right) a c \,d^{3}+2 \left(d x +c \right) b \,c^{4}+a \,c^{2} d^{3}-c^{5} b \right)}{18 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}+\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} a \,d^{3}-\textit{\_R1}^{2} b \,c^{3}+\textit{\_R1} a c \,d^{3}+2 \textit{\_R1} b \,c^{4}+a \,c^{2} d^{3}-c^{5} b +12 \textit{\_R1} b \,c^{2}+2 a \,d^{3}-2 b \,c^{3}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{54 a^{2} b^{2}}-\frac{c \,d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1}^{2} b c -3 \textit{\_RR1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{9 a^{2} b^{2}}-\frac{\sin \left(d x +c \right) c \,d^{3} \left(8 b^{2} c \left(d x +c \right)^{5}-35 b^{2} c^{2} \left(d x +c \right)^{4}+60 b^{2} c^{3} \left(d x +c \right)^{3}+14 \left(d x +c \right)^{2} a b c \,d^{3}-50 \left(d x +c \right)^{2} b^{2} c^{4}-20 \left(d x +c \right) a b \,c^{2} d^{3}+20 \left(d x +c \right) b^{2} c^{5}-3 a^{2} d^{6}+6 a b \,c^{3} d^{3}-3 b^{2} c^{6}\right)}{6 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}+\frac{\cos \left(d x +c \right) c \,d^{3} \left(c^{2} \left(d x +c \right)^{2} b -\left(d x +c \right) a \,d^{3}-2 \left(d x +c \right) b \,c^{3}-a c \,d^{3}+b \,c^{4}\right)}{6 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}+\frac{c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} b \,c^{2}-\textit{\_R1} a \,d^{3}-2 \textit{\_R1} b \,c^{3}-a c \,d^{3}+b \,c^{4}-8 \textit{\_R1} b c -2 b \,c^{2}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{18 a^{2} b^{2}}+\frac{c \,d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(4 \textit{\_RR1}^{2} b c -5 \textit{\_RR1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{9 a^{2} b^{2}}+\frac{\sin \left(d x +c \right) c^{2} d^{3} \left(4 b \left(d x +c \right)^{5}-15 b c \left(d x +c \right)^{4}+20 b \,c^{2} \left(d x +c \right)^{3}+7 \left(d x +c \right)^{2} a \,d^{3}-10 \left(d x +c \right)^{2} b \,c^{3}-6 \left(d x +c \right) a c \,d^{3}-a \,c^{2} d^{3}+c^{5} b \right)}{6 a^{2} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) c^{2} d^{3} \left(c \left(d x +c \right)^{2} b -2 \left(d x +c \right) b \,c^{2}-a \,d^{3}+b \,c^{3}\right)}{6 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{c^{2} d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} b c -2 \textit{\_R1} b \,c^{2}-a \,d^{3}+b \,c^{3}-4 \textit{\_R1} b -6 c b \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{18 a^{2} b^{2}}-\frac{c^{2} d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1} +c \right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{9 a^{2} b}-d^{9} c^{3} \left(\frac{\sin \left(d x +c \right) \left(5 \left(d x +c \right)^{4} b -20 c \left(d x +c \right)^{3} b +30 c^{2} \left(d x +c \right)^{2} b +8 \left(d x +c \right) a \,d^{3}-20 \left(d x +c \right) b \,c^{3}-8 a c \,d^{3}+5 b \,c^{4}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) \left(\left(d x +c \right)^{2}-2 \left(d x +c \right) c +c^{2}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}-10\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{54 a^{2} d^{6} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a^{2} d^{6} b}\right)}{d^{4}}"," ",0,"1/d^4*(1/18*sin(d*x+c)*d^3*(12*b^2*c^2*(d*x+c)^5+(d*x+c)^4*a*b*d^3-55*(d*x+c)^4*b^2*c^3-4*(d*x+c)^3*a*b*c*d^3+100*(d*x+c)^3*b^2*c^4+27*(d*x+c)^2*a*b*c^2*d^3-90*(d*x+c)^2*b^2*c^5-2*(d*x+c)*a^2*d^6-38*(d*x+c)*a*b*c^3*d^3+40*(d*x+c)*b^2*c^6-7*a^2*c*d^6+14*a*b*c^4*d^3-7*b^2*c^7)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2+1/18*cos(d*x+c)*d^3*((d*x+c)^2*a*d^3-(d*x+c)^2*b*c^3+(d*x+c)*a*c*d^3+2*(d*x+c)*b*c^4+a*c^2*d^3-c^5*b)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/54*d^3/a^2/b^2*sum((_R1^2*a*d^3-_R1^2*b*c^3+_R1*a*c*d^3+2*_R1*b*c^4+a*c^2*d^3-b*c^5+12*_R1*b*c^2+2*a*d^3-2*b*c^3)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*c*d^3/a^2/b^2*sum((2*_RR1^2*b*c-3*_RR1*b*c^2-a*d^3+b*c^3)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/6*sin(d*x+c)*c*d^3*(8*b^2*c*(d*x+c)^5-35*b^2*c^2*(d*x+c)^4+60*b^2*c^3*(d*x+c)^3+14*(d*x+c)^2*a*b*c*d^3-50*(d*x+c)^2*b^2*c^4-20*(d*x+c)*a*b*c^2*d^3+20*(d*x+c)*b^2*c^5-3*a^2*d^6+6*a*b*c^3*d^3-3*b^2*c^6)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2+1/6*cos(d*x+c)*c*d^3*(c^2*(d*x+c)^2*b-(d*x+c)*a*d^3-2*(d*x+c)*b*c^3-a*c*d^3+b*c^4)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/18*c*d^3/a^2/b^2*sum((_R1^2*b*c^2-_R1*a*d^3-2*_R1*b*c^3-a*c*d^3+b*c^4-8*_R1*b*c-2*b*c^2)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/9*c*d^3/a^2/b^2*sum((4*_RR1^2*b*c-5*_RR1*b*c^2-a*d^3+b*c^3)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+1/6*sin(d*x+c)*c^2*d^3*(4*b*(d*x+c)^5-15*b*c*(d*x+c)^4+20*b*c^2*(d*x+c)^3+7*(d*x+c)^2*a*d^3-10*(d*x+c)^2*b*c^3-6*(d*x+c)*a*c*d^3-a*c^2*d^3+c^5*b)/a^2/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/6*cos(d*x+c)*c^2*d^3*(c*(d*x+c)^2*b-2*(d*x+c)*b*c^2-a*d^3+b*c^3)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/18*c^2*d^3/a^2/b^2*sum((_R1^2*b*c-2*_R1*b*c^2-a*d^3+b*c^3-4*_R1*b-6*b*c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*c^2*d^3/a^2/b*sum((2*_RR1+c)/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-d^9*c^3*(1/18*sin(d*x+c)*(5*(d*x+c)^4*b-20*c*(d*x+c)^3*b+30*c^2*(d*x+c)^2*b+8*(d*x+c)*a*d^3-20*(d*x+c)*b*c^3-8*a*c*d^3+5*b*c^4)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*((d*x+c)^2-2*(d*x+c)*c+c^2)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54/a^2/d^6/b*sum((_R1^2-2*_R1*c+c^2-10)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a^2/d^6/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
110,1,1394,555,0.137000," ","int(x^2*sin(d*x+c)/(b*x^3+a)^3,x)","\frac{\frac{\sin \left(d x +c \right) d^{3} \left(8 b^{2} c \left(d x +c \right)^{5}-35 b^{2} c^{2} \left(d x +c \right)^{4}+60 b^{2} c^{3} \left(d x +c \right)^{3}+14 \left(d x +c \right)^{2} a b c \,d^{3}-50 \left(d x +c \right)^{2} b^{2} c^{4}-20 \left(d x +c \right) a b \,c^{2} d^{3}+20 \left(d x +c \right) b^{2} c^{5}-3 a^{2} d^{6}+6 a b \,c^{3} d^{3}-3 b^{2} c^{6}\right)}{18 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) d^{3} \left(c^{2} \left(d x +c \right)^{2} b -\left(d x +c \right) a \,d^{3}-2 \left(d x +c \right) b \,c^{3}-a c \,d^{3}+b \,c^{4}\right)}{18 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} b \,c^{2}-\textit{\_R1} a \,d^{3}-2 \textit{\_R1} b \,c^{3}-a c \,d^{3}+b \,c^{4}-8 \textit{\_R1} b c -2 b \,c^{2}\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{54 a^{2} b^{2}}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(4 \textit{\_RR1}^{2} b c -5 \textit{\_RR1} b \,c^{2}-a \,d^{3}+b \,c^{3}\right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{27 a^{2} b^{2}}-\frac{\sin \left(d x +c \right) c \,d^{3} \left(4 b \left(d x +c \right)^{5}-15 b c \left(d x +c \right)^{4}+20 b \,c^{2} \left(d x +c \right)^{3}+7 \left(d x +c \right)^{2} a \,d^{3}-10 \left(d x +c \right)^{2} b \,c^{3}-6 \left(d x +c \right) a c \,d^{3}-a \,c^{2} d^{3}+c^{5} b \right)}{9 a^{2} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}+\frac{\cos \left(d x +c \right) c \,d^{3} \left(c \left(d x +c \right)^{2} b -2 \left(d x +c \right) b \,c^{2}-a \,d^{3}+b \,c^{3}\right)}{9 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}+\frac{c \,d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} b c -2 \textit{\_R1} b \,c^{2}-a \,d^{3}+b \,c^{3}-4 \textit{\_R1} b -6 c b \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{27 a^{2} b^{2}}+\frac{2 c \,d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1} +c \right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{27 a^{2} b}+c^{2} d^{9} \left(\frac{\sin \left(d x +c \right) \left(5 \left(d x +c \right)^{4} b -20 c \left(d x +c \right)^{3} b +30 c^{2} \left(d x +c \right)^{2} b +8 \left(d x +c \right) a \,d^{3}-20 \left(d x +c \right) b \,c^{3}-8 a c \,d^{3}+5 b \,c^{4}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) \left(\left(d x +c \right)^{2}-2 \left(d x +c \right) c +c^{2}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}-10\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{54 a^{2} d^{6} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a^{2} d^{6} b}\right)}{d^{3}}"," ",0,"1/d^3*(1/18*sin(d*x+c)*d^3*(8*b^2*c*(d*x+c)^5-35*b^2*c^2*(d*x+c)^4+60*b^2*c^3*(d*x+c)^3+14*(d*x+c)^2*a*b*c*d^3-50*(d*x+c)^2*b^2*c^4-20*(d*x+c)*a*b*c^2*d^3+20*(d*x+c)*b^2*c^5-3*a^2*d^6+6*a*b*c^3*d^3-3*b^2*c^6)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*d^3*(c^2*(d*x+c)^2*b-(d*x+c)*a*d^3-2*(d*x+c)*b*c^3-a*c*d^3+b*c^4)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54*d^3/a^2/b^2*sum((_R1^2*b*c^2-_R1*a*d^3-2*_R1*b*c^3-a*c*d^3+b*c^4-8*_R1*b*c-2*b*c^2)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/27*d^3/a^2/b^2*sum((4*_RR1^2*b*c-5*_RR1*b*c^2-a*d^3+b*c^3)/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9*sin(d*x+c)*c*d^3*(4*b*(d*x+c)^5-15*b*c*(d*x+c)^4+20*b*c^2*(d*x+c)^3+7*(d*x+c)^2*a*d^3-10*(d*x+c)^2*b*c^3-6*(d*x+c)*a*c*d^3-a*c^2*d^3+c^5*b)/a^2/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2+1/9*cos(d*x+c)*c*d^3*(c*(d*x+c)^2*b-2*(d*x+c)*b*c^2-a*d^3+b*c^3)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)+1/27*c*d^3/a^2/b^2*sum((_R1^2*b*c-2*_R1*b*c^2-a*d^3+b*c^3-4*_R1*b-6*b*c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+2/27*c*d^3/a^2/b*sum((2*_RR1+c)/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))+c^2*d^9*(1/18*sin(d*x+c)*(5*(d*x+c)^4*b-20*c*(d*x+c)^3*b+30*c^2*(d*x+c)^2*b+8*(d*x+c)*a*d^3-20*(d*x+c)*b*c^3-8*a*c*d^3+5*b*c^4)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*((d*x+c)^2-2*(d*x+c)*c+c^2)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54/a^2/d^6/b*sum((_R1^2-2*_R1*c+c^2-10)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a^2/d^6/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
111,1,845,837,0.103000," ","int(x*sin(d*x+c)/(b*x^3+a)^3,x)","\frac{\frac{\sin \left(d x +c \right) d^{3} \left(4 b \left(d x +c \right)^{5}-15 b c \left(d x +c \right)^{4}+20 b \,c^{2} \left(d x +c \right)^{3}+7 \left(d x +c \right)^{2} a \,d^{3}-10 \left(d x +c \right)^{2} b \,c^{3}-6 \left(d x +c \right) a c \,d^{3}-a \,c^{2} d^{3}+c^{5} b \right)}{18 a^{2} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) d^{3} \left(c \left(d x +c \right)^{2} b -2 \left(d x +c \right) b \,c^{2}-a \,d^{3}+b \,c^{3}\right)}{18 a^{2} b \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{d^{3} \left(\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2} b c -2 \textit{\_R1} b \,c^{2}-a \,d^{3}+b \,c^{3}-4 \textit{\_R1} b -6 c b \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}\right)}{54 a^{2} b^{2}}-\frac{d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(2 \textit{\_RR1} +c \right) \left(\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)\right)}{\textit{\_RR1} -c}\right)}{27 a^{2} b}-d^{9} c \left(\frac{\sin \left(d x +c \right) \left(5 \left(d x +c \right)^{4} b -20 c \left(d x +c \right)^{3} b +30 c^{2} \left(d x +c \right)^{2} b +8 \left(d x +c \right) a \,d^{3}-20 \left(d x +c \right) b \,c^{3}-8 a c \,d^{3}+5 b \,c^{4}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) \left(\left(d x +c \right)^{2}-2 \left(d x +c \right) c +c^{2}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}-10\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{54 a^{2} d^{6} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a^{2} d^{6} b}\right)}{d^{2}}"," ",0,"1/d^2*(1/18*sin(d*x+c)*d^3*(4*b*(d*x+c)^5-15*b*c*(d*x+c)^4+20*b*c^2*(d*x+c)^3+7*(d*x+c)^2*a*d^3-10*(d*x+c)^2*b*c^3-6*(d*x+c)*a*c*d^3-a*c^2*d^3+c^5*b)/a^2/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*d^3*(c*(d*x+c)^2*b-2*(d*x+c)*b*c^2-a*d^3+b*c^3)/a^2/b/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54*d^3/a^2/b^2*sum((_R1^2*b*c-2*_R1*b*c^2-a*d^3+b*c^3-4*_R1*b-6*b*c)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/27*d^3/a^2/b*sum((2*_RR1+c)/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-d^9*c*(1/18*sin(d*x+c)*(5*(d*x+c)^4*b-20*c*(d*x+c)^3*b+30*c^2*(d*x+c)^2*b+8*(d*x+c)*a*d^3-20*(d*x+c)*b*c^3-8*a*c*d^3+5*b*c^4)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*((d*x+c)^2-2*(d*x+c)*c+c^2)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54/a^2/d^6/b*sum((_R1^2-2*_R1*c+c^2-10)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a^2/d^6/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))))","C"
112,1,392,855,0.065000," ","int(sin(d*x+c)/(b*x^3+a)^3,x)","d^{8} \left(\frac{\sin \left(d x +c \right) \left(5 \left(d x +c \right)^{4} b -20 c \left(d x +c \right)^{3} b +30 c^{2} \left(d x +c \right)^{2} b +8 \left(d x +c \right) a \,d^{3}-20 \left(d x +c \right) b \,c^{3}-8 a c \,d^{3}+5 b \,c^{4}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) \left(\left(d x +c \right)^{2}-2 \left(d x +c \right) c +c^{2}\right)}{18 a^{2} d^{6} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}-10\right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1}^{2}-2 \textit{\_R1} c +c^{2}}}{54 a^{2} d^{6} b}-\frac{\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1} -c}}{9 a^{2} d^{6} b}\right)"," ",0,"d^8*(1/18*sin(d*x+c)*(5*(d*x+c)^4*b-20*c*(d*x+c)^3*b+30*c^2*(d*x+c)^2*b+8*(d*x+c)*a*d^3-20*(d*x+c)*b*c^3-8*a*c*d^3+5*b*c^4)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*((d*x+c)^2-2*(d*x+c)*c+c^2)/a^2/d^6/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)-1/54/a^2/d^6/b*sum((_R1^2-2*_R1*c+c^2-10)/(_R1^2-2*_R1*c+c^2)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-1/9/a^2/d^6/b*sum(1/(_RR1-c)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3)))","C"
113,1,363,857,0.091000," ","int(sin(d*x+c)/x/(b*x^3+a)^3,x)","\frac{\sin \left(d x +c \right) d^{3} \left(2 \left(d x +c \right)^{3} b -6 c \left(d x +c \right)^{2} b +6 \left(d x +c \right) b \,c^{2}+3 a \,d^{3}-2 b \,c^{3}\right)}{6 a^{2} \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right)^{2}}-\frac{\cos \left(d x +c \right) d^{4} x}{18 \left(\left(d x +c \right)^{3} b -3 c \left(d x +c \right)^{2} b +3 \left(d x +c \right) b \,c^{2}+a \,d^{3}-b \,c^{3}\right) a^{2}}+\frac{\Si \left(d x \right) \cos \left(c \right)+\Ci \left(d x \right) \sin \left(c \right)}{a^{3}}-\frac{\munderset{\textit{\_R1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\left(a \,d^{3}+18 \textit{\_R1} b -18 c b \right) \left(-\Si \left(-d x +\textit{\_R1} -c \right) \cos \left(\textit{\_R1} \right)+\Ci \left(d x -\textit{\_R1} +c \right) \sin \left(\textit{\_R1} \right)\right)}{\textit{\_R1} -c}}{54 b \,a^{3}}-\frac{4 d^{3} \left(\munderset{\textit{\_RR1} =\RootOf \left(b \,\textit{\_Z}^{3}-3 c b \,\textit{\_Z}^{2}+3 b \,c^{2} \textit{\_Z} +a \,d^{3}-b \,c^{3}\right)}{\sum}\frac{\Si \left(-d x +\textit{\_RR1} -c \right) \sin \left(\textit{\_RR1} \right)+\Ci \left(d x -\textit{\_RR1} +c \right) \cos \left(\textit{\_RR1} \right)}{\textit{\_RR1}^{2}-2 \textit{\_RR1} c +c^{2}}\right)}{27 a^{2} b}"," ",0,"1/6*sin(d*x+c)*d^3*(2*(d*x+c)^3*b-6*c*(d*x+c)^2*b+6*(d*x+c)*b*c^2+3*a*d^3-2*b*c^3)/a^2/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)^2-1/18*cos(d*x+c)*d^4*x/((d*x+c)^3*b-3*c*(d*x+c)^2*b+3*(d*x+c)*b*c^2+a*d^3-b*c^3)/a^2+1/a^3*(Si(d*x)*cos(c)+Ci(d*x)*sin(c))-1/54/b/a^3*sum((a*d^3+18*_R1*b-18*b*c)/(_R1-c)*(-Si(-d*x+_R1-c)*cos(_R1)+Ci(d*x-_R1+c)*sin(_R1)),_R1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))-4/27*d^3/a^2/b*sum(1/(_RR1^2-2*_RR1*c+c^2)*(Si(-d*x+_RR1-c)*sin(_RR1)+Ci(d*x-_RR1+c)*cos(_RR1)),_RR1=RootOf(_Z^3*b-3*_Z^2*b*c+3*_Z*b*c^2+a*d^3-b*c^3))","C"