1,1,133,80,0.447000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(5 \left(\cos^{8}\left(f x +e \right)\right)+3 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(\cos^{6}\left(f x +e \right)\right)+7 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+7 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-7 \left(\cos^{2}\left(f x +e \right)\right)+28 \sin \left(f x +e \right)+28\right)}{30 f \cos \left(f x +e \right)^{7}}"," ",0,"1/30/f*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(5*cos(f*x+e)^8+3*cos(f*x+e)^6*sin(f*x+e)+4*cos(f*x+e)^6+7*sin(f*x+e)*cos(f*x+e)^4+7*cos(f*x+e)^2*sin(f*x+e)-7*cos(f*x+e)^2+28*sin(f*x+e)+28)/cos(f*x+e)^7","A"
2,1,106,80,0.420000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(2 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+2 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \sin \left(f x +e \right)+6\right)}{10 f \cos \left(f x +e \right)^{5}}"," ",0,"1/10/f*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(2*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+2*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+6*sin(f*x+e)+6)/cos(f*x+e)^5","A"
3,1,90,80,0.395000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(3 \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right)+5 \sin \left(f x +e \right)+5\right)}{12 f \cos \left(f x +e \right)^{3}}"," ",0,"1/12/f*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(3*cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)+4*cos(f*x+e)^2+5*sin(f*x+e)+5)/cos(f*x+e)^3","A"
4,1,55,80,0.383000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(\cos^{2}\left(f x +e \right)+2\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{3 f \cos \left(f x +e \right)}"," ",0,"1/3/f*(cos(f*x+e)^2+2)*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)","A"
5,1,94,39,0.380000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+\sin \left(f x +e \right)+2 \cos \left(f x +e \right)-1\right)}{2 f \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/2/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(1/2)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2+sin(f*x+e)+2*cos(f*x+e)-1)/(-c*(sin(f*x+e)-1))^(1/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
6,1,138,91,0.376000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(\sin \left(f x +e \right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{f \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/f*(sin(f*x+e)+4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*ln(2/(cos(f*x+e)+1)))*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(1/2)/(1-cos(f*x+e)+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(3/2)","A"
7,1,192,89,0.380000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(2 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \sin \left(f x +e \right)+\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{f \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(2*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(2/(cos(f*x+e)+1))-2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)+ln(2/(cos(f*x+e)+1)))*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(1/2)/(1-cos(f*x+e)+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(5/2)","B"
8,1,96,42,0.381000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right)}{f \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(1-\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"-1/f*(a*(1+sin(f*x+e)))^(1/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(-c*(sin(f*x+e)-1))^(7/2)/(1-cos(f*x+e)+sin(f*x+e))","B"
9,1,133,122,0.422000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(15 \left(\cos^{8}\left(f x +e \right)\right)+5 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+16 \left(\cos^{6}\left(f x +e \right)\right)+13 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+16 \left(\cos^{4}\left(f x +e \right)\right)+29 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+58 \sin \left(f x +e \right)+58\right)}{105 f \cos \left(f x +e \right)^{7}}"," ",0,"1/105/f*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(15*cos(f*x+e)^8+5*cos(f*x+e)^6*sin(f*x+e)+16*cos(f*x+e)^6+13*sin(f*x+e)*cos(f*x+e)^4+16*cos(f*x+e)^4+29*cos(f*x+e)^2*sin(f*x+e)+58*sin(f*x+e)+58)/cos(f*x+e)^7","A"
10,1,116,122,0.363000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(5 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)+11 \sin \left(f x +e \right)+11\right)}{30 f \cos \left(f x +e \right)^{5}}"," ",0,"1/30/f*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(5*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4+6*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2+11*sin(f*x+e)+11)/cos(f*x+e)^5","A"
11,1,67,122,0.339000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(3 \left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{15 f \cos \left(f x +e \right)^{3}}"," ",0,"1/15/f*(3*cos(f*x+e)^4+4*cos(f*x+e)^2+8)*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)/cos(f*x+e)^3","A"
12,1,90,80,0.390000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-3 \left(\cos^{4}\left(f x +e \right)\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right)+5 \sin \left(f x +e \right)-5\right)}{12 f \cos \left(f x +e \right)^{3}}"," ",0,"-1/12/f*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(-3*cos(f*x+e)^4+cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^2+5*sin(f*x+e)-5)/cos(f*x+e)^3","A"
13,1,141,39,0.360000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(\cos^{3}\left(f x +e \right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+2 \left(\cos^{2}\left(f x +e \right)\right)-3 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \cos \left(f x +e \right)-\sin \left(f x +e \right)+1\right)}{3 f \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}"," ",0,"1/3/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(3/2)*(cos(f*x+e)^3+cos(f*x+e)^2*sin(f*x+e)+2*cos(f*x+e)^2-3*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)-sin(f*x+e)+1)/(-c*(sin(f*x+e)-1))^(1/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)","B"
14,1,173,133,0.362000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(-\left(\cos^{2}\left(f x +e \right)\right)+6 \sin \left(f x +e \right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+1\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{2 f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(-cos(f*x+e)^2+6*sin(f*x+e)+16*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*ln(2/(cos(f*x+e)+1))+1)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(3/2)","A"
15,1,223,132,0.368000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(8 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-8 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-5 \sin \left(f x +e \right)+4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+1\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(8*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2-4*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-8*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-5*sin(f*x+e)+4*ln(2/(cos(f*x+e)+1))+1)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
16,1,276,133,0.422000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-2 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-4 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+2 \left(\cos^{2}\left(f x +e \right)\right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+4 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}"," ",0,"-1/f*(cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-2*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-4*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+2*cos(f*x+e)^2-2*ln(2/(cos(f*x+e)+1))+4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-2)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(7/2)","B"
17,1,127,42,0.354000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(\cos^{2}\left(f x +e \right)-4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right)}{3 f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}"," ",0,"-1/3/f*(cos(f*x+e)^2-4)*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(9/2)","B"
18,1,152,85,0.385000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+10\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right)}{6 f \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}}}"," ",0,"1/6/f*(cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^2-4*sin(f*x+e)+10)*(a*(1+sin(f*x+e)))^(3/2)*sin(f*x+e)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(11/2)","A"
19,1,143,164,0.444000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(35 \left(\cos^{8}\left(f x +e \right)\right)+5 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+40 \left(\cos^{6}\left(f x +e \right)\right)+13 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+48 \left(\cos^{4}\left(f x +e \right)\right)+29 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+64 \left(\cos^{2}\left(f x +e \right)\right)+93 \sin \left(f x +e \right)+93\right)}{280 f \cos \left(f x +e \right)^{7}}"," ",0,"1/280/f*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(35*cos(f*x+e)^8+5*cos(f*x+e)^6*sin(f*x+e)+40*cos(f*x+e)^6+13*sin(f*x+e)*cos(f*x+e)^4+48*cos(f*x+e)^4+29*cos(f*x+e)^2*sin(f*x+e)+64*cos(f*x+e)^2+93*sin(f*x+e)+93)/cos(f*x+e)^7","A"
20,1,77,164,0.371000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(5 \left(\cos^{6}\left(f x +e \right)\right)+6 \left(\cos^{4}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right)+16\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{35 f \cos \left(f x +e \right)^{5}}"," ",0,"1/35/f*(5*cos(f*x+e)^6+6*cos(f*x+e)^4+8*cos(f*x+e)^2+16)*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/cos(f*x+e)^5","A"
21,1,116,122,0.388000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-5 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-6 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+11 \sin \left(f x +e \right)-11\right)}{30 f \cos \left(f x +e \right)^{5}}"," ",0,"-1/30/f*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(-5*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4-6*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+11*sin(f*x+e)-11)/cos(f*x+e)^5","A"
22,1,106,80,0.410000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-2 \left(\cos^{6}\left(f x +e \right)\right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-2 \left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \sin \left(f x +e \right)-6\right)}{10 f \cos \left(f x +e \right)^{5}}"," ",0,"-1/10/f*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(-2*cos(f*x+e)^6+sin(f*x+e)*cos(f*x+e)^4-2*cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+6*sin(f*x+e)-6)/cos(f*x+e)^5","A"
23,1,199,39,0.362000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-\left(\cos^{4}\left(f x +e \right)\right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+4 \left(\cos^{3}\left(f x +e \right)\right)-7 \sin \left(f x +e \right) \cos \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right)-\sin \left(f x +e \right)-8 \cos \left(f x +e \right)+1\right)}{4 f \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+2 \cos \left(f x +e \right)-4\right)}"," ",0,"1/4/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)*(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)+4*cos(f*x+e)^3-7*sin(f*x+e)*cos(f*x+e)+4*cos(f*x+e)^2-sin(f*x+e)-8*cos(f*x+e)+1)/(-c*(sin(f*x+e)-1))^(1/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)","B"
24,1,218,175,0.355000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+6 \left(\cos^{2}\left(f x +e \right)\right)+24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-22 \sin \left(f x +e \right)-48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{3 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+2 \cos \left(f x +e \right)-4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/3/f*(cos(f*x+e)^2*sin(f*x+e)+6*cos(f*x+e)^2+24*ln(2/(cos(f*x+e)+1))-22*sin(f*x+e)-48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(3/2)","A"
25,1,273,174,0.374000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+48 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-9 \left(\cos^{2}\left(f x +e \right)\right)-48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-25 \sin \left(f x +e \right)+9\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{2 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+2 \cos \left(f x +e \right)-4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/2/f*(-cos(f*x+e)^2*sin(f*x+e)+48*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-9*cos(f*x+e)^2-48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+24*ln(2/(cos(f*x+e)+1))-25*sin(f*x+e)+9)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(5/2)","A"
26,1,325,175,0.376000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+12 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-10 \left(\cos^{2}\left(f x +e \right)\right)+24 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-12 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6 \sin \left(f x +e \right)-24 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+10\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}"," ",0,"1/f*(cos(f*x+e)^2*sin(f*x+e)+12*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-6*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-10*cos(f*x+e)^2+24*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-12*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-6*sin(f*x+e)-24*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+12*ln(2/(cos(f*x+e)+1))+10)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(7/2)","A"
27,1,397,173,0.377000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x)","\frac{\left(6 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-18 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+9 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+6 \left(\cos^{2}\left(f x +e \right)\right)-24 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+12 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+14 \sin \left(f x +e \right)-12 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-6\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{3 f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}"," ",0,"1/3/f*(6*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-18*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*cos(f*x+e)^2*sin(f*x+e)+9*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+6*cos(f*x+e)^2-24*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+12*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+24*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+14*sin(f*x+e)-12*ln(2/(cos(f*x+e)+1))-6)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(9/2)","B"
28,1,153,42,0.342000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x)","-\frac{\left(\cos^{2}\left(f x +e \right)-2\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}}}"," ",0,"-1/f*(cos(f*x+e)^2-2)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(5/2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(11/2)","B"
29,1,187,85,0.372000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x)","\frac{\left(\cos^{4}\left(f x +e \right)+5 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-17 \left(\cos^{2}\left(f x +e \right)\right)-10 \sin \left(f x +e \right)+26\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right)}{10 f \left(\cos^{3}\left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+4 \sin \left(f x +e \right)+4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}}}"," ",0,"1/10/f*(cos(f*x+e)^4+5*cos(f*x+e)^2*sin(f*x+e)-17*cos(f*x+e)^2-10*sin(f*x+e)+26)*(a*(1+sin(f*x+e)))^(5/2)*sin(f*x+e)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(cos(f*x+e)^3-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-2*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+4*sin(f*x+e)+4)/(-c*(sin(f*x+e)-1))^(13/2)","B"
30,1,169,206,0.512000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(63 \left(\cos^{10}\left(f x +e \right)\right)+7 \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right)+70 \left(\cos^{8}\left(f x +e \right)\right)+17 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+80 \left(\cos^{6}\left(f x +e \right)\right)+33 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+96 \left(\cos^{4}\left(f x +e \right)\right)+65 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+128 \left(\cos^{2}\left(f x +e \right)\right)+193 \sin \left(f x +e \right)+193\right)}{630 f \cos \left(f x +e \right)^{9}}"," ",0,"1/630/f*(-c*(sin(f*x+e)-1))^(9/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(63*cos(f*x+e)^10+7*sin(f*x+e)*cos(f*x+e)^8+70*cos(f*x+e)^8+17*cos(f*x+e)^6*sin(f*x+e)+80*cos(f*x+e)^6+33*sin(f*x+e)*cos(f*x+e)^4+96*cos(f*x+e)^4+65*cos(f*x+e)^2*sin(f*x+e)+128*cos(f*x+e)^2+193*sin(f*x+e)+193)/cos(f*x+e)^9","A"
31,1,87,206,0.394000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x)","\frac{\left(35 \left(\cos^{8}\left(f x +e \right)\right)+40 \left(\cos^{6}\left(f x +e \right)\right)+48 \left(\cos^{4}\left(f x +e \right)\right)+64 \left(\cos^{2}\left(f x +e \right)\right)+128\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{315 f \cos \left(f x +e \right)^{7}}"," ",0,"1/315/f*(35*cos(f*x+e)^8+40*cos(f*x+e)^6+48*cos(f*x+e)^4+64*cos(f*x+e)^2+128)*(-c*(sin(f*x+e)-1))^(7/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)/cos(f*x+e)^7","A"
32,1,143,164,0.411000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(-35 \left(\cos^{8}\left(f x +e \right)\right)+5 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-40 \left(\cos^{6}\left(f x +e \right)\right)+13 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-48 \left(\cos^{4}\left(f x +e \right)\right)+29 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-64 \left(\cos^{2}\left(f x +e \right)\right)+93 \sin \left(f x +e \right)-93\right)}{280 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/280/f*(-c*(sin(f*x+e)-1))^(5/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(-35*cos(f*x+e)^8+5*cos(f*x+e)^6*sin(f*x+e)-40*cos(f*x+e)^6+13*sin(f*x+e)*cos(f*x+e)^4-48*cos(f*x+e)^4+29*cos(f*x+e)^2*sin(f*x+e)-64*cos(f*x+e)^2+93*sin(f*x+e)-93)/cos(f*x+e)^7","A"
33,1,133,122,0.404000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(-15 \left(\cos^{8}\left(f x +e \right)\right)+5 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-16 \left(\cos^{6}\left(f x +e \right)\right)+13 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-16 \left(\cos^{4}\left(f x +e \right)\right)+29 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+58 \sin \left(f x +e \right)-58\right)}{105 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/105/f*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(-15*cos(f*x+e)^8+5*cos(f*x+e)^6*sin(f*x+e)-16*cos(f*x+e)^6+13*sin(f*x+e)*cos(f*x+e)^4-16*cos(f*x+e)^4+29*cos(f*x+e)^2*sin(f*x+e)+58*sin(f*x+e)-58)/cos(f*x+e)^7","A"
34,1,133,80,0.402000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(-5 \left(\cos^{8}\left(f x +e \right)\right)+3 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{6}\left(f x +e \right)\right)+7 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+7 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+7 \left(\cos^{2}\left(f x +e \right)\right)+28 \sin \left(f x +e \right)-28\right)}{30 f \cos \left(f x +e \right)^{7}}"," ",0,"-1/30/f*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(-5*cos(f*x+e)^8+3*cos(f*x+e)^6*sin(f*x+e)-4*cos(f*x+e)^6+7*sin(f*x+e)*cos(f*x+e)^4+7*cos(f*x+e)^2*sin(f*x+e)+7*cos(f*x+e)^2+28*sin(f*x+e)-28)/cos(f*x+e)^7","A"
35,1,245,39,0.398000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(\cos^{5}\left(f x +e \right)+\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{4}\left(f x +e \right)\right)-5 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-12 \left(\cos^{3}\left(f x +e \right)\right)-7 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+15 \sin \left(f x +e \right) \cos \left(f x +e \right)+16 \cos \left(f x +e \right)+\sin \left(f x +e \right)-1\right)}{5 f \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right)}"," ",0,"1/5/f*sin(f*x+e)*(a*(1+sin(f*x+e)))^(7/2)*(cos(f*x+e)^5+sin(f*x+e)*cos(f*x+e)^4+4*cos(f*x+e)^4-5*sin(f*x+e)*cos(f*x+e)^3-12*cos(f*x+e)^3-7*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+15*sin(f*x+e)*cos(f*x+e)+16*cos(f*x+e)+sin(f*x+e)-1)/(-c*(sin(f*x+e)-1))^(1/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)","B"
36,1,250,217,0.388000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(3 \left(\cos^{4}\left(f x +e \right)\right)-20 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-72 \left(\cos^{2}\left(f x +e \right)\right)+384 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+200 \sin \left(f x +e \right)-192 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+69\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{12 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/12/f*(3*cos(f*x+e)^4-20*cos(f*x+e)^2*sin(f*x+e)-72*cos(f*x+e)^2+384*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+200*sin(f*x+e)-192*ln(2/(cos(f*x+e)+1))+69)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(3/2)","A"
37,1,307,216,0.392000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(-\left(\cos^{4}\left(f x +e \right)\right)+8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-192 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+44 \left(\cos^{2}\left(f x +e \right)\right)+91 \sin \left(f x +e \right)+192 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-43\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{3 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/3/f*(-cos(f*x+e)^4+8*cos(f*x+e)^2*sin(f*x+e)-192*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+96*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+44*cos(f*x+e)^2+91*sin(f*x+e)+192*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*ln(2/(cos(f*x+e)+1))-43)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(5/2)","A"
38,1,365,217,0.418000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{\left(-\left(\cos^{4}\left(f x +e \right)\right)+12 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+96 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-48 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+192 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-73 \left(\cos^{2}\left(f x +e \right)\right)-58 \sin \left(f x +e \right)-192 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+74\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{2 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}}}"," ",0,"-1/2/f*(-cos(f*x+e)^4+12*cos(f*x+e)^2*sin(f*x+e)+96*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-48*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))+192*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-73*cos(f*x+e)^2-58*sin(f*x+e)-192*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+96*ln(2/(cos(f*x+e)+1))+74)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(7/2)","A"
39,1,435,217,0.408000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{\left(48 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-24 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-3 \left(\cos^{4}\left(f x +e \right)\right)-49 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-144 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+72 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-192 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+63 \left(\cos^{2}\left(f x +e \right)\right)+76 \sin \left(f x +e \right)+192 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-96 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-60\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{3 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}}}"," ",0,"-1/3/f*(48*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-24*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-3*cos(f*x+e)^4-49*cos(f*x+e)^2*sin(f*x+e)-144*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+72*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-192*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+96*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+63*cos(f*x+e)^2+76*sin(f*x+e)+192*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-96*ln(2/(cos(f*x+e)+1))-60)*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(9/2)","A"
40,1,490,217,0.398000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x)","-\frac{\left(6 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-3 \left(\cos^{4}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+24 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \left(\cos^{4}\left(f x +e \right)\right)-12 \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 \left(\cos^{2}\left(f x +e \right)\right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+28 \left(\cos^{2}\left(f x +e \right)\right)+24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+8 \sin \left(f x +e \right)-24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-20\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{3 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}}}"," ",0,"-1/3/f*(6*cos(f*x+e)^4*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-3*cos(f*x+e)^4*ln(2/(cos(f*x+e)+1))+24*sin(f*x+e)*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*cos(f*x+e)^4-12*sin(f*x+e)*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-48*cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-8*cos(f*x+e)^2*sin(f*x+e)+24*cos(f*x+e)^2*ln(2/(cos(f*x+e)+1))-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+28*cos(f*x+e)^2+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+48*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+8*sin(f*x+e)-24*ln(2/(cos(f*x+e)+1))-20)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(11/2)","B"
41,1,188,42,0.362000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x)","\frac{\left(\cos^{4}\left(f x +e \right)-12 \left(\cos^{2}\left(f x +e \right)\right)+16\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right)}{5 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}}}"," ",0,"1/5/f*(cos(f*x+e)^4-12*cos(f*x+e)^2+16)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(13/2)","B"
42,1,230,85,0.398000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x)","-\frac{\left(3 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-18 \left(\cos^{4}\left(f x +e \right)\right)-36 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+116 \left(\cos^{2}\left(f x +e \right)\right)+48 \sin \left(f x +e \right)-128\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right)}{30 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{15}{2}}}"," ",0,"-1/30/f*(3*sin(f*x+e)*cos(f*x+e)^4-18*cos(f*x+e)^4-36*cos(f*x+e)^2*sin(f*x+e)+116*cos(f*x+e)^2+48*sin(f*x+e)-128)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(15/2)","B"
43,1,240,127,0.433000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x)","-\frac{\left(9 \left(\cos^{6}\left(f x +e \right)\right)+63 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-216 \left(\cos^{4}\left(f x +e \right)\right)-406 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+790 \left(\cos^{2}\left(f x +e \right)\right)+448 \sin \left(f x +e \right)-688\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right)}{105 f \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{3}\left(f x +e \right)\right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+8 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{17}{2}}}"," ",0,"-1/105/f*(9*cos(f*x+e)^6+63*sin(f*x+e)*cos(f*x+e)^4-216*cos(f*x+e)^4-406*cos(f*x+e)^2*sin(f*x+e)+790*cos(f*x+e)^2+448*sin(f*x+e)-688)*(a*(1+sin(f*x+e)))^(7/2)*sin(f*x+e)*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(17/2)","A"
44,1,195,39,0.381000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\sin \left(f x +e \right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+\cos^{4}\left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-4 \left(\cos^{3}\left(f x +e \right)\right)-7 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \left(\cos^{2}\left(f x +e \right)\right)-\sin \left(f x +e \right)+8 \cos \left(f x +e \right)-1\right)}{4 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right)}"," ",0,"1/4/f*sin(f*x+e)*(-c*(sin(f*x+e)-1))^(5/2)*(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4+3*cos(f*x+e)^2*sin(f*x+e)-4*cos(f*x+e)^3-7*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)^2-sin(f*x+e)+8*cos(f*x+e)-1)/(a*(1+sin(f*x+e)))^(1/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)","B"
45,1,147,39,0.368000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right) \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{3}\left(f x +e \right)\right)-3 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \left(\cos^{2}\left(f x +e \right)\right)-\sin \left(f x +e \right)+4 \cos \left(f x +e \right)-1\right)}{3 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right)}"," ",0,"1/3/f*(-c*(sin(f*x+e)-1))^(3/2)*sin(f*x+e)*(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3-3*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)^2-sin(f*x+e)+4*cos(f*x+e)-1)/(a*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)","B"
46,1,90,39,0.370000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{\sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)-2 \cos \left(f x +e \right)+\sin \left(f x +e \right)+1\right)}{2 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right)}"," ",0,"1/2/f*(-c*(sin(f*x+e)-1))^(1/2)*sin(f*x+e)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)+sin(f*x+e)+1)/(a*(1+sin(f*x+e)))^(1/2)/(-1+cos(f*x+e)+sin(f*x+e))","B"
47,1,42,39,0.364000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\cos \left(f x +e \right) \sin \left(f x +e \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/f*cos(f*x+e)*sin(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(1/2)","A"
48,1,138,50,0.368000," ","int(cos(f*x+e)^2/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(2 \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)\right) \left(-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(2/(cos(f*x+e)+1)))*(-1+cos(f*x+e)-sin(f*x+e))*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
49,1,51,38,0.365000," ","int(cos(f*x+e)^2/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(\sin \left(f x +e \right)-1\right) \cos \left(f x +e \right) \sin \left(f x +e \right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/f*(sin(f*x+e)-1)*cos(f*x+e)*sin(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
50,1,252,215,0.395000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(3 \left(\cos^{4}\left(f x +e \right)\right)+20 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-72 \left(\cos^{2}\left(f x +e \right)\right)-192 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-200 \sin \left(f x +e \right)+384 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+69\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{12 f \left(\cos^{4}\left(f x +e \right)-\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+3 \left(\cos^{3}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+4 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \cos \left(f x +e \right)-8 \sin \left(f x +e \right)+8\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/12/f*(3*cos(f*x+e)^4+20*cos(f*x+e)^2*sin(f*x+e)-72*cos(f*x+e)^2-192*ln(2/(cos(f*x+e)+1))-200*sin(f*x+e)+384*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+69)*(-c*(sin(f*x+e)-1))^(7/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(cos(f*x+e)^4-sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3+4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)-8*sin(f*x+e)+8)/(a*(1+sin(f*x+e)))^(3/2)","A"
51,1,214,172,0.364000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-6 \left(\cos^{2}\left(f x +e \right)\right)-22 \sin \left(f x +e \right)-24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+48 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+6\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{3 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/3/f*(cos(f*x+e)^2*sin(f*x+e)-6*cos(f*x+e)^2-22*sin(f*x+e)-24*ln(2/(cos(f*x+e)+1))+48*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+6)*(-c*(sin(f*x+e)-1))^(5/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/(a*(1+sin(f*x+e)))^(3/2)","A"
52,1,175,131,0.351000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x)","\frac{\left(-\left(\cos^{2}\left(f x +e \right)\right)+16 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-6 \sin \left(f x +e \right)-8 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+1\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{2 f \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(-cos(f*x+e)^2+16*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-6*sin(f*x+e)-8*ln(2/(cos(f*x+e)+1))+1)*(-c*(sin(f*x+e)-1))^(3/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(a*(1+sin(f*x+e)))^(3/2)","A"
53,1,137,88,0.371000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x)","-\frac{\left(4 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-\sin \left(f x +e \right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}"," ",0,"-1/f*(4*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*ln(2/(cos(f*x+e)+1))-sin(f*x+e))*(-c*(sin(f*x+e)-1))^(1/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e)+sin(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)","A"
54,1,137,47,0.389000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(-\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/2/f*(-ln(2/(cos(f*x+e)+1))+2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*(-1+cos(f*x+e)+sin(f*x+e))*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(1/2)","B"
55,1,174,48,0.358000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","\frac{\left(\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{2 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"1/2/f*(ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
56,1,244,92,0.352000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","\frac{\left(\sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\sin \left(f x +e \right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{4 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"1/4/f*(sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+sin(f*x+e)-ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))+ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)","B"
57,1,349,257,0.365000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(3 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-25 \left(\cos^{4}\left(f x +e \right)\right)-116 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+500 \left(\cos^{2}\left(f x +e \right)\right)-960 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+1920 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-859 \sin \left(f x +e \right)-960 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+1920 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-475\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{12 f \left(\sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+\cos^{5}\left(f x +e \right)+4 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-5 \left(\cos^{4}\left(f x +e \right)\right)-12 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{3}\left(f x +e \right)\right)-8 \sin \left(f x +e \right) \cos \left(f x +e \right)+20 \left(\cos^{2}\left(f x +e \right)\right)+16 \sin \left(f x +e \right)+8 \cos \left(f x +e \right)-16\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/12/f*(3*sin(f*x+e)*cos(f*x+e)^4-25*cos(f*x+e)^4-116*cos(f*x+e)^2*sin(f*x+e)+500*cos(f*x+e)^2-960*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+1920*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-859*sin(f*x+e)-960*ln(2/(cos(f*x+e)+1))+1920*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-475)*(-c*(sin(f*x+e)-1))^(9/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3-5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)+20*cos(f*x+e)^2+16*sin(f*x+e)+8*cos(f*x+e)-16)/(a*(1+sin(f*x+e)))^(5/2)","A"
58,1,306,215,0.409000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(\cos^{4}\left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-44 \left(\cos^{2}\left(f x +e \right)\right)-192 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+91 \sin \left(f x +e \right)-192 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+96 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+43\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{3 f \left(\cos^{4}\left(f x +e \right)-\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+3 \left(\cos^{3}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-8 \left(\cos^{2}\left(f x +e \right)\right)+4 \sin \left(f x +e \right) \cos \left(f x +e \right)-4 \cos \left(f x +e \right)-8 \sin \left(f x +e \right)+8\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/3/f*(cos(f*x+e)^4+8*cos(f*x+e)^2*sin(f*x+e)-44*cos(f*x+e)^2-192*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+96*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+91*sin(f*x+e)-192*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+96*ln(2/(cos(f*x+e)+1))+43)*(-c*(sin(f*x+e)-1))^(7/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(cos(f*x+e)^4-sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3+4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)-8*sin(f*x+e)+8)/(a*(1+sin(f*x+e)))^(5/2)","A"
59,1,270,173,0.408000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-9 \left(\cos^{2}\left(f x +e \right)\right)+24 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-48 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+24 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+25 \sin \left(f x +e \right)-48 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)+9\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{2 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{3}\left(f x +e \right)+2 \sin \left(f x +e \right) \cos \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-2 \cos \left(f x +e \right)+4\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/2/f*(cos(f*x+e)^2*sin(f*x+e)-9*cos(f*x+e)^2+24*sin(f*x+e)*ln(2/(cos(f*x+e)+1))-48*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+24*ln(2/(cos(f*x+e)+1))+25*sin(f*x+e)-48*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))+9)*(-c*(sin(f*x+e)-1))^(5/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/(a*(1+sin(f*x+e)))^(5/2)","A"
60,1,229,131,0.402000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x)","-\frac{\left(8 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 \sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+\cos^{2}\left(f x +e \right)-5 \sin \left(f x +e \right)+8 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-4 \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)-1\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{f \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-2 \sin \left(f x +e \right)-\cos \left(f x +e \right)+2\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"-1/f*(8*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-4*sin(f*x+e)*ln(2/(cos(f*x+e)+1))+cos(f*x+e)^2-5*sin(f*x+e)+8*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-4*ln(2/(cos(f*x+e)+1))-1)*(-c*(sin(f*x+e)-1))^(3/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/(a*(1+sin(f*x+e)))^(5/2)","A"
61,1,192,89,0.364000," ","int(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x)","\frac{\left(2 \sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right) \ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)+2 \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-2 \sin \left(f x +e \right)-\ln \left(\frac{2}{\cos \left(f x +e \right)+1}\right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{f \left(-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}"," ",0,"1/f*(2*sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(2/(cos(f*x+e)+1))+2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-2*sin(f*x+e)-ln(2/(cos(f*x+e)+1)))*(-c*(sin(f*x+e)-1))^(1/2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e)+sin(f*x+e))/(a*(1+sin(f*x+e)))^(5/2)","B"
62,1,50,39,0.363000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right) \sin \left(f x +e \right)}{f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/f*(1+sin(f*x+e))*cos(f*x+e)*sin(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(1/2)","A"
63,1,246,92,0.354000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{\left(\sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right)+\ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{4 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/4/f*(sin(f*x+e)*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-sin(f*x+e)*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-sin(f*x+e)+ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e)))*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(3/2)","B"
64,1,196,134,0.359000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{\left(\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\left(\cos^{2}\left(f x +e \right)\right) \ln \left(-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}\right)-\sin \left(f x +e \right)\right) \left(\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \left(\cos^{2}\left(f x +e \right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+\cos \left(f x +e \right)-2 \sin \left(f x +e \right)-2\right)}{4 f \left(-1+\cos \left(f x +e \right)\right) \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}"," ",0,"-1/4/f*(cos(f*x+e)^2*ln(-(-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))-cos(f*x+e)^2*ln(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))-sin(f*x+e))*(cos(f*x+e)^2-sin(f*x+e)*cos(f*x+e)+cos(f*x+e)+2*sin(f*x+e)-2)*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(5/2)","A"
65,0,0,94,4.197000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
66,0,0,72,8.860000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","F"
67,0,0,72,7.567000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","F"
68,0,0,70,3.149000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x)","F"
69,0,0,67,1.651000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x)","F"
70,0,0,65,4.023000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","F"
71,0,0,69,3.326000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","F"
72,0,0,72,3.017000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","F"
73,0,0,232,0.796000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","F"
74,0,0,164,0.735000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","F"
75,0,0,103,0.707000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \sqrt{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","F"
76,0,0,48,0.673000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
77,0,0,70,0.652000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","F"
78,0,0,71,0.681000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","F"
79,0,0,48,0.010000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
80,0,0,48,0.864000," ","int(cos(f*x+e)^2*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +c \sin \left(f x +e \right)\right)^{m}}{\sqrt{a -a \sin \left(f x +e \right)}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","F"
81,0,0,180,5.366000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-5-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x)","F"
82,0,0,114,5.396000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-4-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x)","F"
83,0,0,54,4.824000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-3-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","F"
84,0,0,91,3.579000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-2-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","F"
85,0,0,92,1.353000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","F"
86,0,0,94,1.834000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","F"
87,0,0,94,2.962000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{1-m}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","F"
88,1,425,321,0.760000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \left(-21 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+77 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+132 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{231 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+4\right) \cos \left(f x +e \right)^{3} \sin \left(f x +e \right)}"," ",0,"2/231/f*(-c*(sin(f*x+e)-1))^(7/2)*(-21*cos(f*x+e)^6*sin(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+77*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+132*sin(f*x+e)*cos(f*x+e)^4-154*cos(f*x+e)^4-154*cos(f*x+e)^2+231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)/(cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)+4)/cos(f*x+e)^3/sin(f*x+e)","C"
89,1,392,274,0.642000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+35 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+90 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-112 \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{315 f \left(\cos^{2}\left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-2/315/f*(-c*(sin(f*x+e)-1))^(5/2)*(231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+35*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+90*sin(f*x+e)*cos(f*x+e)^4-112*cos(f*x+e)^4-154*cos(f*x+e)^2+231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)/(cos(f*x+e)^2+2*sin(f*x+e)-2)/sin(f*x+e)/cos(f*x+e)^3","C"
90,1,372,227,0.621000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-7 \left(\cos^{4}\left(f x +e \right)\right)-14 \left(\cos^{2}\left(f x +e \right)\right)+21 \cos \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{35 f \left(\sin \left(f x +e \right)-1\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-2/35/f*(21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*sin(f*x+e)*cos(f*x+e)^4+21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-7*cos(f*x+e)^4-14*cos(f*x+e)^2+21*cos(f*x+e))*(-c*(sin(f*x+e)-1))^(3/2)*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)/(sin(f*x+e)-1)/sin(f*x+e)/cos(f*x+e)^3","C"
91,1,346,178,0.671000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x)","\frac{2 \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-\left(\cos^{4}\left(f x +e \right)\right)-2 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}{5 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"2/5/f*(-c*(sin(f*x+e)-1))^(1/2)*(3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-cos(f*x+e)^4-2*cos(f*x+e)^2+3*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)/cos(f*x+e)^3","C"
92,1,362,132,0.581000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right)}{3 f \left(1+\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"2/3/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)*(3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2+3*cos(f*x+e))/(1+sin(f*x+e))/sin(f*x+e)/cos(f*x+e)/(-c*(sin(f*x+e)-1))^(1/2)","C"
93,1,2835,135,0.671000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-1/f*(-1+cos(f*x+e))*(-10*cos(f*x+e)^2-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+6*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+2*cos(f*x+e)^3-cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-6*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+6*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+2*cos(f*x+e)^2*sin(f*x+e)+sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+3*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-12*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)/(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-c*(sin(f*x+e)-1))^(3/2)/sin(f*x+e)/cos(f*x+e)","C"
94,1,2040,182,0.559000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/10/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)*(-1+cos(f*x+e))^3*(sin(f*x+e)-1)*(-12*sin(f*x+e)*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+12*I*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-5*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-20*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+12*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+24*I*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-4*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-5*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+5*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-12*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+5*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)+20*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+24*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+24*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)+12*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e))/(1+sin(f*x+e))/sin(f*x+e)^7/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)","C"
95,1,966,229,0.558000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+12 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \left(\cos^{4}\left(f x +e \right)\right)+9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+10 \left(\cos^{3}\left(f x +e \right)\right)-16 \sin \left(f x +e \right) \cos \left(f x +e \right)-19 \left(\cos^{2}\left(f x +e \right)\right)+10 \sin \left(f x +e \right)-4 \cos \left(f x +e \right)+10\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{45 f \left(1+\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"2/45/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(-9*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4+9*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4-6*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+12*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*cos(f*x+e)^4+6*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+6*cos(f*x+e)^2*sin(f*x+e)+10*cos(f*x+e)^3-16*sin(f*x+e)*cos(f*x+e)-19*cos(f*x+e)^2+10*sin(f*x+e)-4*cos(f*x+e)+10)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(1+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(7/2)/sin(f*x+e)^5/cos(f*x+e)","C"
96,1,1126,276,0.609000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(9/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(27 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-18 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-27 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-3 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+18 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+5 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+9 \left(\cos^{4}\left(f x +e \right)\right)-9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 \left(\cos^{3}\left(f x +e \right)\right)-42 \sin \left(f x +e \right) \cos \left(f x +e \right)-45 \left(\cos^{2}\left(f x +e \right)\right)+30 \sin \left(f x +e \right)-18 \cos \left(f x +e \right)+30\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{195 f \left(1+\sin \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"2/195/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(1/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(9*I*sin(f*x+e)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-18*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-9*I*sin(f*x+e)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*sin(f*x+e)*cos(f*x+e)^4+27*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-27*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+5*sin(f*x+e)*cos(f*x+e)^3+9*cos(f*x+e)^4+18*I*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+10*cos(f*x+e)^2*sin(f*x+e)+24*cos(f*x+e)^3-42*sin(f*x+e)*cos(f*x+e)-45*cos(f*x+e)^2+30*sin(f*x+e)-18*cos(f*x+e)+30)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(1+sin(f*x+e))/(-c*(sin(f*x+e)-1))^(9/2)/sin(f*x+e)^5/cos(f*x+e)","C"
97,1,382,328,0.630000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(45 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-55 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-22 \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{495 f \left(\sin \left(f x +e \right)-1\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{5}}"," ",0,"-2/495/f*(-c*(sin(f*x+e)-1))^(5/2)*(45*cos(f*x+e)^6*sin(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-55*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-22*cos(f*x+e)^4-154*cos(f*x+e)^2+231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)/(sin(f*x+e)-1)/sin(f*x+e)/cos(f*x+e)^5","C"
98,1,356,279,0.564000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 \left(\cos^{6}\left(f x +e \right)\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+2 \left(\cos^{4}\left(f x +e \right)\right)+14 \left(\cos^{2}\left(f x +e \right)\right)-21 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{45 f \sin \left(f x +e \right) \cos \left(f x +e \right)^{5}}"," ",0,"-2/45/f*(-c*(sin(f*x+e)-1))^(3/2)*(21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+5*cos(f*x+e)^6+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+2*cos(f*x+e)^4+14*cos(f*x+e)^2-21*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)/sin(f*x+e)/cos(f*x+e)^5","C"
99,1,372,227,0.604000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+5 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+7 \left(\cos^{4}\left(f x +e \right)\right)+14 \left(\cos^{2}\left(f x +e \right)\right)-21 \cos \left(f x +e \right)\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}}}{35 f \left(1+\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-2/35/f*(-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+5*sin(f*x+e)*cos(f*x+e)^4-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+7*cos(f*x+e)^4+14*cos(f*x+e)^2-21*cos(f*x+e))*(-c*(sin(f*x+e)-1))^(1/2)*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)/(1+sin(f*x+e))/sin(f*x+e)/cos(f*x+e)^3","C"
100,1,384,180,0.535000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 \left(\cos^{4}\left(f x +e \right)\right)+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+24 \left(\cos^{2}\left(f x +e \right)\right)-21 \cos \left(f x +e \right)\right)}{15 f \left(2 \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+2\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-2/15/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)*(21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*cos(f*x+e)^4+10*cos(f*x+e)^2*sin(f*x+e)+24*cos(f*x+e)^2-21*cos(f*x+e))/(2*sin(f*x+e)-cos(f*x+e)^2+2)/sin(f*x+e)/cos(f*x+e)/(-c*(sin(f*x+e)-1))^(1/2)","C"
101,1,2894,186,0.568000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/3/f*(-1+cos(f*x+e))*(-33*cos(f*x+e)^2-3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+42*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8*cos(f*x+e)^3+21*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-cos(f*x+e)^4-12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-18*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+18*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*cos(f*x+e)^2*sin(f*x+e)+3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-12*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+12*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+sin(f*x+e)*cos(f*x+e)^3+3*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-9*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+9*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-9*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-21*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-21*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(3/2)/sin(f*x+e)/cos(f*x+e)","C"
102,1,3499,186,0.552000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/5/f*(-1+cos(f*x+e))*(-38*cos(f*x+e)^2-10*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+10*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+10*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+21*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+9*cos(f*x+e)^3+5*cos(f*x+e)^4-10*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+10*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+46*cos(f*x+e)^2*sin(f*x+e)+63*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-63*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+10*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-10*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-35*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+35*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-10*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*sin(f*x+e)*cos(f*x+e)^3+25*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-25*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+45*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-45*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+35*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-35*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-63*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+63*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)/(cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)+2*cos(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(5/2)/sin(f*x+e)/cos(f*x+e)","C"
103,1,2684,235,0.565000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x)","\text{Expression too large to display}"," ",0,"1/90/f*(cos(f*x+e)+1)*(-1+cos(f*x+e))^4*(-12*sin(f*x+e)*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+168*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+90*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+88*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-90*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+84*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-164*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-180*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+45*sin(f*x+e)*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-45*sin(f*x+e)*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-90*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+248*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+336*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-168*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)+168*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-168*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+336*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)-336*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)-336*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-88*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+168*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-168*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+84*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-84*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+168*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-168*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-84*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+84*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-336*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+336*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(sin(f*x+e)-1)*(a*(1+sin(f*x+e)))^(3/2)*(g*cos(f*x+e))^(3/2)/sin(f*x+e)^9/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(7/2)/(2*sin(f*x+e)-cos(f*x+e)^2+2)","C"
104,1,1138,284,0.561000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-126 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-84 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+84 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-147 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+84 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+126 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-189 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+147 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-84 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-63 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-21 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+189 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+63 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-160 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+63 \left(\cos^{4}\left(f x +e \right)\right)+265 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-222 \left(\cos^{3}\left(f x +e \right)\right)+96 \sin \left(f x +e \right) \cos \left(f x +e \right)+75 \left(\cos^{2}\left(f x +e \right)\right)-180 \sin \left(f x +e \right)+264 \cos \left(f x +e \right)-180\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{585 f \left(2 \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{9}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/585/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(-147*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+84*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-84*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-126*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+84*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+126*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-84*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+189*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+63*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-189*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+147*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*sin(f*x+e)*cos(f*x+e)^4-63*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-160*sin(f*x+e)*cos(f*x+e)^3+63*cos(f*x+e)^4+265*cos(f*x+e)^2*sin(f*x+e)-222*cos(f*x+e)^3+96*sin(f*x+e)*cos(f*x+e)+75*cos(f*x+e)^2-180*sin(f*x+e)+264*cos(f*x+e)-180)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(2*sin(f*x+e)-cos(f*x+e)^2+2)/(-c*(sin(f*x+e)-1))^(9/2)/sin(f*x+e)^5/cos(f*x+e)","C"
105,1,1298,333,0.621000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-780-780 \sin \left(f x +e \right)+948 \cos \left(f x +e \right)+612 \sin \left(f x +e \right) \cos \left(f x +e \right)+154 \left(\cos^{4}\left(f x +e \right)\right)+168 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-168 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 \left(\cos^{6}\left(f x +e \right)\right)+35 \left(\cos^{5}\left(f x +e \right)\right)-941 \left(\cos^{3}\left(f x +e \right)\right)-189 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-336 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+336 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+605 \left(\cos^{2}\left(f x +e \right)\right)-523 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-168 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+168 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+775 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+189 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+336 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-420 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-84 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-84 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+84 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+420 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-336 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-21 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{3315 f \left(2 \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+2\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/3315/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(3/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(-780-780*sin(f*x+e)+948*cos(f*x+e)+605*cos(f*x+e)^2+612*sin(f*x+e)*cos(f*x+e)+35*cos(f*x+e)^5-941*cos(f*x+e)^3+21*I*sin(f*x+e)*cos(f*x+e)^6*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+154*cos(f*x+e)^4-21*cos(f*x+e)^6+168*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-168*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+775*cos(f*x+e)^2*sin(f*x+e)-523*sin(f*x+e)*cos(f*x+e)^3-84*sin(f*x+e)*cos(f*x+e)^4-21*I*sin(f*x+e)*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+336*I*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-336*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-420*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+420*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-168*I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+168*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-84*I*cos(f*x+e)^6*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+84*I*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-189*I*sin(f*x+e)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+189*I*sin(f*x+e)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+336*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-336*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2))*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(2*sin(f*x+e)-cos(f*x+e)^2+2)/(-c*(sin(f*x+e)-1))^(11/2)/sin(f*x+e)^5/cos(f*x+e)","C"
106,1,366,374,0.589000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x)","\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(-45 \left(\cos^{8}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-22 \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{585 f \cos \left(f x +e \right)^{7} \sin \left(f x +e \right)}"," ",0,"2/585/f*(-c*(sin(f*x+e)-1))^(5/2)*(-45*cos(f*x+e)^8+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-22*cos(f*x+e)^4-154*cos(f*x+e)^2+231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/cos(f*x+e)^7/sin(f*x+e)","C"
107,1,382,328,0.677000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(45 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+55 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+22 \left(\cos^{4}\left(f x +e \right)\right)+154 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{495 f \left(1+\sin \left(f x +e \right)\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{5}}"," ",0,"-2/495/f*(-c*(sin(f*x+e)-1))^(3/2)*(45*cos(f*x+e)^6*sin(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+55*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+22*cos(f*x+e)^4+154*cos(f*x+e)^2-231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/(1+sin(f*x+e))/sin(f*x+e)/cos(f*x+e)^5","C"
108,1,394,274,0.647000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-35 \left(\cos^{6}\left(f x +e \right)\right)+90 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+112 \left(\cos^{4}\left(f x +e \right)\right)+154 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}}}{315 f \left(2 \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+2\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-2/315/f*(-c*(sin(f*x+e)-1))^(1/2)*(231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-35*cos(f*x+e)^6+90*sin(f*x+e)*cos(f*x+e)^4+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+112*cos(f*x+e)^4+154*cos(f*x+e)^2-231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/(2*sin(f*x+e)-cos(f*x+e)^2+2)/sin(f*x+e)/cos(f*x+e)^3","C"
109,1,415,226,0.596000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-15 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-63 \left(\cos^{4}\left(f x +e \right)\right)+140 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+294 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right)}{105 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-4\right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"2/105/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)*(231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-15*sin(f*x+e)*cos(f*x+e)^4-63*cos(f*x+e)^4+140*cos(f*x+e)^2*sin(f*x+e)+294*cos(f*x+e)^2-231*cos(f*x+e))/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(1/2)/sin(f*x+e)/cos(f*x+e)","C"
110,1,2945,235,0.646000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/15/f*(-1+cos(f*x+e))*(351*cos(f*x+e)^2+30*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-30*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+30*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^5-94*cos(f*x+e)^3+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+20*cos(f*x+e)^4+120*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-120*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+180*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-180*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-111*cos(f*x+e)^2*sin(f*x+e)-30*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+30*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+120*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-120*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-30*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-17*sin(f*x+e)*cos(f*x+e)^3-30*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+30*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+90*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-90*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+90*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+3*sin(f*x+e)*cos(f*x+e)^4-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/cos(f*x+e)/(-c*(sin(f*x+e)-1))^(3/2)/sin(f*x+e)","C"
111,1,3549,235,0.660000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/15/f*(-1+cos(f*x+e))*(438*cos(f*x+e)^2+90*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-5*cos(f*x+e)^5-89*cos(f*x+e)^3-70*cos(f*x+e)^4-45*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+45*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+90*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+360*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-360*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-486*cos(f*x+e)^2*sin(f*x+e)-90*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+90*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+315*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-315*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+65*sin(f*x+e)*cos(f*x+e)^3-225*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+225*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-405*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+405*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-315*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+315*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-5*sin(f*x+e)*cos(f*x+e)^4-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(5/2)/sin(f*x+e)/cos(f*x+e)","C"
112,1,4183,235,0.713000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x)","\text{output too large to display}"," ",0,"-1/45/f*(-1+cos(f*x+e))*(1928*cos(f*x+e)^2+540*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-540*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1350*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)^5-268*cos(f*x+e)^3-1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-1182*cos(f*x+e)^4-810*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+810*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+135*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-135*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+2025*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2025*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1768*cos(f*x+e)^2*sin(f*x+e)-540*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+540*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+1890*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1890*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+1350*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+348*sin(f*x+e)*cos(f*x+e)^3-945*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+945*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2295*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+2295*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-1890*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+1890*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+90*sin(f*x+e)*cos(f*x+e)^4-135*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+135*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-462*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1848*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1848*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2772*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+135*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-135*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2772*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2772*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2772*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)/(sin(f*x+e)*cos(f*x+e)^3+cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)-8*cos(f*x+e)^2+8*sin(f*x+e)-4*cos(f*x+e)+8)/(-c*(sin(f*x+e)-1))^(7/2)/sin(f*x+e)/cos(f*x+e)","C"
113,1,3455,284,0.712000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x)","\text{output too large to display}"," ",0,"1/1170/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)*(-1+cos(f*x+e))^4*(sin(f*x+e)-1)*(cos(f*x+e)+1)*(3696*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2340*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)^5+585*cos(f*x+e)^5*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-585*cos(f*x+e)^5*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2925*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2772*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4+5544*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^3-5544*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^3-924*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2+924*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2-7392*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)+7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)-924*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^6+1848*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^5-1848*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^5-3696*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4+3696*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4-9240*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3+9240*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-924*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+924*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+3696*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+2752*sin(f*x+e)*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-924*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)*cos(f*x+e)^4-1868*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+1755*sin(f*x+e)*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1755*sin(f*x+e)*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2340*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-2340*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-2925*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+7476*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-2340*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2340*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+432*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1440*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+1008*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3696*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+2256*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+924*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^6-1440*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-5136*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+2772*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4)/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(9/2)/sin(f*x+e)^9","C"
114,1,1313,333,0.780000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-4680-4680 \sin \left(f x +e \right)+2832 \cos \left(f x +e \right)+6528 \sin \left(f x +e \right) \cos \left(f x +e \right)-5009 \left(\cos^{4}\left(f x +e \right)\right)-1848 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+1848 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 \left(\cos^{6}\left(f x +e \right)\right)+2930 \left(\cos^{5}\left(f x +e \right)\right)-6224 \left(\cos^{3}\left(f x +e \right)\right)+2079 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+9920 \left(\cos^{2}\left(f x +e \right)\right)-4192 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+1848 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-1848 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+1420 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-2079 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+4620 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+924 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+924 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-924 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-4620 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+3696 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+231 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{9945 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{11}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"2/9945/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(-4680-4680*sin(f*x+e)+2832*cos(f*x+e)+9920*cos(f*x+e)^2+6528*sin(f*x+e)*cos(f*x+e)+1848*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-1848*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+2930*cos(f*x+e)^5-6224*cos(f*x+e)^3+2079*I*sin(f*x+e)*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-5009*cos(f*x+e)^4+231*cos(f*x+e)^6+1420*cos(f*x+e)^2*sin(f*x+e)-4192*sin(f*x+e)*cos(f*x+e)^3+924*sin(f*x+e)*cos(f*x+e)^4+231*I*sin(f*x+e)*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-231*I*sin(f*x+e)*cos(f*x+e)^6*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-2079*I*sin(f*x+e)*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3696*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3696*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-1848*I*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+1848*I*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-924*I*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+924*I*cos(f*x+e)^6*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3696*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3696*I*cos(f*x+e)^4*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-4620*I*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+4620*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2))*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(11/2)/sin(f*x+e)^5/cos(f*x+e)","C"
115,1,1473,382,0.750000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(26520+26520 \sin \left(f x +e \right)-22824 \cos \left(f x +e \right)-30216 \sin \left(f x +e \right) \cos \left(f x +e \right)+17773 \left(\cos^{4}\left(f x +e \right)\right)+3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-385 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)-1155 \left(\cos^{6}\left(f x +e \right)\right)-11998 \left(\cos^{5}\left(f x +e \right)\right)+35284 \left(\cos^{3}\left(f x +e \right)\right)-5775 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-8316 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+8316 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-43600 \left(\cos^{2}\left(f x +e \right)\right)+24488 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-18020 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5775 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+9471 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10164 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-2618 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+231 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-3234 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3234 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+10164 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-9471 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+1155 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-1155 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{69615 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-4\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/69615/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(5/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(26520+26520*sin(f*x+e)-22824*cos(f*x+e)-43600*cos(f*x+e)^2-30216*sin(f*x+e)*cos(f*x+e)-385*sin(f*x+e)*cos(f*x+e)^5-11998*cos(f*x+e)^5+35284*cos(f*x+e)^3+1155*I*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+17773*cos(f*x+e)^4-1155*cos(f*x+e)^6+3696*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-18020*cos(f*x+e)^2*sin(f*x+e)+24488*sin(f*x+e)*cos(f*x+e)^3-2618*sin(f*x+e)*cos(f*x+e)^4+231*cos(f*x+e)^6*sin(f*x+e)-1155*I*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3234*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3234*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+9471*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-9471*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10164*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+10164*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3696*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-5775*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5775*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8316*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8316*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/(-c*(sin(f*x+e)-1))^(13/2)/sin(f*x+e)^5/cos(f*x+e)","C"
116,1,392,423,0.855000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \left(39 \left(\cos^{8}\left(f x +e \right)\right) \sin \left(f x +e \right)+45 \left(\cos^{8}\left(f x +e \right)\right)+10 \left(\cos^{6}\left(f x +e \right)\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+22 \left(\cos^{4}\left(f x +e \right)\right)+154 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{585 f \left(1+\sin \left(f x +e \right)\right) \cos \left(f x +e \right)^{7} \sin \left(f x +e \right)}"," ",0,"-2/585/f*(-c*(sin(f*x+e)-1))^(5/2)*(39*cos(f*x+e)^8*sin(f*x+e)+45*cos(f*x+e)^8+10*cos(f*x+e)^6-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+22*cos(f*x+e)^4+154*cos(f*x+e)^2-231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(1+sin(f*x+e))/cos(f*x+e)^7/sin(f*x+e)","C"
117,1,404,377,0.729000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x)","-\frac{2 \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \left(-33 \left(\cos^{8}\left(f x +e \right)\right)+78 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+88 \left(\cos^{6}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+22 \left(\cos^{4}\left(f x +e \right)\right)+154 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{429 f \left(2 \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)+2\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{5}}"," ",0,"-2/429/f*(-c*(sin(f*x+e)-1))^(3/2)*(-33*cos(f*x+e)^8+78*cos(f*x+e)^6*sin(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+88*cos(f*x+e)^6+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+22*cos(f*x+e)^4+154*cos(f*x+e)^2-231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(2*sin(f*x+e)-cos(f*x+e)^2+2)/sin(f*x+e)/cos(f*x+e)^5","C"
118,1,425,321,0.717000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(21 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+77 \left(\cos^{6}\left(f x +e \right)\right)-132 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-154 \left(\cos^{4}\left(f x +e \right)\right)-154 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}}}{231 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-4\right) \sin \left(f x +e \right) \cos \left(f x +e \right)^{3}}"," ",0,"-2/231/f*(-c*(sin(f*x+e)-1))^(1/2)*(21*cos(f*x+e)^6*sin(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+77*cos(f*x+e)^6-132*sin(f*x+e)*cos(f*x+e)^4+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-154*cos(f*x+e)^4-154*cos(f*x+e)^2+231*cos(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(cos(f*x+e)^2*sin(f*x+e)+3*cos(f*x+e)^2-4*sin(f*x+e)-4)/sin(f*x+e)/cos(f*x+e)^3","C"
119,1,436,272,0.564000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-7 \left(\cos^{6}\left(f x +e \right)\right)+36 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+98 \left(\cos^{4}\left(f x +e \right)\right)-168 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-322 \left(\cos^{2}\left(f x +e \right)\right)+231 \cos \left(f x +e \right)\right)}{63 f \left(-\left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)-8 \sin \left(f x +e \right)-8\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"-2/63/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)*(231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-7*cos(f*x+e)^6+36*sin(f*x+e)*cos(f*x+e)^4+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+98*cos(f*x+e)^4-168*cos(f*x+e)^2*sin(f*x+e)-322*cos(f*x+e)^2+231*cos(f*x+e))/(-cos(f*x+e)^4+4*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2-8*sin(f*x+e)-8)/sin(f*x+e)/cos(f*x+e)/(-c*(sin(f*x+e)-1))^(1/2)","C"
120,1,2998,284,0.623000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/7/f*(-1+cos(f*x+e))*(343*cos(f*x+e)^2+28*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-28*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+28*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+sin(f*x+e)*cos(f*x+e)^5+6*cos(f*x+e)^5-98*cos(f*x+e)^3+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+28*cos(f*x+e)^4-cos(f*x+e)^6+112*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-112*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+168*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-168*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-119*cos(f*x+e)^2*sin(f*x+e)-28*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+28*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+112*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-112*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-28*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*sin(f*x+e)*cos(f*x+e)^3-28*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+28*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-84*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+84*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-84*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+84*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+7*sin(f*x+e)*cos(f*x+e)^4-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2)*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4-cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3+5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)-20*cos(f*x+e)^2+16*sin(f*x+e)-8*cos(f*x+e)+16)/(-c*(sin(f*x+e)-1))^(3/2)/sin(f*x+e)/cos(f*x+e)","C"
121,1,3601,284,0.620000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/5/f*(-1+cos(f*x+e))*(446*cos(f*x+e)^2+80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-sin(f*x+e)*cos(f*x+e)^5-8*cos(f*x+e)^5-85*cos(f*x+e)^3-78*cos(f*x+e)^4+cos(f*x+e)^6-40*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+40*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-40*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+40*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+80*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+320*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-320*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-478*cos(f*x+e)^2*sin(f*x+e)-80*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+80*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+280*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-280*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+80*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+69*sin(f*x+e)*cos(f*x+e)^3-200*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+200*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-360*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+360*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-280*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+280*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-9*sin(f*x+e)*cos(f*x+e)^4-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4-cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3+5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)-20*cos(f*x+e)^2+16*sin(f*x+e)-8*cos(f*x+e)+16)/cos(f*x+e)/(-c*(sin(f*x+e)-1))^(5/2)/sin(f*x+e)","C"
122,1,4237,284,0.617000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x)","\text{output too large to display}"," ",0,"2/9/f*(-1+cos(f*x+e))*(-940*cos(f*x+e)^2-216*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+216*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+540*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*sin(f*x+e)*cos(f*x+e)^5-54*cos(f*x+e)^5+146*cos(f*x+e)^3-231*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+567*cos(f*x+e)^4+3*cos(f*x+e)^6+324*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-324*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-54*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+54*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+54*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-54*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-810*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+810*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+908*cos(f*x+e)^2*sin(f*x+e)+216*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-216*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-756*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+756*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-540*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-162*sin(f*x+e)*cos(f*x+e)^3+378*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-378*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+918*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-918*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+756*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-756*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-57*sin(f*x+e)*cos(f*x+e)^4-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3+231*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-54*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+54*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-924*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+924*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+924*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-924*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1386*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1386*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1386*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1386*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+924*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-924*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4-cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3+5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)-20*cos(f*x+e)^2+16*sin(f*x+e)-8*cos(f*x+e)+16)/(-c*(sin(f*x+e)-1))^(7/2)/sin(f*x+e)/cos(f*x+e)","C"
123,1,4829,284,0.606000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x)","\text{output too large to display}"," ",0,"2/39/f*(-1+cos(f*x+e))*(1800*cos(f*x+e)^2+624*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-624*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2772*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2772*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2541*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2541*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+924*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-924*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2184*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-78*cos(f*x+e)^7*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-39*sin(f*x+e)*cos(f*x+e)^5+78*cos(f*x+e)^7*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+237*cos(f*x+e)^5-332*cos(f*x+e)^3-1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-1472*cos(f*x+e)^4+39*cos(f*x+e)^6-1092*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+1092*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+858*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-858*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-546*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+546*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2184*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2184*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1896*cos(f*x+e)^2*sin(f*x+e)-624*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+624*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+2184*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2184*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2184*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+284*sin(f*x+e)*cos(f*x+e)^3-546*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+546*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2496*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+2496*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-2184*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+2184*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+660*sin(f*x+e)*cos(f*x+e)^4+1848*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+78*sin(f*x+e)*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-78*sin(f*x+e)*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+546*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-546*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2772*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+2772*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*sin(f*x+e)*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1155*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1155*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^5*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4-cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3+5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)-20*cos(f*x+e)^2+16*sin(f*x+e)-8*cos(f*x+e)+16)/(-c*(sin(f*x+e)-1))^(9/2)/sin(f*x+e)/cos(f*x+e)","C"
124,1,3910,333,0.594000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x)","\text{output too large to display}"," ",0,"-1/1326/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)*(-1+cos(f*x+e))^4*(sin(f*x+e)-1)*(cos(f*x+e)+1)*(-2960*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*cos(f*x+e)^5+2652*cos(f*x+e)^5*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2652*cos(f*x+e)^5*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+7956*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+663*sin(f*x+e)*cos(f*x+e)^5*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-752*sin(f*x+e)*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1044*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)*cos(f*x+e)^4-11840*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+5304*sin(f*x+e)*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5304*sin(f*x+e)*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5304*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-5304*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-7956*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+7856*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-5304*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5304*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5356*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-663*sin(f*x+e)*cos(f*x+e)^5*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2652*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+2496*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-6928*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-3696*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^6*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+9888*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+3696*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^6*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-924*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+2496*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-4896*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+14784*I*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+14784*I*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-14784*I*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+924*I*sin(f*x+e)*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-924*I*sin(f*x+e)*cos(f*x+e)^6*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+1848*I*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^5*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-1848*I*sin(f*x+e)*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6468*I*sin(f*x+e)*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6468*I*sin(f*x+e)*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-14784*I*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-7392*I*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+7392*I*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+7392*I*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-7392*I*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+22176*I*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-22176*I*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3696*I*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-7392*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-14784*I*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+14784*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e))/(-cos(f*x+e)^4+4*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2-8*sin(f*x+e)-8)/sin(f*x+e)^9/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(11/2)","C"
125,1,1484,382,0.624000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-10608-10608 \sin \left(f x +e \right)+14304 \cos \left(f x +e \right)+6912 \sin \left(f x +e \right) \cos \left(f x +e \right)-791 \left(\cos^{4}\left(f x +e \right)\right)+3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+4256 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)-1155 \left(\cos^{6}\left(f x +e \right)\right)+6566 \left(\cos^{5}\left(f x +e \right)\right)-20408 \left(\cos^{3}\left(f x +e \right)\right)-5775 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-8316 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+8316 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+12092 \left(\cos^{2}\left(f x +e \right)\right)-12640 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)-3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3696 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+19108 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5775 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+9471 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10164 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-7259 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+231 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)-3234 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3234 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+10164 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-9471 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+1155 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-1155 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{13923 f \left(-\left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)-8 \sin \left(f x +e \right)-8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{13}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"2/13923/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(-10608-10608*sin(f*x+e)+14304*cos(f*x+e)+12092*cos(f*x+e)^2+6912*sin(f*x+e)*cos(f*x+e)+4256*sin(f*x+e)*cos(f*x+e)^5+6566*cos(f*x+e)^5-20408*cos(f*x+e)^3+1155*I*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-791*cos(f*x+e)^4-1155*cos(f*x+e)^6+3696*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+19108*cos(f*x+e)^2*sin(f*x+e)-12640*sin(f*x+e)*cos(f*x+e)^3-7259*sin(f*x+e)*cos(f*x+e)^4+231*cos(f*x+e)^6*sin(f*x+e)-1155*I*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3234*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3234*I*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+9471*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-9471*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-10164*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+10164*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3696*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3696*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-5775*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+5775*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8316*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8316*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(-cos(f*x+e)^4+4*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2-8*sin(f*x+e)-8)/(-c*(sin(f*x+e)-1))^(13/2)/sin(f*x+e)^5/cos(f*x+e)","C"
126,1,1644,431,0.737000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{7}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(74256+74256 \sin \left(f x +e \right)-81648 \cos \left(f x +e \right)-66864 \sin \left(f x +e \right) \cos \left(f x +e \right)+34757 \left(\cos^{4}\left(f x +e \right)\right)-7392 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+7392 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 \left(\cos^{8}\left(f x +e \right)\right)-20895 \sin \left(f x +e \right) \left(\cos^{5}\left(f x +e \right)\right)+4004 \left(\cos^{6}\left(f x +e \right)\right)-50003 \left(\cos^{5}\left(f x +e \right)\right)+130804 \left(\cos^{3}\left(f x +e \right)\right)+15246 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+18480 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-18480 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-112324 \left(\cos^{2}\left(f x +e \right)\right)+385 \left(\cos^{7}\left(f x +e \right)\right)+85052 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+7392 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-7392 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-99836 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-15246 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-23562 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+22176 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+29673 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-1386 \left(\cos^{6}\left(f x +e \right)\right) \sin \left(f x +e \right)+10164 i \left(\cos^{6}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-10164 i \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-22176 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+23562 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-1386 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+1386 i \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-4389 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+4389 i \sin \left(f x +e \right) \left(\cos^{6}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+231 i \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-231 i \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{8}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{116025 f \left(-\left(\cos^{4}\left(f x +e \right)\right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+8 \left(\cos^{2}\left(f x +e \right)\right)-8 \sin \left(f x +e \right)-8\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{15}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/116025/f*(g*cos(f*x+e))^(3/2)*(a*(1+sin(f*x+e)))^(7/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(74256+74256*sin(f*x+e)-81648*cos(f*x+e)-112324*cos(f*x+e)^2-66864*sin(f*x+e)*cos(f*x+e)-20895*sin(f*x+e)*cos(f*x+e)^5-231*cos(f*x+e)^8-50003*cos(f*x+e)^5+130804*cos(f*x+e)^3+231*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+34757*cos(f*x+e)^4+4004*cos(f*x+e)^6-99836*cos(f*x+e)^2*sin(f*x+e)+85052*sin(f*x+e)*cos(f*x+e)^3+385*cos(f*x+e)^7+29673*sin(f*x+e)*cos(f*x+e)^4-7392*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+7392*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+15246*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-15246*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-18480*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+18480*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-1386*cos(f*x+e)^6*sin(f*x+e)-231*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-1386*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+1386*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^8*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+10164*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-10164*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-23562*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+23562*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+22176*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-22176*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+7392*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-7392*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-4389*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+4389*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^6*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2))*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(-cos(f*x+e)^4+4*cos(f*x+e)^2*sin(f*x+e)+8*cos(f*x+e)^2-8*sin(f*x+e)-8)/(-c*(sin(f*x+e)-1))^(15/2)/sin(f*x+e)^5/cos(f*x+e)","C"
127,1,415,226,0.529000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-231 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+15 \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-63 \left(\cos^{4}\left(f x +e \right)\right)-140 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+294 \left(\cos^{2}\left(f x +e \right)\right)-231 \cos \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}}}{105 f \left(\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)+4\right) \sin \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \cos \left(f x +e \right)}"," ",0,"-2/105/f*(g*cos(f*x+e))^(3/2)*(231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+15*sin(f*x+e)*cos(f*x+e)^4-63*cos(f*x+e)^4-140*cos(f*x+e)^2*sin(f*x+e)+294*cos(f*x+e)^2-231*cos(f*x+e))*(-c*(sin(f*x+e)-1))^(5/2)/(cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)+4)/sin(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)/cos(f*x+e)","C"
128,1,382,180,0.499000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \left(\cos^{4}\left(f x +e \right)\right)+10 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-24 \left(\cos^{2}\left(f x +e \right)\right)+21 \cos \left(f x +e \right)\right) \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}{15 f \left(\cos^{2}\left(f x +e \right)+2 \sin \left(f x +e \right)-2\right) \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}}"," ",0,"-2/15/f*(g*cos(f*x+e))^(3/2)*(21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*cos(f*x+e)^4+10*cos(f*x+e)^2*sin(f*x+e)-24*cos(f*x+e)^2+21*cos(f*x+e))*(-c*(sin(f*x+e)-1))^(3/2)/(cos(f*x+e)^2+2*sin(f*x+e)-2)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(1/2)","C"
129,1,361,132,0.551000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \left(3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-3 \left(\cos^{2}\left(f x +e \right)\right)+3 \cos \left(f x +e \right)\right)}{3 f \left(\sin \left(f x +e \right)-1\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"-2/3/f*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(1/2)*(3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^2+3*cos(f*x+e))/(sin(f*x+e)-1)/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)/cos(f*x+e)","C"
130,1,334,86,0.498000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-\left(\cos^{2}\left(f x +e \right)\right)+\cos \left(f x +e \right)\right)}{f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right) \cos \left(f x +e \right)}"," ",0,"2/f*(g*cos(f*x+e))^(3/2)*(I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-cos(f*x+e)^2+cos(f*x+e))/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(1/2)/sin(f*x+e)/cos(f*x+e)","C"
131,1,925,133,0.598000," ","int((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\sin \left(f x +e \right)-1\right) \left(4 i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-4 i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+8 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-8 i \sin \left(f x +e \right) \cos \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-4 i \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)-4 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right) \sin \left(f x +e \right)+\cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right) \sin \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right)}{2 f \left(\cos \left(f x +e \right)+1\right) \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \sin \left(f x +e \right)^{5} \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}}}"," ",0,"-1/2/f*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(sin(f*x+e)-1)*(4*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-4*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-4*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+4*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))/(cos(f*x+e)+1)/(a*(1+sin(f*x+e)))^(1/2)/sin(f*x+e)^5/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(3/2)","C"
132,1,781,179,0.559000," ","int((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+2 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)-\left(\cos^{2}\left(f x +e \right)\right)-\sin \left(f x +e \right)+2 \cos \left(f x +e \right)-1\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{5 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/5/f*(g*cos(f*x+e))^(3/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-2*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2+2*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2-I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^2*sin(f*x+e)-cos(f*x+e)^2-sin(f*x+e)+2*cos(f*x+e)-1)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(5/2)/sin(f*x+e)^5/cos(f*x+e)","C"
133,1,955,225,0.561000," ","int((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(1/2),x)","\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)-\cos \left(f x +e \right)+1\right) \left(-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-12 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+6 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+12 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-9 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)-3 \left(\cos^{4}\left(f x +e \right)\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{4}\left(f x +e \right)\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+5 \left(\cos^{3}\left(f x +e \right)\right)+\sin \left(f x +e \right) \cos \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right)+5 \sin \left(f x +e \right)-11 \cos \left(f x +e \right)+5\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{45 f \sqrt{a \left(1+\sin \left(f x +e \right)\right)}\, \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"2/45/f*(g*cos(f*x+e))^(3/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)-cos(f*x+e)+1)*(9*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-9*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*sin(f*x+e)*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4-6*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*cos(f*x+e)^4+12*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*cos(f*x+e)^2*sin(f*x+e)+5*cos(f*x+e)^3+sin(f*x+e)*cos(f*x+e)+4*cos(f*x+e)^2+5*sin(f*x+e)-11*cos(f*x+e)+5)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(a*(1+sin(f*x+e)))^(1/2)/(-c*(sin(f*x+e)-1))^(7/2)/sin(f*x+e)^5/cos(f*x+e)","C"
134,1,2994,284,0.620000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/7/f*(-1+cos(f*x+e))*(-343*cos(f*x+e)^2-28*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+28*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-28*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+sin(f*x+e)*cos(f*x+e)^5-6*cos(f*x+e)^5+98*cos(f*x+e)^3-28*cos(f*x+e)^4+cos(f*x+e)^6-112*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+112*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-168*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+168*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-119*cos(f*x+e)^2*sin(f*x+e)-28*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+28*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-112*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+112*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+28*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*sin(f*x+e)*cos(f*x+e)^3-28*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+28*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-84*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+84*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-84*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+84*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+7*sin(f*x+e)*cos(f*x+e)^4-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-231*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2)*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3-5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)+20*cos(f*x+e)^2+16*sin(f*x+e)+8*cos(f*x+e)-16)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)","C"
135,1,2946,235,0.570000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/15/f*(-1+cos(f*x+e))*(351*cos(f*x+e)^2+30*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-30*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+30*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^5-94*cos(f*x+e)^3+231*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+20*cos(f*x+e)^4+120*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-120*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+180*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-180*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+111*cos(f*x+e)^2*sin(f*x+e)+30*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-30*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+120*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-120*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-30*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+17*sin(f*x+e)*cos(f*x+e)^3+30*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-30*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-90*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+90*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-90*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*sin(f*x+e)*cos(f*x+e)^4-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2+462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2-462*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^2+231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3-231*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)^3)*(-c*(sin(f*x+e)-1))^(5/2)*(g*cos(f*x+e))^(3/2)/(cos(f*x+e)^4-sin(f*x+e)*cos(f*x+e)^3+3*cos(f*x+e)^3+4*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^2+4*sin(f*x+e)*cos(f*x+e)-4*cos(f*x+e)-8*sin(f*x+e)+8)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)","C"
136,1,2890,186,0.556000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"-2/3/f*(-1+cos(f*x+e))*(33*cos(f*x+e)^2+3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+3*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-8*cos(f*x+e)^3+21*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^4+12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-12*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+18*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-18*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*cos(f*x+e)^2*sin(f*x+e)+3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+12*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-12*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+sin(f*x+e)*cos(f*x+e)^3+3*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-9*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+9*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-9*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-21*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+42*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(-c*(sin(f*x+e)-1))^(3/2)*(g*cos(f*x+e))^(3/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)","C"
137,1,2838,135,0.600000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x)","\text{output too large to display}"," ",0,"1/f*(-1+cos(f*x+e))*(-10*cos(f*x+e)^2-(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+2*cos(f*x+e)^3-6*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-6*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+6*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-2*cos(f*x+e)^2*sin(f*x+e)-ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+4*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+3*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-3*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+3*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+6*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+12*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+6*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2))*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(1/2)/(sin(f*x+e)*cos(f*x+e)-cos(f*x+e)^2-2*sin(f*x+e)-cos(f*x+e)+2)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(3/2)","C"
138,1,925,133,0.592000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x)","\frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(4 i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-4 i \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+8 i \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-8 i \sin \left(f x +e \right) \cos \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+4 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right)-4 i \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right)+4 \sin \left(f x +e \right) \cos \left(f x +e \right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\cos \left(f x +e \right) \ln \left(-\frac{2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1}{\sin \left(f x +e \right)^{2}}\right) \sin \left(f x +e \right)+\cos \left(f x +e \right) \ln \left(-\frac{2 \left(2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-\left(\cos^{2}\left(f x +e \right)\right)+2 \cos \left(f x +e \right)-2 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}-1\right)}{\sin \left(f x +e \right)^{2}}\right) \sin \left(f x +e \right)+4 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}+4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\, \sin \left(f x +e \right)-4 \sqrt{-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}}\right)}{2 f \left(\cos \left(f x +e \right)+1\right) \sin \left(f x +e \right)^{5} \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-\frac{\cos \left(f x +e \right)}{\left(\cos \left(f x +e \right)+1\right)^{2}}\right)^{\frac{3}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}}"," ",0,"1/2/f*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(4*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-4*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8*I*sin(f*x+e)*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-4*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+4*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+4*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)-4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2))/(cos(f*x+e)+1)/sin(f*x+e)^5/(a*(1+sin(f*x+e)))^(3/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)/(-c*(sin(f*x+e)-1))^(1/2)","C"
139,1,363,182,0.571000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-\cos \left(f x +e \right)+1\right)}{f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-cos(f*x+e)+1)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(3/2)/sin(f*x+e)^5/cos(f*x+e)","C"
140,1,877,231,0.540000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(-3 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)-3 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \sin \left(f x +e \right)-3 \cos \left(f x +e \right)+3\right)}{5 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right)^{5}}"," ",0,"-2/5/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+3*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-3*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*sin(f*x+e)*cos(f*x+e)-2*sin(f*x+e)-3*cos(f*x+e)+3)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(5/2)/cos(f*x+e)/sin(f*x+e)^5","C"
141,1,1177,280,0.598000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)-6 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+3 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+6 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 \left(\cos^{3}\left(f x +e \right)\right)+6 \sin \left(f x +e \right) \cos \left(f x +e \right)-2 \left(\cos^{2}\left(f x +e \right)\right)-4 \sin \left(f x +e \right)-6 \cos \left(f x +e \right)+5\right)}{9 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{3}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right)^{5}}"," ",0,"-2/9/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(-6*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-6*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+3*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+6*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-6*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-6*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+6*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+3*cos(f*x+e)^3+6*sin(f*x+e)*cos(f*x+e)-2*cos(f*x+e)^2-4*sin(f*x+e)-6*cos(f*x+e)+5)/(a*(1+sin(f*x+e)))^(3/2)/(-c*(sin(f*x+e)-1))^(7/2)/cos(f*x+e)/sin(f*x+e)^5","C"
142,1,3654,333,0.654000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"-2/35/f*(-1+cos(f*x+e))*(8554*cos(f*x+e)^2+1400*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1400*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1400*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+39*sin(f*x+e)*cos(f*x+e)^5-4389*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-192*cos(f*x+e)^5-1575*cos(f*x+e)^3-1582*cos(f*x+e)^4+44*cos(f*x+e)^6+5*cos(f*x+e)^7-700*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+700*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+700*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-700*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+1400*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1400*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5600*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5600*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+9002*cos(f*x+e)^2*sin(f*x+e)+1400*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-1400*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+4900*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-4900*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+1400*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-1351*sin(f*x+e)*cos(f*x+e)^3+3500*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-3500*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+6300*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-6300*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+4900*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-4900*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+231*sin(f*x+e)*cos(f*x+e)^4-5*cos(f*x+e)^6*sin(f*x+e)-8778*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+8778*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+4389*I*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-13167*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+13167*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+4389*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8778*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+8778*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-4389*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-13167*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+13167*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(9/2)/(cos(f*x+e)^6-sin(f*x+e)*cos(f*x+e)^5+5*cos(f*x+e)^5+6*sin(f*x+e)*cos(f*x+e)^4-18*cos(f*x+e)^4+12*sin(f*x+e)*cos(f*x+e)^3-20*cos(f*x+e)^3-32*cos(f*x+e)^2*sin(f*x+e)+48*cos(f*x+e)^2-16*sin(f*x+e)*cos(f*x+e)+16*cos(f*x+e)+32*sin(f*x+e)-32)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)","C"
143,1,3598,284,0.596000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"-2/5/f*(-1+cos(f*x+e))*(446*cos(f*x+e)^2+80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+sin(f*x+e)*cos(f*x+e)^5+231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8*cos(f*x+e)^5-85*cos(f*x+e)^3-78*cos(f*x+e)^4+cos(f*x+e)^6-40*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+40*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+40*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-40*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+80*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-80*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+320*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-320*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+478*cos(f*x+e)^2*sin(f*x+e)+80*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-80*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+280*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-280*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+80*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-69*sin(f*x+e)*cos(f*x+e)^3+200*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-200*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+360*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-360*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+280*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-280*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+9*sin(f*x+e)*cos(f*x+e)^4-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e))*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(7/2)/(sin(f*x+e)*cos(f*x+e)^4+cos(f*x+e)^5+4*sin(f*x+e)*cos(f*x+e)^3-5*cos(f*x+e)^4-12*cos(f*x+e)^2*sin(f*x+e)-8*cos(f*x+e)^3-8*sin(f*x+e)*cos(f*x+e)+20*cos(f*x+e)^2+16*sin(f*x+e)+8*cos(f*x+e)-16)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)","C"
144,1,3551,235,0.566000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/15/f*(-1+cos(f*x+e))*(-438*cos(f*x+e)^2-90*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-693*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2+5*cos(f*x+e)^5+89*cos(f*x+e)^3+70*cos(f*x+e)^4+45*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-45*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+45*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-90*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+90*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-360*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+360*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-486*cos(f*x+e)^2*sin(f*x+e)-90*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+90*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-315*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+315*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-90*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+65*sin(f*x+e)*cos(f*x+e)^3-225*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+225*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-405*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+405*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-315*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+315*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-5*sin(f*x+e)*cos(f*x+e)^4-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+462*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+693*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+462*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-231*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(-c*(sin(f*x+e)-1))^(5/2)*(g*cos(f*x+e))^(3/2)/(sin(f*x+e)*cos(f*x+e)^3-cos(f*x+e)^4-4*cos(f*x+e)^2*sin(f*x+e)-3*cos(f*x+e)^3-4*sin(f*x+e)*cos(f*x+e)+8*cos(f*x+e)^2+8*sin(f*x+e)+4*cos(f*x+e)-8)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)","C"
145,1,3497,186,0.558000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{output too large to display}"," ",0,"2/5/f*(-1+cos(f*x+e))*(38*cos(f*x+e)^2+10*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-10*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-10*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-9*cos(f*x+e)^3-5*cos(f*x+e)^4-5*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*cos(f*x+e)^5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4-5*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)*cos(f*x+e)^4+10*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-10*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-40*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+46*cos(f*x+e)^2*sin(f*x+e)+10*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)-10*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*sin(f*x+e)+35*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-35*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+10*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*sin(f*x+e)*cos(f*x+e)^3+25*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-25*sin(f*x+e)*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+45*sin(f*x+e)*cos(f*x+e)^2*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-45*sin(f*x+e)*cos(f*x+e)^2*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+35*sin(f*x+e)*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)-35*sin(f*x+e)*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)+63*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-63*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^4*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-42*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+42*I*cos(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-63*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+63*I*cos(f*x+e)^2*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I))*(g*cos(f*x+e))^(3/2)*(-c*(sin(f*x+e)-1))^(3/2)/(cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^3+2*sin(f*x+e)*cos(f*x+e)-3*cos(f*x+e)^2-4*sin(f*x+e)-2*cos(f*x+e)+4)/sin(f*x+e)/cos(f*x+e)/(a*(1+sin(f*x+e)))^(5/2)","C"
146,1,2040,182,0.553000," ","int((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/10/f*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^3*(1+sin(f*x+e))*(-c*(sin(f*x+e)-1))^(1/2)*(-5*cos(f*x+e)^3*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+12*sin(f*x+e)*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+5*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)-5*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)*sin(f*x+e)+5*cos(f*x+e)^3*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-20*cos(f*x+e)^3*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+5*cos(f*x+e)*ln(-2*(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)-5*cos(f*x+e)*ln(-(2*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-cos(f*x+e)^2+2*cos(f*x+e)-2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-1)/sin(f*x+e)^2)+8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-8*cos(f*x+e)^2*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)-12*I*cos(f*x+e)^4*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-12*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+4*sin(f*x+e)*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+12*I*cos(f*x+e)^4*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-8*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*sin(f*x+e)+20*cos(f*x+e)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)+24*I*sin(f*x+e)*cos(f*x+e)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*sin(f*x+e)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-12*I*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-24*I*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+24*I*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+12*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-12*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)+24*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-24*I*(1/(cos(f*x+e)+1))^(1/2)*(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e))/(sin(f*x+e)-1)/sin(f*x+e)^7/(a*(1+sin(f*x+e)))^(5/2)/(-cos(f*x+e)/(cos(f*x+e)+1)^2)^(3/2)","C"
147,1,777,179,0.551000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x)","-\frac{2 \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(\sin \left(f x +e \right) \cos \left(f x +e \right)-\sin \left(f x +e \right)+\cos \left(f x +e \right)-1\right) \left(-i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+2 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-2 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+\cos^{2}\left(f x +e \right)-\sin \left(f x +e \right)-2 \cos \left(f x +e \right)+1\right) \left(\cos^{2}\left(f x +e \right)+2 \cos \left(f x +e \right)+1\right)}{5 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \sqrt{-c \left(\sin \left(f x +e \right)-1\right)}\, \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/5/f*(g*cos(f*x+e))^(3/2)*(sin(f*x+e)*cos(f*x+e)-sin(f*x+e)+cos(f*x+e)-1)*(-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4+I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2+2*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2-2*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2-I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)+I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)-I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+cos(f*x+e)^2*sin(f*x+e)+cos(f*x+e)^2-sin(f*x+e)-2*cos(f*x+e)+1)*(cos(f*x+e)^2+2*cos(f*x+e)+1)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(1/2)/sin(f*x+e)^5/cos(f*x+e)","C"
148,1,877,231,0.555000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}+3 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \cos \left(f x +e \right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \cos \left(f x +e \right) \sin \left(f x +e \right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 \sin \left(f x +e \right) \cos \left(f x +e \right)+2 \sin \left(f x +e \right)-3 \cos \left(f x +e \right)+3\right)}{5 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{3}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right)^{5}}"," ",0,"-2/5/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(3*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*cos(f*x+e)+3*I*sin(f*x+e)*cos(f*x+e)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)-3*sin(f*x+e)*cos(f*x+e)+2*sin(f*x+e)-3*cos(f*x+e)+3)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(3/2)/cos(f*x+e)/sin(f*x+e)^5","C"
149,1,395,277,0.560000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x)","-\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(3 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-3 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)-3 \left(\cos^{3}\left(f x +e \right)\right)+2 \left(\cos^{2}\left(f x +e \right)\right)+1\right)}{5 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{5}{2}} \sin \left(f x +e \right)^{5} \cos \left(f x +e \right)}"," ",0,"-2/5/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(3*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*sin(f*x+e)*cos(f*x+e)^3*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+3*I*sin(f*x+e)*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-3*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)*cos(f*x+e)^2-3*cos(f*x+e)^3+2*cos(f*x+e)^2+1)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(5/2)/sin(f*x+e)^5/cos(f*x+e)","C"
150,1,947,326,0.646000," ","int((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x)","\frac{2 \left(\cos \left(f x +e \right)+1\right)^{2} \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(1+\sin \left(f x +e \right)\right) \left(\sin \left(f x +e \right)-1\right) \left(-21 i \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \left(\cos^{2}\left(f x +e \right)\right) \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right)+21 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \left(\cos^{4}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{2}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \left(\cos^{4}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \left(\cos^{3}\left(f x +e \right)\right) \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right) \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}-21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)+21 i \sqrt{\frac{1}{\cos \left(f x +e \right)+1}}\, \left(\cos^{5}\left(f x +e \right)\right) \sqrt{\frac{\cos \left(f x +e \right)}{\cos \left(f x +e \right)+1}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(f x +e \right)\right)}{\sin \left(f x +e \right)}, i\right)-21 \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)+14 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right)+21 \left(\cos^{3}\left(f x +e \right)\right)-14 \left(\cos^{2}\left(f x +e \right)\right)+2 \sin \left(f x +e \right)-7\right)}{45 f \left(a \left(1+\sin \left(f x +e \right)\right)\right)^{\frac{5}{2}} \left(-c \left(\sin \left(f x +e \right)-1\right)\right)^{\frac{7}{2}} \cos \left(f x +e \right) \sin \left(f x +e \right)^{5}}"," ",0,"2/45/f*(cos(f*x+e)+1)^2*(g*cos(f*x+e))^(3/2)*(-1+cos(f*x+e))^2*(1+sin(f*x+e))*(sin(f*x+e)-1)*(-21*I*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4+21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^5*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^4*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^5*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)+21*I*cos(f*x+e)^2*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)*sin(f*x+e)-21*I*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)*cos(f*x+e)^2*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*cos(f*x+e)^3*sin(f*x+e)*(1/(cos(f*x+e)+1))^(1/2)*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticE(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^2*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*I*(1/(cos(f*x+e)+1))^(1/2)*cos(f*x+e)^3*(cos(f*x+e)/(cos(f*x+e)+1))^(1/2)*EllipticF(I*(-1+cos(f*x+e))/sin(f*x+e),I)-21*sin(f*x+e)*cos(f*x+e)^3+14*cos(f*x+e)^2*sin(f*x+e)+21*cos(f*x+e)^3-14*cos(f*x+e)^2+2*sin(f*x+e)-7)/(a*(1+sin(f*x+e)))^(5/2)/(-c*(sin(f*x+e)-1))^(7/2)/cos(f*x+e)/sin(f*x+e)^5","C"
151,0,0,97,0.535000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
152,0,0,77,2.957000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x)","F"
153,0,0,77,1.533000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x)","F"
154,0,0,75,0.812000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x)","F"
155,0,0,72,0.307000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x)","F"
156,0,0,70,0.665000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x)","F"
157,0,0,77,1.365000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x)","F"
158,0,0,77,1.403000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x)","F"
159,0,0,96,0.443000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x)","F"
160,0,0,94,0.467000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x)","F"
161,0,0,91,0.451000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \sqrt{c -c \sin \left(f x +e \right)}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x)","F"
162,0,0,88,0.418000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
163,0,0,90,0.395000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{3}{2}}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x)","F"
164,0,0,96,0.392000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c -c \sin \left(f x +e \right)\right)^{\frac{5}{2}}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x)","F"
165,0,0,88,0.008000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m}}{\sqrt{c -c \sin \left(f x +e \right)}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x)","F"
166,0,0,88,0.469000," ","int((g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(c +c \sin \left(f x +e \right)\right)^{m}}{\sqrt{a -a \sin \left(f x +e \right)}}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x)","F"
167,0,0,99,1.389000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-3-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x)","F"
168,0,0,99,1.109000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-2-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x)","F"
169,0,0,96,0.707000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-1-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x)","F"
170,0,0,97,0.467000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x)","F"
171,0,0,99,0.668000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{1-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x)","F"
172,0,0,99,1.002000," ","int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x)","\int \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2-m}\, dx"," ",0,"int((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x)","F"
173,0,0,115,9.720000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
174,1,8507,59,13.417000," ","int((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+m),x)","\text{output too large to display}"," ",0,"result too large to display","C"
175,0,0,203,66.340000," ","int((g*cos(f*x+e))^(5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{5-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
176,0,0,127,26.100000," ","int((g*cos(f*x+e))^(3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{3-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
177,0,0,58,37.176000," ","int((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{1-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
178,0,0,79,25.909000," ","int((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
179,0,0,83,32.330000," ","int((g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{-3-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
180,0,0,86,53.336000," ","int((g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{-5-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
181,0,0,53,0.964000," ","int((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-2 m} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x)","F"
182,0,0,122,1.770000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{3+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n),x)","F"
183,0,0,122,1.474000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{2+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n),x)","F"
184,0,0,119,95.905000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{1+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n),x)","F"
185,0,0,55,1.054000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
186,0,0,125,1.326000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-1+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n),x)","F"
187,0,0,204,1.840000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-2+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n),x)","F"
188,0,0,290,2.977000," ","int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m -n} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{-3+n}\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n),x)","F"
189,0,0,118,10.491000," ","int((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","\int \left(g \sec \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c -c \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x)","F"
190,1,28,29,0.090000," ","int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{4}\left(d x +c \right)\right) a}{4}+\frac{\left(\sin^{3}\left(d x +c \right)\right) a}{3}}{d}"," ",0,"1/d*(1/4*sin(d*x+c)^4*a+1/3*sin(d*x+c)^3*a)","A"
191,1,28,29,0.046000," ","int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{3}\left(d x +c \right)\right) a}{3}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a}{2}}{d}"," ",0,"1/d*(1/3*sin(d*x+c)^3*a+1/2*sin(d*x+c)^2*a)","A"
192,1,25,24,0.129000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{a \sin \left(d x +c \right)}{d}"," ",0,"a*ln(sin(d*x+c))/d+a*sin(d*x+c)/d","A"
193,1,28,25,0.084000," ","int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","-\frac{a}{d \sin \left(d x +c \right)}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-a/d/sin(d*x+c)+a*ln(sin(d*x+c))/d","A"
194,1,27,28,0.128000," ","int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{1}{\sin \left(d x +c \right)}-\frac{1}{2 \sin \left(d x +c \right)^{2}}\right)}{d}"," ",0,"a/d*(-1/sin(d*x+c)-1/2/sin(d*x+c)^2)","A"
195,1,27,29,0.086000," ","int(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a/d*(-1/2/sin(d*x+c)^2-1/3/sin(d*x+c)^3)","A"
196,1,27,29,0.092000," ","int(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{1}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a/d*(-1/4/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
197,1,45,49,0.092000," ","int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{\frac{\left(\sin^{5}\left(d x +c \right)\right) a^{2}}{5}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(1/5*sin(d*x+c)^5*a^2+1/2*a^2*sin(d*x+c)^4+1/3*a^2*sin(d*x+c)^3)","A"
198,1,45,49,0.095000," ","int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{2 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2}}{d}"," ",0,"1/d*(1/4*a^2*sin(d*x+c)^4+2/3*a^2*sin(d*x+c)^3+1/2*sin(d*x+c)^2*a^2)","A"
199,1,46,45,0.175000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{2 a^{2} \sin \left(d x +c \right)}{d}+\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"a^2*ln(sin(d*x+c))/d+2*a^2*sin(d*x+c)/d+1/2*a^2*sin(d*x+c)^2/d","A"
200,1,46,43,0.133000," ","int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \sin \left(d x +c \right)}{d}-\frac{a^{2}}{d \sin \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"a^2*sin(d*x+c)/d-a^2/d/sin(d*x+c)+2*a^2*ln(sin(d*x+c))/d","A"
201,1,48,45,0.185000," ","int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","-\frac{2 a^{2}}{d \sin \left(d x +c \right)}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-2*a^2/d/sin(d*x+c)+a^2*ln(sin(d*x+c))/d-1/2*a^2/d/sin(d*x+c)^2","A"
202,1,39,28,0.146000," ","int(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{1}{\sin \left(d x +c \right)}-\frac{1}{\sin \left(d x +c \right)^{2}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^2/d*(-1/sin(d*x+c)-1/sin(d*x+c)^2-1/3/sin(d*x+c)^3)","A"
203,1,39,49,0.138000," ","int(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}-\frac{2}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^2/d*(-1/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4-2/3/sin(d*x+c)^3)","A"
204,1,39,49,0.136000," ","int(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^2/d*(-1/5/sin(d*x+c)^5-1/2/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
205,1,39,49,0.155000," ","int(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{1}{6 \sin \left(d x +c \right)^{6}}-\frac{2}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}\right)}{d}"," ",0,"a^2/d*(-1/6/sin(d*x+c)^6-2/5/sin(d*x+c)^5-1/4/sin(d*x+c)^4)","A"
206,1,58,65,0.105000," ","int(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}}{d}"," ",0,"1/d*(1/7*a^3*sin(d*x+c)^7+1/2*a^3*sin(d*x+c)^6+3/5*a^3*sin(d*x+c)^5+1/4*a^3*sin(d*x+c)^4)","A"
207,1,58,65,0.095000," ","int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(1/6*a^3*sin(d*x+c)^6+3/5*a^3*sin(d*x+c)^5+3/4*a^3*sin(d*x+c)^4+1/3*a^3*sin(d*x+c)^3)","A"
208,1,57,41,0.095000," ","int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4}+a^{3} \left(\sin^{3}\left(d x +c \right)\right)+\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2}}{d}"," ",0,"1/d*(1/5*a^3*sin(d*x+c)^5+3/4*a^3*sin(d*x+c)^4+a^3*sin(d*x+c)^3+1/2*a^3*sin(d*x+c)^2)","A"
209,1,62,61,0.183000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \sin \left(d x +c \right)}{d}+\frac{3 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"a^3*ln(sin(d*x+c))/d+3*a^3*sin(d*x+c)/d+3/2*a^3*sin(d*x+c)^2/d+1/3*a^3*sin(d*x+c)^3/d","A"
210,1,63,60,0.142000," ","int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \sin \left(d x +c \right)}{d}-\frac{a^{3}}{d \sin \left(d x +c \right)}+\frac{3 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^3*sin(d*x+c)^2/d+3*a^3*sin(d*x+c)/d-a^3/d/sin(d*x+c)+3*a^3*ln(sin(d*x+c))/d","A"
211,1,62,59,0.193000," ","int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \sin \left(d x +c \right)}{d}-\frac{3 a^{3}}{d \sin \left(d x +c \right)}+\frac{3 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{3}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"a^3*sin(d*x+c)/d-3*a^3/d/sin(d*x+c)+3*a^3*ln(sin(d*x+c))/d-1/2*a^3/d/sin(d*x+c)^2","A"
212,1,64,61,0.137000," ","int(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","-\frac{3 a^{3}}{d \sin \left(d x +c \right)}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{3}}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-3*a^3/d/sin(d*x+c)+a^3*ln(sin(d*x+c))/d-3/2*a^3/d/sin(d*x+c)^2-1/3*a^3/d/sin(d*x+c)^3","A"
213,1,49,28,0.144000," ","int(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{1}{\sin \left(d x +c \right)}-\frac{3}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{\sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^3/d*(-1/sin(d*x+c)-3/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4-1/sin(d*x+c)^3)","A"
214,1,49,57,0.142000," ","int(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{3}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{\sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^3/d*(-1/5/sin(d*x+c)^5-1/2/sin(d*x+c)^2-3/4/sin(d*x+c)^4-1/sin(d*x+c)^3)","A"
215,1,49,65,0.161000," ","int(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{1}{6 \sin \left(d x +c \right)^{6}}-\frac{3}{5 \sin \left(d x +c \right)^{5}}-\frac{3}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}\right)}{d}"," ",0,"a^3/d*(-1/6/sin(d*x+c)^6-3/5/sin(d*x+c)^5-3/4/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
216,1,49,65,0.193000," ","int(cos(d*x+c)*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{1}{2 \sin \left(d x +c \right)^{6}}-\frac{3}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}\right)}{d}"," ",0,"a^3/d*(-1/2/sin(d*x+c)^6-3/5/sin(d*x+c)^5-1/7/sin(d*x+c)^7-1/4/sin(d*x+c)^4)","A"
217,1,71,81,0.106000," ","int(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\sin^{9}\left(d x +c \right)\right)}{9}+\frac{a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{2}+\frac{6 a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{2 a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{3}+\frac{a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(1/9*a^4*sin(d*x+c)^9+1/2*a^4*sin(d*x+c)^8+6/7*a^4*sin(d*x+c)^7+2/3*a^4*sin(d*x+c)^6+1/5*a^4*sin(d*x+c)^5)","A"
218,1,70,80,0.099000," ","int(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\sin^{8}\left(d x +c \right)\right)}{8}+\frac{4 a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{7}+a^{4} \left(\sin^{6}\left(d x +c \right)\right)+\frac{4 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{4}}{d}"," ",0,"1/d*(1/8*a^4*sin(d*x+c)^8+4/7*a^4*sin(d*x+c)^7+a^4*sin(d*x+c)^6+4/5*a^4*sin(d*x+c)^5+1/4*a^4*sin(d*x+c)^4)","A"
219,1,70,61,0.097000," ","int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{2 a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{3}+\frac{6 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}+a^{4} \left(\sin^{4}\left(d x +c \right)\right)+\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(1/7*a^4*sin(d*x+c)^7+2/3*a^4*sin(d*x+c)^6+6/5*a^4*sin(d*x+c)^5+a^4*sin(d*x+c)^4+1/3*a^4*sin(d*x+c)^3)","A"
220,1,71,41,0.098000," ","int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^4,x)","\frac{\frac{a^{4} \left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{4 a^{4} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{3 a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{2}+\frac{4 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{2}}{d}"," ",0,"1/d*(1/6*a^4*sin(d*x+c)^6+4/5*a^4*sin(d*x+c)^5+3/2*a^4*sin(d*x+c)^4+4/3*a^4*sin(d*x+c)^3+1/2*a^4*sin(d*x+c)^2)","A"
221,1,78,77,0.184000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{4 a^{4} \sin \left(d x +c \right)}{d}+\frac{3 a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{4 a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}"," ",0,"a^4*ln(sin(d*x+c))/d+4*a^4*sin(d*x+c)/d+3*a^4*sin(d*x+c)^2/d+4/3*a^4*sin(d*x+c)^3/d+1/4*a^4*sin(d*x+c)^4/d","A"
222,1,79,76,0.147000," ","int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{d}+\frac{6 a^{4} \sin \left(d x +c \right)}{d}-\frac{a^{4}}{d \sin \left(d x +c \right)}+\frac{4 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/3*a^4*sin(d*x+c)^3/d+2*a^4*sin(d*x+c)^2/d+6*a^4*sin(d*x+c)/d-a^4/d/sin(d*x+c)+4*a^4*ln(sin(d*x+c))/d","A"
223,1,79,76,0.185000," ","int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}+\frac{4 a^{4} \sin \left(d x +c \right)}{d}-\frac{4 a^{4}}{d \sin \left(d x +c \right)}+\frac{6 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{4}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2*a^4*sin(d*x+c)^2/d+4*a^4*sin(d*x+c)/d-4*a^4/d/sin(d*x+c)+6*a^4*ln(sin(d*x+c))/d-1/2*a^4/d/sin(d*x+c)^2","A"
224,1,80,79,0.121000," ","int(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}-\frac{\sin \left(d x +c \right)}{a d}+\frac{\sin^{2}\left(d x +c \right)}{2 a d}-\frac{\sin^{3}\left(d x +c \right)}{3 d a}+\frac{\sin^{4}\left(d x +c \right)}{4 d a}"," ",0,"ln(1+sin(d*x+c))/a/d-sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d-1/3*sin(d*x+c)^3/d/a+1/4*sin(d*x+c)^4/d/a","A"
225,1,64,63,0.125000," ","int(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}+\frac{\sin \left(d x +c \right)}{a d}-\frac{\sin^{2}\left(d x +c \right)}{2 a d}+\frac{\sin^{3}\left(d x +c \right)}{3 d a}"," ",0,"-ln(1+sin(d*x+c))/a/d+sin(d*x+c)/a/d-1/2*sin(d*x+c)^2/a/d+1/3*sin(d*x+c)^3/d/a","A"
226,1,48,47,0.125000," ","int(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}-\frac{\sin \left(d x +c \right)}{a d}+\frac{\sin^{2}\left(d x +c \right)}{2 a d}"," ",0,"ln(1+sin(d*x+c))/a/d-sin(d*x+c)/a/d+1/2*sin(d*x+c)^2/a/d","A"
227,1,32,31,0.072000," ","int(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}+\frac{\sin \left(d x +c \right)}{a d}"," ",0,"-ln(1+sin(d*x+c))/a/d+sin(d*x+c)/a/d","A"
228,1,33,32,0.199000," ","int(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}"," ",0,"ln(sin(d*x+c))/a/d-ln(1+sin(d*x+c))/a/d","A"
229,1,49,46,0.184000," ","int(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}"," ",0,"-1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d+ln(1+sin(d*x+c))/a/d","A"
230,1,64,61,0.230000," ","int(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{1}{2 a d \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}"," ",0,"-1/2/a/d/sin(d*x+c)^2+ln(sin(d*x+c))/a/d+1/d/a/sin(d*x+c)-ln(1+sin(d*x+c))/a/d","A"
231,1,81,78,0.202000," ","int(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","-\frac{1}{3 a d \sin \left(d x +c \right)^{3}}-\frac{1}{d a \sin \left(d x +c \right)}+\frac{1}{2 a d \sin \left(d x +c \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a d}"," ",0,"-1/3/a/d/sin(d*x+c)^3-1/d/a/sin(d*x+c)+1/2/a/d/sin(d*x+c)^2-ln(sin(d*x+c))/a/d+ln(1+sin(d*x+c))/a/d","A"
232,1,83,85,0.224000," ","int(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\sin^{3}\left(d x +c \right)}{3 a^{2} d}-\frac{\sin^{2}\left(d x +c \right)}{a^{2} d}+\frac{3 \sin \left(d x +c \right)}{a^{2} d}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/3*sin(d*x+c)^3/a^2/d-sin(d*x+c)^2/a^2/d+3*sin(d*x+c)/a^2/d-4*ln(1+sin(d*x+c))/a^2/d-1/d/a^2/(1+sin(d*x+c))","A"
233,1,66,68,0.218000," ","int(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\sin^{2}\left(d x +c \right)}{2 a^{2} d}-\frac{2 \sin \left(d x +c \right)}{a^{2} d}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/2*sin(d*x+c)^2/a^2/d-2*sin(d*x+c)/a^2/d+3*ln(1+sin(d*x+c))/a^2/d+1/d/a^2/(1+sin(d*x+c))","A"
234,1,50,52,0.227000," ","int(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\sin \left(d x +c \right)}{a^{2} d}-\frac{2 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"sin(d*x+c)/a^2/d-2*ln(1+sin(d*x+c))/a^2/d-1/d/a^2/(1+sin(d*x+c))","A"
235,1,35,37,0.191000," ","int(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"ln(1+sin(d*x+c))/a^2/d+1/d/a^2/(1+sin(d*x+c))","A"
236,1,50,52,0.281000," ","int(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"ln(sin(d*x+c))/a^2/d+1/d/a^2/(1+sin(d*x+c))-ln(1+sin(d*x+c))/a^2/d","A"
237,1,68,68,0.261000," ","int(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","-\frac{1}{a^{2} d \sin \left(d x +c \right)}-\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{2 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/a^2/d/sin(d*x+c)-2*ln(sin(d*x+c))/a^2/d-1/d/a^2/(1+sin(d*x+c))+2*ln(1+sin(d*x+c))/a^2/d","A"
238,1,83,83,0.296000," ","int(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{1}{2 a^{2} d \sin \left(d x +c \right)^{2}}+\frac{2}{a^{2} d \sin \left(d x +c \right)}+\frac{3 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/2/a^2/d/sin(d*x+c)^2+2/a^2/d/sin(d*x+c)+3*ln(sin(d*x+c))/a^2/d+1/d/a^2/(1+sin(d*x+c))-3*ln(1+sin(d*x+c))/a^2/d","A"
239,1,99,99,0.292000," ","int(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","-\frac{1}{3 a^{2} d \sin \left(d x +c \right)^{3}}+\frac{1}{a^{2} d \sin \left(d x +c \right)^{2}}-\frac{3}{a^{2} d \sin \left(d x +c \right)}-\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/3/a^2/d/sin(d*x+c)^3+1/a^2/d/sin(d*x+c)^2-3/a^2/d/sin(d*x+c)-4*ln(sin(d*x+c))/a^2/d-1/d/a^2/(1+sin(d*x+c))+4*ln(1+sin(d*x+c))/a^2/d","A"
240,1,101,105,0.239000," ","int(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{\sin^{3}\left(d x +c \right)}{3 a^{3} d}-\frac{3 \left(\sin^{2}\left(d x +c \right)\right)}{2 a^{3} d}+\frac{6 \sin \left(d x +c \right)}{a^{3} d}+\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{10 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{5}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/3*sin(d*x+c)^3/a^3/d-3/2*sin(d*x+c)^2/a^3/d+6*sin(d*x+c)/a^3/d+1/2/d/a^3/(1+sin(d*x+c))^2-10*ln(1+sin(d*x+c))/a^3/d-5/d/a^3/(1+sin(d*x+c))","A"
241,1,85,89,0.236000," ","int(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{\sin^{2}\left(d x +c \right)}{2 a^{3} d}-\frac{3 \sin \left(d x +c \right)}{a^{3} d}-\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{6 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/2*sin(d*x+c)^2/a^3/d-3*sin(d*x+c)/a^3/d-1/2/d/a^3/(1+sin(d*x+c))^2+6*ln(1+sin(d*x+c))/a^3/d+4/d/a^3/(1+sin(d*x+c))","A"
242,1,68,72,0.230000," ","int(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{\sin \left(d x +c \right)}{a^{3} d}+\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{3}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"sin(d*x+c)/a^3/d+1/2/d/a^3/(1+sin(d*x+c))^2-3*ln(1+sin(d*x+c))/a^3/d-3/d/a^3/(1+sin(d*x+c))","A"
243,1,54,58,0.225000," ","int(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","-\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{2}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"-1/2/d/a^3/(1+sin(d*x+c))^2+ln(1+sin(d*x+c))/a^3/d+2/d/a^3/(1+sin(d*x+c))","A"
244,1,33,28,0.201000," ","int(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\frac{1}{2 \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{1+\sin \left(d x +c \right)}}{d \,a^{3}}"," ",0,"1/d/a^3*(1/2/(1+sin(d*x+c))^2-1/(1+sin(d*x+c)))","A"
245,1,68,72,0.286000," ","int(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"ln(sin(d*x+c))/a^3/d+1/2/d/a^3/(1+sin(d*x+c))^2+1/d/a^3/(1+sin(d*x+c))-ln(1+sin(d*x+c))/a^3/d","A"
246,1,86,88,0.287000," ","int(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","-\frac{1}{a^{3} d \sin \left(d x +c \right)}-\frac{3 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{2}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/a^3/d/sin(d*x+c)-3*ln(sin(d*x+c))/a^3/d-1/2/d/a^3/(1+sin(d*x+c))^2-2/d/a^3/(1+sin(d*x+c))+3*ln(1+sin(d*x+c))/a^3/d","A"
247,1,102,104,0.311000," ","int(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{1}{2 a^{3} d \sin \left(d x +c \right)^{2}}+\frac{3}{a^{3} d \sin \left(d x +c \right)}+\frac{6 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{6 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/2/a^3/d/sin(d*x+c)^2+3/a^3/d/sin(d*x+c)+6*ln(sin(d*x+c))/a^3/d+1/2/d/a^3/(1+sin(d*x+c))^2+3/d/a^3/(1+sin(d*x+c))-6*ln(1+sin(d*x+c))/a^3/d","A"
248,1,118,120,0.302000," ","int(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","-\frac{1}{3 a^{3} d \sin \left(d x +c \right)^{3}}+\frac{3}{2 a^{3} d \sin \left(d x +c \right)^{2}}-\frac{6}{a^{3} d \sin \left(d x +c \right)}-\frac{10 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{2 d \,a^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{4}{d \,a^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{10 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/3/a^3/d/sin(d*x+c)^3+3/2/a^3/d/sin(d*x+c)^2-6/a^3/d/sin(d*x+c)-10*ln(sin(d*x+c))/a^3/d-1/2/d/a^3/(1+sin(d*x+c))^2-4/d/a^3/(1+sin(d*x+c))+10*ln(1+sin(d*x+c))/a^3/d","A"
249,1,103,110,0.227000," ","int(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^4,x)","\frac{\sin^{2}\left(d x +c \right)}{2 a^{4} d}-\frac{4 \sin \left(d x +c \right)}{a^{4} d}+\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5}{2 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{10 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{10}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/2*sin(d*x+c)^2/a^4/d-4*sin(d*x+c)/a^4/d+1/3/d/a^4/(1+sin(d*x+c))^3-5/2/d/a^4/(1+sin(d*x+c))^2+10*ln(1+sin(d*x+c))/a^4/d+10/d/a^4/(1+sin(d*x+c))","A"
250,1,86,93,0.235000," ","int(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x)","\frac{\sin \left(d x +c \right)}{a^{4} d}-\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}-\frac{6}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{2}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}"," ",0,"sin(d*x+c)/a^4/d-1/3/d/a^4/(1+sin(d*x+c))^3-4*ln(1+sin(d*x+c))/a^4/d-6/d/a^4/(1+sin(d*x+c))+2/d/a^4/(1+sin(d*x+c))^2","A"
251,1,72,79,0.215000," ","int(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x)","\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{2 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{3}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"1/3/d/a^4/(1+sin(d*x+c))^3-3/2/d/a^4/(1+sin(d*x+c))^2+ln(1+sin(d*x+c))/a^4/d+3/d/a^4/(1+sin(d*x+c))","A"
252,1,43,28,0.221000," ","int(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{3 \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{1}{\left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{1}{1+\sin \left(d x +c \right)}}{d \,a^{4}}"," ",0,"1/d/a^4*(-1/3/(1+sin(d*x+c))^3+1/(1+sin(d*x+c))^2-1/(1+sin(d*x+c)))","A"
253,1,33,42,0.200000," ","int(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{2 \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{3 \left(1+\sin \left(d x +c \right)\right)^{3}}}{d \,a^{4}}"," ",0,"1/d/a^4*(-1/2/(1+sin(d*x+c))^2+1/3/(1+sin(d*x+c))^3)","A"
254,1,86,93,0.253000," ","int(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^4,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{1}{2 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"ln(sin(d*x+c))/a^4/d+1/3/d/a^4/(1+sin(d*x+c))^3+1/2/d/a^4/(1+sin(d*x+c))^2+1/d/a^4/(1+sin(d*x+c))-ln(1+sin(d*x+c))/a^4/d","A"
255,1,104,109,0.262000," ","int(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^4,x)","-\frac{1}{a^{4} d \sin \left(d x +c \right)}-\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}-\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{1}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/a^4/d/sin(d*x+c)-4*ln(sin(d*x+c))/a^4/d-1/3/d/a^4/(1+sin(d*x+c))^3-1/d/a^4/(1+sin(d*x+c))^2-3/d/a^4/(1+sin(d*x+c))+4*ln(1+sin(d*x+c))/a^4/d","A"
256,1,120,125,0.283000," ","int(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^4,x)","-\frac{1}{2 a^{4} d \sin \left(d x +c \right)^{2}}+\frac{4}{a^{4} d \sin \left(d x +c \right)}+\frac{10 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{1}{3 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{3}{2 d \,a^{4} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{6}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{10 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/2/a^4/d/sin(d*x+c)^2+4/a^4/d/sin(d*x+c)+10*ln(sin(d*x+c))/a^4/d+1/3/d/a^4/(1+sin(d*x+c))^3+3/2/d/a^4/(1+sin(d*x+c))^2+6/d/a^4/(1+sin(d*x+c))-10*ln(1+sin(d*x+c))/a^4/d","A"
257,1,42,43,0.154000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \sqrt{a +a \sin \left(d x +c \right)}-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{a +a \sin \left(d x +c \right)}}{\sqrt{a}}\right)}{d}"," ",0,"1/d*(2*(a+a*sin(d*x+c))^(1/2)-2*a^(1/2)*arctanh((a+a*sin(d*x+c))^(1/2)/a^(1/2)))","A"
258,0,0,114,8.357000," ","int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x)","\int \cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{4}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x)","F"
259,0,0,91,6.390000," ","int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","\int \cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","F"
260,0,0,68,6.525000," ","int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","\int \cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","F"
261,0,0,41,3.786000," ","int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","\int \cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","F"
262,0,0,40,1.292000," ","int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","\int \frac{\cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","F"
263,0,0,40,4.023000," ","int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","\int \frac{\cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","F"
264,0,0,40,3.787000," ","int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","\int \frac{\cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","F"
265,0,0,40,3.615000," ","int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","\int \frac{\cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","F"
266,1,95,93,0.132000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)}{d}"," ",0,"1/d*(a*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+a*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3))","A"
267,1,77,71,0.122000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+a \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)}{d}"," ",0,"1/d*(a*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+a*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c))","A"
268,1,57,57,0.081000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{\left(\cos^{3}\left(d x +c \right)\right) a}{3}}{d}"," ",0,"1/d*(a*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/3*cos(d*x+c)^3*a)","A"
269,1,63,47,0.255000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a x}{2}+\frac{c a}{2 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/2*a*cos(d*x+c)*sin(d*x+c)/d+1/2*a*x+1/2/d*c*a+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
270,1,57,41,0.190000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","-a x -\frac{a \cot \left(d x +c \right)}{d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{c a}{d}"," ",0,"-a*x-a*cot(d*x+c)/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*c*a","A"
271,1,81,48,0.252000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-a x -\frac{a \cot \left(d x +c \right)}{d}-\frac{c a}{d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{2 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-a*x-a*cot(d*x+c)/d-1/d*c*a-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/2*a*cos(d*x+c)/d-1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
272,1,80,46,0.221000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{2 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/2*a*cos(d*x+c)/d-1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^3","A"
273,1,102,66,0.219000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{8 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^3-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/8*a*cos(d*x+c)/d-1/8/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
274,1,124,80,0.217000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{8 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/8*a*cos(d*x+c)/d-1/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^3-2/15/d*a/sin(d*x+c)^3*cos(d*x+c)^3","A"
275,1,151,121,0.172000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+2 a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)}{d}"," ",0,"1/d*(a^2*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+2*a^2*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+a^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3))","A"
276,1,142,93,0.171000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+2 a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+a^{2} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)}{d}"," ",0,"1/d*(a^2*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+2*a^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+a^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c))","A"
277,1,95,81,0.155000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+2 a^{2} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(a^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+2*a^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/3*a^2*cos(d*x+c)^3)","A"
278,1,86,69,0.337000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2} \cos \left(d x +c \right)}{d}"," ",0,"-1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)*sin(d*x+c)/d+a^2*x+1/d*a^2*c+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+a^2*cos(d*x+c)/d","A"
279,1,89,70,0.293000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}+\frac{2 a^{2} \cos \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \cot \left(d x +c \right)}{d}"," ",0,"1/2*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c+2*a^2*cos(d*x+c)/d+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-a^2*cot(d*x+c)/d","A"
280,1,93,69,0.352000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \cos \left(d x +c \right)}{2 d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-2 a^{2} x -\frac{2 a^{2} \cot \left(d x +c \right)}{d}-\frac{2 a^{2} c}{d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2*a^2*cos(d*x+c)/d+1/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2*a^2*x-2*a^2*cot(d*x+c)/d-2/d*a^2*c-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3","A"
281,1,117,71,0.317000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","-a^{2} x -\frac{a^{2} \cot \left(d x +c \right)}{d}-\frac{a^{2} c}{d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \cos \left(d x +c \right)}{d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-a^2*x-a^2*cot(d*x+c)/d-1/d*a^2*c-1/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-a^2*cos(d*x+c)/d-1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3","A"
282,1,112,74,0.312000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{5 a^{2} \cos \left(d x +c \right)}{8 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-5/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-5/8*a^2*cos(d*x+c)/d-5/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^3","A"
283,1,136,90,0.312000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","-\frac{7 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \cos \left(d x +c \right)}{4 d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-7/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3-1/2/d*a^2/sin(d*x+c)^4*cos(d*x+c)^3-1/4/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-1/4*a^2*cos(d*x+c)/d-1/4/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^3","A"
284,1,160,112,0.340000," ","int(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} \cos \left(d x +c \right)}{16 d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{4 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-3/8/d*a^2/sin(d*x+c)^4*cos(d*x+c)^3-3/16/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-3/16*a^2*cos(d*x+c)/d-3/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^3-4/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^3","A"
285,1,194,120,0.163000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+a^{3} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)}{d}"," ",0,"1/d*(a^3*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3)+3*a^3*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+3*a^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+a^3*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c))","A"
286,1,156,105,0.168000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 a^{3} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(a^3*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+3*a^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3*a^3*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/3*a^3*cos(d*x+c)^3)","A"
287,1,111,93,0.357000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{13 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{13 a^{3} x}{8}+\frac{13 a^{3} c}{8 d}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{a^{3} \cos \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d+13/8*a^3*cos(d*x+c)*sin(d*x+c)/d+13/8*a^3*x+13/8/d*a^3*c-a^3*cos(d*x+c)^3/d+a^3*cos(d*x+c)/d+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
288,1,105,86,0.317000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} x}{2}+\frac{a^{3} c}{2 d}+\frac{3 a^{3} \cos \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} \cot \left(d x +c \right)}{d}"," ",0,"-1/3*a^3*cos(d*x+c)^3/d+3/2*a^3*cos(d*x+c)*sin(d*x+c)/d+1/2*a^3*x+1/2/d*a^3*c+3*a^3*cos(d*x+c)/d+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-a^3*cot(d*x+c)/d","A"
289,1,113,90,0.415000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{5 a^{3} x}{2}-\frac{5 a^{3} c}{2 d}+\frac{5 a^{3} \cos \left(d x +c \right)}{2 d}+\frac{5 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/2*a^3*cos(d*x+c)*sin(d*x+c)/d-5/2*a^3*x-5/2/d*a^3*c+5/2*a^3*cos(d*x+c)/d+5/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3*a^3*cot(d*x+c)/d-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3","A"
290,1,117,85,0.337000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \cos \left(d x +c \right)}{2 d}-\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-3 a^{3} x -\frac{3 a^{3} \cot \left(d x +c \right)}{d}-\frac{3 a^{3} c}{d}-\frac{3 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/2*a^3*cos(d*x+c)/d-1/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3*a^3*x-3*a^3*cot(d*x+c)/d-3/d*a^3*c-3/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-1/3/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3","A"
291,1,141,94,0.329000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","-a^{3} x -\frac{a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} c}{d}-\frac{13 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{13 a^{3} \cos \left(d x +c \right)}{8 d}-\frac{13 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-a^3*x-a^3*cot(d*x+c)/d-1/d*a^3*c-13/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-13/8*a^3*cos(d*x+c)/d-13/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3-1/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^3","A"
292,1,136,90,0.325000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","-\frac{7 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{7 a^{3} \cos \left(d x +c \right)}{8 d}-\frac{7 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{17 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{3 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-7/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-7/8*a^3*cos(d*x+c)/d-7/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-17/15/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3-3/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^3-1/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^3","A"
293,1,160,112,0.352000," ","int(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","-\frac{11 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{7 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}-\frac{7 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{7 a^{3} \cos \left(d x +c \right)}{16 d}-\frac{7 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-11/15/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3-7/8/d*a^3/sin(d*x+c)^4*cos(d*x+c)^3-7/16/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-7/16*a^3*cos(d*x+c)/d-7/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^3-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^3","A"
294,1,182,125,0.321000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+4 a^{4} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+6 a^{4} \left(-\frac{\left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{4 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3}+a^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a^4*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+4*a^4*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+6*a^4*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-4/3*a^4*cos(d*x+c)^3+a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
295,1,135,109,0.371000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^4,x)","-\frac{a^{4} \left(\cos^{3}\left(d x +c \right)\right) \left(\sin^{2}\left(d x +c \right)\right)}{5 d}-\frac{32 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{15 d}-\frac{a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}+\frac{5 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a^{4} x}{2}+\frac{5 a^{4} c}{2 d}+\frac{a^{4} \cos \left(d x +c \right)}{d}+\frac{a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/5/d*a^4*cos(d*x+c)^3*sin(d*x+c)^2-32/15*a^4*cos(d*x+c)^3/d-a^4*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a^4*cos(d*x+c)*sin(d*x+c)/d+5/2*a^4*x+5/2/d*a^4*c+a^4*cos(d*x+c)/d+1/d*a^4*ln(csc(d*x+c)-cot(d*x+c))","A"
296,1,127,108,0.316000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","-\frac{a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{25 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{17 a^{4} x}{8}+\frac{17 a^{4} c}{8 d}-\frac{4 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{4 a^{4} \cos \left(d x +c \right)}{d}+\frac{4 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{4} \cot \left(d x +c \right)}{d}"," ",0,"-1/4*a^4*cos(d*x+c)^3*sin(d*x+c)/d+25/8*a^4*cos(d*x+c)*sin(d*x+c)/d+17/8*a^4*x+17/8/d*a^4*c-4/3*a^4*cos(d*x+c)^3/d+4*a^4*cos(d*x+c)/d+4/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-a^4*cot(d*x+c)/d","A"
297,1,245,94,0.304000," ","int(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{3 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{7 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{32 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{16}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9+7/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-7/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+16/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5+3/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
298,1,245,79,0.286000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"-3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-11/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+11/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-4/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4-3/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
299,1,141,56,0.277000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+4/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3+1/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
300,1,142,41,0.195000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2-1/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
301,1,37,22,0.383000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"-2/a/d*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))","A"
302,1,56,29,0.376000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))","A"
303,1,94,49,0.418000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}+\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/a/d*tan(1/2*d*x+1/2*c)+1/2/a/d/tan(1/2*d*x+1/2*c)+1/2/a/d*ln(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2","A"
304,1,132,66,0.449000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{3}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2+3/8/a/d*tan(1/2*d*x+1/2*c)-3/8/a/d/tan(1/2*d*x+1/2*c)-1/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/24/a/d/tan(1/2*d*x+1/2*c)^3","A"
305,1,170,87,0.428000," ","int(cos(d*x+c)^2*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{3}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/24/a/d*tan(1/2*d*x+1/2*c)^3+1/8/a/d*tan(1/2*d*x+1/2*c)^2-3/8/a/d*tan(1/2*d*x+1/2*c)+3/8/a/d/tan(1/2*d*x+1/2*c)+3/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/24/a/d/tan(1/2*d*x+1/2*c)^3","A"
306,1,208,104,0.463000," ","int(cos(d*x+c)^2*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{5}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{5}{96 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/a/d*tan(1/2*d*x+1/2*c)^5-1/64/a/d*tan(1/2*d*x+1/2*c)^4+5/96/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2+5/16/a/d*tan(1/2*d*x+1/2*c)-5/16/a/d/tan(1/2*d*x+1/2*c)-3/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/160/a/d/tan(1/2*d*x+1/2*c)^5+1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/64/a/d/tan(1/2*d*x+1/2*c)^4-5/96/a/d/tan(1/2*d*x+1/2*c)^3","A"
307,1,300,103,0.464000," ","int(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","-\frac{11 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{19 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{19 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{68 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{27 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}-\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-11/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6-19/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-20/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+19/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-68/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+11/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-20/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4-27/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","B"
308,1,198,81,0.460000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{16}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+16/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3+6/d/a^2*arctan(tan(1/2*d*x+1/2*c))+4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","B"
309,1,163,65,0.438000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2-5/d/a^2*arctan(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","B"
310,1,64,47,0.385000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{2}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)+4/d/a^2*arctan(tan(1/2*d*x+1/2*c))+4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","A"
311,1,40,40,0.594000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","A"
312,1,77,54,0.716000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","A"
313,1,114,74,0.762000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}-\frac{1}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)-1/8/d/a^2/tan(1/2*d*x+1/2*c)^2+1/d/a^2/tan(1/2*d*x+1/2*c)+5/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","A"
314,1,153,89,0.581000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{1}{24 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{11}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^2*tan(1/2*d*x+1/2*c)^2+11/8/d/a^2*tan(1/2*d*x+1/2*c)-1/24/d/a^2/tan(1/2*d*x+1/2*c)^3+1/4/d/a^2/tan(1/2*d*x+1/2*c)^2-11/8/d/a^2/tan(1/2*d*x+1/2*c)-3/d/a^2*ln(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)+1)","A"
315,1,205,89,0.410000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{11 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{10}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2-11/d/a^3*arctan(tan(1/2*d*x+1/2*c))+8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2-10/d/a^3/(tan(1/2*d*x+1/2*c)+1)","B"
316,1,106,74,0.510000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{2}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{6}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)+6/d/a^3*arctan(tan(1/2*d*x+1/2*c))-8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3+4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+6/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
317,1,83,57,0.418000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-2/d/a^3*arctan(tan(1/2*d*x+1/2*c))+8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2-2/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
318,1,82,64,0.609000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{6}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+6/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
319,1,119,78,0.595000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{10}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^3*ln(tan(1/2*d*x+1/2*c))-8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3+4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2-10/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
320,1,157,98,0.691000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{11 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{8}{3 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{14}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^3*tan(1/2*d*x+1/2*c)-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+3/2/d/a^3/tan(1/2*d*x+1/2*c)+11/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/3/d/a^3/(tan(1/2*d*x+1/2*c)+1)^3-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^2+14/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
321,1,130,134,0.481000," ","int(cos(f*x+e)^2*sin(f*x+e)/(a+a*sin(f*x+e))^6,x)","\frac{-\frac{248}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{6}}+\frac{64}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{9}}+\frac{336}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{32}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{8}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{12}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}-\frac{36}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{464}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{7}}}{f \,a^{6}}"," ",0,"4/f/a^6*(-62/3/(tan(1/2*f*x+1/2*e)+1)^6+16/9/(tan(1/2*f*x+1/2*e)+1)^9+84/5/(tan(1/2*f*x+1/2*e)+1)^5-8/(tan(1/2*f*x+1/2*e)+1)^8-1/2/(tan(1/2*f*x+1/2*e)+1)^2+3/(tan(1/2*f*x+1/2*e)+1)^3-9/(tan(1/2*f*x+1/2*e)+1)^4+116/7/(tan(1/2*f*x+1/2*e)+1)^7)","A"
322,1,85,169,1.042000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{2} \left(315 \left(\sin^{4}\left(d x +c \right)\right)+665 \left(\sin^{3}\left(d x +c \right)\right)+570 \left(\sin^{2}\left(d x +c \right)\right)+456 \sin \left(d x +c \right)+304\right)}{3465 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3465*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^2*(315*sin(d*x+c)^4+665*sin(d*x+c)^3+570*sin(d*x+c)^2+456*sin(d*x+c)+304)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
323,1,75,108,1.017000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{2} \left(7 \left(\sin^{3}\left(d x +c \right)\right)+15 \left(\sin^{2}\left(d x +c \right)\right)+12 \sin \left(d x +c \right)+8\right)}{63 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/63*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^2*(7*sin(d*x+c)^3+15*sin(d*x+c)^2+12*sin(d*x+c)+8)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
324,1,65,80,1.057000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{2} \left(15 \left(\sin^{2}\left(d x +c \right)\right)+33 \sin \left(d x +c \right)+22\right)}{105 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/105*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^2*(15*sin(d*x+c)^2+33*sin(d*x+c)+22)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
325,1,103,79,1.205000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(3 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)+\left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}-3 a \sqrt{a -a \sin \left(d x +c \right)}\right)}{3 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(3*a^(3/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))+(a-a*sin(d*x+c))^(3/2)-3*a*(a-a*sin(d*x+c))^(1/2))/a/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
326,1,125,79,1.095000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(2 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}-\arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{2}\right)-\sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)}{\sin \left(d x +c \right) a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(sin(d*x+c)*(2*(a-a*sin(d*x+c))^(1/2)*a^(3/2)-arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^2)-(a-a*sin(d*x+c))^(1/2)*a^(3/2))/sin(d*x+c)/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
327,1,126,85,1.112000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(5 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+3 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}-5 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{4 a^{\frac{3}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(3/2)*(5*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+3*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)-5*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
328,1,144,117,1.136000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(9 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+9 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(d x +c \right)\right)-8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-9 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}\right)}{24 a^{\frac{7}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*(9*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)+9*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^3-8*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)-9*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
329,1,97,205,0.936000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{2} \left(3465 \left(\sin^{5}\left(d x +c \right)\right)+11340 \left(\sin^{4}\left(d x +c \right)\right)+15085 \left(\sin^{3}\left(d x +c \right)\right)+12930 \left(\sin^{2}\left(d x +c \right)\right)+10344 \sin \left(d x +c \right)+6896\right)}{45045 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/45045*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^2*(3465*sin(d*x+c)^5+11340*sin(d*x+c)^4+15085*sin(d*x+c)^3+12930*sin(d*x+c)^2+10344*sin(d*x+c)+6896)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
330,1,87,136,0.859000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{2} \left(105 \left(\sin^{4}\left(d x +c \right)\right)+350 \left(\sin^{3}\left(d x +c \right)\right)+465 \left(\sin^{2}\left(d x +c \right)\right)+372 \sin \left(d x +c \right)+248\right)}{1155 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/1155*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^2*(105*sin(d*x+c)^4+350*sin(d*x+c)^3+465*sin(d*x+c)^2+372*sin(d*x+c)+248)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
331,1,77,108,0.893000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{2} \left(35 \left(\sin^{3}\left(d x +c \right)\right)+120 \left(\sin^{2}\left(d x +c \right)\right)+159 \sin \left(d x +c \right)+106\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/315*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^2*(35*sin(d*x+c)^3+120*sin(d*x+c)^2+159*sin(d*x+c)+106)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
332,1,121,105,1.079000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-5 a^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)+\left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}-5 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a +5 a^{2} \sqrt{a -a \sin \left(d x +c \right)}\right)}{5 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/5*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-5*a^(5/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))+(a-a*sin(d*x+c))^(5/2)-5*(a-a*sin(d*x+c))^(3/2)*a+5*a^2*(a-a*sin(d*x+c))^(1/2))/a/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
333,1,144,105,1.178000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(2 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}-12 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}+9 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{2}\right)+3 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)}{3 \sin \left(d x +c \right) \sqrt{a}\, \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(sin(d*x+c)*(2*(a-a*sin(d*x+c))^(3/2)*a^(1/2)-12*(a-a*sin(d*x+c))^(1/2)*a^(3/2)+9*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^2)+3*(a-a*sin(d*x+c))^(1/2)*a^(3/2))/sin(d*x+c)/a^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
334,1,151,111,1.199000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(8 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin^{2}\left(d x +c \right)\right) a^{\frac{3}{2}}+\arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+7 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}-9 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{4 \sin \left(d x +c \right)^{2} \sqrt{a}\, \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(8*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)^2*a^(3/2)+arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+7*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)-9*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^2/a^(1/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
335,1,144,119,1.238000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-39 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)+9 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}-40 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}+39 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}\right)}{24 a^{\frac{3}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(3/2)*(-39*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^3+9*(-a*(sin(d*x+c)-1))^(5/2)*a^(1/2)-40*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)+39*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
336,1,74,138,0.967000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{2} \left(35 \left(\sin^{3}\left(d x +c \right)\right)+30 \left(\sin^{2}\left(d x +c \right)\right)+24 \sin \left(d x +c \right)+16\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/315*(1+sin(d*x+c))*(sin(d*x+c)-1)^2*(35*sin(d*x+c)^3+30*sin(d*x+c)^2+24*sin(d*x+c)+16)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
337,1,64,80,1.510000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{2} \left(15 \left(\sin^{2}\left(d x +c \right)\right)+12 \sin \left(d x +c \right)+8\right)}{105 d \cos \left(d x +c \right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"-2/105/d*(1+sin(d*x+c))*(sin(d*x+c)-1)^2*(15*sin(d*x+c)^2+12*sin(d*x+c)+8)/cos(d*x+c)/(a*(1+sin(d*x+c)))^(1/2)","A"
338,1,54,52,0.893000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{2} \left(3 \sin \left(d x +c \right)+2\right)}{15 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/15*(1+sin(d*x+c))*(sin(d*x+c)-1)^2*(3*sin(d*x+c)+2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
339,1,88,55,1.036000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{a}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)-\sqrt{a -a \sin \left(d x +c \right)}\right)}{a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(a^(1/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))-(a-a*sin(d*x+c))^(1/2))/a/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
340,1,103,54,0.905000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-\arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a \sin \left(d x +c \right)+\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)}{a^{\frac{3}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a*sin(d*x+c)+(a-a*sin(d*x+c))^(1/2)*a^(1/2))/a^(3/2)/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
341,1,124,84,1.235000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-\arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}\right)}{4 a^{\frac{7}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*((-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)-arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^2+(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
342,1,144,115,1.133000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(3 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}-8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)-3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}\right)}{24 a^{\frac{11}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(11/2)*(3*(-a*(sin(d*x+c)-1))^(5/2)*a^(5/2)-8*(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+3*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^5*sin(d*x+c)^3-3*(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
343,1,148,159,1.302000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(105 a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-15 \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}+21 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a -35 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}-105 a^{3} \sqrt{a -a \sin \left(d x +c \right)}\right)}{105 a^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/105*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(105*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-15*(a-a*sin(d*x+c))^(7/2)+21*(a-a*sin(d*x+c))^(5/2)*a-35*(a-a*sin(d*x+c))^(3/2)*a^2-105*a^3*(a-a*sin(d*x+c))^(1/2))/a^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
344,1,112,119,1.679000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-5 a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)+\left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}+5 a^{2} \sqrt{a -a \sin \left(d x +c \right)}\right)}{5 d \,a^{4} \cos \left(d x +c \right) \sqrt{a \left(1+\sin \left(d x +c \right)\right)}}"," ",0,"2/5/d/a^4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-5*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+(a-a*sin(d*x+c))^(5/2)+5*a^2*(a-a*sin(d*x+c))^(1/2))/cos(d*x+c)/(a*(1+sin(d*x+c)))^(1/2)","A"
345,1,110,91,1.174000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-3 a^{\frac{3}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)+\left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}+3 a \sqrt{a -a \sin \left(d x +c \right)}\right)}{3 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/3/a^3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-3*a^(3/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+(a-a*sin(d*x+c))^(3/2)+3*a*(a-a*sin(d*x+c))^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
346,1,97,70,1.042000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-\arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)}{a^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))/a^(3/2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
347,1,134,96,1.115000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) a^{2} \left(2 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-3 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)+\sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)}{a^{\frac{7}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/a^(7/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(sin(d*x+c)*a^2*(2*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-3*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))+(a-a*sin(d*x+c))^(1/2)*a^(3/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
348,1,164,128,1.368000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(11 a^{4} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right)+5 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-8 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{4} \left(\sin^{2}\left(d x +c \right)\right)-3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}\right)}{4 a^{\frac{11}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4/a^(11/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(11*a^4*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2+5*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)-8*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^4*sin(d*x+c)^2-3*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
349,1,182,162,1.492000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-69 a^{6} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{3}\left(d x +c \right)\right)+27 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{7}{2}}-40 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{9}{2}}+48 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{6} \left(\sin^{3}\left(d x +c \right)\right)+21 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{11}{2}}\right)}{24 a^{\frac{15}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24/a^(15/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-69*a^6*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3+27*(-a*(sin(d*x+c)-1))^(5/2)*a^(7/2)-40*(-a*(sin(d*x+c)-1))^(3/2)*a^(9/2)+48*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^6*sin(d*x+c)^3+21*(-a*(sin(d*x+c)-1))^(1/2)*a^(11/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
350,1,92,57,0.238000," ","int(cos(d*x+c)^3*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)}{d}"," ",0,"1/d*(a*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*cos(d*x+c)^4*sin(d*x+c)+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+a*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4))","A"
351,1,74,57,0.218000," ","int(cos(d*x+c)^3*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+a \left(-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)}{d}"," ",0,"1/d*(a*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+a*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c)))","A"
352,1,54,43,0.225000," ","int(cos(d*x+c)^3*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{\left(\cos^{4}\left(d x +c \right)\right) a}{4}}{d}"," ",0,"1/d*(a*(-1/5*cos(d*x+c)^4*sin(d*x+c)+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-1/4*cos(d*x+c)^4*a)","A"
353,1,36,41,0.283000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{4}\left(d x +c \right)\right) a}{4}+\frac{a \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(-1/4*cos(d*x+c)^4*a+1/3*a*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
354,1,60,52,0.329000," ","int(cos(d*x+c)^3*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}+\frac{2 a \sin \left(d x +c \right)}{3 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*cos(d*x+c)^2*sin(d*x+c)*a+2/3*a*sin(d*x+c)/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d","A"
355,1,82,51,0.283000," ","int(cos(d*x+c)^3*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{2 a \sin \left(d x +c \right)}{d}"," ",0,"1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/d*a/sin(d*x+c)*cos(d*x+c)^4-1/d*cos(d*x+c)^2*sin(d*x+c)*a-2*a*sin(d*x+c)/d","A"
356,1,83,52,0.345000," ","int(cos(d*x+c)^3*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{2 a \sin \left(d x +c \right)}{d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^4-1/d*cos(d*x+c)^2*sin(d*x+c)*a-2*a*sin(d*x+c)/d-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d","A"
357,1,30,33,0.150000," ","int(cos(d*x+c)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}-\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}}{a d}"," ",0,"-1/a/d*(1/4*sin(d*x+c)^4-1/3*sin(d*x+c)^3)","A"
358,1,30,33,0.098000," ","int(cos(d*x+c)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}}{a d}"," ",0,"-1/a/d*(1/3*sin(d*x+c)^3-1/2*sin(d*x+c)^2)","A"
359,1,28,30,0.187000," ","int(cos(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}-\sin \left(d x +c \right)}{a d}"," ",0,"-1/a/d*(1/2*sin(d*x+c)^2-sin(d*x+c))","A"
360,1,33,29,0.226000," ","int(cos(d*x+c)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{1}{a d \csc \left(d x +c \right)}-\frac{\ln \left(\csc \left(d x +c \right)\right)}{a d}"," ",0,"-1/a/d/csc(d*x+c)-1/a/d*ln(csc(d*x+c))","A"
361,1,30,30,0.181000," ","int(cos(d*x+c)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{\csc \left(d x +c \right)}{a d}+\frac{\ln \left(\csc \left(d x +c \right)\right)}{a d}"," ",0,"-csc(d*x+c)/a/d+1/a/d*ln(csc(d*x+c))","A"
362,1,25,30,0.230000," ","int(cos(d*x+c)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\csc^{2}\left(d x +c \right)\right)}{2}+\csc \left(d x +c \right)}{a d}"," ",0,"1/a/d*(-1/2*csc(d*x+c)^2+csc(d*x+c))","A"
363,1,29,33,0.203000," ","int(cos(d*x+c)^3*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\csc^{3}\left(d x +c \right)\right)}{3}+\frac{\left(\csc^{2}\left(d x +c \right)\right)}{2}}{a d}"," ",0,"1/a/d*(-1/3*csc(d*x+c)^3+1/2*csc(d*x+c)^2)","A"
364,1,29,33,0.212000," ","int(cos(d*x+c)^3*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\csc^{4}\left(d x +c \right)\right)}{4}+\frac{\left(\csc^{3}\left(d x +c \right)\right)}{3}}{a d}"," ",0,"1/a/d*(-1/4*csc(d*x+c)^4+1/3*csc(d*x+c)^3)","A"
365,1,124,127,0.247000," ","int(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(a*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+a*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
366,1,106,113,0.242000," ","int(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)}{d}"," ",0,"1/d*(a*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+a*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5))","A"
367,1,88,91,0.260000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+a*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
368,1,68,77,0.245000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(a*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/5*a*cos(d*x+c)^5)","A"
369,1,97,81,0.360000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 a x}{8}+\frac{3 c a}{8 d}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/4*a*cos(d*x+c)^3*sin(d*x+c)/d+3/8*a*cos(d*x+c)*sin(d*x+c)/d+3/8*a*x+3/8/d*c*a+1/3*a*cos(d*x+c)^3/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
370,1,119,75,0.306000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 a x}{2}-\frac{3 c a}{2 d}"," ",0,"1/3*a*cos(d*x+c)^3/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*a/sin(d*x+c)*cos(d*x+c)^5-a*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a*cos(d*x+c)*sin(d*x+c)/d-3/2*a*x-3/2/d*c*a","A"
371,1,143,82,0.368000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 a x}{2}-\frac{3 c a}{2 d}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a \cos \left(d x +c \right)}{2 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^5-a*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a*cos(d*x+c)*sin(d*x+c)/d-3/2*a*x-3/2/d*c*a-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a*cos(d*x+c)^3/d-3/2*a*cos(d*x+c)/d-3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
372,1,106,74,0.223000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a \cos \left(d x +c \right)}{2 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a*cos(d*x+c)^3/d-3/2*a*cos(d*x+c)/d-3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a","A"
373,1,128,80,0.224000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a \cos \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/8*a*cos(d*x+c)^3/d+3/8*a*cos(d*x+c)/d+3/8/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
374,1,116,66,0.221000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a \cos \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/8*a*cos(d*x+c)^3/d+3/8*a*cos(d*x+c)/d+3/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^5","A"
375,1,138,88,0.250000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{a \cos \left(d x +c \right)}{16 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^5-1/6/d*a/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/48*a*cos(d*x+c)^3/d+1/16*a*cos(d*x+c)/d+1/16/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
376,1,160,102,0.269000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{a \cos \left(d x +c \right)}{16 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/6/d*a/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/48*a*cos(d*x+c)^3/d+1/16*a*cos(d*x+c)/d+1/16/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*a/sin(d*x+c)^5*cos(d*x+c)^5","A"
377,1,182,122,0.265000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{6}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{128 d}+\frac{3 a \cos \left(d x +c \right)}{128 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}"," ",0,"-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*a/sin(d*x+c)^5*cos(d*x+c)^5-1/8/d*a/sin(d*x+c)^8*cos(d*x+c)^5-1/16/d*a/sin(d*x+c)^6*cos(d*x+c)^5-1/64/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/128/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/128*a*cos(d*x+c)^3/d+3/128*a*cos(d*x+c)/d+3/128/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
378,1,218,167,0.280000," ","int(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+2 a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(a^2*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+2*a^2*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+a^2*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
379,1,162,143,0.280000," ","int(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+2 a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)}{d}"," ",0,"1/d*(a^2*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+2*a^2*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+a^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5))","A"
380,1,164,127,0.286000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+2 a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a^2*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+2*a^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
381,1,106,117,0.273000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+2 a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(a^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+2*a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/5*a^2*cos(d*x+c)^5)","A"
382,1,127,109,0.465000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{4 d}+\frac{3 a^{2} x}{4}+\frac{3 a^{2} c}{4 d}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cos \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/5*a^2*cos(d*x+c)^5/d+1/2*a^2*cos(d*x+c)^3*sin(d*x+c)/d+3/4*a^2*cos(d*x+c)*sin(d*x+c)/d+3/4*a^2*x+3/4/d*a^2*c+1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)/d+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))","A"
383,1,137,108,0.415000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{9 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{9 a^{2} x}{8}-\frac{9 a^{2} c}{8 d}+\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2} \cos \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-3/4*a^2*cos(d*x+c)^3*sin(d*x+c)/d-9/8*a^2*cos(d*x+c)*sin(d*x+c)/d-9/8*a^2*x-9/8/d*a^2*c+2/3*a^2*cos(d*x+c)^3/d+2*a^2*cos(d*x+c)/d+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^2/sin(d*x+c)*cos(d*x+c)^5","A"
384,1,161,92,0.486000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{a^{2} \cos \left(d x +c \right)}{2 d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}-3 a^{2} x -\frac{3 a^{2} c}{d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/6*a^2*cos(d*x+c)^3/d-1/2*a^2*cos(d*x+c)/d-1/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/d*a^2/sin(d*x+c)*cos(d*x+c)^5-2*a^2*cos(d*x+c)^3*sin(d*x+c)/d-3*a^2*cos(d*x+c)*sin(d*x+c)/d-3*a^2*x-3/d*a^2*c-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5","A"
385,1,190,92,0.440000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{2} x}{2}-\frac{a^{2} c}{2 d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right)}{d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}"," ",0,"-1/d*a^2/sin(d*x+c)*cos(d*x+c)^5-a^2*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a^2*cos(d*x+c)*sin(d*x+c)/d-1/2*a^2*x-1/2/d*a^2*c-1/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5-a^2*cos(d*x+c)^3/d-3*a^2*cos(d*x+c)/d-3/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d","B"
386,1,149,108,0.332000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}-\frac{9 a^{2} \cos \left(d x +c \right)}{8 d}-\frac{9 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2} \cot \left(d x +c \right)}{d}+2 a^{2} x +\frac{2 a^{2} c}{d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-3/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5-3/8*a^2*cos(d*x+c)^3/d-9/8*a^2*cos(d*x+c)/d-9/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3*a^2*cot(d*x+c)^3/d+2*a^2*cot(d*x+c)/d+2*a^2*x+2/d*a^2*c-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5","A"
387,1,170,108,0.333000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} \cos \left(d x +c \right)}{4 d}+\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d+a^2*x+1/d*a^2*c-1/2/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+1/4/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+1/4*a^2*cos(d*x+c)^3/d+3/4*a^2*cos(d*x+c)/d+3/4/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5","A"
388,1,152,120,0.362000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","-\frac{7 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{7 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{7 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{7 a^{2} \cos \left(d x +c \right)}{16 d}+\frac{7 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-7/24/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+7/48/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+7/48*a^2*cos(d*x+c)^3/d+7/16*a^2*cos(d*x+c)/d+7/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^5","A"
389,1,200,160,0.386000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x)","-\frac{11 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}-\frac{11 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}+\frac{11 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{384 d \sin \left(d x +c \right)^{2}}+\frac{11 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}+\frac{11 a^{2} \cos \left(d x +c \right)}{128 d}+\frac{11 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{4 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}"," ",0,"-11/48/d*a^2/sin(d*x+c)^6*cos(d*x+c)^5-11/192/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+11/384/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+11/384*a^2*cos(d*x+c)^3/d+11/128*a^2*cos(d*x+c)/d+11/128/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/7/d*a^2/sin(d*x+c)^7*cos(d*x+c)^5-4/35/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/8/d*a^2/sin(d*x+c)^8*cos(d*x+c)^5","A"
390,1,224,152,0.411000," ","int(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x)","-\frac{13 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{26 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{315 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{8}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{6}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{32 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{64 d}+\frac{3 a^{2} \cos \left(d x +c \right)}{64 d}+\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{64 d}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}"," ",0,"-13/63/d*a^2/sin(d*x+c)^7*cos(d*x+c)^5-26/315/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/4/d*a^2/sin(d*x+c)^8*cos(d*x+c)^5-1/8/d*a^2/sin(d*x+c)^6*cos(d*x+c)^5-1/32/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+1/64/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+1/64*a^2*cos(d*x+c)^3/d+3/64*a^2*cos(d*x+c)/d+3/64/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/9/d*a^2/sin(d*x+c)^9*cos(d*x+c)^5","A"
391,1,248,198,0.408000," ","int(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{8}}-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{32 d \sin \left(d x +c \right)^{6}}-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{256 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{256 d}+\frac{9 a^{2} \cos \left(d x +c \right)}{256 d}+\frac{9 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{8 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{16 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{315 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}"," ",0,"-3/16/d*a^2/sin(d*x+c)^8*cos(d*x+c)^5-3/32/d*a^2/sin(d*x+c)^6*cos(d*x+c)^5-3/128/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+3/256/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+3/256*a^2*cos(d*x+c)^3/d+9/256*a^2*cos(d*x+c)/d+9/256/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/9/d*a^2/sin(d*x+c)^9*cos(d*x+c)^5-8/63/d*a^2/sin(d*x+c)^7*cos(d*x+c)^5-16/315/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/10/d*a^2/sin(d*x+c)^10*cos(d*x+c)^5","A"
392,1,288,183,0.286000," ","int(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{11}-\frac{2 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{33}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{231}-\frac{16 \left(\cos^{5}\left(d x +c \right)\right)}{1155}\right)+3 a^{3} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+3 a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(a^3*(-1/11*sin(d*x+c)^6*cos(d*x+c)^5-2/33*sin(d*x+c)^4*cos(d*x+c)^5-8/231*sin(d*x+c)^2*cos(d*x+c)^5-16/1155*cos(d*x+c)^5)+3*a^3*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+3*a^3*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+a^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
393,1,252,166,0.288000," ","int(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+3 a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)}{d}"," ",0,"1/d*(a^3*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+3*a^3*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+3*a^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5))","A"
394,1,216,143,0.278000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a^3*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+3*a^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+3*a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
395,1,178,143,0.273000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(a^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+3*a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/5*a^3*cos(d*x+c)^5)","A"
396,1,149,131,0.473000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6 d}+\frac{19 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}+\frac{19 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{19 a^{3} x}{16}+\frac{19 a^{3} c}{16 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cos \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/6*a^3*cos(d*x+c)^5*sin(d*x+c)/d+19/24*a^3*cos(d*x+c)^3*sin(d*x+c)/d+19/16*a^3*cos(d*x+c)*sin(d*x+c)/d+19/16*a^3*x+19/16/d*a^3*c-3/5*a^3*cos(d*x+c)^5/d+1/3*a^3*cos(d*x+c)^3/d+a^3*cos(d*x+c)/d+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
397,1,152,123,0.418000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{3 a^{3} x}{8}-\frac{3 a^{3} c}{8 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} \cos \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-1/5*a^3*cos(d*x+c)^5/d-1/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d-3/8*a^3*cos(d*x+c)*sin(d*x+c)/d-3/8*a^3*x-3/8/d*a^3*c+a^3*cos(d*x+c)^3/d+3*a^3*cos(d*x+c)/d+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^3/sin(d*x+c)*cos(d*x+c)^5","A"
398,1,161,127,0.486000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","-\frac{11 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{33 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{33 a^{3} x}{8}-\frac{33 a^{3} c}{8 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \cos \left(d x +c \right)}{2 d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-11/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d-33/8*a^3*cos(d*x+c)*sin(d*x+c)/d-33/8*a^3*x-33/8/d*a^3*c+1/2*a^3*cos(d*x+c)^3/d+3/2*a^3*cos(d*x+c)/d+3/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/d*a^3/sin(d*x+c)*cos(d*x+c)^5-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5","A"
399,1,190,122,0.446000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","-\frac{7 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{7 a^{3} \cos \left(d x +c \right)}{2 d}-\frac{7 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{3 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{9 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{7 a^{3} x}{2}-\frac{7 a^{3} c}{2 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cot \left(d x +c \right)}{d}"," ",0,"-7/6*a^3*cos(d*x+c)^3/d-7/2*a^3*cos(d*x+c)/d-7/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/d*a^3/sin(d*x+c)*cos(d*x+c)^5-3*a^3*cos(d*x+c)^3*sin(d*x+c)/d-9/2*a^3*cos(d*x+c)*sin(d*x+c)/d-7/2*a^3*x-7/2/d*a^3*c-3/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5-1/3*a^3*cot(d*x+c)^3/d+a^3*cot(d*x+c)/d","A"
400,1,215,128,0.447000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{3} x}{2}+\frac{3 a^{3} c}{2 d}-\frac{11 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{11 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}-\frac{33 a^{3} \cos \left(d x +c \right)}{8 d}-\frac{33 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-1/d*a^3/sin(d*x+c)*cos(d*x+c)^5-a^3*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d+3/2*a^3*x+3/2/d*a^3*c-11/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5-11/8*a^3*cos(d*x+c)^3/d-33/8*a^3*cos(d*x+c)/d-33/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-a^3*cot(d*x+c)^3/d+3*a^3*cot(d*x+c)/d-1/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5","A"
401,1,173,124,0.346000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a^{3} \cos \left(d x +c \right)}{8 d}-\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 a^{3} x +\frac{3 a^{3} \cot \left(d x +c \right)}{d}+\frac{3 a^{3} c}{d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5-1/8*a^3*cos(d*x+c)^3/d-3/8*a^3*cos(d*x+c)/d-3/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-a^3*cot(d*x+c)^3/d+3*a^3*x+3*a^3*cot(d*x+c)/d+3/d*a^3*c-3/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5-1/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5","A"
402,1,194,154,0.365000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cot \left(d x +c \right)}{d}+a^{3} x +\frac{a^{3} c}{d}-\frac{19 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{19 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{19 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{19 a^{3} \cos \left(d x +c \right)}{16 d}+\frac{19 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-1/3*a^3*cot(d*x+c)^3/d+a^3*cot(d*x+c)/d+a^3*x+1/d*a^3*c-19/24/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+19/48/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+19/48*a^3*cos(d*x+c)^3/d+19/16*a^3*cos(d*x+c)/d+19/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5","A"
403,1,176,136,0.378000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x)","-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{16 d}+\frac{9 a^{3} \cos \left(d x +c \right)}{16 d}+\frac{9 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{23 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}"," ",0,"-3/8/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+3/16/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+3/16*a^3*cos(d*x+c)^3/d+9/16*a^3*cos(d*x+c)/d+9/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-23/35/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-1/2/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-1/7/d*a^3/sin(d*x+c)^7*cos(d*x+c)^5","A"
404,1,200,160,0.387000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x)","-\frac{13 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{9 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{6}}-\frac{9 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{4}}+\frac{9 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}+\frac{9 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{128 d}+\frac{27 a^{3} \cos \left(d x +c \right)}{128 d}+\frac{27 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}"," ",0,"-13/35/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-9/16/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-9/64/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+9/128/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+9/128*a^3*cos(d*x+c)^3/d+27/128*a^3*cos(d*x+c)/d+27/128/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/7/d*a^3/sin(d*x+c)^7*cos(d*x+c)^5-1/8/d*a^3/sin(d*x+c)^8*cos(d*x+c)^5","A"
405,1,224,176,0.408000," ","int(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x)","-\frac{17 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}-\frac{17 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}+\frac{17 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{384 d \sin \left(d x +c \right)^{2}}+\frac{17 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}+\frac{17 a^{3} \cos \left(d x +c \right)}{128 d}+\frac{17 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{31 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{62 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{315 d \sin \left(d x +c \right)^{5}}-\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}"," ",0,"-17/48/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-17/192/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+17/384/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+17/384*a^3*cos(d*x+c)^3/d+17/128*a^3*cos(d*x+c)/d+17/128/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-31/63/d*a^3/sin(d*x+c)^7*cos(d*x+c)^5-62/315/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-3/8/d*a^3/sin(d*x+c)^8*cos(d*x+c)^5-1/9/d*a^3/sin(d*x+c)^9*cos(d*x+c)^5","A"
406,1,248,198,0.470000," ","int(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{7}}-\frac{2 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{5}}-\frac{7 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{8}}-\frac{7 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{32 d \sin \left(d x +c \right)^{6}}-\frac{7 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{4}}+\frac{7 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{256 d \sin \left(d x +c \right)^{2}}+\frac{7 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{256 d}+\frac{21 a^{3} \cos \left(d x +c \right)}{256 d}+\frac{21 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{9}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}"," ",0,"-1/3/d*a^3/sin(d*x+c)^7*cos(d*x+c)^5-2/15/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-7/16/d*a^3/sin(d*x+c)^8*cos(d*x+c)^5-7/32/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-7/128/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+7/256/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+7/256*a^3*cos(d*x+c)^3/d+21/256*a^3*cos(d*x+c)/d+21/256/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a^3/sin(d*x+c)^9*cos(d*x+c)^5-1/10/d*a^3/sin(d*x+c)^10*cos(d*x+c)^5","A"
407,1,306,171,0.279000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{16}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{32}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{128}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+4 a^{4} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)+6 a^{4} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+4 a^{4} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+a^{4} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a^4*(-1/10*sin(d*x+c)^5*cos(d*x+c)^5-1/16*sin(d*x+c)^3*cos(d*x+c)^5-1/32*sin(d*x+c)*cos(d*x+c)^5+1/128*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+4*a^4*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5)+6*a^4*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+4*a^4*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+a^4*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
408,1,190,130,0.441000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","-\frac{23 a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{69 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{61 a^{4} x}{8}-\frac{61 a^{4} c}{8 d}-\frac{2 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{4} \cos \left(d x +c \right)}{d}-\frac{2 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{6 a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{4} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} \cot \left(d x +c \right)}{d}"," ",0,"-23/4*a^4*cos(d*x+c)^3*sin(d*x+c)/d-69/8*a^4*cos(d*x+c)*sin(d*x+c)/d-61/8*a^4*x-61/8/d*a^4*c-2/3*a^4*cos(d*x+c)^3/d-2*a^4*cos(d*x+c)/d-2/d*a^4*ln(csc(d*x+c)-cot(d*x+c))-6/d*a^4/sin(d*x+c)*cos(d*x+c)^5-2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^5-1/3*a^4*cot(d*x+c)^3/d+a^4*cot(d*x+c)/d","A"
409,1,381,121,0.269000," ","int(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{97 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{32 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{16 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{97 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{16 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{16}{105 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13+5/6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11-97/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9+32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8-16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6+97/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5+16/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4-5/6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3+16/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2-1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)+16/105/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7+1/8/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
410,1,347,105,0.258000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{17 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{19 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{19 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{17 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"-1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-17/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8+19/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-8/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6-19/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+17/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-8/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2+1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-4/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6-1/8/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
411,1,279,81,0.246000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9-3/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6-4/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+3/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+4/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+4/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5+1/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
412,1,279,65,0.173000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}"," ",0,"-1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6+7/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4-7/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-2/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-2/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4-1/4/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
413,1,159,55,0.359000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2-1/a/d*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))","B"
414,1,97,49,0.393000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))","A"
415,1,112,54,0.433000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/a/d*tan(1/2*d*x+1/2*c)+2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/2/a/d/tan(1/2*d*x+1/2*c)-1/2/a/d*ln(tan(1/2*d*x+1/2*c))","B"
416,1,132,52,0.442000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/8/a/d*tan(1/2*d*x+1/2*c)+1/8/a/d/tan(1/2*d*x+1/2*c)+1/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/24/a/d/tan(1/2*d*x+1/2*c)^3","B"
417,1,132,74,0.432000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/24/a/d*tan(1/2*d*x+1/2*c)^3+1/8/a/d*tan(1/2*d*x+1/2*c)-1/8/a/d/tan(1/2*d*x+1/2*c)-1/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/24/a/d/tan(1/2*d*x+1/2*c)^3","A"
418,1,170,90,0.464000," ","int(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}+\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{96 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/a/d*tan(1/2*d*x+1/2*c)^5-1/64/a/d*tan(1/2*d*x+1/2*c)^4+1/96/a/d*tan(1/2*d*x+1/2*c)^3-1/16/a/d*tan(1/2*d*x+1/2*c)+1/16/a/d/tan(1/2*d*x+1/2*c)+1/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/160/a/d/tan(1/2*d*x+1/2*c)^5+1/64/a/d/tan(1/2*d*x+1/2*c)^4-1/96/a/d/tan(1/2*d*x+1/2*c)^3","A"
419,1,246,112,0.477000," ","int(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 a d}+\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{96 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/384/a/d*tan(1/2*d*x+1/2*c)^6-1/160/a/d*tan(1/2*d*x+1/2*c)^5+1/128/a/d*tan(1/2*d*x+1/2*c)^4-1/96/a/d*tan(1/2*d*x+1/2*c)^3-1/128/a/d*tan(1/2*d*x+1/2*c)^2+1/16/a/d*tan(1/2*d*x+1/2*c)-1/384/a/d/tan(1/2*d*x+1/2*c)^6-1/16/a/d/tan(1/2*d*x+1/2*c)-1/16/a/d*ln(tan(1/2*d*x+1/2*c))+1/160/a/d/tan(1/2*d*x+1/2*c)^5+1/128/a/d/tan(1/2*d*x+1/2*c)^2-1/128/a/d/tan(1/2*d*x+1/2*c)^4+1/96/a/d/tan(1/2*d*x+1/2*c)^3","B"
420,1,381,133,0.442000," ","int(cos(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","-\frac{5 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{25 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{283 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{32 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{176 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{283 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{208 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{25 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{208 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{208}{105 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"-5/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13-25/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11-283/12/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9-32/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8-176/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6+283/12/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5-208/5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4+25/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3-208/15/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2+5/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)-208/105/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^7-5/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
421,1,347,117,0.411000," ","int(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{187 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{47 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{64 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{47 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{32 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{187 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{64 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{32}{15 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{11 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}"," ",0,"11/8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+187/24/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+47/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+64/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6-47/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+32/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4-187/24/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+64/5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2-11/8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+32/15/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^6+11/8/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
422,1,279,94,0.399000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{3 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{20 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{12}{5 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}"," ",0,"-3/2/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9-7/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7-4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6-20/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+7/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3-12/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+3/2/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)-12/5/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^5-3/2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
423,1,245,79,0.360000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{7 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{15 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{15 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{32 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"7/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+15/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4-15/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+32/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2-7/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+8/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4+7/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
424,1,177,68,0.348000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{10}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-10/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
425,1,60,36,0.513000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{2}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"-2/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))+1/d/a^2*ln(tan(1/2*d*x+1/2*c))","A"
426,1,74,35,0.538000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
427,1,93,50,0.602000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}"," ",0,"1/8/a^2/d*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)+1/d/a^2/tan(1/2*d*x+1/2*c)+3/2/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2","A"
428,1,132,64,0.612000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}+\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{7}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/24/a^2/d*tan(1/2*d*x+1/2*c)^3-1/4/a^2/d*tan(1/2*d*x+1/2*c)^2+7/8/d/a^2*tan(1/2*d*x+1/2*c)-7/8/d/a^2/tan(1/2*d*x+1/2*c)-1/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/4/a^2/d/tan(1/2*d*x+1/2*c)^2-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
429,1,170,88,0.605000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{12 d \,a^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2}}+\frac{3}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{12 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/64/a^2/d*tan(1/2*d*x+1/2*c)^4-1/12/a^2/d*tan(1/2*d*x+1/2*c)^3+1/4/a^2/d*tan(1/2*d*x+1/2*c)^2-3/4/d/a^2*tan(1/2*d*x+1/2*c)+3/4/d/a^2/tan(1/2*d*x+1/2*c)+7/8/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/4/a^2/d/tan(1/2*d*x+1/2*c)^2-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+1/12/a^2/d/tan(1/2*d*x+1/2*c)^3","A"
430,1,208,104,0.639000," ","int(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a^{2} d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a^{2} d}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}-\frac{11}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}-\frac{1}{160 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{32 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{3}{32 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/a^2/d*tan(1/2*d*x+1/2*c)^5-1/32/a^2/d*tan(1/2*d*x+1/2*c)^4+3/32/a^2/d*tan(1/2*d*x+1/2*c)^3-1/4/a^2/d*tan(1/2*d*x+1/2*c)^2+11/16/d/a^2*tan(1/2*d*x+1/2*c)-11/16/d/a^2/tan(1/2*d*x+1/2*c)-3/4/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/160/a^2/d/tan(1/2*d*x+1/2*c)^5+1/4/a^2/d/tan(1/2*d*x+1/2*c)^2+1/32/a^2/d/tan(1/2*d*x+1/2*c)^4-3/32/a^2/d/tan(1/2*d*x+1/2*c)^3","A"
431,1,246,126,0.663000," ","int(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a^{2} d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{80 a^{2} d}+\frac{5 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{48 d \,a^{2}}+\frac{31 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{1}{384 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{5}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{11 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2}}+\frac{1}{80 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{31}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{5}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{5}{48 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/384/a^2/d*tan(1/2*d*x+1/2*c)^6-1/80/a^2/d*tan(1/2*d*x+1/2*c)^5+5/128/a^2/d*tan(1/2*d*x+1/2*c)^4-5/48/a^2/d*tan(1/2*d*x+1/2*c)^3+31/128/a^2/d*tan(1/2*d*x+1/2*c)^2-5/8/d/a^2*tan(1/2*d*x+1/2*c)-1/384/a^2/d/tan(1/2*d*x+1/2*c)^6+5/8/d/a^2/tan(1/2*d*x+1/2*c)+11/16/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/80/a^2/d/tan(1/2*d*x+1/2*c)^5-31/128/a^2/d/tan(1/2*d*x+1/2*c)^2-5/128/a^2/d/tan(1/2*d*x+1/2*c)^4+5/48/a^2/d/tan(1/2*d*x+1/2*c)^3","A"
432,1,300,103,0.415000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{19 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{27 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{36 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{27 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{19 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{12}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{51 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}+\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"19/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6+27/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+36/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4-27/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+40/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2-19/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+12/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4+51/4/d/a^3*arctan(tan(1/2*d*x+1/2*c))+8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","B"
433,1,198,81,0.384000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{20 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{28}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{11 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5-8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-20/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-28/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3-11/d/a^3*arctan(tan(1/2*d*x+1/2*c))-8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","B"
434,1,163,74,0.403000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2+9/d/a^3*arctan(tan(1/2*d*x+1/2*c))+8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","B"
435,1,58,45,0.577000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"2/d/a^3*arctan(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
436,1,77,54,0.589000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^3*ln(tan(1/2*d*x+1/2*c))-8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
437,1,115,74,0.678000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^3*tan(1/2*d*x+1/2*c)-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+3/2/d/a^3/tan(1/2*d*x+1/2*c)+9/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
438,1,153,98,0.673000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{19 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{19}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{11 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/d/a^3*tan(1/2*d*x+1/2*c)^2+19/8/d/a^3*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3+3/8/d/a^3/tan(1/2*d*x+1/2*c)^2-19/8/d/a^3/tan(1/2*d*x+1/2*c)-11/2/d/a^3*ln(tan(1/2*d*x+1/2*c))-8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
439,1,191,111,0.683000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}-\frac{25 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{1}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{25}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{51 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{8}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/64/d/a^3*tan(1/2*d*x+1/2*c)^4-1/8/d/a^3*tan(1/2*d*x+1/2*c)^3+5/8/d/a^3*tan(1/2*d*x+1/2*c)^2-25/8/d/a^3*tan(1/2*d*x+1/2*c)-1/64/d/a^3/tan(1/2*d*x+1/2*c)^4+1/8/d/a^3/tan(1/2*d*x+1/2*c)^3-5/8/d/a^3/tan(1/2*d*x+1/2*c)^2+25/8/d/a^3/tan(1/2*d*x+1/2*c)+51/8/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/d/a^3/(tan(1/2*d*x+1/2*c)+1)","A"
440,1,100,54,0.455000," ","int(cos(f*x+e)^4*sin(f*x+e)/(a+a*sin(f*x+e))^6,x)","\frac{\frac{224}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{2}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{2}}+\frac{64}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{7}}-\frac{32}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{6}}-\frac{32}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}+\frac{12}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}}{f \,a^{6}}"," ",0,"4/f/a^6*(56/5/(tan(1/2*f*x+1/2*e)+1)^5-1/2/(tan(1/2*f*x+1/2*e)+1)^2+16/7/(tan(1/2*f*x+1/2*e)+1)^7-8/(tan(1/2*f*x+1/2*e)+1)^6-8/(tan(1/2*f*x+1/2*e)+1)^4+3/(tan(1/2*f*x+1/2*e)+1)^3)","A"
441,1,115,83,0.455000," ","int(cos(f*x+e)^4*sin(f*x+e)^2/(a+a*sin(f*x+e))^7,x)","\frac{\frac{352}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{6}}-\frac{832}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{7}}+\frac{20}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}-\frac{8}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{3}}+\frac{64}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{8}}-\frac{328}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}-\frac{128}{9 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{9}}}{f \,a^{7}}"," ",0,"8/f/a^7*(44/3/(tan(1/2*f*x+1/2*e)+1)^6-104/7/(tan(1/2*f*x+1/2*e)+1)^7+5/2/(tan(1/2*f*x+1/2*e)+1)^4-1/3/(tan(1/2*f*x+1/2*e)+1)^3+8/(tan(1/2*f*x+1/2*e)+1)^8-41/5/(tan(1/2*f*x+1/2*e)+1)^5-16/9/(tan(1/2*f*x+1/2*e)+1)^9)","A"
442,1,130,145,0.534000," ","int(cos(f*x+e)^4*sin(f*x+e)^3/(a+a*sin(f*x+e))^8,x)","\frac{\frac{256}{11 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{11}}+\frac{2064}{7 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{7}}-\frac{136}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{6}}-\frac{384}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{8}}-\frac{128}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{10}}+\frac{176}{5 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{5}}+\frac{896}{3 \left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{9}}-\frac{4}{\left(\tan \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)^{4}}}{f \,a^{8}}"," ",0,"16/f/a^8*(16/11/(tan(1/2*f*x+1/2*e)+1)^11+129/7/(tan(1/2*f*x+1/2*e)+1)^7-17/2/(tan(1/2*f*x+1/2*e)+1)^6-24/(tan(1/2*f*x+1/2*e)+1)^8-8/(tan(1/2*f*x+1/2*e)+1)^10+11/5/(tan(1/2*f*x+1/2*e)+1)^5+56/3/(tan(1/2*f*x+1/2*e)+1)^9-1/4/(tan(1/2*f*x+1/2*e)+1)^4)","A"
443,1,85,136,0.985000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{3} \left(3465 \left(\sin^{4}\left(d x +c \right)\right)+10710 \left(\sin^{3}\left(d x +c \right)\right)+12145 \left(\sin^{2}\left(d x +c \right)\right)+6940 \sin \left(d x +c \right)+2776\right)}{45045 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/45045*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^3*(3465*sin(d*x+c)^4+10710*sin(d*x+c)^3+12145*sin(d*x+c)^2+6940*sin(d*x+c)+2776)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
444,1,75,108,0.882000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a \left(\sin \left(d x +c \right)-1\right)^{3} \left(315 \left(\sin^{3}\left(d x +c \right)\right)+980 \left(\sin^{2}\left(d x +c \right)\right)+1055 \sin \left(d x +c \right)+422\right)}{3465 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/3465*(1+sin(d*x+c))*a*(sin(d*x+c)-1)^3*(315*sin(d*x+c)^3+980*sin(d*x+c)^2+1055*sin(d*x+c)+422)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
445,1,141,137,1.334000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(105 a^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)-15 \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}+63 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a -35 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}-105 a^{3} \sqrt{a -a \sin \left(d x +c \right)}\right)}{105 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/105*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(105*a^(7/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))-15*(a-a*sin(d*x+c))^(7/2)+63*(a-a*sin(d*x+c))^(5/2)*a-35*(a-a*sin(d*x+c))^(3/2)*a^2-105*a^3*(a-a*sin(d*x+c))^(1/2))/a^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
446,1,162,128,1.278000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(6 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}-20 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-30 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{7}{2}}+15 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{4}\right)+15 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{7}{2}}\right)}{15 a^{\frac{7}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/15*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*(sin(d*x+c)*(6*(a-a*sin(d*x+c))^(5/2)*a^(3/2)-20*(a-a*sin(d*x+c))^(3/2)*a^(5/2)-30*(a-a*sin(d*x+c))^(1/2)*a^(7/2)+15*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^4)+15*(a-a*sin(d*x+c))^(1/2)*a^(7/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
447,1,178,132,1.392000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(24 a^{\frac{3}{2}} \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin^{2}\left(d x +c \right)\right)-8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right) \sqrt{a}-39 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+15 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}-9 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\right)}{12 a^{\frac{3}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/12*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(24*a^(3/2)*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)^2-8*(-a*(sin(d*x+c)-1))^(3/2)*sin(d*x+c)^2*a^(1/2)-39*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+15*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)-9*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2))/a^(3/2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
448,1,170,141,1.383000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(48 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}} \left(\sin^{3}\left(d x +c \right)\right)-15 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}+56 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-33 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}-33 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(d x +c \right)\right)\right)}{24 a^{\frac{7}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(48*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2)*sin(d*x+c)^3-15*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2)+56*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)-33*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)-33*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^3)/a^(7/2)/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
449,1,162,149,1.412000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-201 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{4}\left(d x +c \right)\right)+201 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}-737 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}+671 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}-183 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} \sqrt{a}\right)}{192 a^{\frac{7}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/192*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-201*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^4+201*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2)-737*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)+671*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)-183*(-a*(sin(d*x+c)-1))^(7/2)*a^(1/2))/a^(7/2)/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
450,1,180,181,1.402000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(465 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{3}{2}}+465 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{6} \left(\sin^{5}\left(d x +c \right)\right)-890 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{5}{2}}-896 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{7}{2}}+2170 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{9}{2}}-465 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{11}{2}}\right)}{1920 a^{\frac{11}{2}} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/1920*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(11/2)*(465*(-a*(sin(d*x+c)-1))^(9/2)*a^(3/2)+465*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^6*sin(d*x+c)^5-890*(-a*(sin(d*x+c)-1))^(7/2)*a^(5/2)-896*(-a*(sin(d*x+c)-1))^(5/2)*a^(7/2)+2170*(-a*(sin(d*x+c)-1))^(3/2)*a^(9/2)-465*(-a*(sin(d*x+c)-1))^(1/2)*a^(11/2))/sin(d*x+c)^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
451,1,198,213,1.323000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-825 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{15}{2}}+4675 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{13}{2}}+1398 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{11}{2}}-7818 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{9}{2}}+4675 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{7}{2}}-825 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{11}{2}} a^{\frac{5}{2}}+825 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{8} \left(\sin^{6}\left(d x +c \right)\right)\right)}{7680 a^{\frac{15}{2}} \sin \left(d x +c \right)^{6} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/7680*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-825*(-a*(sin(d*x+c)-1))^(1/2)*a^(15/2)+4675*(-a*(sin(d*x+c)-1))^(3/2)*a^(13/2)+1398*(-a*(sin(d*x+c)-1))^(5/2)*a^(11/2)-7818*(-a*(sin(d*x+c)-1))^(7/2)*a^(9/2)+4675*(-a*(sin(d*x+c)-1))^(9/2)*a^(7/2)-825*(-a*(sin(d*x+c)-1))^(11/2)*a^(5/2)+825*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^8*sin(d*x+c)^6)/a^(15/2)/sin(d*x+c)^6/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
452,1,216,245,1.391000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(6405 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{13}{2}} a^{\frac{7}{2}}-42700 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{11}{2}} a^{\frac{9}{2}}+120841 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{11}{2}}+6405 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{10} \left(\sin^{7}\left(d x +c \right)\right)-156672 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{13}{2}}+51191 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{15}{2}}+42700 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{17}{2}}-6405 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{19}{2}}\right)}{107520 a^{\frac{19}{2}} \sin \left(d x +c \right)^{7} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/107520*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(19/2)*(6405*(-a*(sin(d*x+c)-1))^(13/2)*a^(7/2)-42700*(-a*(sin(d*x+c)-1))^(11/2)*a^(9/2)+120841*(-a*(sin(d*x+c)-1))^(9/2)*a^(11/2)+6405*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^10*sin(d*x+c)^7-156672*(-a*(sin(d*x+c)-1))^(7/2)*a^(13/2)+51191*(-a*(sin(d*x+c)-1))^(5/2)*a^(15/2)+42700*(-a*(sin(d*x+c)-1))^(3/2)*a^(17/2)-6405*(-a*(sin(d*x+c)-1))^(1/2)*a^(19/2))/sin(d*x+c)^7/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
453,1,97,164,1.112000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{3} \left(429 \left(\sin^{5}\left(d x +c \right)\right)+1815 \left(\sin^{4}\left(d x +c \right)\right)+3075 \left(\sin^{3}\left(d x +c \right)\right)+2765 \left(\sin^{2}\left(d x +c \right)\right)+1580 \sin \left(d x +c \right)+632\right)}{6435 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/6435*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^3*(429*sin(d*x+c)^5+1815*sin(d*x+c)^4+3075*sin(d*x+c)^3+2765*sin(d*x+c)^2+1580*sin(d*x+c)+632)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
454,1,87,136,0.862000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) a^{2} \left(\sin \left(d x +c \right)-1\right)^{3} \left(385 \left(\sin^{4}\left(d x +c \right)\right)+1645 \left(\sin^{3}\left(d x +c \right)\right)+2765 \left(\sin^{2}\left(d x +c \right)\right)+2295 \sin \left(d x +c \right)+918\right)}{5005 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/5005*(1+sin(d*x+c))*a^2*(sin(d*x+c)-1)^3*(385*sin(d*x+c)^4+1645*sin(d*x+c)^3+2765*sin(d*x+c)^2+2295*sin(d*x+c)+918)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
455,1,159,173,1.293000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(315 a^{\frac{9}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)+35 \left(a -a \sin \left(d x +c \right)\right)^{\frac{9}{2}}-225 a \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}+441 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a^{2}-105 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{3}-315 a^{4} \sqrt{a -a \sin \left(d x +c \right)}\right)}{315 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/315*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(315*a^(9/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))+35*(a-a*sin(d*x+c))^(9/2)-225*a*(a-a*sin(d*x+c))^(7/2)+441*(a-a*sin(d*x+c))^(5/2)*a^2-105*(a-a*sin(d*x+c))^(3/2)*a^3-315*a^4*(a-a*sin(d*x+c))^(1/2))/a^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
456,1,180,154,1.275000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(140 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{7}{2}}+70 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-56 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+10 \sqrt{a}\, \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}-105 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{4}\right)-35 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{7}{2}}\right)}{35 a^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/35*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(5/2)*(sin(d*x+c)*(140*(a-a*sin(d*x+c))^(1/2)*a^(7/2)+70*(a-a*sin(d*x+c))^(3/2)*a^(5/2)-56*(a-a*sin(d*x+c))^(5/2)*a^(3/2)+10*a^(1/2)*(a-a*sin(d*x+c))^(7/2)-105*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^4)-35*(a-a*sin(d*x+c))^(1/2)*a^(7/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
457,1,178,158,1.174000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(40 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} \left(\sin^{2}\left(d x +c \right)\right)-8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} \left(\sin^{2}\left(d x +c \right)\right) \sqrt{a}+45 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-45 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}+35 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}\right)}{20 a^{\frac{3}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/20*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(40*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)*sin(d*x+c)^2-8*(-a*(sin(d*x+c)-1))^(5/2)*sin(d*x+c)^2*a^(1/2)+45*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^2-45*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2)+35*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2))/a^(3/2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
458,1,196,169,1.500000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(96 a^{\frac{5}{2}} \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin^{3}\left(d x +c \right)\right)-16 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}} \left(\sin^{3}\left(d x +c \right)\right)-111 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)+15 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}+8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-15 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}\right)}{24 a^{\frac{3}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(96*a^(5/2)*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)^3-16*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)*sin(d*x+c)^3-111*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^3+15*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2)+8*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)-15*(-a*(sin(d*x+c)-1))^(5/2)*a^(1/2))/a^(3/2)/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
459,1,188,179,1.418000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(128 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}} \left(\sin^{4}\left(d x +c \right)\right)-21 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{4}\left(d x +c \right)\right)+149 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} \sqrt{a}-461 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+435 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-107 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}\right)}{64 a^{\frac{5}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/64*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(5/2)*(128*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2)*sin(d*x+c)^4-21*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^4+149*(-a*(sin(d*x+c)-1))^(7/2)*a^(1/2)-461*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)+435*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)-107*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2))/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
460,1,180,187,1.480000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-825 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{5} \left(\sin^{5}\left(d x +c \right)\right)+455 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} \sqrt{a}-2550 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{3}{2}}+4992 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}-3850 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+825 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}\right)}{640 a^{\frac{7}{2}} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/640*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(7/2)*(-825*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^5*sin(d*x+c)^5+455*(-a*(sin(d*x+c)-1))^(9/2)*a^(1/2)-2550*(-a*(sin(d*x+c)-1))^(7/2)*a^(3/2)+4992*(-a*(sin(d*x+c)-1))^(5/2)*a^(5/2)-3850*(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+825*(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2))/sin(d*x+c)^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
461,1,198,221,1.463000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(2685 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{11}{2}} a^{\frac{3}{2}}-2685 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{7} \left(\sin^{6}\left(d x +c \right)\right)-10095 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{5}{2}}+7794 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{7}{2}}+10866 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{9}{2}}-15215 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{11}{2}}+2685 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{13}{2}}\right)}{7680 a^{\frac{11}{2}} \sin \left(d x +c \right)^{6} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/7680*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(11/2)*(2685*(-a*(sin(d*x+c)-1))^(11/2)*a^(3/2)-2685*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^7*sin(d*x+c)^6-10095*(-a*(sin(d*x+c)-1))^(9/2)*a^(5/2)+7794*(-a*(sin(d*x+c)-1))^(7/2)*a^(7/2)+10866*(-a*(sin(d*x+c)-1))^(5/2)*a^(9/2)-15215*(-a*(sin(d*x+c)-1))^(3/2)*a^(11/2)+2685*(-a*(sin(d*x+c)-1))^(1/2)*a^(13/2))/sin(d*x+c)^6/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
462,1,216,255,1.660000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(5985 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{17}{2}}-39900 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{15}{2}}-1771 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{13}{2}}+95232 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{11}{2}}-98581 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{9}{2}}+39900 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{11}{2}} a^{\frac{7}{2}}-5985 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{13}{2}} a^{\frac{5}{2}}-5985 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{9} \left(\sin^{7}\left(d x +c \right)\right)\right)}{35840 a^{\frac{15}{2}} \sin \left(d x +c \right)^{7} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/35840*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(5985*(-a*(sin(d*x+c)-1))^(1/2)*a^(17/2)-39900*(-a*(sin(d*x+c)-1))^(3/2)*a^(15/2)-1771*(-a*(sin(d*x+c)-1))^(5/2)*a^(13/2)+95232*(-a*(sin(d*x+c)-1))^(7/2)*a^(11/2)-98581*(-a*(sin(d*x+c)-1))^(9/2)*a^(9/2)+39900*(-a*(sin(d*x+c)-1))^(11/2)*a^(7/2)-5985*(-a*(sin(d*x+c)-1))^(13/2)*a^(5/2)-5985*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^9*sin(d*x+c)^7)/a^(15/2)/sin(d*x+c)^7/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
463,1,234,289,1.877000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(55545 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{15}{2}} a^{\frac{7}{2}}-425845 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{13}{2}} a^{\frac{9}{2}}+1418249 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{11}{2}} a^{\frac{11}{2}}-55545 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{11} \left(\sin^{8}\left(d x +c \right)\right)-2509197 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{13}{2}}+2176627 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{15}{2}}-416759 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{17}{2}}-425845 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{19}{2}}+55545 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{21}{2}}\right)}{573440 a^{\frac{19}{2}} \sin \left(d x +c \right)^{8} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/573440*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(19/2)*(55545*(-a*(sin(d*x+c)-1))^(15/2)*a^(7/2)-425845*(-a*(sin(d*x+c)-1))^(13/2)*a^(9/2)+1418249*(-a*(sin(d*x+c)-1))^(11/2)*a^(11/2)-55545*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^11*sin(d*x+c)^8-2509197*(-a*(sin(d*x+c)-1))^(9/2)*a^(13/2)+2176627*(-a*(sin(d*x+c)-1))^(7/2)*a^(15/2)-416759*(-a*(sin(d*x+c)-1))^(5/2)*a^(17/2)-425845*(-a*(sin(d*x+c)-1))^(3/2)*a^(19/2)+55545*(-a*(sin(d*x+c)-1))^(1/2)*a^(21/2))/sin(d*x+c)^8/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
464,1,74,108,1.353000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(315 \left(\sin^{3}\left(d x +c \right)\right)+595 \left(\sin^{2}\left(d x +c \right)\right)+340 \sin \left(d x +c \right)+136\right)}{3465 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/3465*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(315*sin(d*x+c)^3+595*sin(d*x+c)^2+340*sin(d*x+c)+136)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
465,1,64,80,1.405000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(35 \left(\sin^{2}\left(d x +c \right)\right)+65 \sin \left(d x +c \right)+26\right)}{315 \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(35*sin(d*x+c)^2+65*sin(d*x+c)+26)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
466,1,123,112,1.896000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(15 a^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)+3 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}-5 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a -15 a^{2} \sqrt{a -a \sin \left(d x +c \right)}\right)}{15 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/15*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(15*a^(5/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))+3*(a-a*sin(d*x+c))^(5/2)-5*(a-a*sin(d*x+c))^(3/2)*a-15*a^2*(a-a*sin(d*x+c))^(1/2))/a^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
467,1,126,103,2.039000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(2 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} \sqrt{a}+3 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a^{2}\right)-3 \sqrt{a -a \sin \left(d x +c \right)}\, a^{\frac{3}{2}}\right)}{3 a^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(5/2)*(sin(d*x+c)*(2*(a-a*sin(d*x+c))^(3/2)*a^(1/2)+3*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a^2)-3*(a-a*sin(d*x+c))^(1/2)*a^(3/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
468,1,150,107,2.046000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(8 a^{\frac{3}{2}} \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin^{2}\left(d x +c \right)\right)-9 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+\left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}+\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}\right)}{4 a^{\frac{5}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(5/2)*(8*a^(3/2)*(-a*(sin(d*x+c)-1))^(1/2)*sin(d*x+c)^2-9*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2)+(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2))/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
469,1,144,115,2.099000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(21 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)-21 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}+56 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-27 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} \sqrt{a}\right)}{24 a^{\frac{7}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(21*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^3-21*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2)+56*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)-27*(-a*(sin(d*x+c)-1))^(5/2)*a^(1/2))/a^(7/2)/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
470,1,162,146,2.051000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(33 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{3}{2}}-33 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)+7 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}-121 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+33 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}\right)}{192 a^{\frac{11}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/192*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)/a^(11/2)*(33*(-a*(sin(d*x+c)-1))^(7/2)*a^(3/2)-33*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^5*sin(d*x+c)^4+7*(-a*(sin(d*x+c)-1))^(5/2)*a^(5/2)-121*(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+33*(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2))/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
471,1,180,177,2.096000," ","int(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(45 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{13}{2}}-210 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{11}{2}}-128 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{9}{2}}+210 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{7}{2}}-45 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{5}{2}}-45 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{7} \left(\sin^{5}\left(d x +c \right)\right)\right)}{640 a^{\frac{15}{2}} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/640*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(45*(-a*(sin(d*x+c)-1))^(1/2)*a^(13/2)-210*(-a*(sin(d*x+c)-1))^(3/2)*a^(11/2)-128*(-a*(sin(d*x+c)-1))^(5/2)*a^(9/2)+210*(-a*(sin(d*x+c)-1))^(7/2)*a^(7/2)-45*(-a*(sin(d*x+c)-1))^(9/2)*a^(5/2)-45*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^7*sin(d*x+c)^5)/a^(15/2)/sin(d*x+c)^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
472,1,77,181,0.997000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(105 \left(\sin^{3}\left(d x +c \right)\right)+70 \left(\sin^{2}\left(d x +c \right)\right)+40 \sin \left(d x +c \right)+16\right)}{1155 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/1155/a*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(105*sin(d*x+c)^3+70*sin(d*x+c)^2+40*sin(d*x+c)+16)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
473,1,67,80,1.017000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(35 \left(\sin^{2}\left(d x +c \right)\right)+20 \sin \left(d x +c \right)+8\right)}{315 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315/a*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(35*sin(d*x+c)^2+20*sin(d*x+c)+8)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
474,1,57,52,0.874000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \left(\sin \left(d x +c \right)-1\right)^{3} \left(5 \sin \left(d x +c \right)+2\right)}{35 a \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/35/a*(1+sin(d*x+c))*(sin(d*x+c)-1)^3*(5*sin(d*x+c)+2)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
475,1,103,84,1.096000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-3 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)+\left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}+3 a \sqrt{a -a \sin \left(d x +c \right)}\right)}{3 a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/3/a^3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-3*a^(3/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))+(a-a*sin(d*x+c))^(3/2)+3*a*(a-a*sin(d*x+c))^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
476,1,123,84,1.098000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) \left(2 \sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}-3 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right) a \right)+\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)}{a^{\frac{5}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/a^(5/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(sin(d*x+c)*(2*(a-a*sin(d*x+c))^(1/2)*a^(1/2)-3*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))*a)+(a-a*sin(d*x+c))^(1/2)*a^(1/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
477,1,126,90,1.281000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{2}\left(d x +c \right)\right) a^{2}+3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{3}{2}}-5 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} \sqrt{a}\right)}{4 a^{\frac{7}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-3*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^2*a^2+3*(-a*(sin(d*x+c)-1))^(1/2)*a^(3/2)-5*(-a*(sin(d*x+c)-1))^(3/2)*a^(1/2))/a^(7/2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
478,1,144,124,1.239000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(3 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{3}{2}}+3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{4} \left(\sin^{3}\left(d x +c \right)\right)+8 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{5}{2}}-3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{7}{2}}\right)}{24 a^{\frac{11}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24/a^(11/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(3*(-a*(sin(d*x+c)-1))^(5/2)*a^(3/2)+3*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^4*sin(d*x+c)^3+8*(-a*(sin(d*x+c)-1))^(3/2)*a^(5/2)-3*(-a*(sin(d*x+c)-1))^(1/2)*a^(7/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
479,1,162,158,1.294000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-3 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{5}{2}}+11 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{7}{2}}+11 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{9}{2}}-3 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{11}{2}}+3 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{6} \left(\sin^{4}\left(d x +c \right)\right)\right)}{64 a^{\frac{15}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/64*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-3*(-a*(sin(d*x+c)-1))^(7/2)*a^(5/2)+11*(-a*(sin(d*x+c)-1))^(5/2)*a^(7/2)+11*(-a*(sin(d*x+c)-1))^(3/2)*a^(9/2)-3*(-a*(sin(d*x+c)-1))^(1/2)*a^(11/2)+3*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^6*sin(d*x+c)^4)/a^(15/2)/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
480,1,180,192,1.359000," ","int(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(15 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{9}{2}} a^{\frac{7}{2}}-70 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{9}{2}}+128 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{11}{2}}+15 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{8} \left(\sin^{5}\left(d x +c \right)\right)+70 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{13}{2}}-15 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{15}{2}}\right)}{640 a^{\frac{19}{2}} \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/640/a^(19/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(15*(-a*(sin(d*x+c)-1))^(9/2)*a^(7/2)-70*(-a*(sin(d*x+c)-1))^(7/2)*a^(9/2)+128*(-a*(sin(d*x+c)-1))^(5/2)*a^(11/2)+15*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^8*sin(d*x+c)^5+70*(-a*(sin(d*x+c)-1))^(3/2)*a^(13/2)-15*(-a*(sin(d*x+c)-1))^(1/2)*a^(15/2))/sin(d*x+c)^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
481,1,166,227,1.234000," ","int(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-1386 a^{\frac{11}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)+63 \left(a -a \sin \left(d x +c \right)\right)^{\frac{11}{2}}-154 a \left(a -a \sin \left(d x +c \right)\right)^{\frac{9}{2}}+198 \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}} a^{2}+231 a^{4} \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}}+1386 a^{5} \sqrt{a -a \sin \left(d x +c \right)}\right)}{693 a^{8} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/693/a^8*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-1386*a^(11/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))+63*(a-a*sin(d*x+c))^(11/2)-154*a*(a-a*sin(d*x+c))^(9/2)+198*(a-a*sin(d*x+c))^(7/2)*a^2+231*a^4*(a-a*sin(d*x+c))^(3/2)+1386*a^5*(a-a*sin(d*x+c))^(1/2))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
482,1,166,193,1.283000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(630 a^{\frac{9}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-35 \left(a -a \sin \left(d x +c \right)\right)^{\frac{9}{2}}+45 a \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}-63 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}} a^{2}-105 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{3}-630 a^{4} \sqrt{a -a \sin \left(d x +c \right)}\right)}{315 a^{7} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(630*a^(9/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-35*(a-a*sin(d*x+c))^(9/2)+45*a*(a-a*sin(d*x+c))^(7/2)-63*(a-a*sin(d*x+c))^(5/2)*a^2-105*(a-a*sin(d*x+c))^(3/2)*a^3-630*a^4*(a-a*sin(d*x+c))^(1/2))/a^7/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
483,1,132,146,1.095000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(42 a^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-3 \left(a -a \sin \left(d x +c \right)\right)^{\frac{7}{2}}-7 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a^{2}-42 a^{3} \sqrt{a -a \sin \left(d x +c \right)}\right)}{21 a^{6} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/21*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(42*a^(7/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-3*(a-a*sin(d*x+c))^(7/2)-7*(a-a*sin(d*x+c))^(3/2)*a^2-42*a^3*(a-a*sin(d*x+c))^(1/2))/a^6/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
484,1,130,118,1.195000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(30 a^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-3 \left(a -a \sin \left(d x +c \right)\right)^{\frac{5}{2}}-5 \left(a -a \sin \left(d x +c \right)\right)^{\frac{3}{2}} a -30 a^{2} \sqrt{a -a \sin \left(d x +c \right)}\right)}{15 a^{5} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"2/15*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(30*a^(5/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-3*(a-a*sin(d*x+c))^(5/2)-5*(a-a*sin(d*x+c))^(3/2)*a-30*a^2*(a-a*sin(d*x+c))^(1/2))/a^5/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
485,1,116,96,1.005000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x)","-\frac{2 \left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sqrt{a -a \sin \left(d x +c \right)}+\sqrt{a}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)-2 \sqrt{a}\, \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)\right)}{a^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-2/a^3*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*((a-a*sin(d*x+c))^(1/2)+a^(1/2)*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2))-2*a^(1/2)*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2)))/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
486,1,132,96,1.070000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(\sin \left(d x +c \right) a \left(4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{2}}{2 \sqrt{a}}\right)-5 \arctanh \left(\frac{\sqrt{a -a \sin \left(d x +c \right)}}{\sqrt{a}}\right)\right)+\sqrt{a -a \sin \left(d x +c \right)}\, \sqrt{a}\right)}{a^{\frac{7}{2}} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/a^(7/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(sin(d*x+c)*a*(4*2^(1/2)*arctanh(1/2*(a-a*sin(d*x+c))^(1/2)*2^(1/2)/a^(1/2))-5*arctanh((a-a*sin(d*x+c))^(1/2)/a^(1/2)))+(a-a*sin(d*x+c))^(1/2)*a^(1/2))/sin(d*x+c)/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
487,1,164,128,1.291000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(16 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+7 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{5}{2}}-9 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{3}{2}}-23 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)\right)}{4 a^{\frac{11}{2}} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/4*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(16*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^3*sin(d*x+c)^2+7*(-a*(sin(d*x+c)-1))^(1/2)*a^(5/2)-9*(-a*(sin(d*x+c)-1))^(3/2)*a^(3/2)-23*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*a^3*sin(d*x+c)^2)/a^(11/2)/sin(d*x+c)^2/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
488,1,182,162,1.484000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x)","-\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(-135 \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)+57 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{5}{2}}+96 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)-88 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{7}{2}}+39 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{9}{2}}\right)}{24 a^{\frac{15}{2}} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"-1/24/a^(15/2)*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(-135*a^5*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^3+57*(-a*(sin(d*x+c)-1))^(5/2)*a^(5/2)+96*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^5*sin(d*x+c)^3-88*(-a*(sin(d*x+c)-1))^(3/2)*a^(7/2)+39*(-a*(sin(d*x+c)-1))^(1/2)*a^(9/2))/sin(d*x+c)^3/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
489,1,200,196,1.396000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x)","\frac{\left(1+\sin \left(d x +c \right)\right) \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \left(321 \sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, a^{\frac{13}{2}}-1049 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{3}{2}} a^{\frac{11}{2}}+1127 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{5}{2}} a^{\frac{9}{2}}-447 \left(-a \left(\sin \left(d x +c \right)-1\right)\right)^{\frac{7}{2}} a^{\frac{7}{2}}+768 \sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) a^{7} \left(\sin^{4}\left(d x +c \right)\right)-1089 a^{7} \arctanh \left(\frac{\sqrt{-a \left(\sin \left(d x +c \right)-1\right)}}{\sqrt{a}}\right) \left(\sin^{4}\left(d x +c \right)\right)\right)}{192 a^{\frac{19}{2}} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +a \sin \left(d x +c \right)}\, d}"," ",0,"1/192*(1+sin(d*x+c))*(-a*(sin(d*x+c)-1))^(1/2)*(321*(-a*(sin(d*x+c)-1))^(1/2)*a^(13/2)-1049*(-a*(sin(d*x+c)-1))^(3/2)*a^(11/2)+1127*(-a*(sin(d*x+c)-1))^(5/2)*a^(9/2)-447*(-a*(sin(d*x+c)-1))^(7/2)*a^(7/2)+768*2^(1/2)*arctanh(1/2*(-a*(sin(d*x+c)-1))^(1/2)*2^(1/2)/a^(1/2))*a^7*sin(d*x+c)^4-1089*a^7*arctanh((-a*(sin(d*x+c)-1))^(1/2)/a^(1/2))*sin(d*x+c)^4)/a^(19/2)/sin(d*x+c)^4/cos(d*x+c)/(a+a*sin(d*x+c))^(1/2)/d","A"
490,0,0,182,11.093000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","F"
491,0,0,117,6.119000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","F"
492,0,0,122,4.783000," ","int(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","\int \frac{\left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","F"
493,0,0,161,6.952000," ","int(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","\int \frac{\left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","F"
494,1,138,85,0.227000," ","int(cos(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{11}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{99}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)+a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)}{d}"," ",0,"1/d*(a*(-1/11*sin(d*x+c)^5*cos(d*x+c)^6-5/99*sin(d*x+c)^3*cos(d*x+c)^6-5/231*sin(d*x+c)*cos(d*x+c)^6+1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6))","A"
495,1,120,85,0.244000," ","int(cos(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)}{d}"," ",0,"1/d*(a*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+a*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
496,1,102,71,0.283000," ","int(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(a*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6))","A"
497,1,84,71,0.241000," ","int(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(a*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+a*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
498,1,64,57,0.245000," ","int(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*a*cos(d*x+c)^6)","A"
499,1,94,80,0.374000," ","int(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{8 a \sin \left(d x +c \right)}{15 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}+\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{15 d}+\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"8/15*a*sin(d*x+c)/d+1/5/d*cos(d*x+c)^4*sin(d*x+c)*a+4/15/d*a*sin(d*x+c)*cos(d*x+c)^2+1/4*a*cos(d*x+c)^4/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d","A"
500,1,116,79,0.308000," ","int(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 a \sin \left(d x +c \right)}{3 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}"," ",0,"1/4*a*cos(d*x+c)^4/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/d*a/sin(d*x+c)*cos(d*x+c)^6-8/3*a*sin(d*x+c)/d-1/d*cos(d*x+c)^4*sin(d*x+c)*a-4/3/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
501,1,139,80,0.385000," ","int(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 a \sin \left(d x +c \right)}{3 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^6-8/3*a*sin(d*x+c)/d-1/d*cos(d*x+c)^4*sin(d*x+c)*a-4/3/d*a*sin(d*x+c)*cos(d*x+c)^2-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^6-1/2*a*cos(d*x+c)^4/d-a*cos(d*x+c)^2/d-2*a*ln(sin(d*x+c))/d","A"
502,1,159,79,0.336000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}+\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^6-1/2*a*cos(d*x+c)^4/d-a*cos(d*x+c)^2/d-2*a*ln(sin(d*x+c))/d-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^6+1/d*a/sin(d*x+c)*cos(d*x+c)^6+8/3*a*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*a+4/3/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
503,1,136,77,0.324000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}+\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^6+1/d*a/sin(d*x+c)*cos(d*x+c)^6+8/3*a*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*a+4/3/d*a*sin(d*x+c)*cos(d*x+c)^2-1/4/d*a*cot(d*x+c)^4+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d","A"
504,1,160,80,0.321000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}-\frac{8 a \sin \left(d x +c \right)}{15 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{4 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{15 d}"," ",0,"-1/4/d*a*cot(d*x+c)^4+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^6+1/15/d*a/sin(d*x+c)^3*cos(d*x+c)^6-1/5/d*a/sin(d*x+c)*cos(d*x+c)^6-8/15*a*sin(d*x+c)/d-1/5/d*cos(d*x+c)^4*sin(d*x+c)*a-4/15/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
505,1,110,55,0.337000," ","int(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}\right)-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6 \sin \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(a*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*a/sin(d*x+c)^6*cos(d*x+c)^6)","A"
506,1,128,57,0.359000," ","int(cos(d*x+c)^5*csc(d*x+c)^8*(a+a*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6 \sin \left(d x +c \right)^{6}}+a \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(-1/6*a/sin(d*x+c)^6*cos(d*x+c)^6+a*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
507,1,148,71,0.364000," ","int(cos(d*x+c)^5*csc(d*x+c)^9*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+a \left(-\frac{\cos^{6}\left(d x +c \right)}{8 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{24 \sin \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(a*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/8/sin(d*x+c)^8*cos(d*x+c)^6-1/24/sin(d*x+c)^6*cos(d*x+c)^6))","B"
508,1,166,71,0.375000," ","int(cos(d*x+c)^5*csc(d*x+c)^10*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{8 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{24 \sin \left(d x +c \right)^{6}}\right)+a \left(-\frac{\cos^{6}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{6}\left(d x +c \right)}{21 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)}{d}"," ",0,"1/d*(a*(-1/8/sin(d*x+c)^8*cos(d*x+c)^6-1/24/sin(d*x+c)^6*cos(d*x+c)^6)+a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^6-1/21/sin(d*x+c)^7*cos(d*x+c)^6-1/105/sin(d*x+c)^5*cos(d*x+c)^6+1/315/sin(d*x+c)^3*cos(d*x+c)^6-1/105/sin(d*x+c)*cos(d*x+c)^6-1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
509,1,184,85,0.373000," ","int(cos(d*x+c)^5*csc(d*x+c)^11*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{6}\left(d x +c \right)}{21 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+a \left(-\frac{\cos^{6}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{6}\left(d x +c \right)}{20 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{60 \sin \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^6-1/21/sin(d*x+c)^7*cos(d*x+c)^6-1/105/sin(d*x+c)^5*cos(d*x+c)^6+1/315/sin(d*x+c)^3*cos(d*x+c)^6-1/105/sin(d*x+c)*cos(d*x+c)^6-1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/10/sin(d*x+c)^10*cos(d*x+c)^6-1/20/sin(d*x+c)^8*cos(d*x+c)^6-1/60/sin(d*x+c)^6*cos(d*x+c)^6))","B"
510,1,202,85,0.288000," ","int(cos(d*x+c)^5*csc(d*x+c)^12*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{6}\left(d x +c \right)}{20 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{60 \sin \left(d x +c \right)^{6}}\right)+a \left(-\frac{\cos^{6}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right)}{99 \sin \left(d x +c \right)^{9}}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right)}{231 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{693 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{231 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)}{d}"," ",0,"1/d*(a*(-1/10/sin(d*x+c)^10*cos(d*x+c)^6-1/20/sin(d*x+c)^8*cos(d*x+c)^6-1/60/sin(d*x+c)^6*cos(d*x+c)^6)+a*(-1/11/sin(d*x+c)^11*cos(d*x+c)^6-5/99/sin(d*x+c)^9*cos(d*x+c)^6-5/231/sin(d*x+c)^7*cos(d*x+c)^6-1/231/sin(d*x+c)^5*cos(d*x+c)^6+1/693/sin(d*x+c)^3*cos(d*x+c)^6-1/231/sin(d*x+c)*cos(d*x+c)^6-1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
511,1,158,113,0.171000," ","int(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+2 a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(a^2*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+2*a^2*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+a^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6))","A"
512,1,156,101,0.267000," ","int(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+2 a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(a^2*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+2*a^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
513,1,102,81,0.237000," ","int(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+2 a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+2*a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*a^2*cos(d*x+c)^6)","A"
514,1,122,109,0.471000," ","int(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6 d}+\frac{16 a^{2} \sin \left(d x +c \right)}{15 d}+\frac{2 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{5 d}+\frac{8 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{15 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{4 d}+\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/6/d*a^2*cos(d*x+c)^6+16/15*a^2*sin(d*x+c)/d+2/5/d*sin(d*x+c)*a^2*cos(d*x+c)^4+8/15/d*sin(d*x+c)*a^2*cos(d*x+c)^2+1/4/d*cos(d*x+c)^4*a^2+1/2/d*a^2*cos(d*x+c)^2+a^2*ln(sin(d*x+c))/d","A"
515,1,130,108,0.408000," ","int(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","-\frac{32 a^{2} \sin \left(d x +c \right)}{15 d}-\frac{4 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{16 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{15 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{2 d}+\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-32/15*a^2*sin(d*x+c)/d-4/5/d*sin(d*x+c)*a^2*cos(d*x+c)^4-16/15/d*sin(d*x+c)*a^2*cos(d*x+c)^2+1/2/d*cos(d*x+c)^4*a^2+1/d*a^2*cos(d*x+c)^2+2*a^2*ln(sin(d*x+c))/d-1/d*a^2/sin(d*x+c)*cos(d*x+c)^6","A"
516,1,155,108,0.472000," ","int(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","-\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{4 d}-\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a^{2} \sin \left(d x +c \right)}{3 d}-\frac{2 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{8 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-1/4/d*cos(d*x+c)^4*a^2-1/2/d*a^2*cos(d*x+c)^2-a^2*ln(sin(d*x+c))/d-2/d*a^2/sin(d*x+c)*cos(d*x+c)^6-16/3*a^2*sin(d*x+c)/d-2/d*sin(d*x+c)*a^2*cos(d*x+c)^4-8/3/d*sin(d*x+c)*a^2*cos(d*x+c)^2-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^6","A"
517,1,97,106,0.424000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{d}-\frac{2 a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/d*a^2/sin(d*x+c)^2*cos(d*x+c)^6-1/d*cos(d*x+c)^4*a^2-2/d*a^2*cos(d*x+c)^2-4*a^2*ln(sin(d*x+c))/d-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6","A"
518,1,211,108,0.425000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{2}}{2 d}-\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{16 a^{2} \sin \left(d x +c \right)}{3 d}+\frac{2 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{8 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^6-1/2/d*cos(d*x+c)^4*a^2-1/d*a^2*cos(d*x+c)^2-a^2*ln(sin(d*x+c))/d-2/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6+2/d*a^2/sin(d*x+c)*cos(d*x+c)^6+16/3*a^2*sin(d*x+c)/d+2/d*sin(d*x+c)*a^2*cos(d*x+c)^4+8/3/d*sin(d*x+c)*a^2*cos(d*x+c)^2-1/4/d*a^2*cot(d*x+c)^4+1/2/d*a^2*cot(d*x+c)^2","A"
519,1,178,106,0.425000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","-\frac{4 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}+\frac{4 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}+\frac{32 a^{2} \sin \left(d x +c \right)}{15 d}+\frac{4 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{5 d}+\frac{16 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-4/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6+4/5/d*a^2/sin(d*x+c)*cos(d*x+c)^6+32/15*a^2*sin(d*x+c)/d+4/5/d*sin(d*x+c)*a^2*cos(d*x+c)^4+16/15/d*sin(d*x+c)*a^2*cos(d*x+c)^2-1/2/d*a^2*cot(d*x+c)^4+1/d*a^2*cot(d*x+c)^2+2*a^2*ln(sin(d*x+c))/d-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^6","A"
520,1,202,109,0.444000," ","int(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{2 a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}-\frac{16 a^{2} \sin \left(d x +c \right)}{15 d}-\frac{2 \sin \left(d x +c \right) a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 \sin \left(d x +c \right) a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-1/4/d*a^2*cot(d*x+c)^4+1/2/d*a^2*cot(d*x+c)^2+a^2*ln(sin(d*x+c))/d-2/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^6+2/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6-2/5/d*a^2/sin(d*x+c)*cos(d*x+c)^6-16/15*a^2*sin(d*x+c)/d-2/5/d*sin(d*x+c)*a^2*cos(d*x+c)^4-8/15/d*sin(d*x+c)*a^2*cos(d*x+c)^2-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^6","A"
521,1,208,101,0.265000," ","int(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(a^3*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+3*a^3*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+3*a^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+a^3*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
522,1,170,81,0.259000," ","int(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+3 a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a^3*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+3*a^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+3*a^3*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*a^3*cos(d*x+c)^6)","B"
523,1,144,125,0.471000," ","int(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right)}{7 d}+\frac{176 a^{3} \sin \left(d x +c \right)}{105 d}+\frac{22 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35 d}+\frac{88 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{105 d}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{3}}{4 d}+\frac{a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/7/d*a^3*cos(d*x+c)^6*sin(d*x+c)+176/105*a^3*sin(d*x+c)/d+22/35/d*a^3*cos(d*x+c)^4*sin(d*x+c)+88/105/d*a^3*cos(d*x+c)^2*sin(d*x+c)-1/2/d*a^3*cos(d*x+c)^6+1/4/d*cos(d*x+c)^4*a^3+1/2/d*a^3*cos(d*x+c)^2+a^3*ln(sin(d*x+c))/d","A"
524,1,147,123,0.398000," ","int(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{6 d}-\frac{16 a^{3} \sin \left(d x +c \right)}{15 d}-\frac{2 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{8 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15 d}+\frac{3 \left(\cos^{4}\left(d x +c \right)\right) a^{3}}{4 d}+\frac{3 a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-1/6/d*a^3*cos(d*x+c)^6-16/15*a^3*sin(d*x+c)/d-2/5/d*a^3*cos(d*x+c)^4*sin(d*x+c)-8/15/d*a^3*cos(d*x+c)^2*sin(d*x+c)+3/4/d*cos(d*x+c)^4*a^3+3/2/d*a^3*cos(d*x+c)^2+3*a^3*ln(sin(d*x+c))/d-1/d*a^3/sin(d*x+c)*cos(d*x+c)^6","A"
525,1,154,123,0.462000," ","int(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","-\frac{112 a^{3} \sin \left(d x +c \right)}{15 d}-\frac{14 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{56 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{3}}{4 d}+\frac{a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-112/15*a^3*sin(d*x+c)/d-14/5/d*a^3*cos(d*x+c)^4*sin(d*x+c)-56/15/d*a^3*cos(d*x+c)^2*sin(d*x+c)+1/4/d*cos(d*x+c)^4*a^3+1/2/d*a^3*cos(d*x+c)^2+a^3*ln(sin(d*x+c))/d-3/d*a^3/sin(d*x+c)*cos(d*x+c)^6-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^6","A"
526,1,179,123,0.428000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","-\frac{5 \left(\cos^{4}\left(d x +c \right)\right) a^{3}}{4 d}-\frac{5 a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{5 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a^{3} \sin \left(d x +c \right)}{3 d}-\frac{2 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{8 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{3 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-5/4/d*cos(d*x+c)^4*a^3-5/2/d*a^3*cos(d*x+c)^2-5*a^3*ln(sin(d*x+c))/d-2/d*a^3/sin(d*x+c)*cos(d*x+c)^6-16/3*a^3*sin(d*x+c)/d-2/d*a^3*cos(d*x+c)^4*sin(d*x+c)-8/3/d*a^3*cos(d*x+c)^2*sin(d*x+c)-3/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^6-1/3/d*a^3/sin(d*x+c)^3*cos(d*x+c)^6","A"
527,1,211,123,0.428000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{2 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{16 a^{3} \sin \left(d x +c \right)}{3 d}+\frac{2 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}+\frac{8 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{3 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 \left(\cos^{4}\left(d x +c \right)\right) a^{3}}{2 d}-\frac{3 a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{5 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}-\frac{a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"2/d*a^3/sin(d*x+c)*cos(d*x+c)^6+16/3*a^3*sin(d*x+c)/d+2/d*a^3*cos(d*x+c)^4*sin(d*x+c)+8/3/d*a^3*cos(d*x+c)^2*sin(d*x+c)-3/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^6-3/2/d*cos(d*x+c)^4*a^3-3/d*a^3*cos(d*x+c)^2-5*a^3*ln(sin(d*x+c))/d-1/d*a^3/sin(d*x+c)^3*cos(d*x+c)^6-1/4/d*a^3*cot(d*x+c)^4+1/2/d*a^3*cot(d*x+c)^2","A"
528,1,234,123,0.441000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{\left(\cos^{4}\left(d x +c \right)\right) a^{3}}{2 d}-\frac{a^{3} \left(\cos^{2}\left(d x +c \right)\right)}{d}+\frac{a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{14 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}+\frac{14 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}+\frac{112 a^{3} \sin \left(d x +c \right)}{15 d}+\frac{14 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}+\frac{56 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15 d}-\frac{3 a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^6-1/2/d*cos(d*x+c)^4*a^3-1/d*a^3*cos(d*x+c)^2+a^3*ln(sin(d*x+c))/d-14/15/d*a^3/sin(d*x+c)^3*cos(d*x+c)^6+14/5/d*a^3/sin(d*x+c)*cos(d*x+c)^6+112/15*a^3*sin(d*x+c)/d+14/5/d*a^3*cos(d*x+c)^4*sin(d*x+c)+56/15/d*a^3*cos(d*x+c)^2*sin(d*x+c)-3/4/d*a^3*cot(d*x+c)^4+3/2/d*a^3*cot(d*x+c)^2-1/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^6","A"
529,1,203,123,0.519000," ","int(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","-\frac{2 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}+\frac{2 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}+\frac{16 a^{3} \sin \left(d x +c \right)}{15 d}+\frac{2 a^{3} \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}+\frac{8 a^{3} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15 d}-\frac{3 a^{3} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-2/15/d*a^3/sin(d*x+c)^3*cos(d*x+c)^6+2/5/d*a^3/sin(d*x+c)*cos(d*x+c)^6+16/15*a^3*sin(d*x+c)/d+2/5/d*a^3*cos(d*x+c)^4*sin(d*x+c)+8/15/d*a^3*cos(d*x+c)^2*sin(d*x+c)-3/4/d*a^3*cot(d*x+c)^4+3/2/d*a^3*cot(d*x+c)^2+3*a^3*ln(sin(d*x+c))/d-3/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^6-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^6","A"
530,1,179,139,0.454000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","-\frac{64 a^{4} \sin \left(d x +c \right)}{5 d}-\frac{24 a^{4} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{32 a^{4} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{a^{4} \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{2 a^{4} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{5 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-64/5*a^4*sin(d*x+c)/d-24/5/d*a^4*sin(d*x+c)*cos(d*x+c)^4-32/5/d*a^4*cos(d*x+c)^2*sin(d*x+c)-1/d*a^4*cos(d*x+c)^4-2/d*a^4*cos(d*x+c)^2-4*a^4*ln(sin(d*x+c))/d-5/d*a^4/sin(d*x+c)*cos(d*x+c)^6-2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^6-1/3/d*a^4/sin(d*x+c)^3*cos(d*x+c)^6","A"
531,1,129,140,0.441000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^4,x)","-\frac{11 a^{4} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}-\frac{11 a^{4} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{10 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{3 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{4 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"-11/4/d*a^4*cos(d*x+c)^4-11/2/d*a^4*cos(d*x+c)^2-10*a^4*ln(sin(d*x+c))/d-3/d*a^4/sin(d*x+c)^2*cos(d*x+c)^6-4/3/d*a^4/sin(d*x+c)^3*cos(d*x+c)^6-1/4/d*a^4*cot(d*x+c)^4+1/2/d*a^4*cot(d*x+c)^2","A"
532,1,235,140,0.432000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^4,x)","\frac{24 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}+\frac{64 a^{4} \sin \left(d x +c \right)}{5 d}+\frac{24 a^{4} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}+\frac{32 a^{4} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{5 d}-\frac{2 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{2 a^{4} \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{4 a^{4} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{4 a^{4} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{29 a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a^{4} \left(\cot^{4}\left(d x +c \right)\right)}{d}+\frac{2 a^{4} \left(\cot^{2}\left(d x +c \right)\right)}{d}-\frac{a^{4} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"24/5/d*a^4/sin(d*x+c)*cos(d*x+c)^6+64/5*a^4*sin(d*x+c)/d+24/5/d*a^4*sin(d*x+c)*cos(d*x+c)^4+32/5/d*a^4*cos(d*x+c)^2*sin(d*x+c)-2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^6-2/d*a^4*cos(d*x+c)^4-4/d*a^4*cos(d*x+c)^2-4*a^4*ln(sin(d*x+c))/d-29/15/d*a^4/sin(d*x+c)^3*cos(d*x+c)^6-1/d*a^4*cot(d*x+c)^4+2/d*a^4*cot(d*x+c)^2-1/5/d*a^4/sin(d*x+c)^5*cos(d*x+c)^6","A"
533,1,49,65,0.253000," ","int(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}-\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}}{d a}"," ",0,"1/d/a*(1/7*sin(d*x+c)^7-1/6*sin(d*x+c)^6-1/5*sin(d*x+c)^5+1/4*sin(d*x+c)^4)","A"
534,1,49,65,0.242000," ","int(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}-\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}}{d a}"," ",0,"1/d/a*(1/6*sin(d*x+c)^6-1/5*sin(d*x+c)^5-1/4*sin(d*x+c)^4+1/3*sin(d*x+c)^3)","A"
535,1,49,49,0.189000," ","int(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}-\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(1/5*sin(d*x+c)^5-1/4*sin(d*x+c)^4-1/3*sin(d*x+c)^3+1/2*sin(d*x+c)^2)","A"
536,1,62,61,0.383000," ","int(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\sin \left(d x +c \right)}{a d}-\frac{\sin^{2}\left(d x +c \right)}{2 a d}+\frac{\sin^{3}\left(d x +c \right)}{3 d a}"," ",0,"ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d-1/2*sin(d*x+c)^2/a/d+1/3*sin(d*x+c)^3/d/a","A"
537,1,63,60,0.426000," ","int(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\sin^{2}\left(d x +c \right)}{2 a d}-\frac{\sin \left(d x +c \right)}{a d}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}"," ",0,"1/2*sin(d*x+c)^2/a/d-sin(d*x+c)/a/d-1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d","A"
538,1,61,58,0.461000," ","int(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\sin \left(d x +c \right)}{a d}+\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{1}{2 a d \sin \left(d x +c \right)^{2}}"," ",0,"sin(d*x+c)/a/d+1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d-1/2/a/d/sin(d*x+c)^2","A"
539,1,63,60,0.457000," ","int(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{1}{d a \sin \left(d x +c \right)}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{2 a d \sin \left(d x +c \right)^{2}}-\frac{1}{3 a d \sin \left(d x +c \right)^{3}}"," ",0,"1/d/a/sin(d*x+c)+ln(sin(d*x+c))/a/d+1/2/a/d/sin(d*x+c)^2-1/3/a/d/sin(d*x+c)^3","A"
540,1,49,47,0.464000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{\sin \left(d x +c \right)}+\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/sin(d*x+c)+1/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3)","A"
541,1,49,49,0.483000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}+\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/5/sin(d*x+c)^5-1/2/sin(d*x+c)^2+1/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3)","A"
542,1,49,65,0.493000," ","int(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{5 \sin \left(d x +c \right)^{5}}+\frac{1}{4 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/6/sin(d*x+c)^6+1/5/sin(d*x+c)^5+1/4/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
543,1,49,65,0.539000," ","int(cos(d*x+c)^5*csc(d*x+c)^8/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}}{d a}"," ",0,"1/d/a*(1/6/sin(d*x+c)^6+1/5/sin(d*x+c)^5-1/7/sin(d*x+c)^7-1/4/sin(d*x+c)^4)","A"
544,1,39,49,0.380000," ","int(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}-\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/6*sin(d*x+c)^6-2/5*sin(d*x+c)^5+1/4*sin(d*x+c)^4)","A"
545,1,39,49,0.362000," ","int(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\sin^{4}\left(d x +c \right)\right)}{2}+\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/5*sin(d*x+c)^5-1/2*sin(d*x+c)^4+1/3*sin(d*x+c)^3)","A"
546,1,39,49,0.299000," ","int(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}}{d \,a^{2}}"," ",0,"1/d/a^2*(1/4*sin(d*x+c)^4-2/3*sin(d*x+c)^3+1/2*sin(d*x+c)^2)","A"
547,1,46,45,0.455000," ","int(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{2 \sin \left(d x +c \right)}{a^{2} d}+\frac{\sin^{2}\left(d x +c \right)}{2 a^{2} d}"," ",0,"ln(sin(d*x+c))/a^2/d-2*sin(d*x+c)/a^2/d+1/2*sin(d*x+c)^2/a^2/d","A"
548,1,46,43,0.482000," ","int(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\sin \left(d x +c \right)}{a^{2} d}-\frac{1}{a^{2} d \sin \left(d x +c \right)}-\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"sin(d*x+c)/a^2/d-1/a^2/d/sin(d*x+c)-2*ln(sin(d*x+c))/a^2/d","A"
549,1,48,45,0.526000," ","int(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{2}{a^{2} d \sin \left(d x +c \right)}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{2 d \,a^{2} \sin \left(d x +c \right)^{2}}"," ",0,"2/a^2/d/sin(d*x+c)+ln(sin(d*x+c))/a^2/d-1/2/d/a^2/sin(d*x+c)^2","A"
550,1,37,29,0.537000," ","int(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{\sin \left(d x +c \right)}+\frac{1}{\sin \left(d x +c \right)^{2}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/sin(d*x+c)+1/sin(d*x+c)^2-1/3/sin(d*x+c)^3)","A"
551,1,39,49,0.532000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/2/sin(d*x+c)^2-1/4/sin(d*x+c)^4+2/3/sin(d*x+c)^3)","A"
552,1,39,49,0.563000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{5 \sin \left(d x +c \right)^{5}}+\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/5/sin(d*x+c)^5+1/2/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
553,1,39,49,0.585000," ","int(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{2}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/6/sin(d*x+c)^6+2/5/sin(d*x+c)^5-1/4/sin(d*x+c)^4)","A"
554,1,97,96,0.421000," ","int(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4 \sin \left(d x +c \right)}{a^{3} d}-\frac{2 \left(\sin^{2}\left(d x +c \right)\right)}{a^{3} d}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{3 a^{3} d}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{4 a^{3} d}+\frac{\sin^{5}\left(d x +c \right)}{5 a^{3} d}"," ",0,"-4*ln(1+sin(d*x+c))/a^3/d+4*sin(d*x+c)/a^3/d-2*sin(d*x+c)^2/a^3/d+4/3*sin(d*x+c)^3/a^3/d-3/4*sin(d*x+c)^4/a^3/d+1/5*sin(d*x+c)^5/a^3/d","A"
555,1,81,80,0.440000," ","int(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 \sin \left(d x +c \right)}{a^{3} d}+\frac{2 \left(\sin^{2}\left(d x +c \right)\right)}{a^{3} d}-\frac{\sin^{3}\left(d x +c \right)}{a^{3} d}+\frac{\sin^{4}\left(d x +c \right)}{4 a^{3} d}"," ",0,"4*ln(1+sin(d*x+c))/a^3/d-4*sin(d*x+c)/a^3/d+2*sin(d*x+c)^2/a^3/d-sin(d*x+c)^3/a^3/d+1/4*sin(d*x+c)^4/a^3/d","A"
556,1,65,64,0.392000," ","int(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4 \sin \left(d x +c \right)}{a^{3} d}-\frac{3 \left(\sin^{2}\left(d x +c \right)\right)}{2 a^{3} d}+\frac{\sin^{3}\left(d x +c \right)}{3 a^{3} d}"," ",0,"-4*ln(1+sin(d*x+c))/a^3/d+4*sin(d*x+c)/a^3/d-3/2*sin(d*x+c)^2/a^3/d+1/3*sin(d*x+c)^3/a^3/d","A"
557,1,46,45,0.553000," ","int(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{\sin \left(d x +c \right)}{a^{3} d}"," ",0,"ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d+sin(d*x+c)/a^3/d","A"
558,1,50,47,0.582000," ","int(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","-\frac{1}{a^{3} d \sin \left(d x +c \right)}-\frac{3 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/a^3/d/sin(d*x+c)-3*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d","A"
559,1,66,63,0.668000," ","int(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{1}{2 a^{3} d \sin \left(d x +c \right)^{2}}+\frac{3}{a^{3} d \sin \left(d x +c \right)}+\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/2/a^3/d/sin(d*x+c)^2+3/a^3/d/sin(d*x+c)+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d","A"
560,1,82,79,0.676000," ","int(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","-\frac{1}{3 d \,a^{3} \sin \left(d x +c \right)^{3}}+\frac{3}{2 a^{3} d \sin \left(d x +c \right)^{2}}-\frac{4}{a^{3} d \sin \left(d x +c \right)}-\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/3/d/a^3/sin(d*x+c)^3+3/2/a^3/d/sin(d*x+c)^2-4/a^3/d/sin(d*x+c)-4*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d","A"
561,1,97,94,0.680000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","-\frac{1}{4 d \,a^{3} \sin \left(d x +c \right)^{4}}+\frac{1}{d \,a^{3} \sin \left(d x +c \right)^{3}}-\frac{2}{a^{3} d \sin \left(d x +c \right)^{2}}+\frac{4}{a^{3} d \sin \left(d x +c \right)}+\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/4/d/a^3/sin(d*x+c)^4+1/d/a^3/sin(d*x+c)^3-2/a^3/d/sin(d*x+c)^2+4/a^3/d/sin(d*x+c)+4*ln(sin(d*x+c))/a^3/d-4*ln(1+sin(d*x+c))/a^3/d","A"
562,1,114,111,0.661000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","-\frac{1}{5 d \,a^{3} \sin \left(d x +c \right)^{5}}+\frac{3}{4 d \,a^{3} \sin \left(d x +c \right)^{4}}-\frac{4}{3 d \,a^{3} \sin \left(d x +c \right)^{3}}+\frac{2}{a^{3} d \sin \left(d x +c \right)^{2}}-\frac{4}{a^{3} d \sin \left(d x +c \right)}-\frac{4 \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{4 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"-1/5/d/a^3/sin(d*x+c)^5+3/4/d/a^3/sin(d*x+c)^4-4/3/d/a^3/sin(d*x+c)^3+2/a^3/d/sin(d*x+c)^2-4/a^3/d/sin(d*x+c)-4*ln(sin(d*x+c))/a^3/d+4*ln(1+sin(d*x+c))/a^3/d","A"
563,1,116,116,0.684000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^4,x)","-\frac{1}{4 d \,a^{4} \sin \left(d x +c \right)^{4}}+\frac{4}{3 d \,a^{4} \sin \left(d x +c \right)^{3}}-\frac{4}{d \,a^{4} \sin \left(d x +c \right)^{2}}+\frac{12}{d \,a^{4} \sin \left(d x +c \right)}+\frac{16 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}+\frac{4}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{16 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/4/d/a^4/sin(d*x+c)^4+4/3/d/a^4/sin(d*x+c)^3-4/d/a^4/sin(d*x+c)^2+12/d/a^4/sin(d*x+c)+16*ln(sin(d*x+c))/a^4/d+4/d/a^4/(1+sin(d*x+c))-16*ln(1+sin(d*x+c))/a^4/d","A"
564,1,131,131,0.685000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^4,x)","-\frac{1}{5 d \,a^{4} \sin \left(d x +c \right)^{5}}+\frac{1}{d \,a^{4} \sin \left(d x +c \right)^{4}}-\frac{8}{3 d \,a^{4} \sin \left(d x +c \right)^{3}}+\frac{6}{d \,a^{4} \sin \left(d x +c \right)^{2}}-\frac{16}{d \,a^{4} \sin \left(d x +c \right)}-\frac{20 \ln \left(\sin \left(d x +c \right)\right)}{a^{4} d}-\frac{4}{d \,a^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{20 \ln \left(1+\sin \left(d x +c \right)\right)}{a^{4} d}"," ",0,"-1/5/d/a^4/sin(d*x+c)^5+1/d/a^4/sin(d*x+c)^4-8/3/d/a^4/sin(d*x+c)^3+6/d/a^4/sin(d*x+c)^2-16/d/a^4/sin(d*x+c)-20*ln(sin(d*x+c))/a^4/d-4/d/a^4/(1+sin(d*x+c))+20*ln(1+sin(d*x+c))/a^4/d","A"
565,0,0,181,21.576000," ","int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","F"
566,0,0,160,16.812000," ","int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","F"
567,0,0,123,9.863000," ","int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","F"
568,0,0,91,5.916000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","F"
569,0,0,68,13.917000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","F"
570,0,0,87,6.211000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","F"
571,0,0,90,12.282000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","F"
572,1,134,147,0.243000," ","int(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)}{d}"," ",0,"1/d*(a*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+a*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c))","A"
573,1,116,133,0.246000," ","int(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)}{d}"," ",0,"1/d*(a*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+a*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7))","A"
574,1,98,111,0.237000," ","int(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+a \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)}{d}"," ",0,"1/d*(a*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+a*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c))","A"
575,1,78,97,0.247000," ","int(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{7}}{d}"," ",0,"1/d*(a*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/7*a*cos(d*x+c)^7)","A"
576,1,131,115,0.377000," ","int(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}+\frac{5 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 a x}{16}+\frac{5 c a}{16 d}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/6*a*cos(d*x+c)^5*sin(d*x+c)/d+5/24*a*cos(d*x+c)^3*sin(d*x+c)/d+5/16*a*cos(d*x+c)*sin(d*x+c)/d+5/16*a*x+5/16/d*c*a+1/5*a*cos(d*x+c)^5/d+1/3*a*cos(d*x+c)^3/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
577,1,153,109,0.291000," ","int(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{15 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 a x}{8}-\frac{15 c a}{8 d}"," ",0,"1/5*a*cos(d*x+c)^5/d+1/3*a*cos(d*x+c)^3/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*a/sin(d*x+c)*cos(d*x+c)^7-a*cos(d*x+c)^5*sin(d*x+c)/d-5/4*a*cos(d*x+c)^3*sin(d*x+c)/d-15/8*a*cos(d*x+c)*sin(d*x+c)/d-15/8*a*x-15/8/d*c*a","A"
578,1,177,118,0.370000," ","int(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{15 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 a x}{8}-\frac{15 c a}{8 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{5 a \cos \left(d x +c \right)}{2 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^7-a*cos(d*x+c)^5*sin(d*x+c)/d-5/4*a*cos(d*x+c)^3*sin(d*x+c)/d-15/8*a*cos(d*x+c)*sin(d*x+c)/d-15/8*a*x-15/8/d*c*a-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/2*a*cos(d*x+c)^5/d-5/6*a*cos(d*x+c)^3/d-5/2*a*cos(d*x+c)/d-5/2/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
579,1,199,114,0.321000," ","int(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{5 a \cos \left(d x +c \right)}{2 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 a \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 a \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a x}{2}+\frac{5 c a}{2 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/2*a*cos(d*x+c)^5/d-5/6*a*cos(d*x+c)^3/d-5/2*a*cos(d*x+c)/d-5/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*a/sin(d*x+c)*cos(d*x+c)^7+4/3*a*cos(d*x+c)^5*sin(d*x+c)/d+5/3*a*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a*cos(d*x+c)*sin(d*x+c)/d+5/2*a*x+5/2/d*c*a","A"
580,1,221,118,0.332000," ","int(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 a \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 a \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a x}{2}+\frac{5 c a}{2 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 a \cos \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*a/sin(d*x+c)*cos(d*x+c)^7+4/3*a*cos(d*x+c)^5*sin(d*x+c)/d+5/3*a*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a*cos(d*x+c)*sin(d*x+c)/d+5/2*a*x+5/2/d*c*a-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*a/sin(d*x+c)^2*cos(d*x+c)^7+3/8*a*cos(d*x+c)^5/d+5/8*a*cos(d*x+c)^3/d+15/8*a*cos(d*x+c)/d+15/8/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
581,1,159,110,0.226000," ","int(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 a \cos \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*a/sin(d*x+c)^2*cos(d*x+c)^7+3/8*a*cos(d*x+c)^5/d+5/8*a*cos(d*x+c)^3/d+15/8*a*cos(d*x+c)/d+15/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a","A"
582,1,181,116,0.251000," ","int(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a \cot \left(d x +c \right)}{d}-a x -\frac{c a}{d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{48 d}-\frac{5 a \cos \left(d x +c \right)}{16 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}"," ",0,"-1/5*a*cot(d*x+c)^5/d+1/3*a*cot(d*x+c)^3/d-a*cot(d*x+c)/d-a*x-1/d*c*a-1/6/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/24/d*a/sin(d*x+c)^4*cos(d*x+c)^7-1/16/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/16*a*cos(d*x+c)^5/d-5/48*a*cos(d*x+c)^3/d-5/16*a*cos(d*x+c)/d-5/16/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
583,1,152,86,0.270000," ","int(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{48 d}-\frac{5 a \cos \left(d x +c \right)}{16 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/6/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/24/d*a/sin(d*x+c)^4*cos(d*x+c)^7-1/16/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/16*a*cos(d*x+c)^5/d-5/48*a*cos(d*x+c)^3/d-5/16*a*cos(d*x+c)/d-5/16/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^7","A"
584,1,174,110,0.268000," ","int(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{5 a \cos \left(d x +c \right)}{128 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}"," ",0,"-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^7-1/8/d*a/sin(d*x+c)^8*cos(d*x+c)^7-1/48/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/192/d*a/sin(d*x+c)^4*cos(d*x+c)^7-1/128/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/128*a*cos(d*x+c)^5/d-5/384*a*cos(d*x+c)^3/d-5/128*a*cos(d*x+c)/d-5/128/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
585,1,196,124,0.287000," ","int(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{5 a \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{5 a \cos \left(d x +c \right)}{128 d}-\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{2 a \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/8/d*a/sin(d*x+c)^8*cos(d*x+c)^7-1/48/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/192/d*a/sin(d*x+c)^4*cos(d*x+c)^7-1/128/d*a/sin(d*x+c)^2*cos(d*x+c)^7-1/128*a*cos(d*x+c)^5/d-5/384*a*cos(d*x+c)^3/d-5/128*a*cos(d*x+c)/d-5/128/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/9/d*a/sin(d*x+c)^9*cos(d*x+c)^7-2/63/d*a/sin(d*x+c)^7*cos(d*x+c)^7","A"
586,1,218,144,0.292000," ","int(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{2 a \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}-\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{160 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{4}}-\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{3 a \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{256 d}-\frac{3 a \cos \left(d x +c \right)}{256 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}"," ",0,"-1/9/d*a/sin(d*x+c)^9*cos(d*x+c)^7-2/63/d*a/sin(d*x+c)^7*cos(d*x+c)^7-1/10/d*a/sin(d*x+c)^10*cos(d*x+c)^7-3/80/d*a/sin(d*x+c)^8*cos(d*x+c)^7-1/160/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/640/d*a/sin(d*x+c)^4*cos(d*x+c)^7-3/1280/d*a/sin(d*x+c)^2*cos(d*x+c)^7-3/1280*a*cos(d*x+c)^5/d-1/256*a*cos(d*x+c)^3/d-3/256*a*cos(d*x+c)/d-3/256/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
587,1,240,158,0.294000," ","int(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}-\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{160 d \sin \left(d x +c \right)^{6}}+\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{4}}-\frac{3 a \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{3 a \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{256 d}-\frac{3 a \cos \left(d x +c \right)}{256 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{a \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}-\frac{4 a \left(\cos^{7}\left(d x +c \right)\right)}{99 d \sin \left(d x +c \right)^{9}}-\frac{8 a \left(\cos^{7}\left(d x +c \right)\right)}{693 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/10/d*a/sin(d*x+c)^10*cos(d*x+c)^7-3/80/d*a/sin(d*x+c)^8*cos(d*x+c)^7-1/160/d*a/sin(d*x+c)^6*cos(d*x+c)^7+1/640/d*a/sin(d*x+c)^4*cos(d*x+c)^7-3/1280/d*a/sin(d*x+c)^2*cos(d*x+c)^7-3/1280*a*cos(d*x+c)^5/d-1/256*a*cos(d*x+c)^3/d-3/256*a*cos(d*x+c)/d-3/256/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/11/d*a/sin(d*x+c)^11*cos(d*x+c)^7-4/99/d*a/sin(d*x+c)^9*cos(d*x+c)^7-8/693/d*a/sin(d*x+c)^7*cos(d*x+c)^7","A"
588,1,238,189,0.280000," ","int(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)+2 a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)}{d}"," ",0,"1/d*(a^2*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*cos(d*x+c)^7*sin(d*x+c)+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c)+2*a^2*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+a^2*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c))","A"
589,1,172,165,0.276000," ","int(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+2 a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)}{d}"," ",0,"1/d*(a^2*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+2*a^2*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+a^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7))","A"
590,1,184,149,0.275000," ","int(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+2 a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+a^{2} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)}{d}"," ",0,"1/d*(a^2*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+2*a^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+a^2*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c))","A"
591,1,116,139,0.247000," ","int(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+2 a^{2} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7}}{d}"," ",0,"1/d*(a^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+2*a^2*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/7*a^2*cos(d*x+c)^7)","A"
592,1,165,147,0.479000," ","int(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{12 d}+\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{5 a^{2} x}{8}+\frac{5 a^{2} c}{8 d}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cos \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/7*a^2*cos(d*x+c)^7/d+1/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d+5/12*a^2*cos(d*x+c)^3*sin(d*x+c)/d+5/8*a^2*cos(d*x+c)*sin(d*x+c)/d+5/8*a^2*x+5/8/d*a^2*c+1/5*a^2*cos(d*x+c)^5/d+1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)/d+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))","A"
593,1,175,146,0.423000," ","int(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","-\frac{5 a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6 d}-\frac{25 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}-\frac{25 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{25 a^{2} x}{16}-\frac{25 a^{2} c}{16 d}+\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2} \cos \left(d x +c \right)}{d}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-5/6*a^2*cos(d*x+c)^5*sin(d*x+c)/d-25/24*a^2*cos(d*x+c)^3*sin(d*x+c)/d-25/16*a^2*cos(d*x+c)*sin(d*x+c)/d-25/16*a^2*x-25/16/d*a^2*c+2/5*a^2*cos(d*x+c)^5/d+2/3*a^2*cos(d*x+c)^3/d+2*a^2*cos(d*x+c)/d+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^2/sin(d*x+c)*cos(d*x+c)^7","A"
594,1,199,128,0.485000," ","int(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{10 d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} \cos \left(d x +c \right)}{2 d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}-\frac{15 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{4 d}-\frac{15 a^{2} x}{4}-\frac{15 a^{2} c}{4 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-3/10*a^2*cos(d*x+c)^5/d-1/2*a^2*cos(d*x+c)^3/d-3/2*a^2*cos(d*x+c)/d-3/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/d*a^2/sin(d*x+c)*cos(d*x+c)^7-2*a^2*cos(d*x+c)^5*sin(d*x+c)/d-5/2*a^2*cos(d*x+c)^3*sin(d*x+c)/d-15/4*a^2*cos(d*x+c)*sin(d*x+c)/d-15/4*a^2*x-15/4/d*a^2*c-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7","A"
595,1,223,143,0.431000," ","int(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{12 d}+\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{5 a^{2} x}{8}+\frac{5 a^{2} c}{8 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"1/3/d*a^2/sin(d*x+c)*cos(d*x+c)^7+1/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d+5/12*a^2*cos(d*x+c)^3*sin(d*x+c)/d+5/8*a^2*cos(d*x+c)*sin(d*x+c)/d+5/8*a^2*x+5/8/d*a^2*c-1/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-a^2*cos(d*x+c)^5/d-5/3*a^2*cos(d*x+c)^3/d-5*a^2*cos(d*x+c)/d-5/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^7","A"
596,1,247,143,0.441000," ","int(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{8 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{8 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{8 a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{10 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+5 a^{2} x +\frac{5 a^{2} c}{d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"-1/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/8*a^2*cos(d*x+c)^5/d-5/24*a^2*cos(d*x+c)^3/d-5/8*a^2*cos(d*x+c)/d-5/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^7+8/3/d*a^2/sin(d*x+c)*cos(d*x+c)^7+8/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d+10/3*a^2*cos(d*x+c)^3*sin(d*x+c)/d+5*a^2*cos(d*x+c)*sin(d*x+c)/d+5*a^2*x+5/d*a^2*c-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7","A"
597,1,293,127,0.449000," ","int(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} x}{2}+\frac{3 a^{2} c}{2 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{15 a^{2} \cos \left(d x +c \right)}{4 d}+\frac{15 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right)}{d}"," ",0,"-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*a^2/sin(d*x+c)*cos(d*x+c)^7+4/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d+5/3*a^2*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a^2*cos(d*x+c)*sin(d*x+c)/d+3/2*a^2*x+3/2/d*a^2*c-1/2/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7+3/4/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7+3/4*a^2*cos(d*x+c)^5/d+5/4*a^2*cos(d*x+c)^3/d+15/4*a^2*cos(d*x+c)/d+15/4/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/5*a^2*cot(d*x+c)^5/d+1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)/d","B"
598,1,205,145,0.366000," ","int(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x)","-\frac{5 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{5 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}+\frac{5 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{16 d}+\frac{25 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{25 a^{2} \cos \left(d x +c \right)}{16 d}+\frac{25 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{2 a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a^{2} \cot \left(d x +c \right)}{d}-2 a^{2} x -\frac{2 a^{2} c}{d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}"," ",0,"-5/24/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7+5/16/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7+5/16*a^2*cos(d*x+c)^5/d+25/48*a^2*cos(d*x+c)^3/d+25/16*a^2*cos(d*x+c)/d+25/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5*a^2*cot(d*x+c)^5/d+2/3*a^2*cot(d*x+c)^3/d-2*a^2*cot(d*x+c)/d-2*a^2*x-2/d*a^2*c-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7","A"
599,1,229,148,0.382000," ","int(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{8 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/5*a^2*cot(d*x+c)^5/d+1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)/d-a^2*x-1/d*a^2*c-1/3/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/12/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-1/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/8*a^2*cos(d*x+c)^5/d-5/24*a^2*cos(d*x+c)^3/d-5/8*a^2*cos(d*x+c)/d-5/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/7/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7","A"
600,1,192,166,0.388000," ","int(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x)","-\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{6}}+\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{4}}-\frac{9 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{9 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{15 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{128 d}-\frac{45 a^{2} \cos \left(d x +c \right)}{128 d}-\frac{45 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}"," ",0,"-3/16/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+3/64/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-9/128/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-9/128*a^2*cos(d*x+c)^5/d-15/128*a^2*cos(d*x+c)^3/d-45/128*a^2*cos(d*x+c)/d-45/128/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/7/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/8/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7","A"
601,1,216,138,0.416000," ","int(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x)","-\frac{11 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{8}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{96 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{64 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{192 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{64 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{64 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}"," ",0,"-11/63/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/4/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-1/24/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/96/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-1/64/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/64*a^2*cos(d*x+c)^5/d-5/192*a^2*cos(d*x+c)^3/d-5/64*a^2*cos(d*x+c)/d-5/64/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/9/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7","A"
602,1,240,208,0.398000," ","int(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x)","-\frac{13 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{13 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{480 d \sin \left(d x +c \right)^{6}}+\frac{13 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{1920 d \sin \left(d x +c \right)^{4}}-\frac{13 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{13 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{13 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{768 d}-\frac{13 a^{2} \cos \left(d x +c \right)}{256 d}-\frac{13 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{4 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}"," ",0,"-13/80/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-13/480/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+13/1920/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-13/1280/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-13/1280*a^2*cos(d*x+c)^5/d-13/768*a^2*cos(d*x+c)^3/d-13/256*a^2*cos(d*x+c)/d-13/256/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/9/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7-4/63/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/10/d*a^2/sin(d*x+c)^10*cos(d*x+c)^7","A"
603,1,264,176,0.389000," ","int(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^2,x)","-\frac{5 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{33 d \sin \left(d x +c \right)^{9}}-\frac{10 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{231 d \sin \left(d x +c \right)^{7}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{10}}-\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{40 d \sin \left(d x +c \right)^{8}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{320 d \sin \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{640 d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{128 d}-\frac{3 a^{2} \cos \left(d x +c \right)}{128 d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}"," ",0,"-5/33/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7-10/231/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/5/d*a^2/sin(d*x+c)^10*cos(d*x+c)^7-3/40/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-1/80/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/320/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-3/640/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-3/640*a^2*cos(d*x+c)^5/d-1/128*a^2*cos(d*x+c)^3/d-3/128*a^2*cos(d*x+c)/d-3/128/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-1/11/d*a^2/sin(d*x+c)^11*cos(d*x+c)^7","A"
604,1,288,246,0.408000," ","int(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^2,x)","-\frac{17 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{120 d \sin \left(d x +c \right)^{10}}-\frac{17 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{320 d \sin \left(d x +c \right)^{8}}-\frac{17 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{1920 d \sin \left(d x +c \right)^{6}}+\frac{17 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7680 d \sin \left(d x +c \right)^{4}}-\frac{17 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{5120 d \sin \left(d x +c \right)^{2}}-\frac{17 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5120 d}-\frac{17 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3072 d}-\frac{17 a^{2} \cos \left(d x +c \right)}{1024 d}-\frac{17 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{1024 d}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}-\frac{8 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{99 d \sin \left(d x +c \right)^{9}}-\frac{16 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{693 d \sin \left(d x +c \right)^{7}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{12}}"," ",0,"-17/120/d*a^2/sin(d*x+c)^10*cos(d*x+c)^7-17/320/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-17/1920/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+17/7680/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-17/5120/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-17/5120*a^2*cos(d*x+c)^5/d-17/3072*a^2*cos(d*x+c)^3/d-17/1024*a^2*cos(d*x+c)/d-17/1024/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/11/d*a^2/sin(d*x+c)^11*cos(d*x+c)^7-8/99/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7-16/693/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/12/d*a^2/sin(d*x+c)^12*cos(d*x+c)^7","A"
605,1,308,204,0.287000," ","int(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{13}-\frac{6 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{143}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{429}-\frac{16 \left(\cos^{7}\left(d x +c \right)\right)}{3003}\right)+3 a^{3} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)+3 a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)}{d}"," ",0,"1/d*(a^3*(-1/13*sin(d*x+c)^6*cos(d*x+c)^7-6/143*sin(d*x+c)^4*cos(d*x+c)^7-8/429*sin(d*x+c)^2*cos(d*x+c)^7-16/3003*cos(d*x+c)^7)+3*a^3*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*cos(d*x+c)^7*sin(d*x+c)+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c)+3*a^3*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+a^3*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c))","A"
606,1,272,189,0.275000," ","int(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)+3 a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)}{d}"," ",0,"1/d*(a^3*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*cos(d*x+c)^7*sin(d*x+c)+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c)+3*a^3*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+3*a^3*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7))","A"
607,1,236,165,0.286000," ","int(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+3 a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+a^{3} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)}{d}"," ",0,"1/d*(a^3*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+3*a^3*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+3*a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+a^3*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c))","A"
608,1,198,165,0.275000," ","int(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+3 a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+3 a^{3} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7}}{d}"," ",0,"1/d*(a^3*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+3*a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+3*a^3*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/7*a^3*cos(d*x+c)^7)","A"
609,1,187,169,0.491000," ","int(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8 d}+\frac{25 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{48 d}+\frac{125 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{192 d}+\frac{125 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{128 d}+\frac{125 a^{3} x}{128}+\frac{125 a^{3} c}{128 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7 d}+\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cos \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/8*a^3*cos(d*x+c)^7*sin(d*x+c)/d+25/48*a^3*cos(d*x+c)^5*sin(d*x+c)/d+125/192*a^3*cos(d*x+c)^3*sin(d*x+c)/d+125/128*a^3*cos(d*x+c)*sin(d*x+c)/d+125/128*a^3*x+125/128/d*a^3*c-3/7*a^3*cos(d*x+c)^7/d+1/5*a^3*cos(d*x+c)^5/d+1/3*a^3*cos(d*x+c)^3/d+a^3*cos(d*x+c)/d+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
610,1,190,161,0.419000," ","int(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7 d}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}-\frac{5 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8 d}-\frac{15 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{15 a^{3} x}{16}-\frac{15 a^{3} c}{16 d}+\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} \cos \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}"," ",0,"-1/7*a^3*cos(d*x+c)^7/d-1/2*a^3*cos(d*x+c)^5*sin(d*x+c)/d-5/8*a^3*cos(d*x+c)^3*sin(d*x+c)/d-15/16*a^3*cos(d*x+c)*sin(d*x+c)/d-15/16*a^3*x-15/16/d*a^3*c+3/5*a^3*cos(d*x+c)^5/d+a^3*cos(d*x+c)^3/d+3*a^3*cos(d*x+c)/d+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^3/sin(d*x+c)*cos(d*x+c)^7","A"
611,1,199,165,0.501000," ","int(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","-\frac{17 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6 d}-\frac{85 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}-\frac{85 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{85 a^{3} x}{16}-\frac{85 a^{3} c}{16 d}+\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{10 d}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}+\frac{a^{3} \cos \left(d x +c \right)}{2 d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"-17/6*a^3*cos(d*x+c)^5*sin(d*x+c)/d-85/24*a^3*cos(d*x+c)^3*sin(d*x+c)/d-85/16*a^3*cos(d*x+c)*sin(d*x+c)/d-85/16*a^3*x-85/16/d*a^3*c+1/10*a^3*cos(d*x+c)^5/d+1/6*a^3*cos(d*x+c)^3/d+1/2*a^3*cos(d*x+c)/d+1/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/d*a^3/sin(d*x+c)*cos(d*x+c)^7-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7","A"
612,1,223,160,0.453000," ","int(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","-\frac{13 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{10 d}-\frac{13 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{13 a^{3} \cos \left(d x +c \right)}{2 d}-\frac{13 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{5 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}-\frac{5 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}-\frac{25 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{12 d}-\frac{25 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{25 a^{3} x}{8}-\frac{25 a^{3} c}{8 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-13/10*a^3*cos(d*x+c)^5/d-13/6*a^3*cos(d*x+c)^3/d-13/2*a^3*cos(d*x+c)/d-13/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-5/3/d*a^3/sin(d*x+c)*cos(d*x+c)^7-5/3*a^3*cos(d*x+c)^5*sin(d*x+c)/d-25/12*a^3*cos(d*x+c)^3*sin(d*x+c)/d-25/8*a^3*cos(d*x+c)*sin(d*x+c)/d-25/8*a^3*x-25/8/d*a^3*c-3/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-1/3/d*a^3/sin(d*x+c)^3*cos(d*x+c)^7","A"
613,1,247,166,0.428000," ","int(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}+\frac{15 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{45 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{45 a^{3} x}{8}+\frac{45 a^{3} c}{8 d}-\frac{9 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{9 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}-\frac{15 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}-\frac{45 a^{3} \cos \left(d x +c \right)}{8 d}-\frac{45 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}"," ",0,"3/d*a^3/sin(d*x+c)*cos(d*x+c)^7+3*a^3*cos(d*x+c)^5*sin(d*x+c)/d+15/4*a^3*cos(d*x+c)^3*sin(d*x+c)/d+45/8*a^3*cos(d*x+c)*sin(d*x+c)/d+45/8*a^3*x+45/8/d*a^3*c-9/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-9/8*a^3*cos(d*x+c)^5/d-15/8*a^3*cos(d*x+c)^3/d-45/8*a^3*cos(d*x+c)/d-45/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^3/sin(d*x+c)^3*cos(d*x+c)^7-1/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7","A"
614,1,293,159,0.449000," ","int(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x)","\frac{5 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{5 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{25 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{24 d}+\frac{25 a^{3} \cos \left(d x +c \right)}{8 d}+\frac{25 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}+\frac{4 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{4 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}+\frac{5 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}+\frac{15 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 a^{3} x}{2}+\frac{13 a^{3} c}{2 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right)}{d}"," ",0,"5/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7+5/8*a^3*cos(d*x+c)^5/d+25/24*a^3*cos(d*x+c)^3/d+25/8*a^3*cos(d*x+c)/d+25/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^3/sin(d*x+c)^3*cos(d*x+c)^7+4/d*a^3/sin(d*x+c)*cos(d*x+c)^7+4*a^3*cos(d*x+c)^5*sin(d*x+c)/d+5*a^3*cos(d*x+c)^3*sin(d*x+c)/d+15/2*a^3*cos(d*x+c)*sin(d*x+c)/d+13/2*a^3*x+13/2/d*a^3*c-3/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-1/5*a^3*cot(d*x+c)^5/d+1/3*a^3*cot(d*x+c)^3/d-a^3*cot(d*x+c)/d","A"
615,1,316,166,0.477000," ","int(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x)","\frac{4 a^{3} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{17 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{3 a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{3} \cot \left(d x +c \right)}{d}-\frac{17 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{17 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{5 a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{a^{3} x}{2}+\frac{85 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{85 a^{3} \cos \left(d x +c \right)}{16 d}+\frac{85 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{a^{3} c}{2 d}"," ",0,"4/3*a^3*cos(d*x+c)^5*sin(d*x+c)/d+17/16*a^3*cos(d*x+c)^5/d-3/5*a^3*cot(d*x+c)^5/d+a^3*cot(d*x+c)^3/d-3*a^3*cot(d*x+c)/d-17/24/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7+17/16/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7-1/3/d*a^3/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*a^3/sin(d*x+c)*cos(d*x+c)^7+5/3*a^3*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a^3*cos(d*x+c)*sin(d*x+c)/d-1/2*a^3*x+85/48*a^3*cos(d*x+c)^3/d+85/16*a^3*cos(d*x+c)/d+85/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/2/d*a^3*c","A"
616,1,228,160,0.385000," ","int(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d}+\frac{5 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{16 d}+\frac{15 a^{3} \cos \left(d x +c \right)}{16 d}+\frac{15 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{3} \cot \left(d x +c \right)}{d}-3 a^{3} x -\frac{3 a^{3} c}{d}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/8/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7+3/16/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7+3/16*a^3*cos(d*x+c)^5/d+5/16*a^3*cos(d*x+c)^3/d+15/16*a^3*cos(d*x+c)/d+15/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/5*a^3*cot(d*x+c)^5/d+a^3*cot(d*x+c)^3/d-3*a^3*cot(d*x+c)/d-3*a^3*x-3/d*a^3*c-1/2/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7-1/7/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7","A"
617,1,253,218,0.450000," ","int(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{3} \cot \left(d x +c \right)}{d}-a^{3} x -\frac{a^{3} c}{d}-\frac{25 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{25 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{25 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{25 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{125 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{125 a^{3} \cos \left(d x +c \right)}{128 d}-\frac{125 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}"," ",0,"-1/5*a^3*cot(d*x+c)^5/d+1/3*a^3*cot(d*x+c)^3/d-a^3*cot(d*x+c)/d-a^3*x-1/d*a^3*c-25/48/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+25/192/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-25/128/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-25/128*a^3*cos(d*x+c)^5/d-125/384*a^3*cos(d*x+c)^3/d-125/128*a^3*cos(d*x+c)/d-125/128/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/7/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-1/8/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7","A"
618,1,216,182,0.401000," ","int(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x)","-\frac{11 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{11 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{11 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{11 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{55 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{55 a^{3} \cos \left(d x +c \right)}{128 d}-\frac{55 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{29 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}"," ",0,"-11/48/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+11/192/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-11/128/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-11/128*a^3*cos(d*x+c)^5/d-55/384*a^3*cos(d*x+c)^3/d-55/128*a^3*cos(d*x+c)/d-55/128/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-29/63/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-3/8/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7-1/9/d*a^3/sin(d*x+c)^9*cos(d*x+c)^7","A"
619,1,240,208,0.403000," ","int(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x)","-\frac{5 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{21 d \sin \left(d x +c \right)^{7}}-\frac{33 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{11 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{160 d \sin \left(d x +c \right)^{6}}+\frac{11 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{4}}-\frac{33 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{33 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{11 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{256 d}-\frac{33 a^{3} \cos \left(d x +c \right)}{256 d}-\frac{33 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{9}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}"," ",0,"-5/21/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-33/80/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7-11/160/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+11/640/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-33/1280/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-33/1280*a^3*cos(d*x+c)^5/d-11/256*a^3*cos(d*x+c)^3/d-33/256*a^3*cos(d*x+c)/d-33/256/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a^3/sin(d*x+c)^9*cos(d*x+c)^7-1/10/d*a^3/sin(d*x+c)^10*cos(d*x+c)^7","A"
620,1,264,224,0.407000," ","int(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^3,x)","-\frac{19 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{19 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{480 d \sin \left(d x +c \right)^{6}}+\frac{19 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{1920 d \sin \left(d x +c \right)^{4}}-\frac{19 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{19 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{19 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{768 d}-\frac{19 a^{3} \cos \left(d x +c \right)}{256 d}-\frac{19 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{37 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{99 d \sin \left(d x +c \right)^{9}}-\frac{74 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{693 d \sin \left(d x +c \right)^{7}}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}"," ",0,"-19/80/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7-19/480/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+19/1920/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-19/1280/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-19/1280*a^3*cos(d*x+c)^5/d-19/768*a^3*cos(d*x+c)^3/d-19/256*a^3*cos(d*x+c)/d-19/256/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-37/99/d*a^3/sin(d*x+c)^9*cos(d*x+c)^7-74/693/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-3/10/d*a^3/sin(d*x+c)^10*cos(d*x+c)^7-1/11/d*a^3/sin(d*x+c)^11*cos(d*x+c)^7","A"
621,1,288,246,0.408000," ","int(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^3,x)","-\frac{23 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{99 d \sin \left(d x +c \right)^{9}}-\frac{46 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{693 d \sin \left(d x +c \right)^{7}}-\frac{41 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{120 d \sin \left(d x +c \right)^{10}}-\frac{41 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{320 d \sin \left(d x +c \right)^{8}}-\frac{41 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{1920 d \sin \left(d x +c \right)^{6}}+\frac{41 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7680 d \sin \left(d x +c \right)^{4}}-\frac{41 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{5120 d \sin \left(d x +c \right)^{2}}-\frac{41 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5120 d}-\frac{41 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3072 d}-\frac{41 a^{3} \cos \left(d x +c \right)}{1024 d}-\frac{41 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{1024 d}-\frac{3 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{12}}"," ",0,"-23/99/d*a^3/sin(d*x+c)^9*cos(d*x+c)^7-46/693/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-41/120/d*a^3/sin(d*x+c)^10*cos(d*x+c)^7-41/320/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7-41/1920/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+41/7680/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-41/5120/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-41/5120*a^3*cos(d*x+c)^5/d-41/3072*a^3*cos(d*x+c)^3/d-41/1024*a^3*cos(d*x+c)/d-41/1024/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/11/d*a^3/sin(d*x+c)^11*cos(d*x+c)^7-1/12/d*a^3/sin(d*x+c)^12*cos(d*x+c)^7","A"
622,1,312,262,0.408000," ","int(cos(d*x+c)^6*csc(d*x+c)^14*(a+a*sin(d*x+c))^3,x)","-\frac{9 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{6}}+\frac{9 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{2560 d \sin \left(d x +c \right)^{4}}-\frac{27 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{5120 d \sin \left(d x +c \right)^{2}}-\frac{45 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{143 d \sin \left(d x +c \right)^{11}}-\frac{20 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{143 d \sin \left(d x +c \right)^{9}}-\frac{9 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{40 d \sin \left(d x +c \right)^{10}}-\frac{27 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{320 d \sin \left(d x +c \right)^{8}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{12}}-\frac{a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{13 d \sin \left(d x +c \right)^{13}}-\frac{40 a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{1001 d \sin \left(d x +c \right)^{7}}-\frac{27 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5120 d}-\frac{9 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{1024 d}-\frac{27 a^{3} \cos \left(d x +c \right)}{1024 d}-\frac{27 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{1024 d}"," ",0,"-9/640/d*a^3/sin(d*x+c)^6*cos(d*x+c)^7+9/2560/d*a^3/sin(d*x+c)^4*cos(d*x+c)^7-27/5120/d*a^3/sin(d*x+c)^2*cos(d*x+c)^7-45/143/d*a^3/sin(d*x+c)^11*cos(d*x+c)^7-20/143/d*a^3/sin(d*x+c)^9*cos(d*x+c)^7-9/40/d*a^3/sin(d*x+c)^10*cos(d*x+c)^7-27/320/d*a^3/sin(d*x+c)^8*cos(d*x+c)^7-1/4/d*a^3/sin(d*x+c)^12*cos(d*x+c)^7-1/13/d*a^3/sin(d*x+c)^13*cos(d*x+c)^7-40/1001/d*a^3/sin(d*x+c)^7*cos(d*x+c)^7-27/5120*a^3*cos(d*x+c)^5/d-9/1024*a^3*cos(d*x+c)^3/d-27/1024*a^3*cos(d*x+c)/d-27/1024/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
623,1,223,166,0.444000," ","int(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","-\frac{9 a^{4} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}-\frac{6 a^{4} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}-\frac{a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{14 a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}-\frac{2 a^{4} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{135 a^{4} x}{16}-\frac{45 a^{4} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8 d}-\frac{135 a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}-\frac{135 a^{4} c}{16 d}-\frac{2 a^{4} \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{6 a^{4} \cos \left(d x +c \right)}{d}-\frac{6 a^{4} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-9/2*a^4*cos(d*x+c)^5*sin(d*x+c)/d-6/5*a^4*cos(d*x+c)^5/d-1/3/d*a^4/sin(d*x+c)^3*cos(d*x+c)^7-14/3/d*a^4/sin(d*x+c)*cos(d*x+c)^7-2/d*a^4/sin(d*x+c)^2*cos(d*x+c)^7-135/16*a^4*x-45/8*a^4*cos(d*x+c)^3*sin(d*x+c)/d-135/16*a^4*cos(d*x+c)*sin(d*x+c)/d-135/16/d*a^4*c-2*a^4*cos(d*x+c)^3/d-6*a^4*cos(d*x+c)/d-6/d*a^4*ln(csc(d*x+c)-cot(d*x+c))","A"
624,1,517,143,0.296000," ","int(cos(d*x+c)^6*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{16}{315 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{64 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{155 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{32 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{169 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{112 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{16 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{169 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{32 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{155 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{13 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{3 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d}"," ",0,"16/315/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9-3/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)+16/35/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^2-13/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^3+64/35/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^4+155/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^5-32/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^6-169/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^7+112/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^8-16/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^10+169/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^11+32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^12-155/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^13+13/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^15+3/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^17+3/64/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
625,1,483,127,0.275000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{4}{35 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{32 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{333 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{32 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{671 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{671 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{333 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{4 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{23 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{3 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d}"," ",0,"-4/35/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8+3/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)-32/35/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2+23/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3+4/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4-333/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5-32/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6+671/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8-671/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9+333/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12-23/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13-3/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-3/64/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
626,1,415,103,0.270000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{4 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{31 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{31 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{4}{35 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13-11/6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10+31/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8+8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6-31/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5-8/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4+11/6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3+4/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2-1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)+4/35/a/d/(1+tan(1/2*d*x+1/2*c)^2)^7+1/8/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
627,1,415,87,0.207000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{47 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{13 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{13 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{47 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"-1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10+47/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8-13/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6+13/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4-47/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-2/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2+1/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-2/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6-1/8/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
628,1,296,93,0.406000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{20 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"5/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6-3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+3/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+20/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2-5/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+8/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4-3/4/a/d*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))","B"
629,1,230,87,0.443000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-8/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3-3/a/d*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))","B"
630,1,234,94,0.473000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/a/d*tan(1/2*d*x+1/2*c)-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2+3/a/d*arctan(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/2/a/d/tan(1/2*d*x+1/2*c)-3/2/a/d*ln(tan(1/2*d*x+1/2*c))","B"
631,1,173,86,0.495000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}"," ",0,"1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2-5/8/a/d*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)+2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/24/a/d/tan(1/2*d*x+1/2*c)^3+1/8/a/d/tan(1/2*d*x+1/2*c)^2+5/8/a/d/tan(1/2*d*x+1/2*c)+3/2/a/d*ln(tan(1/2*d*x+1/2*c))","A"
632,1,188,94,0.483000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{5}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2+5/8/a/d*tan(1/2*d*x+1/2*c)-2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/24/a/d/tan(1/2*d*x+1/2*c)^3+1/8/a/d/tan(1/2*d*x+1/2*c)^2-5/8/a/d/tan(1/2*d*x+1/2*c)+3/8/a/d*ln(tan(1/2*d*x+1/2*c))","A"
633,1,208,74,0.502000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{32 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/a/d*tan(1/2*d*x+1/2*c)^5-1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/32/a/d*tan(1/2*d*x+1/2*c)^3+1/8/a/d*tan(1/2*d*x+1/2*c)^2+1/16/a/d*tan(1/2*d*x+1/2*c)-1/16/a/d/tan(1/2*d*x+1/2*c)-3/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/160/a/d/tan(1/2*d*x+1/2*c)^5-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/32/a/d/tan(1/2*d*x+1/2*c)^3","B"
634,1,415,121,0.337000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{4 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{97 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{52 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{97 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{24 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{44 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{44}{105 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"-1/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13-5/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10+97/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9-52/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8+8/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6-97/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5-24/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4+5/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3-44/15/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2+1/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)-44/105/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7-1/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
635,1,347,94,0.330000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{3 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{13 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{8 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{25 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{16 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{25 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{8}{15 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}"," ",0,"3/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-13/24/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8-25/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+16/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6+25/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+13/24/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+16/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2-3/8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+8/15/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^6+3/8/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
636,1,313,90,0.303000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{14}{15 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}"," ",0,"-1/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8+3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7-8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6-4/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3-8/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+1/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)-14/15/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5-1/2/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
637,1,160,71,0.514000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+4/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))+1/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
638,1,196,70,0.533000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2-1/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
639,1,134,69,0.559000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}+\frac{2}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)+4/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2+1/d/a^2/tan(1/2*d*x+1/2*c)+1/2/d/a^2*ln(tan(1/2*d*x+1/2*c))","A"
640,1,149,71,0.569000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^2*tan(1/2*d*x+1/2*c)^2+3/8/d/a^2*tan(1/2*d*x+1/2*c)-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3+1/4/a^2/d/tan(1/2*d*x+1/2*c)^2-3/8/d/a^2/tan(1/2*d*x+1/2*c)+1/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
641,1,170,74,0.628000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{12 d \,a^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2}}-\frac{1}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{12 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/64/d/a^2*tan(1/2*d*x+1/2*c)^4-1/12/d/a^2*tan(1/2*d*x+1/2*c)^3+1/8/d/a^2*tan(1/2*d*x+1/2*c)^2+1/4/d/a^2*tan(1/2*d*x+1/2*c)-1/4/d/a^2/tan(1/2*d*x+1/2*c)-5/8/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+1/12/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
642,1,170,90,0.656000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a^{2} d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a^{2} d}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{2}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}+\frac{3}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}-\frac{1}{160 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{32 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{5}{96 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/d/a^2*tan(1/2*d*x+1/2*c)^5-1/32/d/a^2*tan(1/2*d*x+1/2*c)^4+5/96/d/a^2*tan(1/2*d*x+1/2*c)^3-3/16/d/a^2*tan(1/2*d*x+1/2*c)+3/16/d/a^2/tan(1/2*d*x+1/2*c)+1/4/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/160/a^2/d/tan(1/2*d*x+1/2*c)^5+1/32/a^2/d/tan(1/2*d*x+1/2*c)^4-5/96/a^2/d/tan(1/2*d*x+1/2*c)^3","A"
643,1,246,112,0.679000," ","int(cos(d*x+c)^6*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d \,a^{2}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{80 a^{2} d}+\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{48 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{2} d}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{1}{384 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{1}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2}}+\frac{1}{80 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{48 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/384/d/a^2*tan(1/2*d*x+1/2*c)^6-1/80/d/a^2*tan(1/2*d*x+1/2*c)^5+3/128/d/a^2*tan(1/2*d*x+1/2*c)^4-1/48/d/a^2*tan(1/2*d*x+1/2*c)^3-1/128/d/a^2*tan(1/2*d*x+1/2*c)^2+1/8/d/a^2*tan(1/2*d*x+1/2*c)-1/384/d/a^2/tan(1/2*d*x+1/2*c)^6-1/8/d/a^2/tan(1/2*d*x+1/2*c)-3/16/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/80/a^2/d/tan(1/2*d*x+1/2*c)^5+1/128/a^2/d/tan(1/2*d*x+1/2*c)^2-3/128/a^2/d/tan(1/2*d*x+1/2*c)^4+1/48/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
644,1,381,117,0.470000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{23 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{391 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{75 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{136 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{75 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{64 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{391 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{136 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{23 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{68}{15 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{23 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}"," ",0,"-23/8/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-391/24/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8-75/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-136/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6+75/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-64/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4+391/24/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-136/5/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2+23/8/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-68/15/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6-23/8/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
645,1,279,95,0.431000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{13 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{25 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{116 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{25 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{76 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{13 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{76}{15 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d}"," ",0,"13/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9+25/2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+12/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+116/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-25/2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+76/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-13/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+76/15/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^5+13/4/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
646,1,279,78,0.427000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{15 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{23 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{18 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{22 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{15 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d}"," ",0,"-15/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6-23/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-18/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+23/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-22/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+15/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-6/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^4-15/4/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
647,1,159,56,0.619000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}"," ",0,"-1/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-6/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^2-7/a^3/d*arctan(tan(1/2*d*x+1/2*c))+1/a^3/d*ln(tan(1/2*d*x+1/2*c))","B"
648,1,97,49,0.665000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{2}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)+2/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)+6/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/a^3/d*ln(tan(1/2*d*x+1/2*c))","A"
649,1,112,56,0.682000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{8 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d}"," ",0,"1/8/a^3/d*tan(1/2*d*x+1/2*c)^2-3/2/d/a^3*tan(1/2*d*x+1/2*c)-2/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/8/a^3/d/tan(1/2*d*x+1/2*c)^2+3/2/d/a^3/tan(1/2*d*x+1/2*c)+7/2/a^3/d*ln(tan(1/2*d*x+1/2*c))","A"
650,1,132,66,0.678000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}+\frac{15 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{15}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a^{3} d}+\frac{3}{8 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/a^3/d*tan(1/2*d*x+1/2*c)^2+15/8/d/a^3*tan(1/2*d*x+1/2*c)-15/8/d/a^3/tan(1/2*d*x+1/2*c)-5/2/a^3/d*ln(tan(1/2*d*x+1/2*c))+3/8/a^3/d/tan(1/2*d*x+1/2*c)^2-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3","A"
651,1,170,87,0.680000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{3} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{3} d}-\frac{13 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{13}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}-\frac{1}{2 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{64 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/64/a^3/d*tan(1/2*d*x+1/2*c)^4-1/8/d/a^3*tan(1/2*d*x+1/2*c)^3+1/2/a^3/d*tan(1/2*d*x+1/2*c)^2-13/8/d/a^3*tan(1/2*d*x+1/2*c)+13/8/d/a^3/tan(1/2*d*x+1/2*c)+15/8/a^3/d*ln(tan(1/2*d*x+1/2*c))-1/2/a^3/d/tan(1/2*d*x+1/2*c)^2-1/64/a^3/d/tan(1/2*d*x+1/2*c)^4+1/8/d/a^3/tan(1/2*d*x+1/2*c)^3","A"
652,1,208,104,0.678000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d \,a^{3}}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a^{3} d}+\frac{17 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a^{3} d}+\frac{23 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}-\frac{23}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}-\frac{1}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{2 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{64 a^{3} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{17}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/d/a^3*tan(1/2*d*x+1/2*c)^5-3/64/a^3/d*tan(1/2*d*x+1/2*c)^4+17/96/d/a^3*tan(1/2*d*x+1/2*c)^3-1/2/a^3/d*tan(1/2*d*x+1/2*c)^2+23/16/d/a^3*tan(1/2*d*x+1/2*c)-23/16/d/a^3/tan(1/2*d*x+1/2*c)-13/8/a^3/d*ln(tan(1/2*d*x+1/2*c))-1/160/d/a^3/tan(1/2*d*x+1/2*c)^5+1/2/a^3/d/tan(1/2*d*x+1/2*c)^2+3/64/a^3/d/tan(1/2*d*x+1/2*c)^4-17/96/d/a^3/tan(1/2*d*x+1/2*c)^3","A"
653,0,0,243,27.622000," ","int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","\int \left(\cos^{6}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","F"
654,0,0,182,20.091000," ","int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","\int \left(\cos^{6}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","F"
655,0,0,117,11.869000," ","int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","\int \left(\cos^{6}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","F"
656,1,166,113,0.238000," ","int(cos(d*x+c)^7*sin(d*x+c)^6*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{14}-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{28}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{70}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{280}\right)+a \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{13}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{143}-\frac{5 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{429}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{3003}\right)}{d}"," ",0,"1/d*(a*(-1/14*sin(d*x+c)^6*cos(d*x+c)^8-1/28*sin(d*x+c)^4*cos(d*x+c)^8-1/70*sin(d*x+c)^2*cos(d*x+c)^8-1/280*cos(d*x+c)^8)+a*(-1/13*sin(d*x+c)^5*cos(d*x+c)^8-5/143*sin(d*x+c)^3*cos(d*x+c)^8-5/429*sin(d*x+c)*cos(d*x+c)^8+5/3003*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","A"
657,1,148,99,0.231000," ","int(cos(d*x+c)^7*sin(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{13}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{143}-\frac{5 \sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{429}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{3003}\right)+a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{30}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{120}\right)}{d}"," ",0,"1/d*(a*(-1/13*sin(d*x+c)^5*cos(d*x+c)^8-5/143*sin(d*x+c)^3*cos(d*x+c)^8-5/429*sin(d*x+c)*cos(d*x+c)^8+5/3003*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/12*sin(d*x+c)^4*cos(d*x+c)^8-1/30*sin(d*x+c)^2*cos(d*x+c)^8-1/120*cos(d*x+c)^8))","A"
658,1,130,99,0.236000," ","int(cos(d*x+c)^7*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{30}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{120}\right)+a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{11}-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)}{d}"," ",0,"1/d*(a*(-1/12*sin(d*x+c)^4*cos(d*x+c)^8-1/30*sin(d*x+c)^2*cos(d*x+c)^8-1/120*cos(d*x+c)^8)+a*(-1/11*sin(d*x+c)^3*cos(d*x+c)^8-1/33*sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","A"
659,1,112,85,0.239000," ","int(cos(d*x+c)^7*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{11}-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)+a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)}{d}"," ",0,"1/d*(a*(-1/11*sin(d*x+c)^3*cos(d*x+c)^8-1/33*sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8))","A"
660,1,94,85,0.236000," ","int(cos(d*x+c)^7*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)+a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)}{d}"," ",0,"1/d*(a*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)+a*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","A"
661,1,74,71,0.235000," ","int(cos(d*x+c)^7*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{8}}{d}"," ",0,"1/d*(a*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-1/8*a*cos(d*x+c)^8)","A"
662,1,128,108,0.339000," ","int(cos(d*x+c)^7*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{16 a \sin \left(d x +c \right)}{35 d}+\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{7 d}+\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35 d}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{35 d}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"16/35*a*sin(d*x+c)/d+1/7/d*cos(d*x+c)^6*sin(d*x+c)*a+6/35/d*a*sin(d*x+c)*cos(d*x+c)^4+8/35/d*a*sin(d*x+c)*cos(d*x+c)^2+1/6*a*cos(d*x+c)^6/d+1/4*a*cos(d*x+c)^4/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d","A"
663,1,150,106,0.290000," ","int(cos(d*x+c)^7*csc(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a \sin \left(d x +c \right)}{5 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}"," ",0,"1/6*a*cos(d*x+c)^6/d+1/4*a*cos(d*x+c)^4/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/d*a/sin(d*x+c)*cos(d*x+c)^8-16/5*a*sin(d*x+c)/d-1/d*cos(d*x+c)^6*sin(d*x+c)*a-6/5/d*a*sin(d*x+c)*cos(d*x+c)^4-8/5/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
664,1,173,107,0.352000," ","int(cos(d*x+c)^7*csc(d*x+c)^3*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a \sin \left(d x +c \right)}{5 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^8-16/5*a*sin(d*x+c)/d-1/d*cos(d*x+c)^6*sin(d*x+c)*a-6/5/d*a*sin(d*x+c)*cos(d*x+c)^4-8/5/d*a*sin(d*x+c)*cos(d*x+c)^2-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^8-1/2*a*cos(d*x+c)^6/d-3/4*a*cos(d*x+c)^4/d-3/2*a*cos(d*x+c)^2/d-3*a*ln(sin(d*x+c))/d","A"
665,1,195,108,0.310000," ","int(cos(d*x+c)^7*csc(d*x+c)^4*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{5 a \left(\cos^{8}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{16 a \sin \left(d x +c \right)}{3 d}+\frac{5 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}+\frac{2 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^8-1/2*a*cos(d*x+c)^6/d-3/4*a*cos(d*x+c)^4/d-3/2*a*cos(d*x+c)^2/d-3*a*ln(sin(d*x+c))/d-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^8+5/3/d*a/sin(d*x+c)*cos(d*x+c)^8+16/3*a*sin(d*x+c)/d+5/3/d*cos(d*x+c)^6*sin(d*x+c)*a+2/d*a*sin(d*x+c)*cos(d*x+c)^4+8/3/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
666,1,217,108,0.296000," ","int(cos(d*x+c)^7*csc(d*x+c)^5*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{5 a \left(\cos^{8}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{16 a \sin \left(d x +c \right)}{3 d}+\frac{5 \left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}+\frac{2 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{3 d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d}+\frac{3 a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^8+5/3/d*a/sin(d*x+c)*cos(d*x+c)^8+16/3*a*sin(d*x+c)/d+5/3/d*cos(d*x+c)^6*sin(d*x+c)*a+2/d*a*sin(d*x+c)*cos(d*x+c)^4+8/3/d*a*sin(d*x+c)*cos(d*x+c)^2-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^8+1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^8+1/2*a*cos(d*x+c)^6/d+3/4*a*cos(d*x+c)^4/d+3/2*a*cos(d*x+c)^2/d+3*a*ln(sin(d*x+c))/d","A"
667,1,239,107,0.312000," ","int(cos(d*x+c)^7*csc(d*x+c)^6*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d}+\frac{3 a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{3 a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a \sin \left(d x +c \right)}{5 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^8+1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^8+1/2*a*cos(d*x+c)^6/d+3/4*a*cos(d*x+c)^4/d+3/2*a*cos(d*x+c)^2/d+3*a*ln(sin(d*x+c))/d-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^8+1/5/d*a/sin(d*x+c)^3*cos(d*x+c)^8-1/d*a/sin(d*x+c)*cos(d*x+c)^8-16/5*a*sin(d*x+c)/d-1/d*cos(d*x+c)^6*sin(d*x+c)*a-6/5/d*a*sin(d*x+c)*cos(d*x+c)^4-8/5/d*a*sin(d*x+c)*cos(d*x+c)^2","B"
668,1,195,107,0.339000," ","int(cos(d*x+c)^7*csc(d*x+c)^7*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a \sin \left(d x +c \right)}{5 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{a \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^8+1/5/d*a/sin(d*x+c)^3*cos(d*x+c)^8-1/d*a/sin(d*x+c)*cos(d*x+c)^8-16/5*a*sin(d*x+c)/d-1/d*cos(d*x+c)^6*sin(d*x+c)*a-6/5/d*a*sin(d*x+c)*cos(d*x+c)^4-8/5/d*a*sin(d*x+c)*cos(d*x+c)^2-1/6*a*cot(d*x+c)^6/d+1/4/d*a*cot(d*x+c)^4-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d","A"
669,1,217,109,0.359000," ","int(cos(d*x+c)^7*csc(d*x+c)^8*(a+a*sin(d*x+c)),x)","-\frac{a \left(\cot^{6}\left(d x +c \right)\right)}{6 d}+\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{3}}+\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)}+\frac{16 a \sin \left(d x +c \right)}{35 d}+\frac{\left(\cos^{6}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{7 d}+\frac{6 a \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35 d}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{35 d}"," ",0,"-1/6*a*cot(d*x+c)^6/d+1/4/d*a*cot(d*x+c)^4-1/2*a*cot(d*x+c)^2/d-a*ln(sin(d*x+c))/d-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^8+1/35/d*a/sin(d*x+c)^5*cos(d*x+c)^8-1/35/d*a/sin(d*x+c)^3*cos(d*x+c)^8+1/7/d*a/sin(d*x+c)*cos(d*x+c)^8+16/35*a*sin(d*x+c)/d+1/7/d*cos(d*x+c)^6*sin(d*x+c)*a+6/35/d*a*sin(d*x+c)*cos(d*x+c)^4+8/35/d*a*sin(d*x+c)*cos(d*x+c)^2","A"
670,1,138,68,0.363000," ","int(cos(d*x+c)^7*csc(d*x+c)^9*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{7 \sin \left(d x +c \right)}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}\right)-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{8 \sin \left(d x +c \right)^{8}}}{d}"," ",0,"1/d*(a*(-1/7/sin(d*x+c)^7*cos(d*x+c)^8+1/35/sin(d*x+c)^5*cos(d*x+c)^8-1/35/sin(d*x+c)^3*cos(d*x+c)^8+1/7/sin(d*x+c)*cos(d*x+c)^8+1/7*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-1/8*a/sin(d*x+c)^8*cos(d*x+c)^8)","B"
671,1,156,71,0.379000," ","int(cos(d*x+c)^7*csc(d*x+c)^10*(a+a*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{8}\left(d x +c \right)\right)}{8 \sin \left(d x +c \right)^{8}}+a \left(-\frac{\cos^{8}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)}{d}"," ",0,"1/d*(-1/8*a/sin(d*x+c)^8*cos(d*x+c)^8+a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^8-1/63/sin(d*x+c)^7*cos(d*x+c)^8+1/315/sin(d*x+c)^5*cos(d*x+c)^8-1/315/sin(d*x+c)^3*cos(d*x+c)^8+1/63/sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","B"
672,1,176,85,0.377000," ","int(cos(d*x+c)^7*csc(d*x+c)^11*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{63 \sin \left(d x +c \right)}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{8}\left(d x +c \right)}{40 \sin \left(d x +c \right)^{8}}\right)}{d}"," ",0,"1/d*(a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^8-1/63/sin(d*x+c)^7*cos(d*x+c)^8+1/315/sin(d*x+c)^5*cos(d*x+c)^8-1/315/sin(d*x+c)^3*cos(d*x+c)^8+1/63/sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/10/sin(d*x+c)^10*cos(d*x+c)^8-1/40/sin(d*x+c)^8*cos(d*x+c)^8))","B"
673,1,194,85,0.388000," ","int(cos(d*x+c)^7*csc(d*x+c)^12*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{8}\left(d x +c \right)}{40 \sin \left(d x +c \right)^{8}}\right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}-\frac{\cos^{8}\left(d x +c \right)}{33 \sin \left(d x +c \right)^{9}}-\frac{\cos^{8}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{1155 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{1155 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{231 \sin \left(d x +c \right)}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)}{d}"," ",0,"1/d*(a*(-1/10/sin(d*x+c)^10*cos(d*x+c)^8-1/40/sin(d*x+c)^8*cos(d*x+c)^8)+a*(-1/11/sin(d*x+c)^11*cos(d*x+c)^8-1/33/sin(d*x+c)^9*cos(d*x+c)^8-1/231/sin(d*x+c)^7*cos(d*x+c)^8+1/1155/sin(d*x+c)^5*cos(d*x+c)^8-1/1155/sin(d*x+c)^3*cos(d*x+c)^8+1/231/sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","B"
674,1,212,99,0.375000," ","int(cos(d*x+c)^7*csc(d*x+c)^13*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}-\frac{\cos^{8}\left(d x +c \right)}{33 \sin \left(d x +c \right)^{9}}-\frac{\cos^{8}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{1155 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{1155 \sin \left(d x +c \right)^{3}}+\frac{\cos^{8}\left(d x +c \right)}{231 \sin \left(d x +c \right)}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{12 \sin \left(d x +c \right)^{12}}-\frac{\cos^{8}\left(d x +c \right)}{30 \sin \left(d x +c \right)^{10}}-\frac{\cos^{8}\left(d x +c \right)}{120 \sin \left(d x +c \right)^{8}}\right)}{d}"," ",0,"1/d*(a*(-1/11/sin(d*x+c)^11*cos(d*x+c)^8-1/33/sin(d*x+c)^9*cos(d*x+c)^8-1/231/sin(d*x+c)^7*cos(d*x+c)^8+1/1155/sin(d*x+c)^5*cos(d*x+c)^8-1/1155/sin(d*x+c)^3*cos(d*x+c)^8+1/231/sin(d*x+c)*cos(d*x+c)^8+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/12/sin(d*x+c)^12*cos(d*x+c)^8-1/30/sin(d*x+c)^10*cos(d*x+c)^8-1/120/sin(d*x+c)^8*cos(d*x+c)^8))","B"
675,1,230,99,0.388000," ","int(cos(d*x+c)^7*csc(d*x+c)^14*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{12 \sin \left(d x +c \right)^{12}}-\frac{\cos^{8}\left(d x +c \right)}{30 \sin \left(d x +c \right)^{10}}-\frac{\cos^{8}\left(d x +c \right)}{120 \sin \left(d x +c \right)^{8}}\right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{13 \sin \left(d x +c \right)^{13}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{143 \sin \left(d x +c \right)^{11}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{429 \sin \left(d x +c \right)^{9}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{3003 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{3003 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{3003 \sin \left(d x +c \right)^{3}}+\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{3003 \sin \left(d x +c \right)}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{3003}\right)}{d}"," ",0,"1/d*(a*(-1/12/sin(d*x+c)^12*cos(d*x+c)^8-1/30/sin(d*x+c)^10*cos(d*x+c)^8-1/120/sin(d*x+c)^8*cos(d*x+c)^8)+a*(-1/13/sin(d*x+c)^13*cos(d*x+c)^8-5/143/sin(d*x+c)^11*cos(d*x+c)^8-5/429/sin(d*x+c)^9*cos(d*x+c)^8-5/3003/sin(d*x+c)^7*cos(d*x+c)^8+1/3003/sin(d*x+c)^5*cos(d*x+c)^8-1/3003/sin(d*x+c)^3*cos(d*x+c)^8+5/3003/sin(d*x+c)*cos(d*x+c)^8+5/3003*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)))","B"
676,1,248,113,0.376000," ","int(cos(d*x+c)^7*csc(d*x+c)^15*(a+a*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{8}\left(d x +c \right)}{13 \sin \left(d x +c \right)^{13}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{143 \sin \left(d x +c \right)^{11}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{429 \sin \left(d x +c \right)^{9}}-\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{3003 \sin \left(d x +c \right)^{7}}+\frac{\cos^{8}\left(d x +c \right)}{3003 \sin \left(d x +c \right)^{5}}-\frac{\cos^{8}\left(d x +c \right)}{3003 \sin \left(d x +c \right)^{3}}+\frac{5 \left(\cos^{8}\left(d x +c \right)\right)}{3003 \sin \left(d x +c \right)}+\frac{5 \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{3003}\right)+a \left(-\frac{\cos^{8}\left(d x +c \right)}{14 \sin \left(d x +c \right)^{14}}-\frac{\cos^{8}\left(d x +c \right)}{28 \sin \left(d x +c \right)^{12}}-\frac{\cos^{8}\left(d x +c \right)}{70 \sin \left(d x +c \right)^{10}}-\frac{\cos^{8}\left(d x +c \right)}{280 \sin \left(d x +c \right)^{8}}\right)}{d}"," ",0,"1/d*(a*(-1/13/sin(d*x+c)^13*cos(d*x+c)^8-5/143/sin(d*x+c)^11*cos(d*x+c)^8-5/429/sin(d*x+c)^9*cos(d*x+c)^8-5/3003/sin(d*x+c)^7*cos(d*x+c)^8+1/3003/sin(d*x+c)^5*cos(d*x+c)^8-1/3003/sin(d*x+c)^3*cos(d*x+c)^8+5/3003/sin(d*x+c)*cos(d*x+c)^8+5/3003*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+a*(-1/14/sin(d*x+c)^14*cos(d*x+c)^8-1/28/sin(d*x+c)^12*cos(d*x+c)^8-1/70/sin(d*x+c)^10*cos(d*x+c)^8-1/280/sin(d*x+c)^8*cos(d*x+c)^8))","B"
677,1,69,97,0.318000," ","int(cos(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{12}\left(d x +c \right)\right)}{12}+\frac{\left(\sin^{11}\left(d x +c \right)\right)}{11}+\frac{\left(\sin^{10}\left(d x +c \right)\right)}{5}-\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{9}-\frac{\left(\sin^{8}\left(d x +c \right)\right)}{8}+\frac{\left(\sin^{7}\left(d x +c \right)\right)}{7}}{d a}"," ",0,"1/d/a*(-1/12*sin(d*x+c)^12+1/11*sin(d*x+c)^11+1/5*sin(d*x+c)^10-2/9*sin(d*x+c)^9-1/8*sin(d*x+c)^8+1/7*sin(d*x+c)^7)","A"
678,1,69,97,0.306000," ","int(cos(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{11}\left(d x +c \right)\right)}{11}+\frac{\left(\sin^{10}\left(d x +c \right)\right)}{10}+\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{9}-\frac{\left(\sin^{8}\left(d x +c \right)\right)}{4}-\frac{\left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}}{d a}"," ",0,"1/d/a*(-1/11*sin(d*x+c)^11+1/10*sin(d*x+c)^10+2/9*sin(d*x+c)^9-1/4*sin(d*x+c)^8-1/7*sin(d*x+c)^7+1/6*sin(d*x+c)^6)","A"
679,1,69,97,0.300000," ","int(cos(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{10}\left(d x +c \right)\right)}{10}+\frac{\left(\sin^{9}\left(d x +c \right)\right)}{9}+\frac{\left(\sin^{8}\left(d x +c \right)\right)}{4}-\frac{2 \left(\sin^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}}{d a}"," ",0,"1/d/a*(-1/10*sin(d*x+c)^10+1/9*sin(d*x+c)^9+1/4*sin(d*x+c)^8-2/7*sin(d*x+c)^7-1/6*sin(d*x+c)^6+1/5*sin(d*x+c)^5)","A"
680,1,69,81,0.256000," ","int(cos(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{9}\left(d x +c \right)\right)}{9}+\frac{\left(\sin^{8}\left(d x +c \right)\right)}{8}+\frac{2 \left(\sin^{7}\left(d x +c \right)\right)}{7}-\frac{\left(\sin^{6}\left(d x +c \right)\right)}{3}-\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}}{d a}"," ",0,"1/d/a*(-1/9*sin(d*x+c)^9+1/8*sin(d*x+c)^8+2/7*sin(d*x+c)^7-1/3*sin(d*x+c)^6-1/5*sin(d*x+c)^5+1/4*sin(d*x+c)^4)","A"
681,1,69,81,0.217000," ","int(cos(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{8}\left(d x +c \right)\right)}{8}+\frac{\left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\sin^{6}\left(d x +c \right)\right)}{3}-\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}}{d a}"," ",0,"1/d/a*(-1/8*sin(d*x+c)^8+1/7*sin(d*x+c)^7+1/3*sin(d*x+c)^6-2/5*sin(d*x+c)^5-1/4*sin(d*x+c)^4+1/3*sin(d*x+c)^3)","A"
682,1,69,65,0.187000," ","int(cos(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{5}-\frac{\left(\sin^{4}\left(d x +c \right)\right)}{2}-\frac{\left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}}{d a}"," ",0,"1/d/a*(-1/7*sin(d*x+c)^7+1/6*sin(d*x+c)^6+2/5*sin(d*x+c)^5-1/2*sin(d*x+c)^4-1/3*sin(d*x+c)^3+1/2*sin(d*x+c)^2)","A"
683,1,65,64,0.308000," ","int(cos(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{-\frac{\left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{\left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(\sin^{4}\left(d x +c \right)\right)}{2}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{3}-\frac{\left(\sin^{2}\left(d x +c \right)\right)}{2}+\sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*(-1/6*sin(d*x+c)^6+1/5*sin(d*x+c)^5+1/2*sin(d*x+c)^4-2/3*sin(d*x+c)^3-1/2*sin(d*x+c)^2+sin(d*x+c))","A"
684,1,94,93,0.368000," ","int(cos(d*x+c)^7*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\sin \left(d x +c \right)}{a d}-\frac{\sin^{2}\left(d x +c \right)}{a d}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{3 d a}+\frac{\sin^{4}\left(d x +c \right)}{4 d a}-\frac{\sin^{5}\left(d x +c \right)}{5 d a}"," ",0,"ln(sin(d*x+c))/a/d-sin(d*x+c)/a/d-sin(d*x+c)^2/a/d+2/3*sin(d*x+c)^3/d/a+1/4*sin(d*x+c)^4/d/a-1/5*sin(d*x+c)^5/d/a","A"
685,1,94,91,0.418000," ","int(cos(d*x+c)^7*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{\sin^{4}\left(d x +c \right)}{4 d a}+\frac{\sin^{3}\left(d x +c \right)}{3 d a}+\frac{\sin^{2}\left(d x +c \right)}{a d}-\frac{2 \sin \left(d x +c \right)}{a d}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}"," ",0,"-1/4*sin(d*x+c)^4/d/a+1/3*sin(d*x+c)^3/d/a+sin(d*x+c)^2/a/d-2*sin(d*x+c)/a/d-1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d","A"
686,1,94,91,0.468000," ","int(cos(d*x+c)^7*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{\sin^{3}\left(d x +c \right)}{3 d a}+\frac{\sin^{2}\left(d x +c \right)}{2 a d}+\frac{2 \sin \left(d x +c \right)}{a d}+\frac{1}{d a \sin \left(d x +c \right)}-\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{1}{2 a d \sin \left(d x +c \right)^{2}}"," ",0,"-1/3*sin(d*x+c)^3/d/a+1/2*sin(d*x+c)^2/a/d+2*sin(d*x+c)/a/d+1/d/a/sin(d*x+c)-2*ln(sin(d*x+c))/a/d-1/2/a/d/sin(d*x+c)^2","A"
687,1,94,91,0.472000," ","int(cos(d*x+c)^7*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","-\frac{\sin^{2}\left(d x +c \right)}{2 a d}+\frac{\sin \left(d x +c \right)}{a d}+\frac{2}{d a \sin \left(d x +c \right)}+\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{2 a d \sin \left(d x +c \right)^{2}}-\frac{1}{3 a d \sin \left(d x +c \right)^{3}}"," ",0,"-1/2*sin(d*x+c)^2/a/d+sin(d*x+c)/a/d+2/d/a/sin(d*x+c)+2*ln(sin(d*x+c))/a/d+1/2/a/d/sin(d*x+c)^2-1/3/a/d/sin(d*x+c)^3","A"
688,1,93,90,0.459000," ","int(cos(d*x+c)^7*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","-\frac{\sin \left(d x +c \right)}{a d}-\frac{2}{d a \sin \left(d x +c \right)}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{a d \sin \left(d x +c \right)^{2}}-\frac{1}{4 a d \sin \left(d x +c \right)^{4}}+\frac{1}{3 a d \sin \left(d x +c \right)^{3}}"," ",0,"-sin(d*x+c)/a/d-2/d/a/sin(d*x+c)+ln(sin(d*x+c))/a/d+1/a/d/sin(d*x+c)^2-1/4/a/d/sin(d*x+c)^4+1/3/a/d/sin(d*x+c)^3","A"
689,1,97,94,0.480000," ","int(cos(d*x+c)^7*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","-\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{1}{5 a d \sin \left(d x +c \right)^{5}}-\frac{1}{a d \sin \left(d x +c \right)^{2}}+\frac{1}{4 a d \sin \left(d x +c \right)^{4}}+\frac{2}{3 a d \sin \left(d x +c \right)^{3}}"," ",0,"-1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d-1/5/a/d/sin(d*x+c)^5-1/a/d/sin(d*x+c)^2+1/4/a/d/sin(d*x+c)^4+2/3/a/d/sin(d*x+c)^3","A"
690,1,67,62,0.470000," ","int(cos(d*x+c)^7*csc(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{\sin \left(d x +c \right)}+\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{2 \sin \left(d x +c \right)^{2}}+\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{2}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(-1/6/sin(d*x+c)^6+1/sin(d*x+c)+1/5/sin(d*x+c)^5-1/2/sin(d*x+c)^2+1/2/sin(d*x+c)^4-2/3/sin(d*x+c)^3)","A"
691,1,69,65,0.522000," ","int(cos(d*x+c)^7*csc(d*x+c)^8/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{2}{5 \sin \left(d x +c \right)^{5}}-\frac{1}{7 \sin \left(d x +c \right)^{7}}+\frac{1}{2 \sin \left(d x +c \right)^{2}}-\frac{1}{2 \sin \left(d x +c \right)^{4}}-\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(1/6/sin(d*x+c)^6+2/5/sin(d*x+c)^5-1/7/sin(d*x+c)^7+1/2/sin(d*x+c)^2-1/2/sin(d*x+c)^4-1/3/sin(d*x+c)^3)","A"
692,1,69,81,0.530000," ","int(cos(d*x+c)^7*csc(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{3 \sin \left(d x +c \right)^{6}}-\frac{2}{5 \sin \left(d x +c \right)^{5}}+\frac{1}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}-\frac{1}{4 \sin \left(d x +c \right)^{4}}+\frac{1}{3 \sin \left(d x +c \right)^{3}}}{d a}"," ",0,"1/d/a*(1/3/sin(d*x+c)^6-2/5/sin(d*x+c)^5+1/7/sin(d*x+c)^7-1/8/sin(d*x+c)^8-1/4/sin(d*x+c)^4+1/3/sin(d*x+c)^3)","A"
693,1,69,81,0.557000," ","int(cos(d*x+c)^7*csc(d*x+c)^10/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{3 \sin \left(d x +c \right)^{6}}-\frac{1}{5 \sin \left(d x +c \right)^{5}}+\frac{2}{7 \sin \left(d x +c \right)^{7}}-\frac{1}{9 \sin \left(d x +c \right)^{9}}+\frac{1}{8 \sin \left(d x +c \right)^{8}}+\frac{1}{4 \sin \left(d x +c \right)^{4}}}{d a}"," ",0,"1/d/a*(-1/3/sin(d*x+c)^6-1/5/sin(d*x+c)^5+2/7/sin(d*x+c)^7-1/9/sin(d*x+c)^9+1/8/sin(d*x+c)^8+1/4/sin(d*x+c)^4)","A"
694,1,69,97,0.577000," ","int(cos(d*x+c)^7*csc(d*x+c)^11/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \sin \left(d x +c \right)^{6}}+\frac{1}{5 \sin \left(d x +c \right)^{5}}-\frac{2}{7 \sin \left(d x +c \right)^{7}}+\frac{1}{9 \sin \left(d x +c \right)^{9}}+\frac{1}{4 \sin \left(d x +c \right)^{8}}-\frac{1}{10 \sin \left(d x +c \right)^{10}}}{d a}"," ",0,"1/d/a*(-1/6/sin(d*x+c)^6+1/5/sin(d*x+c)^5-2/7/sin(d*x+c)^7+1/9/sin(d*x+c)^9+1/4/sin(d*x+c)^8-1/10/sin(d*x+c)^10)","A"
695,1,69,97,0.684000," ","int(cos(d*x+c)^7*csc(d*x+c)^12/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{6 \sin \left(d x +c \right)^{6}}-\frac{1}{7 \sin \left(d x +c \right)^{7}}+\frac{2}{9 \sin \left(d x +c \right)^{9}}-\frac{1}{4 \sin \left(d x +c \right)^{8}}-\frac{1}{11 \sin \left(d x +c \right)^{11}}+\frac{1}{10 \sin \left(d x +c \right)^{10}}}{d a}"," ",0,"1/d/a*(1/6/sin(d*x+c)^6-1/7/sin(d*x+c)^7+2/9/sin(d*x+c)^9-1/4/sin(d*x+c)^8-1/11/sin(d*x+c)^11+1/10/sin(d*x+c)^10)","A"
696,1,69,97,0.658000," ","int(cos(d*x+c)^7*csc(d*x+c)^13/(a+a*sin(d*x+c)),x)","\frac{\frac{1}{7 \sin \left(d x +c \right)^{7}}-\frac{2}{9 \sin \left(d x +c \right)^{9}}-\frac{1}{8 \sin \left(d x +c \right)^{8}}+\frac{1}{11 \sin \left(d x +c \right)^{11}}-\frac{1}{12 \sin \left(d x +c \right)^{12}}+\frac{1}{5 \sin \left(d x +c \right)^{10}}}{d a}"," ",0,"1/d/a*(1/7/sin(d*x+c)^7-2/9/sin(d*x+c)^9-1/8/sin(d*x+c)^8+1/11/sin(d*x+c)^11-1/12/sin(d*x+c)^12+1/5/sin(d*x+c)^10)","A"
697,0,0,184,41.963000," ","int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","\int \left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x)","F"
698,0,0,184,28.834000," ","int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","\int \left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x)","F"
699,0,0,167,17.354000," ","int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","\int \left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x)","F"
700,0,0,137,9.335000," ","int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","\int \frac{\left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{a +a \sin \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x)","F"
701,0,0,92,22.115000," ","int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","\int \frac{\left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x)","F"
702,0,0,92,5.837000," ","int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","\int \frac{\left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{3}}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x)","F"
703,0,0,111,9.074000," ","int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","\int \frac{\left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{4}}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x)","F"
704,0,0,162,2.804000," ","int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x)","\int \frac{\left(\cos^{7}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +a \sin \left(d x +c \right)\right)^{5}}\, dx"," ",0,"int(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x)","F"
705,1,755,189,0.341000," ","int(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c)),x)","-\frac{16}{693 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{64 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{231 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{175 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1536 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{32 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{21 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{311 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{352 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{8361 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{192 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{42259 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{768 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{96 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{25295 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{32 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{25295 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{32 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{42259 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{768 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{16 \left(\tan^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}+\frac{8361 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{32 \left(\tan^{18}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{311 \left(\tan^{19}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{175 \left(\tan^{21}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{1536 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{5 \left(\tan^{23}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{12}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a d}"," ",0,"-16/693/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12+5/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)-64/231/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^2+175/1536/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^3-32/21/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^4+311/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^5+352/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^6-8361/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^7-192/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^8+42259/768/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^9+96/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^10-25295/256/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^11-32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^12+25295/256/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^13-32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^14-42259/768/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^15+16/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^16+8361/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^17-32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^18-311/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^19-175/1536/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^21-5/512/a/d/(1+tan(1/2*d*x+1/2*c)^2)^12*tan(1/2*d*x+1/2*c)^23-5/512/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
706,1,653,165,0.322000," ","int(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{16}{693 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{16 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{80 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{3323 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{640 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{48 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{54 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{240 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{841 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{48 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{176 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{841 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{80 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{54 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{32 \left(\tan^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{3323 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{640 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{\tan^{19}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{3 \left(\tan^{21}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}"," ",0,"16/693/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11-3/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)+16/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^2-1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^3+80/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^4+3323/640/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^5-48/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^6-54/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^7+240/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^8+841/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^9-48/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^10+176/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^12-841/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^13-80/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^14+54/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^15+32/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^16-3323/640/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^17+1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^19+3/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^21+3/128/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
707,1,619,149,0.312000," ","int(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{4}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{29 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{867 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{72 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{519 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{1879 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{8 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{1879 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{40 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{519 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{8 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{867 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{4 \left(\tan^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{29 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{3 \left(\tan^{19}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}"," ",0,"-4/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10+3/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)-40/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^2+29/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^3+8/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^4-867/160/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^5-72/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^6+519/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^7-1879/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^9-8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^10+1879/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^11-40/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^12-519/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^13+8/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^14+867/160/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^15-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^16-29/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^17-3/128/a/d/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^19-3/128/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
708,1,551,125,0.306000," ","int(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{4}{63 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{191 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{83 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{145 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{12 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{20 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{145 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{20 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{83 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{4 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{191 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{5 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d}"," ",0,"4/63/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9-5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)+4/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^2+191/96/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^3-12/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^4-83/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^5+12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^6+145/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^7-12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^8+20/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^10-145/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^11-20/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^12+83/32/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^13+4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^14-191/96/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^15+5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^17+5/64/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
709,1,551,109,0.212000," ","int(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c)),x)","-\frac{2}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{397 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{895 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{6 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{1765 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{1765 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{10 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{895 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{2 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{397 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{2 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{5 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a d}"," ",0,"-2/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8+5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)-2/7/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2-397/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3-6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4+895/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5-6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6-1765/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7-10/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8+1765/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9-10/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10-895/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12+397/192/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^14-5/64/a/d/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-5/64/a/d*arctan(tan(1/2*d*x+1/2*c))","B"
710,1,432,131,0.436000," ","int(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{6 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{18 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{92 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{28 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{62 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{46}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"11/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10-5/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+18/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8+15/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+92/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6-15/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+28/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4+5/24/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+62/5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2-11/8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+46/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^6-5/8/a/d*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))","B"
711,1,367,125,0.447000," ","int(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}+\frac{9 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{56 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{46}{15 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)+9/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9-6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8+5/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7-12/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6-56/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-5/2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3-28/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-9/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)-46/15/a/d/(1+tan(1/2*d*x+1/2*c)^2)^5-15/4/a/d*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))","B"
712,1,371,134,0.562000," ","int(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{9 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{14 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{38 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{14}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a d}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/a/d*tan(1/2*d*x+1/2*c)-9/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6-1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-14/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4+1/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-38/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+9/4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-14/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^4+15/4/a/d*arctan(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2+1/2/a/d/tan(1/2*d*x+1/2*c)-5/2/a/d*ln(tan(1/2*d*x+1/2*c))","B"
713,1,306,130,0.644000," ","int(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{14}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{9}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}"," ",0,"1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2-9/8/a/d*tan(1/2*d*x+1/2*c)-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+6/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+8/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+14/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3+5/a/d*arctan(tan(1/2*d*x+1/2*c))-1/24/a/d/tan(1/2*d*x+1/2*c)^3+1/8/a/d/tan(1/2*d*x+1/2*c)^2+9/8/a/d/tan(1/2*d*x+1/2*c)+5/2/a/d*ln(tan(1/2*d*x+1/2*c))","B"
714,1,310,134,0.546000," ","int(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{24 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{4 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{9}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"1/64/a/d*tan(1/2*d*x+1/2*c)^4-1/24/a/d*tan(1/2*d*x+1/2*c)^3-1/4/a/d*tan(1/2*d*x+1/2*c)^2+9/8/a/d*tan(1/2*d*x+1/2*c)+1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2-5/a/d*arctan(tan(1/2*d*x+1/2*c))-1/64/a/d/tan(1/2*d*x+1/2*c)^4+1/24/a/d/tan(1/2*d*x+1/2*c)^3+1/4/a/d/tan(1/2*d*x+1/2*c)^2-9/8/a/d/tan(1/2*d*x+1/2*c)+15/8/a/d*ln(tan(1/2*d*x+1/2*c))","B"
715,1,249,126,0.519000," ","int(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a d}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{64 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{7}{96 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{4 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{11}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}"," ",0,"1/160/a/d*tan(1/2*d*x+1/2*c)^5-1/64/a/d*tan(1/2*d*x+1/2*c)^4-7/96/a/d*tan(1/2*d*x+1/2*c)^3+1/4/a/d*tan(1/2*d*x+1/2*c)^2+11/16/a/d*tan(1/2*d*x+1/2*c)-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/160/a/d/tan(1/2*d*x+1/2*c)^5+1/64/a/d/tan(1/2*d*x+1/2*c)^4+7/96/a/d/tan(1/2*d*x+1/2*c)^3-1/4/a/d/tan(1/2*d*x+1/2*c)^2-11/16/a/d/tan(1/2*d*x+1/2*c)-15/8/a/d*ln(tan(1/2*d*x+1/2*c))","A"
716,1,264,130,0.553000," ","int(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c)),x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a d}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 a d}+\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{1}{160 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{7}{96 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{15}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{11}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 a d}"," ",0,"1/384/a/d*tan(1/2*d*x+1/2*c)^6-1/160/a/d*tan(1/2*d*x+1/2*c)^5-3/128/a/d*tan(1/2*d*x+1/2*c)^4+7/96/a/d*tan(1/2*d*x+1/2*c)^3+15/128/a/d*tan(1/2*d*x+1/2*c)^2-11/16/a/d*tan(1/2*d*x+1/2*c)+2/a/d*arctan(tan(1/2*d*x+1/2*c))-1/384/a/d/tan(1/2*d*x+1/2*c)^6+1/160/a/d/tan(1/2*d*x+1/2*c)^5+3/128/a/d/tan(1/2*d*x+1/2*c)^4-7/96/a/d/tan(1/2*d*x+1/2*c)^3-15/128/a/d/tan(1/2*d*x+1/2*c)^2+11/16/a/d/tan(1/2*d*x+1/2*c)-5/16/a/d*ln(tan(1/2*d*x+1/2*c))","B"
717,1,284,96,0.552000," ","int(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c)),x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 a d}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{5}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 a d}+\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{896 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{15}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/896/a/d*tan(1/2*d*x+1/2*c)^7-1/384/a/d*tan(1/2*d*x+1/2*c)^6-1/128/a/d*tan(1/2*d*x+1/2*c)^5+3/128/a/d*tan(1/2*d*x+1/2*c)^4+3/128/a/d*tan(1/2*d*x+1/2*c)^3-15/128/a/d*tan(1/2*d*x+1/2*c)^2-5/128/a/d*tan(1/2*d*x+1/2*c)+1/384/a/d/tan(1/2*d*x+1/2*c)^6+5/128/a/d/tan(1/2*d*x+1/2*c)+5/16/a/d*ln(tan(1/2*d*x+1/2*c))+1/128/a/d/tan(1/2*d*x+1/2*c)^5-1/896/a/d/tan(1/2*d*x+1/2*c)^7+15/128/a/d/tan(1/2*d*x+1/2*c)^2-3/128/a/d/tan(1/2*d*x+1/2*c)^4-3/128/a/d/tan(1/2*d*x+1/2*c)^3","B"
718,1,322,122,0.559000," ","int(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 a d}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 a d}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{256 a d}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{5}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{896 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{2048 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{1}{256 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{3}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/2048/a/d*tan(1/2*d*x+1/2*c)^8-1/896/a/d*tan(1/2*d*x+1/2*c)^7-1/384/a/d*tan(1/2*d*x+1/2*c)^6+1/128/a/d*tan(1/2*d*x+1/2*c)^5+1/256/a/d*tan(1/2*d*x+1/2*c)^4-3/128/a/d*tan(1/2*d*x+1/2*c)^3+1/128/a/d*tan(1/2*d*x+1/2*c)^2+5/128/a/d*tan(1/2*d*x+1/2*c)+1/384/a/d/tan(1/2*d*x+1/2*c)^6-5/128/a/d/tan(1/2*d*x+1/2*c)-5/128/a/d*ln(tan(1/2*d*x+1/2*c))-1/128/a/d/tan(1/2*d*x+1/2*c)^5+1/896/a/d/tan(1/2*d*x+1/2*c)^7-1/128/a/d/tan(1/2*d*x+1/2*c)^2-1/2048/a/d/tan(1/2*d*x+1/2*c)^8-1/256/a/d/tan(1/2*d*x+1/2*c)^4+3/128/a/d/tan(1/2*d*x+1/2*c)^3","B"
719,1,322,138,0.601000," ","int(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c)),x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4608 a d}-\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 a d}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3584 a d}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{256 a d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{192 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{256 a d}-\frac{1}{384 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{3}{256 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{3}{3584 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{4608 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}+\frac{1}{2048 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}+\frac{1}{256 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{192 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/4608/a/d*tan(1/2*d*x+1/2*c)^9-1/2048/a/d*tan(1/2*d*x+1/2*c)^8-3/3584/a/d*tan(1/2*d*x+1/2*c)^7+1/384/a/d*tan(1/2*d*x+1/2*c)^6-1/256/a/d*tan(1/2*d*x+1/2*c)^4+1/192/a/d*tan(1/2*d*x+1/2*c)^3-1/128/a/d*tan(1/2*d*x+1/2*c)^2-3/256/a/d*tan(1/2*d*x+1/2*c)-1/384/a/d/tan(1/2*d*x+1/2*c)^6+3/256/a/d/tan(1/2*d*x+1/2*c)+5/128/a/d*ln(tan(1/2*d*x+1/2*c))+3/3584/a/d/tan(1/2*d*x+1/2*c)^7+1/128/a/d/tan(1/2*d*x+1/2*c)^2-1/4608/a/d/tan(1/2*d*x+1/2*c)^9+1/2048/a/d/tan(1/2*d*x+1/2*c)^8+1/256/a/d/tan(1/2*d*x+1/2*c)^4-1/192/a/d/tan(1/2*d*x+1/2*c)^3","B"
720,1,360,160,0.619000," ","int(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c)),x)","\frac{\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)}{10240 a d}-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4608 a d}-\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4096 a d}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3584 a d}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 a d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{512 a d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{192 a d}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 a d}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{256 a d}+\frac{1}{2048 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{3}{256 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 a d}-\frac{3}{3584 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{1024 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{4608 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}+\frac{1}{4096 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{1}{512 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{192 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{10240 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{10}}"," ",0,"1/10240/a/d*tan(1/2*d*x+1/2*c)^10-1/4608/a/d*tan(1/2*d*x+1/2*c)^9-1/4096/a/d*tan(1/2*d*x+1/2*c)^8+3/3584/a/d*tan(1/2*d*x+1/2*c)^7-1/2048/a/d*tan(1/2*d*x+1/2*c)^6+1/512/a/d*tan(1/2*d*x+1/2*c)^4-1/192/a/d*tan(1/2*d*x+1/2*c)^3+1/1024/a/d*tan(1/2*d*x+1/2*c)^2+3/256/a/d*tan(1/2*d*x+1/2*c)+1/2048/a/d/tan(1/2*d*x+1/2*c)^6-3/256/a/d/tan(1/2*d*x+1/2*c)-3/256/a/d*ln(tan(1/2*d*x+1/2*c))-3/3584/a/d/tan(1/2*d*x+1/2*c)^7-1/1024/a/d/tan(1/2*d*x+1/2*c)^2+1/4608/a/d/tan(1/2*d*x+1/2*c)^9+1/4096/a/d/tan(1/2*d*x+1/2*c)^8-1/512/a/d/tan(1/2*d*x+1/2*c)^4+1/192/a/d/tan(1/2*d*x+1/2*c)^3-1/10240/a/d/tan(1/2*d*x+1/2*c)^10","B"
721,1,436,176,0.629000," ","int(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c)),x)","\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{22528 a d}-\frac{\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)}{10240 a d}-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{18432 a d}+\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4096 a d}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{14336 a d}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 a d}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 a d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{512 a d}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3072 a d}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 a d}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 a d}-\frac{1}{2048 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{5}{1024 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 a d}-\frac{1}{2048 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{5}{14336 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{1}{1024 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{18432 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}-\frac{1}{4096 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}+\frac{1}{512 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{22528 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{11}}-\frac{5}{3072 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{10240 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{10}}"," ",0,"1/22528/a/d*tan(1/2*d*x+1/2*c)^11-1/10240/a/d*tan(1/2*d*x+1/2*c)^10-1/18432/a/d*tan(1/2*d*x+1/2*c)^9+1/4096/a/d*tan(1/2*d*x+1/2*c)^8-5/14336/a/d*tan(1/2*d*x+1/2*c)^7+1/2048/a/d*tan(1/2*d*x+1/2*c)^6+1/2048/a/d*tan(1/2*d*x+1/2*c)^5-1/512/a/d*tan(1/2*d*x+1/2*c)^4+5/3072/a/d*tan(1/2*d*x+1/2*c)^3-1/1024/a/d*tan(1/2*d*x+1/2*c)^2-5/1024/a/d*tan(1/2*d*x+1/2*c)-1/2048/a/d/tan(1/2*d*x+1/2*c)^6+5/1024/a/d/tan(1/2*d*x+1/2*c)+3/256/a/d*ln(tan(1/2*d*x+1/2*c))-1/2048/a/d/tan(1/2*d*x+1/2*c)^5+5/14336/a/d/tan(1/2*d*x+1/2*c)^7+1/1024/a/d/tan(1/2*d*x+1/2*c)^2+1/18432/a/d/tan(1/2*d*x+1/2*c)^9-1/4096/a/d/tan(1/2*d*x+1/2*c)^8+1/512/a/d/tan(1/2*d*x+1/2*c)^4-1/22528/a/d/tan(1/2*d*x+1/2*c)^11-5/3072/a/d/tan(1/2*d*x+1/2*c)^3+1/10240/a/d/tan(1/2*d*x+1/2*c)^10","B"
722,1,653,183,0.511000," ","int(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","-\frac{272}{3465 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{272 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{315 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{272 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{773 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{320 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{16 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{148 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{80 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{1207 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{464 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{848 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{1207 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{112 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}+\frac{148 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{32 \left(\tan^{16}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{773 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{320 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{\tan^{19}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{3 \left(\tan^{21}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{11}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2}}"," ",0,"-272/3465/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11+3/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)-272/315/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^2+1/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^3-272/63/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^4+773/320/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^5-16/7/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^6-148/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^7+80/7/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^8+1207/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^9-464/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^10+848/15/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^12-1207/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^13-112/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^14+148/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^15-32/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^16-773/320/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^17-1/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^19-3/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^11*tan(1/2*d*x+1/2*c)^21-3/64/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
723,1,619,167,0.456000," ","int(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{32}{315 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{64 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{63 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{87 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{32 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{553 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{64 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{491 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{32 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{2555 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{64 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{2555 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{32 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{491 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{64 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}-\frac{553 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{87 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{9 \left(\tan^{19}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{10}}+\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}"," ",0,"32/315/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10-9/128/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)+64/63/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^2-87/128/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^3+32/7/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^4+553/160/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^5-64/7/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^6+491/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^7+32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^8-2555/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^9+64/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^10+2555/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^11-32/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^12-491/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^13+64/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^14-553/160/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^15+87/128/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^17+9/128/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^10*tan(1/2*d*x+1/2*c)^19+9/128/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
724,1,551,143,0.443000," ","int(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","-\frac{52}{315 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{52 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{68 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{155 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{169 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{164 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{12 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{169 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{44 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}+\frac{155 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{4 \left(\tan^{14}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{13 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{3 \left(\tan^{17}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{9}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{32 d \,a^{2}}"," ",0,"-52/315/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9+3/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)-52/35/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^2+13/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^3-68/35/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^4-155/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^5+4/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^6+169/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^7-164/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^8+12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^10-169/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^11-44/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^12+155/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^13-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^14-13/16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^15-3/32/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^9*tan(1/2*d*x+1/2*c)^17-3/32/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
725,1,483,127,0.379000," ","int(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{8}{35 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{64 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{35 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{259 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{1103 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{64 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{2261 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{8 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{2261 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{1103 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{8 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{259 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{11 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{11 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2}}"," ",0,"8/35/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8-11/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)+64/35/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2+259/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3-8/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4+1103/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5+64/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6-2261/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7+8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8+2261/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9-1103/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11+8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12-259/192/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13+11/64/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15+11/64/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
726,1,449,112,0.309000," ","int(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","-\frac{\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{2 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{8 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{31 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{16 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{31 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{14 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{18}{35 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"-1/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12+11/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11-8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10-31/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8-16/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6+31/12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5-14/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4-11/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3-8/5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2+1/4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)-18/35/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^7-1/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))","B"
727,1,329,109,0.538000," ","int(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{32 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{34}{15 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"5/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7+12/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+32/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3+28/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2-5/2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)+34/15/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^5-3/2/d/a^2*arctan(tan(1/2*d*x+1/2*c))+1/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
728,1,333,108,0.541000," ","int(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{16 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{16}{3 a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-8/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6+7/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-16/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4-7/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-40/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2+1/4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-16/3/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^4-9/4/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
729,1,234,91,0.623000," ","int(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)+2/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3+6/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2+1/d/a^2/tan(1/2*d*x+1/2*c)-1/2/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
730,1,272,91,0.651000," ","int(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{4}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^2*tan(1/2*d*x+1/2*c)^2-1/8/d/a^2*tan(1/2*d*x+1/2*c)+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2-1/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3+1/4/a^2/d/tan(1/2*d*x+1/2*c)^2+1/8/d/a^2/tan(1/2*d*x+1/2*c)+3/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
731,1,173,108,0.707000," ","int(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{12 d \,a^{2}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{2}}-\frac{2}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{12 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}"," ",0,"1/64/d/a^2*tan(1/2*d*x+1/2*c)^4-1/12/d/a^2*tan(1/2*d*x+1/2*c)^3+5/4/d/a^2*tan(1/2*d*x+1/2*c)-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+1/12/a^2/d/tan(1/2*d*x+1/2*c)^3-5/4/d/a^2/tan(1/2*d*x+1/2*c)-9/8/d/a^2*ln(tan(1/2*d*x+1/2*c))","A"
732,1,226,108,0.744000," ","int(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a^{2} d}-\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a^{2} d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 d \,a^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{160 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{96 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{32 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{9}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{2}}"," ",0,"1/160/d/a^2*tan(1/2*d*x+1/2*c)^5-1/32/d/a^2*tan(1/2*d*x+1/2*c)^4+1/96/d/a^2*tan(1/2*d*x+1/2*c)^3+1/4/d/a^2*tan(1/2*d*x+1/2*c)^2-9/16/d/a^2*tan(1/2*d*x+1/2*c)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-1/160/a^2/d/tan(1/2*d*x+1/2*c)^5-1/96/a^2/d/tan(1/2*d*x+1/2*c)^3+1/32/a^2/d/tan(1/2*d*x+1/2*c)^4-1/4/a^2/d/tan(1/2*d*x+1/2*c)^2+9/16/d/a^2/tan(1/2*d*x+1/2*c)-3/4/d/a^2*ln(tan(1/2*d*x+1/2*c))","B"
733,1,246,120,0.655000," ","int(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d \,a^{2}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{80 a^{2} d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{2} d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}-\frac{17 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}-\frac{1}{384 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{1}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2}}+\frac{1}{80 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{17}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{16 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/384/d/a^2*tan(1/2*d*x+1/2*c)^6-1/80/d/a^2*tan(1/2*d*x+1/2*c)^5+1/128/d/a^2*tan(1/2*d*x+1/2*c)^4+1/16/d/a^2*tan(1/2*d*x+1/2*c)^3-17/128/d/a^2*tan(1/2*d*x+1/2*c)^2-1/8/d/a^2*tan(1/2*d*x+1/2*c)-1/384/d/a^2/tan(1/2*d*x+1/2*c)^6+1/8/d/a^2/tan(1/2*d*x+1/2*c)+7/16/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/80/a^2/d/tan(1/2*d*x+1/2*c)^5+17/128/a^2/d/tan(1/2*d*x+1/2*c)^2-1/128/a^2/d/tan(1/2*d*x+1/2*c)^4-1/16/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
734,1,284,112,0.737000," ","int(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 d \,a^{2}}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{192 d \,a^{2}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{640 a^{2} d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{2}}+\frac{1}{192 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{11}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{3}{640 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{896 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{5}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/896/d/a^2*tan(1/2*d*x+1/2*c)^7-1/192/d/a^2*tan(1/2*d*x+1/2*c)^6+3/640/d/a^2*tan(1/2*d*x+1/2*c)^5+1/64/d/a^2*tan(1/2*d*x+1/2*c)^4-5/128/d/a^2*tan(1/2*d*x+1/2*c)^3+1/64/d/a^2*tan(1/2*d*x+1/2*c)^2+11/128/d/a^2*tan(1/2*d*x+1/2*c)+1/192/d/a^2/tan(1/2*d*x+1/2*c)^6-11/128/d/a^2/tan(1/2*d*x+1/2*c)-1/8/d/a^2*ln(tan(1/2*d*x+1/2*c))-3/640/a^2/d/tan(1/2*d*x+1/2*c)^5-1/896/d/a^2/tan(1/2*d*x+1/2*c)^7-1/64/a^2/d/tan(1/2*d*x+1/2*c)^2-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+5/128/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
735,1,322,160,0.695000," ","int(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 d \,a^{2}}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{448 d \,a^{2}}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d \,a^{2}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{320 a^{2} d}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 a^{2} d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{2} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{2}}-\frac{1}{384 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{3}{64 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{11 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}-\frac{1}{320 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{448 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{1}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{2048 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}+\frac{3}{256 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/2048/d/a^2*tan(1/2*d*x+1/2*c)^8-1/448/d/a^2*tan(1/2*d*x+1/2*c)^7+1/384/d/a^2*tan(1/2*d*x+1/2*c)^6+1/320/d/a^2*tan(1/2*d*x+1/2*c)^5-3/256/d/a^2*tan(1/2*d*x+1/2*c)^4+1/64/d/a^2*tan(1/2*d*x+1/2*c)^3-1/128/d/a^2*tan(1/2*d*x+1/2*c)^2-3/64/d/a^2*tan(1/2*d*x+1/2*c)-1/384/d/a^2/tan(1/2*d*x+1/2*c)^6+3/64/d/a^2/tan(1/2*d*x+1/2*c)+11/128/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/320/a^2/d/tan(1/2*d*x+1/2*c)^5+1/448/d/a^2/tan(1/2*d*x+1/2*c)^7+1/128/a^2/d/tan(1/2*d*x+1/2*c)^2-1/2048/d/a^2/tan(1/2*d*x+1/2*c)^8+3/256/a^2/d/tan(1/2*d*x+1/2*c)^4-1/64/a^2/d/tan(1/2*d*x+1/2*c)^3","B"
736,1,284,152,0.712000," ","int(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4608 d \,a^{2}}-\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 d \,a^{2}}+\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3584 d \,a^{2}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{320 a^{2} d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{2} d}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 d \,a^{2}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{256 d \,a^{2}}-\frac{9}{256 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{2}}+\frac{1}{320 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{5}{3584 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{4608 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}+\frac{1}{1024 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{1}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{96 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/4608/d/a^2*tan(1/2*d*x+1/2*c)^9-1/1024/d/a^2*tan(1/2*d*x+1/2*c)^8+5/3584/d/a^2*tan(1/2*d*x+1/2*c)^7-1/320/d/a^2*tan(1/2*d*x+1/2*c)^5+1/128/d/a^2*tan(1/2*d*x+1/2*c)^4-1/96/d/a^2*tan(1/2*d*x+1/2*c)^3+9/256/d/a^2*tan(1/2*d*x+1/2*c)-9/256/d/a^2/tan(1/2*d*x+1/2*c)-3/64/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/320/a^2/d/tan(1/2*d*x+1/2*c)^5-5/3584/d/a^2/tan(1/2*d*x+1/2*c)^7-1/4608/d/a^2/tan(1/2*d*x+1/2*c)^9+1/1024/d/a^2/tan(1/2*d*x+1/2*c)^8-1/128/a^2/d/tan(1/2*d*x+1/2*c)^4+1/96/a^2/d/tan(1/2*d*x+1/2*c)^3","A"
737,1,398,198,0.751000," ","int(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)}{10240 d \,a^{2}}-\frac{\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2304 d \,a^{2}}+\frac{3 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4096 d \,a^{2}}-\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1792 d \,a^{2}}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 d \,a^{2}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{320 a^{2} d}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{512 a^{2} d}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{192 d \,a^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 a^{2} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{2}}+\frac{1}{2048 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{3}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \,a^{2}}-\frac{1}{320 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{1792 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{1}{1024 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{2304 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}-\frac{3}{4096 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}+\frac{3}{512 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{192 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{10240 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{10}}"," ",0,"1/10240/d/a^2*tan(1/2*d*x+1/2*c)^10-1/2304/d/a^2*tan(1/2*d*x+1/2*c)^9+3/4096/d/a^2*tan(1/2*d*x+1/2*c)^8-1/1792/d/a^2*tan(1/2*d*x+1/2*c)^7-1/2048/d/a^2*tan(1/2*d*x+1/2*c)^6+1/320/d/a^2*tan(1/2*d*x+1/2*c)^5-3/512/d/a^2*tan(1/2*d*x+1/2*c)^4+1/192/d/a^2*tan(1/2*d*x+1/2*c)^3+1/1024/d/a^2*tan(1/2*d*x+1/2*c)^2-3/128/d/a^2*tan(1/2*d*x+1/2*c)+1/2048/d/a^2/tan(1/2*d*x+1/2*c)^6+3/128/d/a^2/tan(1/2*d*x+1/2*c)+9/256/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/320/a^2/d/tan(1/2*d*x+1/2*c)^5+1/1792/d/a^2/tan(1/2*d*x+1/2*c)^7-1/1024/a^2/d/tan(1/2*d*x+1/2*c)^2+1/2304/d/a^2/tan(1/2*d*x+1/2*c)^9-3/4096/d/a^2/tan(1/2*d*x+1/2*c)^8+3/512/a^2/d/tan(1/2*d*x+1/2*c)^4-1/192/a^2/d/tan(1/2*d*x+1/2*c)^3-1/10240/d/a^2/tan(1/2*d*x+1/2*c)^10","B"
738,1,436,190,0.765000," ","int(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c))^2,x)","\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{22528 d \,a^{2}}-\frac{\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)}{5120 d \,a^{2}}+\frac{7 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{18432 d \,a^{2}}-\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 d \,a^{2}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{14336 d \,a^{2}}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 d \,a^{2}}-\frac{27 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{10240 a^{2} d}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{256 a^{2} d}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3072 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{512 a^{2} d}+\frac{19 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{1024 d \,a^{2}}-\frac{1}{1024 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{19}{1024 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}+\frac{27}{10240 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{3}{14336 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{1}{512 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{7}{18432 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{9}}+\frac{1}{2048 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{1}{256 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{1}{22528 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{11}}+\frac{11}{3072 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{5120 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{10}}"," ",0,"1/22528/d/a^2*tan(1/2*d*x+1/2*c)^11-1/5120/d/a^2*tan(1/2*d*x+1/2*c)^10+7/18432/d/a^2*tan(1/2*d*x+1/2*c)^9-1/2048/d/a^2*tan(1/2*d*x+1/2*c)^8+3/14336/d/a^2*tan(1/2*d*x+1/2*c)^7+1/1024/d/a^2*tan(1/2*d*x+1/2*c)^6-27/10240/d/a^2*tan(1/2*d*x+1/2*c)^5+1/256/d/a^2*tan(1/2*d*x+1/2*c)^4-11/3072/d/a^2*tan(1/2*d*x+1/2*c)^3-1/512/d/a^2*tan(1/2*d*x+1/2*c)^2+19/1024/d/a^2*tan(1/2*d*x+1/2*c)-1/1024/d/a^2/tan(1/2*d*x+1/2*c)^6-19/1024/d/a^2/tan(1/2*d*x+1/2*c)-3/128/d/a^2*ln(tan(1/2*d*x+1/2*c))+27/10240/a^2/d/tan(1/2*d*x+1/2*c)^5-3/14336/d/a^2/tan(1/2*d*x+1/2*c)^7+1/512/a^2/d/tan(1/2*d*x+1/2*c)^2-7/18432/d/a^2/tan(1/2*d*x+1/2*c)^9+1/2048/d/a^2/tan(1/2*d*x+1/2*c)^8-1/256/a^2/d/tan(1/2*d*x+1/2*c)^4-1/22528/d/a^2/tan(1/2*d*x+1/2*c)^11+11/3072/a^2/d/tan(1/2*d*x+1/2*c)^3+1/5120/d/a^2/tan(1/2*d*x+1/2*c)^10","B"
739,1,517,145,0.414000," ","int(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","-\frac{76}{105 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{29 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{608 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{105 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{667 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{244 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{1465 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{32 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{15 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{5117 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{76 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{5117 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{128 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}+\frac{1465 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{4 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{667 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{192 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{29 \left(\tan^{15}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{8}}-\frac{29 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 a^{3} d}"," ",0,"-76/105/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8+29/64/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)-608/105/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2+667/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3-244/15/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4-1465/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5+32/15/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6-5117/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7-76/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8+5117/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9-128/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10+1465/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12-667/192/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13-29/64/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-29/64/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
740,1,415,121,0.395000," ","int(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{5 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{3 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{12 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{119 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{92 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{119 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{20 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{20}{21 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}"," ",0,"5/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13+3/2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11+12/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10-119/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9+92/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8+8/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6+119/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5+8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4-3/2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3+20/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2-5/8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)+20/21/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^7+5/8/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
741,1,415,119,0.387000," ","int(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","-\frac{7 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{73 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{18 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{37 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{44 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{37 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{73 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{34 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{22}{15 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}"," ",0,"-7/8/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10+73/24/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-18/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8+37/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-44/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6-37/4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4-73/24/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-34/5/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2+7/8/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-22/15/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^6-7/8/a^3/d*arctan(tan(1/2*d*x+1/2*c))","B"
742,1,239,93,0.569000," ","int(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{11 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{19 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{19 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 a^{3} d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"11/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6+19/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-19/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2-11/4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-13/4/a^3/d*arctan(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))","B"
743,1,230,86,0.608000," ","int(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{16}{3 a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5-4/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-12/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)-16/3/a^3/d/(1+tan(1/2*d*x+1/2*c)^2)^3+1/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^3*ln(tan(1/2*d*x+1/2*c))","B"
744,1,234,90,0.675000," ","int(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^3*tan(1/2*d*x+1/2*c)+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2+5/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+3/2/d/a^3/tan(1/2*d*x+1/2*c)+5/2/d/a^3*ln(tan(1/2*d*x+1/2*c))","B"
745,1,173,86,0.701000," ","int(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{2}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{11}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/d/a^3*tan(1/2*d*x+1/2*c)^2+11/8/d/a^3*tan(1/2*d*x+1/2*c)-2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)-6/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3+3/8/d/a^3/tan(1/2*d*x+1/2*c)^2-11/8/d/a^3/tan(1/2*d*x+1/2*c)+1/2/d/a^3*ln(tan(1/2*d*x+1/2*c))","A"
746,1,188,91,0.710000," ","int(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a^{3} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{1}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{3}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}"," ",0,"1/64/d/a^3*tan(1/2*d*x+1/2*c)^4-1/8/d/a^3*tan(1/2*d*x+1/2*c)^3+3/8/d/a^3*tan(1/2*d*x+1/2*c)^2-1/8/d/a^3*tan(1/2*d*x+1/2*c)+2/a^3/d*arctan(tan(1/2*d*x+1/2*c))-1/64/d/a^3/tan(1/2*d*x+1/2*c)^4+1/8/d/a^3/tan(1/2*d*x+1/2*c)^3-3/8/d/a^3/tan(1/2*d*x+1/2*c)^2+1/8/d/a^3/tan(1/2*d*x+1/2*c)-13/8/d/a^3*ln(tan(1/2*d*x+1/2*c))","B"
747,1,208,90,0.712000," ","int(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d \,a^{3}}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{64 d \,a^{3}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{3} d}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}+\frac{7}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}-\frac{1}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{13}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/160/d/a^3*tan(1/2*d*x+1/2*c)^5-3/64/d/a^3*tan(1/2*d*x+1/2*c)^4+13/96/d/a^3*tan(1/2*d*x+1/2*c)^3-1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-7/16/d/a^3*tan(1/2*d*x+1/2*c)+7/16/d/a^3/tan(1/2*d*x+1/2*c)+7/8/d/a^3*ln(tan(1/2*d*x+1/2*c))-1/160/d/a^3/tan(1/2*d*x+1/2*c)^5+1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+3/64/d/a^3/tan(1/2*d*x+1/2*c)^4-13/96/d/a^3/tan(1/2*d*x+1/2*c)^3","B"
748,1,246,112,0.715000," ","int(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d \,a^{3}}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 d \,a^{3}}+\frac{7 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a^{3} d}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}-\frac{1}{384 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{5}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{3}}+\frac{3}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{7}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{7}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/384/d/a^3*tan(1/2*d*x+1/2*c)^6-3/160/d/a^3*tan(1/2*d*x+1/2*c)^5+7/128/d/a^3*tan(1/2*d*x+1/2*c)^4-7/96/d/a^3*tan(1/2*d*x+1/2*c)^3-1/128/d/a^3*tan(1/2*d*x+1/2*c)^2+5/16/d/a^3*tan(1/2*d*x+1/2*c)-1/384/d/a^3/tan(1/2*d*x+1/2*c)^6-5/16/d/a^3/tan(1/2*d*x+1/2*c)-7/16/d/a^3*ln(tan(1/2*d*x+1/2*c))+3/160/d/a^3/tan(1/2*d*x+1/2*c)^5+1/128/d/a^3/tan(1/2*d*x+1/2*c)^2-7/128/d/a^3/tan(1/2*d*x+1/2*c)^4+7/96/d/a^3/tan(1/2*d*x+1/2*c)^3","B"
749,1,284,128,0.734000," ","int(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 d \,a^{3}}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}-\frac{5 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{384 d \,a^{3}}+\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{3} d}-\frac{29 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}+\frac{1}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{29}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{3}}-\frac{3}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{896 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{3}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{13}{384 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/896/d/a^3*tan(1/2*d*x+1/2*c)^7-1/128/d/a^3*tan(1/2*d*x+1/2*c)^6+3/128/d/a^3*tan(1/2*d*x+1/2*c)^5-5/128/d/a^3*tan(1/2*d*x+1/2*c)^4+13/384/d/a^3*tan(1/2*d*x+1/2*c)^3+3/128/d/a^3*tan(1/2*d*x+1/2*c)^2-29/128/d/a^3*tan(1/2*d*x+1/2*c)+1/128/d/a^3/tan(1/2*d*x+1/2*c)^6+29/128/d/a^3/tan(1/2*d*x+1/2*c)+5/16/d/a^3*ln(tan(1/2*d*x+1/2*c))-3/128/d/a^3/tan(1/2*d*x+1/2*c)^5-1/896/d/a^3/tan(1/2*d*x+1/2*c)^7-3/128/d/a^3/tan(1/2*d*x+1/2*c)^2+5/128/d/a^3/tan(1/2*d*x+1/2*c)^4-13/384/d/a^3/tan(1/2*d*x+1/2*c)^3","B"
750,1,322,150,0.758000," ","int(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^3,x)","\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 d \,a^{3}}-\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{896 d \,a^{3}}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 d \,a^{3}}-\frac{13 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{640 d \,a^{3}}+\frac{7 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{256 d \,a^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{384 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 a^{3} d}+\frac{23 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}-\frac{1}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{23}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{29 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}+\frac{13}{640 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{3}{896 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{1}{32 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{2048 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{7}{256 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{7}{384 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}"," ",0,"1/2048/d/a^3*tan(1/2*d*x+1/2*c)^8-3/896/d/a^3*tan(1/2*d*x+1/2*c)^7+1/96/d/a^3*tan(1/2*d*x+1/2*c)^6-13/640/d/a^3*tan(1/2*d*x+1/2*c)^5+7/256/d/a^3*tan(1/2*d*x+1/2*c)^4-7/384/d/a^3*tan(1/2*d*x+1/2*c)^3-1/32/d/a^3*tan(1/2*d*x+1/2*c)^2+23/128/d/a^3*tan(1/2*d*x+1/2*c)-1/96/d/a^3/tan(1/2*d*x+1/2*c)^6-23/128/d/a^3/tan(1/2*d*x+1/2*c)-29/128/d/a^3*ln(tan(1/2*d*x+1/2*c))+13/640/d/a^3/tan(1/2*d*x+1/2*c)^5+3/896/d/a^3/tan(1/2*d*x+1/2*c)^7+1/32/d/a^3/tan(1/2*d*x+1/2*c)^2-1/2048/d/a^3/tan(1/2*d*x+1/2*c)^8-7/256/d/a^3/tan(1/2*d*x+1/2*c)^4+7/384/d/a^3/tan(1/2*d*x+1/2*c)^3","B"
751,1,104,74,0.399000," ","int(sec(d*x+c)^2*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","A"
752,1,94,59,0.389000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+a \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+a*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
753,1,59,39,0.305000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a*(tan(d*x+c)-d*x-c))","A"
754,1,32,27,0.143000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(\tan \left(d x +c \right)-d x -c \right)+\frac{a}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a*(tan(d*x+c)-d*x-c)+a/cos(d*x+c))","A"
755,1,47,36,0.414000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \tan \left(d x +c \right)}{d}+\frac{a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"a*tan(d*x+c)/d+1/d*a/cos(d*x+c)+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
756,1,69,48,0.379000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a \cot \left(d x +c \right)}{d}"," ",0,"1/d*a/cos(d*x+c)+1/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/d*a/sin(d*x+c)/cos(d*x+c)-2*a*cot(d*x+c)/d","A"
757,1,93,69,0.455000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a \cot \left(d x +c \right)}{d}-\frac{a}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a}{2 d \cos \left(d x +c \right)}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"1/d*a/sin(d*x+c)/cos(d*x+c)-2*a*cot(d*x+c)/d-1/2/d*a/sin(d*x+c)^2/cos(d*x+c)+3/2/d*a/cos(d*x+c)+3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
758,1,116,83,0.442000," ","int(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c)),x)","-\frac{a}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a}{2 d \cos \left(d x +c \right)}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{a}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a \cot \left(d x +c \right)}{3 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2/cos(d*x+c)+3/2/d*a/cos(d*x+c)+3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*a/sin(d*x+c)^3/cos(d*x+c)+4/3/d*a/sin(d*x+c)/cos(d*x+c)-8/3*a*cot(d*x+c)/d","A"
759,1,148,87,0.499000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+2 a^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^2*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+2*a^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
760,1,117,67,0.420000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+2 a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a^{2} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+2*a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a^2*(tan(d*x+c)-d*x-c))","A"
761,1,76,43,0.322000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+2 a^{2} \left(\tan \left(d x +c \right)-d x -c \right)+\frac{a^{2}}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+2*a^2*(tan(d*x+c)-d*x-c)+a^2/cos(d*x+c))","A"
762,1,55,44,0.551000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{2 a^{2}}{d \cos \left(d x +c \right)}+\frac{2 a^{2} \tan \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"2/d*a^2/cos(d*x+c)+2*a^2*tan(d*x+c)/d+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))","A"
763,1,92,58,0.602000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right)}{d}+\frac{2 a^{2}}{d \cos \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a^{2} \cot \left(d x +c \right)}{d}"," ",0,"a^2*tan(d*x+c)/d+2/d*a^2/cos(d*x+c)+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+1/d*a^2/sin(d*x+c)/cos(d*x+c)-2*a^2*cot(d*x+c)/d","A"
764,1,104,80,0.599000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{5 a^{2}}{2 d \cos \left(d x +c \right)}+\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{4 a^{2} \cot \left(d x +c \right)}{d}-\frac{a^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"5/2/d*a^2/cos(d*x+c)+5/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2/d*a^2/sin(d*x+c)/cos(d*x+c)-4*a^2*cot(d*x+c)/d-1/2/d*a^2/sin(d*x+c)^2/cos(d*x+c)","A"
765,1,212,105,0.598000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{7}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)-\frac{15 d x}{8}-\frac{15 c}{8}\right)+3 a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^7/cos(d*x+c)+(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)-15/8*d*x-15/8*c)+3*a^3*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","B"
766,1,167,83,0.509000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+3 a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+a^{3} \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+3*a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+a^3*(tan(d*x+c)-d*x-c))","A"
767,1,130,63,0.423000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+3 a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\tan \left(d x +c \right)-d x -c \right)+\frac{a^{3}}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+3*a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(tan(d*x+c)-d*x-c)+a^3/cos(d*x+c))","B"
768,1,70,48,0.562000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","-a^{3} x +\frac{4 a^{3} \tan \left(d x +c \right)}{d}-\frac{a^{3} c}{d}+\frac{4 a^{3}}{d \cos \left(d x +c \right)}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-a^3*x+4*a^3*tan(d*x+c)/d-1/d*a^3*c+4/d*a^3/cos(d*x+c)+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
769,1,93,56,0.609000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{4 a^{3}}{d \cos \left(d x +c \right)}+\frac{3 a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a^{3} \cot \left(d x +c \right)}{d}"," ",0,"4/d*a^3/cos(d*x+c)+3*a^3*tan(d*x+c)/d+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+1/d*a^3/sin(d*x+c)/cos(d*x+c)-2*a^3*cot(d*x+c)/d","A"
770,1,117,76,0.699000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right)}{d}+\frac{9 a^{3}}{2 d \cos \left(d x +c \right)}+\frac{9 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{6 a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"a^3*tan(d*x+c)/d+9/2/d*a^3/cos(d*x+c)+9/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3/d*a^3/sin(d*x+c)/cos(d*x+c)-6*a^3*cot(d*x+c)/d-1/2/d*a^3/sin(d*x+c)^2/cos(d*x+c)","A"
771,1,128,92,0.590000," ","int(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{11 a^{3}}{2 d \cos \left(d x +c \right)}+\frac{11 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{13 a^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{26 a^{3} \cot \left(d x +c \right)}{3 d}-\frac{3 a^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"11/2/d*a^3/cos(d*x+c)+11/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+13/3/d*a^3/sin(d*x+c)/cos(d*x+c)-26/3*a^3*cot(d*x+c)/d-3/2/d*a^3/sin(d*x+c)^2/cos(d*x+c)-1/3/d*a^3/sin(d*x+c)^3/cos(d*x+c)","A"
772,1,126,79,0.365000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/2/a/d/(tan(1/2*d*x+1/2*c)-1)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)+2/a/d*arctan(tan(1/2*d*x+1/2*c))-2/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/a/d/(tan(1/2*d*x+1/2*c)+1)^2+5/2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
773,1,104,66,0.355000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/2/a/d/(tan(1/2*d*x+1/2*c)-1)-2/a/d*arctan(tan(1/2*d*x+1/2*c))+2/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3-1/a/d/(tan(1/2*d*x+1/2*c)+1)^2-3/2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
774,1,70,46,0.318000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16}}{d a}"," ",0,"8/d/a*(-1/16/(tan(1/2*d*x+1/2*c)-1)-1/12/(tan(1/2*d*x+1/2*c)+1)^3+1/8/(tan(1/2*d*x+1/2*c)+1)^2+1/16/(tan(1/2*d*x+1/2*c)+1))","A"
775,1,70,33,0.280000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{4}{8 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+8}}{d a}"," ",0,"4/d/a*(-1/8/(tan(1/2*d*x+1/2*c)-1)+1/6/(tan(1/2*d*x+1/2*c)+1)^3-1/4/(tan(1/2*d*x+1/2*c)+1)^2+1/8/(tan(1/2*d*x+1/2*c)+1))","B"
776,1,103,75,0.423000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/2/a/d/(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c))+2/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3-1/a/d/(tan(1/2*d*x+1/2*c)+1)^2+5/2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
777,1,139,89,0.433000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{7}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))-2/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3+1/a/d/(tan(1/2*d*x+1/2*c)+1)^2-7/2/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
778,1,267,137,0.474000," ","int(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{7}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{31}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2+1/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)^2-9/d/a^2*arctan(tan(1/2*d*x+1/2*c))-4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+1/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-7/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-31/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
779,1,169,112,0.443000," ","int(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{17}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2/a^2/d/(1+tan(1/2*d*x+1/2*c)^2)+4/d/a^2*arctan(tan(1/2*d*x+1/2*c))+4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-1/3/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+5/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+17/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
780,1,146,98,0.432000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{7}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-1/3/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-3/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-7/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
781,1,100,62,0.426000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{64 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+64}}{a^{2} d}"," ",0,"16/d/a^2*(-1/64/(tan(1/2*d*x+1/2*c)-1)+1/20/(tan(1/2*d*x+1/2*c)+1)^5-1/8/(tan(1/2*d*x+1/2*c)+1)^4+1/16/(tan(1/2*d*x+1/2*c)+1)^3+1/32/(tan(1/2*d*x+1/2*c)+1)^2+1/64/(tan(1/2*d*x+1/2*c)+1))","A"
782,1,100,65,0.409000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{5}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{32 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+32}}{a^{2} d}"," ",0,"8/d/a^2*(-1/32/(tan(1/2*d*x+1/2*c)-1)-1/10/(tan(1/2*d*x+1/2*c)+1)^5+1/4/(tan(1/2*d*x+1/2*c)+1)^4-5/24/(tan(1/2*d*x+1/2*c)+1)^3+1/16/(tan(1/2*d*x+1/2*c)+1)^2+1/32/(tan(1/2*d*x+1/2*c)+1))","A"
783,1,100,65,0.356000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{7}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{4}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16}}{a^{2} d}"," ",0,"4/d/a^2*(-1/16/(tan(1/2*d*x+1/2*c)-1)+1/5/(tan(1/2*d*x+1/2*c)+1)^5-1/2/(tan(1/2*d*x+1/2*c)+1)^4+7/12/(tan(1/2*d*x+1/2*c)+1)^3-3/8/(tan(1/2*d*x+1/2*c)+1)^2+1/16/(tan(1/2*d*x+1/2*c)+1))","A"
784,1,145,107,0.556000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{11}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{7}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{17}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+11/3/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-7/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+17/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
785,1,182,122,0.561000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{13}{3 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{9}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{31}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))-4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-13/3/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+9/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-31/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
786,1,219,146,0.615000," ","int(csc(d*x+c)^3*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","-\frac{1}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{4}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{11}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{49}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)+1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2+1/d/a^2/tan(1/2*d*x+1/2*c)+9/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-11/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+49/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
787,1,211,143,0.526000," ","int(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","-\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{a^{3} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}-\frac{8}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{4}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{14}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{3}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{17}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{49}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)+6/a^3/d*arctan(tan(1/2*d*x+1/2*c))-8/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7+4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6-14/5/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-3/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+1/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+17/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+49/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
788,1,187,130,0.500000," ","int(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","-\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}+\frac{8}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{4}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{18}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{5}{6 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{7}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{15}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)-2/a^3/d*arctan(tan(1/2*d*x+1/2*c))+8/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7-4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6+18/5/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5+1/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4-5/6/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-7/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-15/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
789,1,130,94,0.497000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{22}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{32}{256 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+256}}{d \,a^{3}}"," ",0,"32/d/a^3*(-1/256/(tan(1/2*d*x+1/2*c)-1)-1/28/(tan(1/2*d*x+1/2*c)+1)^7+1/8/(tan(1/2*d*x+1/2*c)+1)^6-11/80/(tan(1/2*d*x+1/2*c)+1)^5+1/32/(tan(1/2*d*x+1/2*c)+1)^4+1/64/(tan(1/2*d*x+1/2*c)+1)^3+1/128/(tan(1/2*d*x+1/2*c)+1)^2+1/256/(tan(1/2*d*x+1/2*c)+1))","A"
790,1,130,80,0.488000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{26}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{128 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+128}}{d \,a^{3}}"," ",0,"16/d/a^3*(-1/128/(tan(1/2*d*x+1/2*c)-1)+1/14/(tan(1/2*d*x+1/2*c)+1)^7-1/4/(tan(1/2*d*x+1/2*c)+1)^6+13/40/(tan(1/2*d*x+1/2*c)+1)^5-3/16/(tan(1/2*d*x+1/2*c)+1)^4+1/32/(tan(1/2*d*x+1/2*c)+1)^3+1/64/(tan(1/2*d*x+1/2*c)+1)^2+1/128/(tan(1/2*d*x+1/2*c)+1))","A"
791,1,130,95,0.466000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{6}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{5}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{13}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{64 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+64}}{d \,a^{3}}"," ",0,"8/d/a^3*(-1/64/(tan(1/2*d*x+1/2*c)-1)-1/7/(tan(1/2*d*x+1/2*c)+1)^7+1/2/(tan(1/2*d*x+1/2*c)+1)^6-3/4/(tan(1/2*d*x+1/2*c)+1)^5+5/8/(tan(1/2*d*x+1/2*c)+1)^4-13/48/(tan(1/2*d*x+1/2*c)+1)^3+1/32/(tan(1/2*d*x+1/2*c)+1)^2+1/64/(tan(1/2*d*x+1/2*c)+1))","A"
792,1,130,91,0.453000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{8}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{34}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{7}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{9}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{7}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{4}{32 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+32}}{d \,a^{3}}"," ",0,"4/d/a^3*(-1/32/(tan(1/2*d*x+1/2*c)-1)+2/7/(tan(1/2*d*x+1/2*c)+1)^7-1/(tan(1/2*d*x+1/2*c)+1)^6+17/10/(tan(1/2*d*x+1/2*c)+1)^5-7/4/(tan(1/2*d*x+1/2*c)+1)^4+9/8/(tan(1/2*d*x+1/2*c)+1)^3-7/16/(tan(1/2*d*x+1/2*c)+1)^2+1/32/(tan(1/2*d*x+1/2*c)+1))","A"
793,1,187,139,0.651000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","-\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{4}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{42}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{11}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{67}{6 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{31}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{49}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)+1/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7-4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6+42/5/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-11/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+67/6/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-31/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+49/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
794,1,224,154,0.647000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{4}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{46}{5 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{13}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{31}{2 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{49}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{111}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/8/a^3/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^3*ln(tan(1/2*d*x+1/2*c))-8/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7+4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6-46/5/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5+13/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4-31/2/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+49/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-111/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
795,1,164,105,0.464000," ","int(sec(d*x+c)^4*sin(d*x+c)^6*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+a \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)}{d}"," ",0,"1/d*(a*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+a*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c))","A"
796,1,154,91,0.456000," ","int(sec(d*x+c)^4*sin(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+a \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+a*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
797,1,98,68,0.361000," ","int(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","A"
798,1,88,56,0.369000," ","int(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+a \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+a*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
799,1,82,41,0.363000," ","int(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+1/3*a*sin(d*x+c)^3/cos(d*x+c)^3)","A"
800,1,36,29,0.204000," ","int(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{a}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(1/3*a*sin(d*x+c)^3/cos(d*x+c)^3+1/3*a/cos(d*x+c)^3)","A"
801,1,82,64,0.429000," ","int(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{2 a \tan \left(d x +c \right)}{3 d}+\frac{a \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a}{3 d \cos \left(d x +c \right)^{3}}+\frac{a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"2/3*a*tan(d*x+c)/d+1/3/d*a*tan(d*x+c)*sec(d*x+c)^2+1/3/d*a/cos(d*x+c)^3+1/d*a/cos(d*x+c)+1/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
802,1,106,77,0.462000," ","int(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a}{3 d \cos \left(d x +c \right)^{3}}+\frac{a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a \cot \left(d x +c \right)}{3 d}"," ",0,"1/3/d*a/cos(d*x+c)^3+1/d*a/cos(d*x+c)+1/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/3/d*a/sin(d*x+c)/cos(d*x+c)^3+4/3/d*a/sin(d*x+c)/cos(d*x+c)-8/3*a*cot(d*x+c)/d","A"
803,1,138,100,0.510000," ","int(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 a}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a \cot \left(d x +c \right)}{3 d}+\frac{a}{3 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{3}}-\frac{5 a}{6 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{5 a}{2 d \cos \left(d x +c \right)}+\frac{5 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"1/3/d*a/sin(d*x+c)/cos(d*x+c)^3+4/3/d*a/sin(d*x+c)/cos(d*x+c)-8/3*a*cot(d*x+c)/d+1/3/d*a/sin(d*x+c)^2/cos(d*x+c)^3-5/6/d*a/sin(d*x+c)^2/cos(d*x+c)+5/2/d*a/cos(d*x+c)+5/2/d*a*ln(csc(d*x+c)-cot(d*x+c))","A"
804,1,186,93,0.487000," ","int(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+2 a^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^2*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+2*a^2*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^2*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","A"
805,1,162,82,0.475000," ","int(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+2 a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a^2*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+2*a^2*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+a^2*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
806,1,114,59,0.402000," ","int(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+2 a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+2*a^2*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+1/3*a^2*sin(d*x+c)^3/cos(d*x+c)^3)","A"
807,1,99,54,0.372000," ","int(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{2 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+\frac{a^{2}}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^2*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+2/3*a^2*sin(d*x+c)^3/cos(d*x+c)^3+1/3*a^2/cos(d*x+c)^3)","A"
808,1,92,69,0.605000," ","int(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{2 a^{2}}{3 d \cos \left(d x +c \right)^{3}}+\frac{4 a^{2} \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{2}}{d \cos \left(d x +c \right)}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"2/3/d*a^2/cos(d*x+c)^3+4/3*a^2*tan(d*x+c)/d+2/3/d*a^2*tan(d*x+c)*sec(d*x+c)^2+1/d*a^2/cos(d*x+c)+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))","A"
809,1,156,83,0.727000," ","int(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{2 a^{2} \tan \left(d x +c \right)}{3 d}+\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 a^{2}}{3 d \cos \left(d x +c \right)^{3}}+\frac{2 a^{2}}{d \cos \left(d x +c \right)}+\frac{2 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a^{2} \cot \left(d x +c \right)}{3 d}"," ",0,"2/3*a^2*tan(d*x+c)/d+1/3/d*a^2*tan(d*x+c)*sec(d*x+c)^2+2/3/d*a^2/cos(d*x+c)^3+2/d*a^2/cos(d*x+c)+2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+1/3/d*a^2/sin(d*x+c)/cos(d*x+c)^3+4/3/d*a^2/sin(d*x+c)/cos(d*x+c)-8/3*a^2*cot(d*x+c)/d","A"
810,1,168,115,0.710000," ","int(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2}}{3 d \cos \left(d x +c \right)^{3}}+\frac{7 a^{2}}{2 d \cos \left(d x +c \right)}+\frac{7 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{8 a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{16 a^{2} \cot \left(d x +c \right)}{3 d}+\frac{a^{2}}{3 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{3}}-\frac{5 a^{2}}{6 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"1/3/d*a^2/cos(d*x+c)^3+7/2/d*a^2/cos(d*x+c)+7/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2/3/d*a^2/sin(d*x+c)/cos(d*x+c)^3+8/3/d*a^2/sin(d*x+c)/cos(d*x+c)-16/3*a^2*cot(d*x+c)/d+1/3/d*a^2/sin(d*x+c)^2/cos(d*x+c)^3-5/6/d*a^2/sin(d*x+c)^2/cos(d*x+c)","A"
811,1,266,109,0.606000," ","int(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+3 a^{3} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+3 a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^3*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+3*a^3*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","B"
812,1,246,93,0.585000," ","int(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+3 a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)}{d}"," ",0,"1/d*(a^3*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+3*a^3*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+a^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c)))","B"
813,1,184,75,0.503000," ","int(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+3 a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+3 a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^3*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+3*a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+3*a^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+1/3*a^3*sin(d*x+c)^3/cos(d*x+c)^3)","B"
814,1,126,62,0.399000," ","int(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+3 a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+\frac{a^{3}}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+3*a^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+a^3*sin(d*x+c)^3/cos(d*x+c)^3+1/3*a^3/cos(d*x+c)^3)","B"
815,1,115,68,0.639000," ","int(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{3}}+\frac{4 a^{3}}{3 d \cos \left(d x +c \right)^{3}}+\frac{2 a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{a^{3}}{d \cos \left(d x +c \right)}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*a^3*sin(d*x+c)^3/cos(d*x+c)^3+4/3/d*a^3/cos(d*x+c)^3+2*a^3*tan(d*x+c)/d+1/d*a^3*tan(d*x+c)*sec(d*x+c)^2+1/d*a^3/cos(d*x+c)+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))","A"
816,1,155,82,0.717000," ","int(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{4 a^{3}}{3 d \cos \left(d x +c \right)^{3}}+\frac{2 a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 a^{3}}{d \cos \left(d x +c \right)}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 a^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a^{3} \cot \left(d x +c \right)}{3 d}"," ",0,"4/3/d*a^3/cos(d*x+c)^3+2*a^3*tan(d*x+c)/d+1/d*a^3*tan(d*x+c)*sec(d*x+c)^2+3/d*a^3/cos(d*x+c)+3/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+1/3/d*a^3/sin(d*x+c)/cos(d*x+c)^3+4/3/d*a^3/sin(d*x+c)/cos(d*x+c)-8/3*a^3*cot(d*x+c)/d","A"
817,1,202,102,0.835000," ","int(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{2 a^{3} \tan \left(d x +c \right)}{3 d}+\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{3}}{d \cos \left(d x +c \right)^{3}}+\frac{11 a^{3}}{2 d \cos \left(d x +c \right)}+\frac{11 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{4 a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a^{3} \cot \left(d x +c \right)}{d}+\frac{a^{3}}{3 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{3}}-\frac{5 a^{3}}{6 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"2/3*a^3*tan(d*x+c)/d+1/3/d*a^3*tan(d*x+c)*sec(d*x+c)^2+1/d*a^3/cos(d*x+c)^3+11/2/d*a^3/cos(d*x+c)+11/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+1/d*a^3/sin(d*x+c)/cos(d*x+c)^3+4/d*a^3/sin(d*x+c)/cos(d*x+c)-8*a^3*cot(d*x+c)/d+1/3/d*a^3/sin(d*x+c)^2/cos(d*x+c)^3-5/6/d*a^3/sin(d*x+c)^2/cos(d*x+c)","A"
818,1,214,118,0.695000," ","int(csc(d*x+c)^4*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3}}{3 d \cos \left(d x +c \right)^{3}}+\frac{17 a^{3}}{2 d \cos \left(d x +c \right)}+\frac{17 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}+\frac{20 a^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{40 a^{3} \cot \left(d x +c \right)}{3 d}+\frac{a^{3}}{d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{3}}-\frac{5 a^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{a^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{3}}-\frac{2 a^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}"," ",0,"1/3/d*a^3/cos(d*x+c)^3+17/2/d*a^3/cos(d*x+c)+17/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+1/d*a^3/sin(d*x+c)/cos(d*x+c)^3+20/3/d*a^3/sin(d*x+c)/cos(d*x+c)-40/3*a^3*cot(d*x+c)/d+1/d*a^3/sin(d*x+c)^2/cos(d*x+c)^3-5/2/d*a^3/sin(d*x+c)^2/cos(d*x+c)+1/3/d*a^3/sin(d*x+c)^3/cos(d*x+c)^3-2/3/d*a^3/sin(d*x+c)^3/cos(d*x+c)","A"
819,1,360,131,0.680000," ","int(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\sin^{9}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{2 \left(\sin^{9}\left(d x +c \right)\right)}{\cos \left(d x +c \right)}-2 \left(\sin^{7}\left(d x +c \right)+\frac{7 \left(\sin^{5}\left(d x +c \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(d x +c \right)\right)}{24}+\frac{35 \sin \left(d x +c \right)}{16}\right) \cos \left(d x +c \right)+\frac{35 d x}{8}+\frac{35 c}{8}\right)+4 a^{4} \left(\frac{\sin^{8}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{5 \left(\sin^{8}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{5 \left(\frac{16}{5}+\sin^{6}\left(d x +c \right)+\frac{6 \left(\sin^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\sin^{2}\left(d x +c \right)\right)}{5}\right) \cos \left(d x +c \right)}{3}\right)+6 a^{4} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+4 a^{4} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+a^{4} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)}{d}"," ",0,"1/d*(a^4*(1/3*sin(d*x+c)^9/cos(d*x+c)^3-2*sin(d*x+c)^9/cos(d*x+c)-2*(sin(d*x+c)^7+7/6*sin(d*x+c)^5+35/24*sin(d*x+c)^3+35/16*sin(d*x+c))*cos(d*x+c)+35/8*d*x+35/8*c)+4*a^4*(1/3*sin(d*x+c)^8/cos(d*x+c)^3-5/3*sin(d*x+c)^8/cos(d*x+c)-5/3*(16/5+sin(d*x+c)^6+6/5*sin(d*x+c)^4+8/5*sin(d*x+c)^2)*cos(d*x+c))+6*a^4*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+4*a^4*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+a^4*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c))","B"
820,1,268,93,0.573000," ","int(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x)","\frac{a^{4} \left(\frac{\sin^{7}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{4 \left(\sin^{7}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)}-\frac{4 \left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)}{3}+\frac{5 d x}{2}+\frac{5 c}{2}\right)+4 a^{4} \left(\frac{\sin^{6}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}-\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+6 a^{4} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+4 a^{4} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^4*(1/3*sin(d*x+c)^7/cos(d*x+c)^3-4/3*sin(d*x+c)^7/cos(d*x+c)-4/3*(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)+5/2*d*x+5/2*c)+4*a^4*(1/3*sin(d*x+c)^6/cos(d*x+c)^3-sin(d*x+c)^6/cos(d*x+c)-(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+6*a^4*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+4*a^4*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+1/3*a^4*sin(d*x+c)^3/cos(d*x+c)^3)","B"
821,1,210,111,0.436000," ","int(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c)),x)","-\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{23}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/6/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^2+7/8/a/d/(tan(1/2*d*x+1/2*c)-1)-2/a/d/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*arctan(tan(1/2*d*x+1/2*c))-2/5/a/d/(tan(1/2*d*x+1/2*c)+1)^5+1/a/d/(tan(1/2*d*x+1/2*c)+1)^4+1/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3-3/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2-23/8/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
822,1,166,97,0.429000," ","int(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c)),x)","-\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{11}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/6/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^2+5/8/a/d/(tan(1/2*d*x+1/2*c)-1)+2/a/d*arctan(tan(1/2*d*x+1/2*c))+2/5/a/d/(tan(1/2*d*x+1/2*c)+1)^5-1/a/d/(tan(1/2*d*x+1/2*c)+1)^4+1/a/d/(tan(1/2*d*x+1/2*c)+1)^2+11/8/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
823,1,130,63,0.412000," ","int(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"32/d/a*(-1/192/(tan(1/2*d*x+1/2*c)-1)^3-1/128/(tan(1/2*d*x+1/2*c)-1)^2+3/256/(tan(1/2*d*x+1/2*c)-1)-1/80/(tan(1/2*d*x+1/2*c)+1)^5+1/32/(tan(1/2*d*x+1/2*c)+1)^4-1/96/(tan(1/2*d*x+1/2*c)+1)^3-1/64/(tan(1/2*d*x+1/2*c)+1)^2-3/256/(tan(1/2*d*x+1/2*c)+1))","B"
824,1,115,49,0.408000," ","int(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{16}{128 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-128}+\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{2}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"16/d/a*(-1/96/(tan(1/2*d*x+1/2*c)-1)^3-1/64/(tan(1/2*d*x+1/2*c)-1)^2+1/128/(tan(1/2*d*x+1/2*c)-1)+1/40/(tan(1/2*d*x+1/2*c)+1)^5-1/16/(tan(1/2*d*x+1/2*c)+1)^4+1/24/(tan(1/2*d*x+1/2*c)+1)^3-1/128/(tan(1/2*d*x+1/2*c)+1))","B"
825,1,130,65,0.384000," ","int(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{64 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+64}}{d a}"," ",0,"8/d/a*(-1/48/(tan(1/2*d*x+1/2*c)-1)^3-1/32/(tan(1/2*d*x+1/2*c)-1)^2-1/64/(tan(1/2*d*x+1/2*c)-1)-1/20/(tan(1/2*d*x+1/2*c)+1)^5+1/8/(tan(1/2*d*x+1/2*c)+1)^4-1/8/(tan(1/2*d*x+1/2*c)+1)^3+1/16/(tan(1/2*d*x+1/2*c)+1)^2+1/64/(tan(1/2*d*x+1/2*c)+1))","A"
826,1,130,49,0.345000," ","int(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{-\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{2}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{4}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{d a}"," ",0,"4/d/a*(-1/24/(tan(1/2*d*x+1/2*c)-1)^3-1/16/(tan(1/2*d*x+1/2*c)-1)^2-3/32/(tan(1/2*d*x+1/2*c)-1)-1/4/(tan(1/2*d*x+1/2*c)+1)^4+1/10/(tan(1/2*d*x+1/2*c)+1)^5+1/3/(tan(1/2*d*x+1/2*c)+1)^3-1/4/(tan(1/2*d*x+1/2*c)+1)^2+3/32/(tan(1/2*d*x+1/2*c)+1))","B"
827,1,187,107,0.497000," ","int(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c)),x)","-\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{7}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{2}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{23}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/6/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^2-7/8/a/d/(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c))+2/5/a/d/(tan(1/2*d*x+1/2*c)+1)^5-1/a/d/(tan(1/2*d*x+1/2*c)+1)^4+2/a/d/(tan(1/2*d*x+1/2*c)+1)^3-2/a/d/(tan(1/2*d*x+1/2*c)+1)^2+23/8/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
828,1,223,120,0.500000," ","int(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{6 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{4 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{9}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2}{5 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{7}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{39}{8 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/6/a/d/(tan(1/2*d*x+1/2*c)-1)^3-1/4/a/d/(tan(1/2*d*x+1/2*c)-1)^2-9/8/a/d/(tan(1/2*d*x+1/2*c)-1)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c))-2/5/a/d/(tan(1/2*d*x+1/2*c)+1)^5+1/a/d/(tan(1/2*d*x+1/2*c)+1)^4-7/3/a/d/(tan(1/2*d*x+1/2*c)+1)^3+5/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2-39/8/a/d/(tan(1/2*d*x+1/2*c)+1)","A"
829,1,253,145,0.585000," ","int(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^2,x)","-\frac{1}{12 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{a^{2} d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{7 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{6}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{2}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{23}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{9}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/12/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))+4/7/d/a^2/(tan(1/2*d*x+1/2*c)+1)^7-2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^6+6/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+2/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-1/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-23/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-9/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
830,1,230,130,0.560000," ","int(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x)","-\frac{1}{12 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{7 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{8}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{11}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{13}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/12/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2+3/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))-4/7/d/a^2/(tan(1/2*d*x+1/2*c)+1)^7+2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^6-8/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-1/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+5/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+11/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+13/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
831,1,145,79,0.560000," ","int(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{64}{256 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-256}+\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{5}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{2} d}"," ",0,"64/d/a^2*(-1/768/(tan(1/2*d*x+1/2*c)-1)^3-1/512/(tan(1/2*d*x+1/2*c)-1)^2+1/256/(tan(1/2*d*x+1/2*c)-1)+1/112/(tan(1/2*d*x+1/2*c)+1)^7-1/32/(tan(1/2*d*x+1/2*c)+1)^6+1/32/(tan(1/2*d*x+1/2*c)+1)^5-5/768/(tan(1/2*d*x+1/2*c)+1)^3-3/512/(tan(1/2*d*x+1/2*c)+1)^2-1/256/(tan(1/2*d*x+1/2*c)+1))","A"
832,1,160,81,0.566000," ","int(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{32}{256 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-256}-\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{12}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{2} d}"," ",0,"32/d/a^2*(-1/384/(tan(1/2*d*x+1/2*c)-1)^3-1/256/(tan(1/2*d*x+1/2*c)-1)^2+1/256/(tan(1/2*d*x+1/2*c)-1)-1/56/(tan(1/2*d*x+1/2*c)+1)^7+1/16/(tan(1/2*d*x+1/2*c)+1)^6-3/40/(tan(1/2*d*x+1/2*c)+1)^5+1/32/(tan(1/2*d*x+1/2*c)+1)^4+1/384/(tan(1/2*d*x+1/2*c)+1)^3-1/256/(tan(1/2*d*x+1/2*c)+1)^2-1/256/(tan(1/2*d*x+1/2*c)+1))","A"
833,1,130,81,0.513000," ","int(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{14}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{7}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}}{a^{2} d}"," ",0,"16/d/a^2*(-1/192/(tan(1/2*d*x+1/2*c)-1)^3-1/128/(tan(1/2*d*x+1/2*c)-1)^2+1/28/(tan(1/2*d*x+1/2*c)+1)^7-1/8/(tan(1/2*d*x+1/2*c)+1)^6+7/40/(tan(1/2*d*x+1/2*c)+1)^5-1/8/(tan(1/2*d*x+1/2*c)+1)^4+7/192/(tan(1/2*d*x+1/2*c)+1)^3+1/128/(tan(1/2*d*x+1/2*c)+1)^2)","A"
834,1,160,81,0.495000," ","int(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{16}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{3}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{19}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{64 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+64}}{a^{2} d}"," ",0,"8/d/a^2*(-1/96/(tan(1/2*d*x+1/2*c)-1)^3-1/64/(tan(1/2*d*x+1/2*c)-1)^2-1/64/(tan(1/2*d*x+1/2*c)-1)-1/14/(tan(1/2*d*x+1/2*c)+1)^7+1/4/(tan(1/2*d*x+1/2*c)+1)^6-2/5/(tan(1/2*d*x+1/2*c)+1)^5+3/8/(tan(1/2*d*x+1/2*c)+1)^4-19/96/(tan(1/2*d*x+1/2*c)+1)^3+3/64/(tan(1/2*d*x+1/2*c)+1)^2+1/64/(tan(1/2*d*x+1/2*c)+1))","A"
835,1,160,85,0.464000," ","int(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{18}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{35}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{11}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{4}{16 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+16}}{a^{2} d}"," ",0,"4/d/a^2*(-1/48/(tan(1/2*d*x+1/2*c)-1)^3-1/32/(tan(1/2*d*x+1/2*c)-1)^2-1/16/(tan(1/2*d*x+1/2*c)-1)+1/7/(tan(1/2*d*x+1/2*c)+1)^7-1/2/(tan(1/2*d*x+1/2*c)+1)^6+9/10/(tan(1/2*d*x+1/2*c)+1)^5-1/(tan(1/2*d*x+1/2*c)+1)^4+35/48/(tan(1/2*d*x+1/2*c)+1)^3-11/32/(tan(1/2*d*x+1/2*c)+1)^2+1/16/(tan(1/2*d*x+1/2*c)+1))","A"
836,1,229,139,0.765000," ","int(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","-\frac{1}{12 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{4}{7 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{22}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{6}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{79}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{39}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{9}{2 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/12/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-1/2/a^2/d/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/7/d/a^2/(tan(1/2*d*x+1/2*c)+1)^7-2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^6+22/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-6/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+79/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-39/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+9/2/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
837,1,266,154,0.645000," ","int(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{12 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{4}{7 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{24}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{7}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{107}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{59}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{75}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/12/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-5/8/a^2/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^2*ln(tan(1/2*d*x+1/2*c))-4/7/d/a^2/(tan(1/2*d*x+1/2*c)+1)^7+2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^6-24/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5+7/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4-107/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3+59/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2-75/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
838,1,303,178,0.697000," ","int(csc(d*x+c)^3*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x)","-\frac{1}{12 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{8 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{1}{d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{11 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{4}{7 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{2}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{26}{5 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{8}{a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{139}{12 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{83}{8 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{67}{4 a^{2} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/12/d/a^2/(tan(1/2*d*x+1/2*c)-1)^3-1/8/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2-3/4/a^2/d/(tan(1/2*d*x+1/2*c)-1)+1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^2*tan(1/2*d*x+1/2*c)-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2+1/d/a^2/tan(1/2*d*x+1/2*c)+11/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+4/7/d/a^2/(tan(1/2*d*x+1/2*c)+1)^7-2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^6+26/5/a^2/d/(tan(1/2*d*x+1/2*c)+1)^5-8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^4+139/12/a^2/d/(tan(1/2*d*x+1/2*c)+1)^3-83/8/a^2/d/(tan(1/2*d*x+1/2*c)+1)^2+67/4/a^2/d/(tan(1/2*d*x+1/2*c)+1)","A"
839,1,272,162,0.569000," ","int(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^3,x)","-\frac{1}{24 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a^{3} d}+\frac{8}{9 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{40}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{4}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{21}{10 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{3}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{13}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{57}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/24/d/a^3/(tan(1/2*d*x+1/2*c)-1)^3-1/16/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2+7/32/a^3/d/(tan(1/2*d*x+1/2*c)-1)+2/a^3/d*arctan(tan(1/2*d*x+1/2*c))+8/9/d/a^3/(tan(1/2*d*x+1/2*c)+1)^9-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^8+40/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7-4/3/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6-21/10/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-3/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+3/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+13/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+57/32/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
840,1,190,111,0.571000," ","int(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{5}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{44}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{10}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"128/d/a^3*(-1/3072/(tan(1/2*d*x+1/2*c)-1)^3-1/2048/(tan(1/2*d*x+1/2*c)-1)^2+5/4096/(tan(1/2*d*x+1/2*c)-1)-1/144/(tan(1/2*d*x+1/2*c)+1)^9+1/32/(tan(1/2*d*x+1/2*c)+1)^8-11/224/(tan(1/2*d*x+1/2*c)+1)^7+5/192/(tan(1/2*d*x+1/2*c)+1)^6+1/256/(tan(1/2*d*x+1/2*c)+1)^5-1/512/(tan(1/2*d*x+1/2*c)+1)^4-1/384/(tan(1/2*d*x+1/2*c)+1)^3-1/512/(tan(1/2*d*x+1/2*c)+1)^2-5/4096/(tan(1/2*d*x+1/2*c)+1))","A"
841,1,190,97,0.559000," ","int(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{48}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{16}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{3}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{1}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{3}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"64/d/a^3*(-1/1536/(tan(1/2*d*x+1/2*c)-1)^3-1/1024/(tan(1/2*d*x+1/2*c)-1)^2+3/2048/(tan(1/2*d*x+1/2*c)-1)+1/72/(tan(1/2*d*x+1/2*c)+1)^9-1/16/(tan(1/2*d*x+1/2*c)+1)^8+3/28/(tan(1/2*d*x+1/2*c)+1)^7-1/12/(tan(1/2*d*x+1/2*c)+1)^6+3/128/(tan(1/2*d*x+1/2*c)+1)^5+1/256/(tan(1/2*d*x+1/2*c)+1)^4-1/768/(tan(1/2*d*x+1/2*c)+1)^3-1/512/(tan(1/2*d*x+1/2*c)+1)^2-3/2048/(tan(1/2*d*x+1/2*c)+1))","A"
842,1,175,113,0.547000," ","int(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{32}{1024 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1024}-\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{52}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{22}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{39}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{3}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{1}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"32/d/a^3*(-1/768/(tan(1/2*d*x+1/2*c)-1)^3-1/512/(tan(1/2*d*x+1/2*c)-1)^2+1/1024/(tan(1/2*d*x+1/2*c)-1)-1/36/(tan(1/2*d*x+1/2*c)+1)^9+1/8/(tan(1/2*d*x+1/2*c)+1)^8-13/56/(tan(1/2*d*x+1/2*c)+1)^7+11/48/(tan(1/2*d*x+1/2*c)+1)^6-39/320/(tan(1/2*d*x+1/2*c)+1)^5+3/128/(tan(1/2*d*x+1/2*c)+1)^4+1/192/(tan(1/2*d*x+1/2*c)+1)^3-1/1024/(tan(1/2*d*x+1/2*c)+1))","A"
843,1,190,97,0.559000," ","int(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{8}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{28}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{67}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{11}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{5}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{512 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+512}}{a^{3} d}"," ",0,"16/d/a^3*(-1/384/(tan(1/2*d*x+1/2*c)-1)^3-1/256/(tan(1/2*d*x+1/2*c)-1)^2-1/512/(tan(1/2*d*x+1/2*c)-1)+1/18/(tan(1/2*d*x+1/2*c)+1)^9-1/4/(tan(1/2*d*x+1/2*c)+1)^8+1/2/(tan(1/2*d*x+1/2*c)+1)^7-7/12/(tan(1/2*d*x+1/2*c)+1)^6+67/160/(tan(1/2*d*x+1/2*c)+1)^5-11/64/(tan(1/2*d*x+1/2*c)+1)^4+5/192/(tan(1/2*d*x+1/2*c)+1)^3+1/128/(tan(1/2*d*x+1/2*c)+1)^2+1/512/(tan(1/2*d*x+1/2*c)+1))","A"
844,1,190,113,0.543000," ","int(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{60}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{34}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{99}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{23}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{2}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"8/d/a^3*(-1/192/(tan(1/2*d*x+1/2*c)-1)^3-1/128/(tan(1/2*d*x+1/2*c)-1)^2-3/256/(tan(1/2*d*x+1/2*c)-1)-1/9/(tan(1/2*d*x+1/2*c)+1)^9+1/2/(tan(1/2*d*x+1/2*c)+1)^8-15/14/(tan(1/2*d*x+1/2*c)+1)^7+17/12/(tan(1/2*d*x+1/2*c)+1)^6-99/80/(tan(1/2*d*x+1/2*c)+1)^5+23/32/(tan(1/2*d*x+1/2*c)+1)^4-1/4/(tan(1/2*d*x+1/2*c)+1)^3+1/32/(tan(1/2*d*x+1/2*c)+1)^2+3/256/(tan(1/2*d*x+1/2*c)+1))","A"
845,1,190,113,0.595000," ","int(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x)","\frac{-\frac{1}{24 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{5}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{8}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{64}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{40}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{27}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{39}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{59}{12 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{13}{8 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{5}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}}{a^{3} d}"," ",0,"4/d/a^3*(-1/96/(tan(1/2*d*x+1/2*c)-1)^3-1/64/(tan(1/2*d*x+1/2*c)-1)^2-5/128/(tan(1/2*d*x+1/2*c)-1)+2/9/(tan(1/2*d*x+1/2*c)+1)^9-1/(tan(1/2*d*x+1/2*c)+1)^8+16/7/(tan(1/2*d*x+1/2*c)+1)^7-10/3/(tan(1/2*d*x+1/2*c)+1)^6+27/8/(tan(1/2*d*x+1/2*c)+1)^5-39/16/(tan(1/2*d*x+1/2*c)+1)^4+59/48/(tan(1/2*d*x+1/2*c)+1)^3-13/32/(tan(1/2*d*x+1/2*c)+1)^2+5/128/(tan(1/2*d*x+1/2*c)+1))","A"
846,1,271,171,0.789000," ","int(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","-\frac{1}{24 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{9}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{8}{9 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{72}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{52}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{219}{10 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{83}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{193}{12 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{75}{8 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{201}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/24/d/a^3/(tan(1/2*d*x+1/2*c)-1)^3-1/16/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2-9/32/a^3/d/(tan(1/2*d*x+1/2*c)-1)+1/d/a^3*ln(tan(1/2*d*x+1/2*c))+8/9/d/a^3/(tan(1/2*d*x+1/2*c)+1)^9-4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^8+72/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7-52/3/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6+219/10/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5-83/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4+193/12/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3-75/8/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2+201/32/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
847,1,308,186,0.804000," ","int(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{24 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{16 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{11}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{8}{9 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{4}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{76}{7 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{58}{3 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{267}{10 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{111}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{25}{a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{67}{4 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{501}{32 a^{3} d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/24/d/a^3/(tan(1/2*d*x+1/2*c)-1)^3-1/16/d/a^3/(tan(1/2*d*x+1/2*c)-1)^2-11/32/a^3/d/(tan(1/2*d*x+1/2*c)-1)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^3*ln(tan(1/2*d*x+1/2*c))-8/9/d/a^3/(tan(1/2*d*x+1/2*c)+1)^9+4/d/a^3/(tan(1/2*d*x+1/2*c)+1)^8-76/7/a^3/d/(tan(1/2*d*x+1/2*c)+1)^7+58/3/a^3/d/(tan(1/2*d*x+1/2*c)+1)^6-267/10/a^3/d/(tan(1/2*d*x+1/2*c)+1)^5+111/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^4-25/a^3/d/(tan(1/2*d*x+1/2*c)+1)^3+67/4/a^3/d/(tan(1/2*d*x+1/2*c)+1)^2-501/32/a^3/d/(tan(1/2*d*x+1/2*c)+1)","A"
848,1,190,129,0.721000," ","int(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{16}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}+\frac{8}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}-\frac{176}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{28}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{179}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{89}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{49}{10 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{1}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{7}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}}{a^{4} d}"," ",0,"32/d/a^4*(-1/1536/(tan(1/2*d*x+1/2*c)-1)^3-1/1024/(tan(1/2*d*x+1/2*c)-1)^2-1/22/(tan(1/2*d*x+1/2*c)+1)^11+1/4/(tan(1/2*d*x+1/2*c)+1)^10-11/18/(tan(1/2*d*x+1/2*c)+1)^9+7/8/(tan(1/2*d*x+1/2*c)+1)^8-179/224/(tan(1/2*d*x+1/2*c)+1)^7+89/192/(tan(1/2*d*x+1/2*c)+1)^6-49/320/(tan(1/2*d*x+1/2*c)+1)^5+1/64/(tan(1/2*d*x+1/2*c)+1)^4+7/1536/(tan(1/2*d*x+1/2*c)+1)^3+1/1024/(tan(1/2*d*x+1/2*c)+1)^2)","A"
849,1,220,129,0.729000," ","int(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{16}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}-\frac{8}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}+\frac{184}{9 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}-\frac{32}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}+\frac{235}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}-\frac{145}{6 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}+\frac{58}{5 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}-\frac{13}{4 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}+\frac{13}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{512 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+512}}{a^{4} d}"," ",0,"16/d/a^4*(-1/768/(tan(1/2*d*x+1/2*c)-1)^3-1/512/(tan(1/2*d*x+1/2*c)-1)^2-1/512/(tan(1/2*d*x+1/2*c)-1)+1/11/(tan(1/2*d*x+1/2*c)+1)^11-1/2/(tan(1/2*d*x+1/2*c)+1)^10+23/18/(tan(1/2*d*x+1/2*c)+1)^9-2/(tan(1/2*d*x+1/2*c)+1)^8+235/112/(tan(1/2*d*x+1/2*c)+1)^7-145/96/(tan(1/2*d*x+1/2*c)+1)^6+29/40/(tan(1/2*d*x+1/2*c)+1)^5-13/64/(tan(1/2*d*x+1/2*c)+1)^4+13/768/(tan(1/2*d*x+1/2*c)+1)^3+3/512/(tan(1/2*d*x+1/2*c)+1)^2+1/512/(tan(1/2*d*x+1/2*c)+1))","A"
850,1,218,129,0.726000," ","int(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x)","\frac{-\frac{1}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{1}{16 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{16}{11 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{11}}+\frac{8}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{10}}-\frac{64}{3 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{9}}+\frac{36}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{8}}-\frac{295}{7 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{7}}+\frac{71}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{6}}-\frac{43}{2 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{5}}+\frac{9}{\left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{4}}-\frac{109}{48 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{5}{32 \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{8}{128 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+128}}{a^{4} d}"," ",0,"8/d/a^4*(-1/384/(tan(1/2*d*x+1/2*c)-1)^3-1/256/(tan(1/2*d*x+1/2*c)-1)^2-1/128/(tan(1/2*d*x+1/2*c)-1)-2/11/(tan(1/2*d*x+1/2*c)+1)^11+1/(tan(1/2*d*x+1/2*c)+1)^10-8/3/(tan(1/2*d*x+1/2*c)+1)^9+9/2/(tan(1/2*d*x+1/2*c)+1)^8-295/56/(tan(1/2*d*x+1/2*c)+1)^7+71/16/(tan(1/2*d*x+1/2*c)+1)^6-43/16/(tan(1/2*d*x+1/2*c)+1)^5+9/8/(tan(1/2*d*x+1/2*c)+1)^4-109/384/(tan(1/2*d*x+1/2*c)+1)^3+5/256/(tan(1/2*d*x+1/2*c)+1)^2+1/128/(tan(1/2*d*x+1/2*c)+1))","A"
851,1,205,121,0.280000," ","int(sec(d*x+c)^5*sin(d*x+c)^6*(a+a*sin(d*x+c)),x)","\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a \sin \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*a*sin(d*x+c)^8/cos(d*x+c)^2-1/2*a*sin(d*x+c)^6/d-3/4*a*sin(d*x+c)^4/d-3/2*a*sin(d*x+c)^2/d-3*a*ln(cos(d*x+c))/d+1/4/d*a*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a*sin(d*x+c)^5/d-5/8*a*sin(d*x+c)^3/d-15/8*a*sin(d*x+c)/d+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
852,1,147,107,0.270000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a \sin \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a*sin(d*x+c)^5/d-5/8*a*sin(d*x+c)^3/d-15/8*a*sin(d*x+c)/d+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d","A"
853,1,133,95,0.247000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x)","\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a \sin \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d+1/4/d*a*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a*sin(d*x+c)^3/d-3/8*a*sin(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
854,1,114,76,0.240000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x)","\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a \sin \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a*sin(d*x+c)^3/d-3/8*a*sin(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a*sin(d*x+c)^4/cos(d*x+c)^4","A"
855,1,100,76,0.235000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x)","\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a \sin \left(d x +c \right)}{8 d}-\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*a*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a*sin(d*x+c)/d-1/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
856,1,92,55,0.179000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a \sin \left(d x +c \right)}{8 d}-\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a*sin(d*x+c)/d-1/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a/cos(d*x+c)^4","A"
857,1,100,107,0.396000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a}{4 d \cos \left(d x +c \right)^{4}}+\frac{a}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4*a*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a/cos(d*x+c)^4+1/2/d*a/cos(d*x+c)^2+a*ln(tan(d*x+c))/d","A"
858,1,120,119,0.349000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a}{4 d \cos \left(d x +c \right)^{4}}+\frac{a}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a}{8 d \sin \left(d x +c \right)}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/cos(d*x+c)^4+1/2/d*a/cos(d*x+c)^2+a*ln(tan(d*x+c))/d+1/4/d*a/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a/sin(d*x+c)/cos(d*x+c)^2-15/8*a/d/sin(d*x+c)+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
859,1,151,133,0.370000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a}{8 d \sin \left(d x +c \right)}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a/sin(d*x+c)/cos(d*x+c)^2-15/8*a/d/sin(d*x+c)+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a/sin(d*x+c)^2+3*a*ln(tan(d*x+c))/d","A"
860,1,173,148,0.398000," ","int(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c)),x)","\frac{a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a}{4 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{4}}-\frac{7 a}{12 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{35 a}{24 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{35 a}{8 d \sin \left(d x +c \right)}+\frac{35 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a/sin(d*x+c)^2+3*a*ln(tan(d*x+c))/d+1/4/d*a/sin(d*x+c)^3/cos(d*x+c)^4-7/12/d*a/sin(d*x+c)^3/cos(d*x+c)^2+35/24/d*a/sin(d*x+c)/cos(d*x+c)^2-35/8*a/d/sin(d*x+c)+35/8/d*a*ln(sec(d*x+c)+tan(d*x+c))","A"
861,1,261,109,0.296000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d}-\frac{5 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{15 a^{2} \sin \left(d x +c \right)}{4 d}+\frac{15 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*a^2*sin(d*x+c)^8/cos(d*x+c)^2-1/2*a^2*sin(d*x+c)^6/d-3/4*a^2*sin(d*x+c)^4/d-3/2*a^2*sin(d*x+c)^2/d-4/d*a^2*ln(cos(d*x+c))+1/2/d*a^2*sin(d*x+c)^7/cos(d*x+c)^4-3/4/d*a^2*sin(d*x+c)^7/cos(d*x+c)^2-3/4*a^2*sin(d*x+c)^5/d-5/4*a^2*sin(d*x+c)^3/d-15/4*a^2*sin(d*x+c)/d+15/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2*tan(d*x+c)^4-1/2/d*a^2*tan(d*x+c)^2","B"
862,1,213,93,0.289000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{3 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{9 a^{2} \sin \left(d x +c \right)}{4 d}+\frac{9 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^2*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a^2*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a^2*sin(d*x+c)^5/d-3/4*a^2*sin(d*x+c)^3/d-9/4*a^2*sin(d*x+c)/d+9/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2*tan(d*x+c)^4-1/d*a^2*tan(d*x+c)^2-2/d*a^2*ln(cos(d*x+c))+1/4/d*a^2*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2","B"
863,1,173,79,0.288000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} \sin \left(d x +c \right)}{4 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2*tan(d*x+c)^4-1/2/d*a^2*tan(d*x+c)^2-1/d*a^2*ln(cos(d*x+c))+1/2/d*a^2*sin(d*x+c)^5/cos(d*x+c)^4-1/4/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2-1/4*a^2*sin(d*x+c)^3/d-3/4*a^2*sin(d*x+c)/d+3/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2*sin(d*x+c)^4/cos(d*x+c)^4","B"
864,1,174,58,0.271000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{a^{2} \sin \left(d x +c \right)}{4 d}+\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^2*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a^2*sin(d*x+c)^3/d-1/4*a^2*sin(d*x+c)/d+1/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2","B"
865,1,126,58,0.263000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{4 d}-\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2*sin(d*x+c)^4/cos(d*x+c)^4+1/2/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/4*a^2*sin(d*x+c)/d-1/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2/cos(d*x+c)^4","B"
866,1,112,93,0.662000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2}}{2 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{4 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a^2/cos(d*x+c)^4+1/2/d*a^2*tan(d*x+c)*sec(d*x+c)^3+3/4/d*a^2*tan(d*x+c)*sec(d*x+c)+3/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2/cos(d*x+c)^2+1/d*a^2*ln(tan(d*x+c))","A"
867,1,176,108,0.616000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{9 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{2 d \cos \left(d x +c \right)^{4}}+\frac{a^{2}}{d \cos \left(d x +c \right)^{2}}+\frac{2 a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a^{2}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a^{2}}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a^{2}}{8 d \sin \left(d x +c \right)}"," ",0,"1/4/d*a^2*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^2*tan(d*x+c)*sec(d*x+c)+9/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2/cos(d*x+c)^4+1/d*a^2/cos(d*x+c)^2+2/d*a^2*ln(tan(d*x+c))+1/4/d*a^2/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a^2/sin(d*x+c)/cos(d*x+c)^2-15/8/d*a^2/sin(d*x+c)","A"
868,1,199,124,0.566000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{4 a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a^{2}}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a^{2}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a^{2}}{4 d \sin \left(d x +c \right)}+\frac{15 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{2}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a^{2}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^2/cos(d*x+c)^4+1/2/d*a^2/cos(d*x+c)^2+4/d*a^2*ln(tan(d*x+c))+1/2/d*a^2/sin(d*x+c)/cos(d*x+c)^4+5/4/d*a^2/sin(d*x+c)/cos(d*x+c)^2-15/4/d*a^2/sin(d*x+c)+15/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a^2/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a^2/sin(d*x+c)^2","A"
869,1,215,140,0.559000," ","int(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{25 a^{2}}{12 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{25 a^{2}}{4 d \sin \left(d x +c \right)}+\frac{25 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a^{2}}{d \sin \left(d x +c \right)^{2}}+\frac{6 a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a^{2}}{4 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{4}}-\frac{7 a^{2}}{12 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^2/sin(d*x+c)/cos(d*x+c)^4+25/12/d*a^2/sin(d*x+c)/cos(d*x+c)^2-25/4/d*a^2/sin(d*x+c)+25/4/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2/sin(d*x+c)^2/cos(d*x+c)^4+3/2/d*a^2/sin(d*x+c)^2/cos(d*x+c)^2-3/d*a^2/sin(d*x+c)^2+6/d*a^2*ln(tan(d*x+c))+1/4/d*a^2/sin(d*x+c)^3/cos(d*x+c)^4-7/12/d*a^2/sin(d*x+c)^3/cos(d*x+c)^2","A"
870,1,325,108,0.309000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 a^{3} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{2 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{d}-\frac{10 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{10 a^{3} \sin \left(d x +c \right)}{d}+\frac{10 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{9 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{9 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{10 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{9 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}"," ",0,"1/4/d*a^3*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*a^3*sin(d*x+c)^9/cos(d*x+c)^2-5/8*a^3*sin(d*x+c)^7/d-2*a^3*sin(d*x+c)^5/d-10/3*a^3*sin(d*x+c)^3/d-10*a^3*sin(d*x+c)/d+10/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^3*sin(d*x+c)^8/cos(d*x+c)^4-3/2/d*a^3*sin(d*x+c)^8/cos(d*x+c)^2-3/2*a^3*sin(d*x+c)^6/d-9/4*a^3*sin(d*x+c)^4/d-9/2*a^3*sin(d*x+c)^2/d-10/d*a^3*ln(cos(d*x+c))+3/4/d*a^3*sin(d*x+c)^7/cos(d*x+c)^4-9/8/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2+1/4/d*a^3*tan(d*x+c)^4-1/2/d*a^3*tan(d*x+c)^2","B"
871,1,309,92,0.298000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{3} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{6 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{9 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{9 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{2 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{6 a^{3} \sin \left(d x +c \right)}{d}+\frac{6 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^3*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*a^3*sin(d*x+c)^8/cos(d*x+c)^2-1/2*a^3*sin(d*x+c)^6/d-3/4*a^3*sin(d*x+c)^4/d-3/2*a^3*sin(d*x+c)^2/d-6/d*a^3*ln(cos(d*x+c))+3/4/d*a^3*sin(d*x+c)^7/cos(d*x+c)^4-9/8/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2-9/8*a^3*sin(d*x+c)^5/d-2*a^3*sin(d*x+c)^3/d-6*a^3*sin(d*x+c)/d+6/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^3*tan(d*x+c)^4-3/2/d*a^3*tan(d*x+c)^2+1/4/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2","B"
872,1,237,76,0.316000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{d}-\frac{3 a^{3} \sin \left(d x +c \right)}{d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^3*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a^3*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a^3*sin(d*x+c)^5/d-a^3*sin(d*x+c)^3/d-3*a^3*sin(d*x+c)/d+3/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^3*tan(d*x+c)^4-3/2/d*a^3*tan(d*x+c)^2-3/d*a^3*ln(cos(d*x+c))+3/4/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-3/8/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2+1/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4","B"
873,1,220,62,0.288000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{a^{3} \sin \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^3*tan(d*x+c)^4-1/2/d*a^3*tan(d*x+c)^2-1/d*a^3*ln(cos(d*x+c))+3/4/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-3/8/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2-3/8*a^3*sin(d*x+c)^3/d-a^3*sin(d*x+c)/d+1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2","B"
874,1,154,29,0.273000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a^3*sin(d*x+c)^3/d+3/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+3/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/4/d*a^3/cos(d*x+c)^4","B"
875,1,172,75,0.609000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \sin \left(d x +c \right)}{8 d}+\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{3}}{d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{a^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a^3*sin(d*x+c)/d+1/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3/cos(d*x+c)^4+3/4/d*a^3*tan(d*x+c)*sec(d*x+c)^3+9/8/d*a^3*tan(d*x+c)*sec(d*x+c)+1/2/d*a^3/cos(d*x+c)^2+1/d*a^3*ln(tan(d*x+c))","B"
876,1,176,91,0.623000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3}}{d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a^{3}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a^{3}}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a^{3}}{8 d \sin \left(d x +c \right)}"," ",0,"1/d*a^3/cos(d*x+c)^4+3/4/d*a^3*tan(d*x+c)*sec(d*x+c)^3+9/8/d*a^3*tan(d*x+c)*sec(d*x+c)+3/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a^3/cos(d*x+c)^2+3/d*a^3*ln(tan(d*x+c))+1/4/d*a^3/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a^3/sin(d*x+c)/cos(d*x+c)^2-15/8/d*a^3/sin(d*x+c)","A"
877,1,241,107,0.689000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x)","\frac{a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{6 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3}}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{6 a^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{15 a^{3}}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{45 a^{3}}{8 d \sin \left(d x +c \right)}+\frac{a^{3}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{3}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a^{3}}{2 d \sin \left(d x +c \right)^{2}}"," ",0,"1/4/d*a^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^3*tan(d*x+c)*sec(d*x+c)+6/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^3/cos(d*x+c)^4+3/2/d*a^3/cos(d*x+c)^2+6/d*a^3*ln(tan(d*x+c))+3/4/d*a^3/sin(d*x+c)/cos(d*x+c)^4+15/8/d*a^3/sin(d*x+c)/cos(d*x+c)^2-45/8/d*a^3/sin(d*x+c)+1/4/d*a^3/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a^3/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a^3/sin(d*x+c)^2","B"
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880,1,175,183,0.460000," ","int(sec(d*x+c)^7*sin(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{\sin \left(d x +c \right)}{a d}-\frac{1}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{13}{128 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{69}{128 a d \left(\sin \left(d x +c \right)-1\right)}+\frac{187 \ln \left(\sin \left(d x +c \right)-1\right)}{256 a d}+\frac{1}{64 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{7}{48 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{41}{64 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{2}{a d \left(1+\sin \left(d x +c \right)\right)}-\frac{443 \ln \left(1+\sin \left(d x +c \right)\right)}{256 a d}"," ",0,"sin(d*x+c)/a/d-1/96/a/d/(sin(d*x+c)-1)^3-13/128/a/d/(sin(d*x+c)-1)^2-69/128/a/d/(sin(d*x+c)-1)+187/256/a/d*ln(sin(d*x+c)-1)+1/64/a/d/(1+sin(d*x+c))^4-7/48/a/d/(1+sin(d*x+c))^3+41/64/a/d/(1+sin(d*x+c))^2-2/a/d/(1+sin(d*x+c))-443/256*ln(1+sin(d*x+c))/a/d","A"
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902,1,180,176,0.395000," ","int(sec(d*x+c)^9*sin(d*x+c)^5/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}+\frac{1}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{1}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3}{256 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}+\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{5}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{5}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{5}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4+1/96/a/d/(sin(d*x+c)-1)^3+1/512/a/d/(sin(d*x+c)-1)^2-3/256/a/d/(sin(d*x+c)-1)-3/512/a/d*ln(sin(d*x+c)-1)+1/160/a/d/(1+sin(d*x+c))^5-5/256/a/d/(1+sin(d*x+c))^4+5/384/a/d/(1+sin(d*x+c))^3+5/512/a/d/(1+sin(d*x+c))^2+3/512*ln(1+sin(d*x+c))/a/d","A"
903,1,180,174,0.395000," ","int(sec(d*x+c)^9*sin(d*x+c)^4/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}+\frac{1}{192 a d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{3}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}-\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{3}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{1}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3}{256 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4+1/192/a/d/(sin(d*x+c)-1)^3-3/512/a/d/(sin(d*x+c)-1)^2-3/512/a/d*ln(sin(d*x+c)-1)-1/160/a/d/(1+sin(d*x+c))^5+3/256/a/d/(1+sin(d*x+c))^4+1/384/a/d/(1+sin(d*x+c))^3-3/512/a/d/(1+sin(d*x+c))^2-3/256/a/d/(1+sin(d*x+c))+3/512*ln(1+sin(d*x+c))/a/d","A"
904,1,162,158,0.382000," ","int(sec(d*x+c)^9*sin(d*x+c)^3/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{3}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3}{256 a d \left(\sin \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}+\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{1}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{1}{128 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-3/512/a/d/(sin(d*x+c)-1)^2+3/256/a/d/(sin(d*x+c)-1)+3/512/a/d*ln(sin(d*x+c)-1)+1/160/a/d/(1+sin(d*x+c))^5-1/256/a/d/(1+sin(d*x+c))^4-1/128/a/d/(1+sin(d*x+c))^3-3/512/a/d/(1+sin(d*x+c))^2-3/512*ln(1+sin(d*x+c))/a/d","A"
905,1,198,156,0.352000," ","int(sec(d*x+c)^9*sin(d*x+c)^2/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{1}{192 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{1}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{1}{128 a d \left(\sin \left(d x +c \right)-1\right)}+\frac{7 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}-\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{1}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{1}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{5}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5}{256 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{7 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-1/192/a/d/(sin(d*x+c)-1)^3+1/512/a/d/(sin(d*x+c)-1)^2+1/128/a/d/(sin(d*x+c)-1)+7/512/a/d*ln(sin(d*x+c)-1)-1/160/a/d/(1+sin(d*x+c))^5-1/256/a/d/(1+sin(d*x+c))^4+1/384/a/d/(1+sin(d*x+c))^3+5/512/a/d/(1+sin(d*x+c))^2+5/256/a/d/(1+sin(d*x+c))-7/512*ln(1+sin(d*x+c))/a/d","A"
906,1,180,140,0.319000," ","int(sec(d*x+c)^9*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{1}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{9}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{7}{256 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{7 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}+\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{3}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{5}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{5}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{7 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-1/96/a/d/(sin(d*x+c)-1)^3+9/512/a/d/(sin(d*x+c)-1)^2-7/256/a/d/(sin(d*x+c)-1)-7/512/a/d*ln(sin(d*x+c)-1)+1/160/a/d/(1+sin(d*x+c))^5+3/256/a/d/(1+sin(d*x+c))^4+5/384/a/d/(1+sin(d*x+c))^3+5/512/a/d/(1+sin(d*x+c))^2+7/512*ln(1+sin(d*x+c))/a/d","A"
907,1,198,190,0.406000," ","int(sec(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{1}{64 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{21}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{7}{64 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{63 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}-\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{5}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{5}{128 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{35}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{35}{256 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{63 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-1/64/a/d/(sin(d*x+c)-1)^3+21/512/a/d/(sin(d*x+c)-1)^2-7/64/a/d/(sin(d*x+c)-1)-63/512/a/d*ln(sin(d*x+c)-1)-1/160/a/d/(1+sin(d*x+c))^5-5/256/a/d/(1+sin(d*x+c))^4-5/128/a/d/(1+sin(d*x+c))^3-35/512/a/d/(1+sin(d*x+c))^2-35/256/a/d/(1+sin(d*x+c))+63/512*ln(1+sin(d*x+c))/a/d","A"
908,1,212,225,0.457000," ","int(csc(d*x+c)*sec(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{1}{48 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{37}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{65}{256 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{193 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{7}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{29}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{93}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{1}{2 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{319 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-1/48/a/d/(sin(d*x+c)-1)^3+37/512/a/d/(sin(d*x+c)-1)^2-65/256/a/d/(sin(d*x+c)-1)-193/512/a/d*ln(sin(d*x+c)-1)+ln(sin(d*x+c))/a/d+1/160/a/d/(1+sin(d*x+c))^5+7/256/a/d/(1+sin(d*x+c))^4+29/384/a/d/(1+sin(d*x+c))^3+93/512/a/d/(1+sin(d*x+c))^2+1/2/a/d/(1+sin(d*x+c))-319/512*ln(1+sin(d*x+c))/a/d","A"
909,1,229,240,0.466000," ","int(csc(d*x+c)^2*sec(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{5}{192 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{57}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{61}{128 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{437 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{9}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{47}{384 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{187}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{315}{256 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{949 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-5/192/a/d/(sin(d*x+c)-1)^3+57/512/a/d/(sin(d*x+c)-1)^2-61/128/a/d/(sin(d*x+c)-1)-437/512/a/d*ln(sin(d*x+c)-1)-1/d/a/sin(d*x+c)-ln(sin(d*x+c))/a/d-1/160/a/d/(1+sin(d*x+c))^5-9/256/a/d/(1+sin(d*x+c))^4-47/384/a/d/(1+sin(d*x+c))^3-187/512/a/d/(1+sin(d*x+c))^2-315/256/a/d/(1+sin(d*x+c))+949/512*ln(1+sin(d*x+c))/a/d","A"
910,1,244,255,0.516000," ","int(csc(d*x+c)^3*sec(d*x+c)^9/(a+a*sin(d*x+c)),x)","\frac{1}{256 a d \left(\sin \left(d x +c \right)-1\right)^{4}}-\frac{1}{32 a d \left(\sin \left(d x +c \right)-1\right)^{3}}+\frac{81}{512 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{203}{256 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{843 \ln \left(\sin \left(d x +c \right)-1\right)}{512 a d}-\frac{1}{2 a d \sin \left(d x +c \right)^{2}}+\frac{1}{d a \sin \left(d x +c \right)}+\frac{6 \ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{160 a d \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{11}{256 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{23}{128 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{325}{512 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5}{2 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{2229 \ln \left(1+\sin \left(d x +c \right)\right)}{512 a d}"," ",0,"1/256/a/d/(sin(d*x+c)-1)^4-1/32/a/d/(sin(d*x+c)-1)^3+81/512/a/d/(sin(d*x+c)-1)^2-203/256/a/d/(sin(d*x+c)-1)-843/512/a/d*ln(sin(d*x+c)-1)-1/2/a/d/sin(d*x+c)^2+1/d/a/sin(d*x+c)+6*ln(sin(d*x+c))/a/d+1/160/a/d/(1+sin(d*x+c))^5+11/256/a/d/(1+sin(d*x+c))^4+23/128/a/d/(1+sin(d*x+c))^3+325/512/a/d/(1+sin(d*x+c))^2+5/2/a/d/(1+sin(d*x+c))-2229/512*ln(1+sin(d*x+c))/a/d","A"
911,0,0,119,19.459000," ","int((g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x)","\int \left(g \sec \left(f x +e \right)\right)^{p} \left(d \sin \left(f x +e \right)\right)^{n} \left(a +a \sin \left(f x +e \right)\right)^{m}\, dx"," ",0,"int((g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x)","F"
912,0,0,90,0.615000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
913,0,0,175,4.380000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{4} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x)","F"
914,0,0,139,4.436000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{3} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","F"
915,0,0,101,3.248000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
916,0,0,61,1.163000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
917,0,0,62,2.424000," ","int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\cos \left(f x +e \right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
918,0,0,62,3.895000," ","int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\cos \left(f x +e \right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
919,0,0,65,3.974000," ","int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","\int \frac{\cos \left(f x +e \right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","F"
920,0,0,170,19.374000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{4}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x)","F"
921,0,0,133,8.888000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{3}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x)","F"
922,0,0,96,6.351000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{2}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x)","F"
923,0,0,59,4.617000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x)","F"
924,0,0,61,2.113000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","\int \frac{\cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{c +d \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x)","F"
925,0,0,61,4.577000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","\int \frac{\cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x)","F"
926,0,0,61,4.353000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","\int \frac{\cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m}}{\left(c +d \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x)","F"
927,0,0,56,5.194000," ","int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x)","F"
928,0,0,134,6.763000," ","int(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\sin^{4}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x)","F"
929,0,0,108,3.231000," ","int(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\sin^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","F"
930,0,0,80,4.776000," ","int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\sin^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","F"
931,0,0,54,1.785000," ","int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \sin \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x)","F"
932,0,0,45,1.882000," ","int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \csc \left(d x +c \right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x)","F"
933,0,0,44,1.145000," ","int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\csc^{2}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x)","F"
934,0,0,45,1.197000," ","int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","\int \cos \left(d x +c \right) \left(\csc^{3}\left(d x +c \right)\right) \left(a +a \sin \left(d x +c \right)\right)^{m}\, dx"," ",0,"int(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^m,x)","F"
935,1,96,71,0.358000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\frac{d a \left(-\frac{\sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right)}{4}+\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{8}+\frac{f x}{8}+\frac{e}{8}\right)-\frac{\left(\cos^{3}\left(f x +e \right)\right) a c}{3}-\frac{d a \left(\cos^{3}\left(f x +e \right)\right)}{3}+c a \left(\frac{\sin \left(f x +e \right) \cos \left(f x +e \right)}{2}+\frac{f x}{2}+\frac{e}{2}\right)}{f}"," ",0,"1/f*(d*a*(-1/4*sin(f*x+e)*cos(f*x+e)^3+1/8*sin(f*x+e)*cos(f*x+e)+1/8*f*x+1/8*e)-1/3*cos(f*x+e)^3*a*c-1/3*d*a*cos(f*x+e)^3+c*a*(1/2*sin(f*x+e)*cos(f*x+e)+1/2*f*x+1/2*e))","A"
936,1,160,100,1.861000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x)","-\frac{2 \left(1+\sin \left(f x +e \right)\right) \sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, \sqrt{2}}{2 \sqrt{a}}\right) \sqrt{a \left(c +d \right) d}-\arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sqrt{a}\, c -\arctanh \left(\frac{\sqrt{-a \left(\sin \left(f x +e \right)-1\right)}\, d}{\sqrt{a \left(c +d \right) d}}\right) \sqrt{a}\, d \right)}{a^{\frac{3}{2}} \left(c -d \right) \sqrt{a \left(c +d \right) d}\, \cos \left(f x +e \right) \sqrt{a +a \sin \left(f x +e \right)}\, f}"," ",0,"-2/a^(3/2)*(1+sin(f*x+e))*(-a*(sin(f*x+e)-1))^(1/2)*(2^(1/2)*arctanh(1/2*(-a*(sin(f*x+e)-1))^(1/2)*2^(1/2)/a^(1/2))*(a*(c+d)*d)^(1/2)-arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(1/2)*c-arctanh((-a*(sin(f*x+e)-1))^(1/2)*d/(a*(c+d)*d)^(1/2))*a^(1/2)*d)/(c-d)/(a*(c+d)*d)^(1/2)/cos(f*x+e)/(a+a*sin(f*x+e))^(1/2)/f","A"
937,1,4463,114,0.604000," ","int(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"1/2/f*(2*(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2+(d^2/c^2)^(1/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*cos(f*x+e)-(d^2/c^2)^(1/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*sin(f*x+e)-(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3+((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*d^4-4*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(-2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(-1+cos(f*x+e)-sin(f*x+e)))*(-(d^2/c^2)^(1/2)*c)^(1/2)*c^2*d^2*sin(f*x+e)+8*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(-2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(-1+cos(f*x+e)-sin(f*x+e)))*(-(d^2/c^2)^(1/2)*c)^(1/2)*c*d^3*sin(f*x+e)-(d^2/c^2)^(1/2)*(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*c+(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^3*d*cos(f*x+e)-2*(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2*cos(f*x+e)+(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3*cos(f*x+e)+(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^3*d*sin(f*x+e)-2*(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2*sin(f*x+e)+(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3*sin(f*x+e)+(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*d*cos(f*x+e)-(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*d*sin(f*x+e)-(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((d^2/c^2)^(1/2)*c*sin(f*x+e)+d*cos(f*x+e)-d)/((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/((d^2/c^2)^(1/2)*c*sin(f*x+e)-d*cos(f*x+e)+d)*((d^2/c^2)^(1/2)*c^2-d^2)*c*((d^2/c^2)^(1/2)-1)/(((d^2/c^2)^(1/2)*c^4+6*(d^2/c^2)^(1/2)*d^2*c^2+d^4*(d^2/c^2)^(1/2)-4*c^2*d^2-4*d^4)*c)^(1/2))*(2*c-2*d)^(1/2)*(-(d^2/c^2)^(1/2)*c)^(1/2)*d-4*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*ln(-2*((2*c-2*d)^(1/2)*2^(1/2)*((c+d*sin(f*x+e))/(cos(f*x+e)+1))^(1/2)*sin(f*x+e)+c*sin(f*x+e)-d*sin(f*x+e)+c*cos(f*x+e)-d*cos(f*x+e)-c+d)/(-1+cos(f*x+e)-sin(f*x+e)))*(-(d^2/c^2)^(1/2)*c)^(1/2)*d^4*sin(f*x+e)-(d^2/c^2)^(1/2)*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^3*d-((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2*cos(f*x+e)-2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3+((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2-((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*d^4*cos(f*x+e)-((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*d^4*sin(f*x+e)+2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3*cos(f*x+e)-((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c^2*d^2*sin(f*x+e)+2*((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)*arctan(((c+d*sin(f*x+e))/((d^2/c^2)^(1/2)*c*sin(f*x+e)+d)*d)^(1/2)/(-(d^2/c^2)^(1/2)*c)^(1/2))*(2*c-2*d)^(1/2)*c*d^3*sin(f*x+e))*(cos(f*x+e)^2+sin(f*x+e)*cos(f*x+e)+cos(f*x+e)-2*sin(f*x+e)-2)/(-1+cos(f*x+e))/(a*(1+sin(f*x+e)))^(3/2)/(c+d*sin(f*x+e))^(1/2)/d^2/(-(d^2/c^2)^(1/2)*c)^(1/2)/(c^2-2*c*d+d^2)/(2*c-2*d)^(1/2)","B"
938,0,0,123,1.112000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
939,0,0,103,3.483000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{3} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x)","F"
940,0,0,103,3.280000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
941,0,0,101,1.350000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
942,0,0,103,1.327000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
943,0,0,103,5.727000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
944,0,0,103,4.015000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","F"
945,0,0,123,1.239000," ","int(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
946,0,0,105,3.581000," ","int(cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
947,0,0,103,1.559000," ","int(cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
948,0,0,105,1.293000," ","int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(\cos^{4}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
949,0,0,105,5.531000," ","int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(\cos^{4}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
950,0,0,105,3.888000," ","int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(\cos^{4}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","F"
951,0,0,105,6.306000," ","int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x)","\int \frac{\left(\cos^{4}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{4}}\, dx"," ",0,"int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x)","F"
952,0,0,105,4.479000," ","int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x)","\int \frac{\left(\cos^{4}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{5}}\, dx"," ",0,"int(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x)","F"
953,1,128,124,0.457000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{a A \left(\cos^{8}\left(d x +c \right)\right)}{8}-\frac{a B \left(\cos^{8}\left(d x +c \right)\right)}{8}+\frac{a A \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(a*B*(-1/9*cos(d*x+c)^8*sin(d*x+c)+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-1/8*a*A*cos(d*x+c)^8-1/8*a*B*cos(d*x+c)^8+1/7*a*A*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
954,1,108,96,0.451000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a A \left(\cos^{6}\left(d x +c \right)\right)}{6}-\frac{a B \left(\cos^{6}\left(d x +c \right)\right)}{6}+\frac{a A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(a*B*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*a*A*cos(d*x+c)^6-1/6*a*B*cos(d*x+c)^6+1/5*a*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
955,1,88,72,0.456000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{a A \left(\cos^{4}\left(d x +c \right)\right)}{4}-\frac{a B \left(\cos^{4}\left(d x +c \right)\right)}{4}+\frac{a A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(a*B*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-1/4*a*A*cos(d*x+c)^4-1/4*a*B*cos(d*x+c)^4+1/3*a*A*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
956,1,44,45,0.230000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(a A +a B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right) a}{d}"," ",0,"1/d*(1/3*a*B*sin(d*x+c)^3+1/2*(A*a+B*a)*sin(d*x+c)^2+A*sin(d*x+c)*a)","A"
957,1,47,34,0.360000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","-\frac{a \ln \left(\sin \left(d x +c \right)-1\right) A}{d}-\frac{a B \sin \left(d x +c \right)}{d}-\frac{a \ln \left(\sin \left(d x +c \right)-1\right) B}{d}"," ",0,"-a/d*ln(sin(d*x+c)-1)*A-a*B*sin(d*x+c)/d-a/d*ln(sin(d*x+c)-1)*B","A"
958,1,129,43,0.569000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A}{2 d \cos \left(d x +c \right)^{2}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a B \sin \left(d x +c \right)}{2 d}-\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a B}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"1/2/d*a*A/cos(d*x+c)^2+1/2/d*a*B*sin(d*x+c)^3/cos(d*x+c)^2+1/2*a*B*sin(d*x+c)/d-1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*A*sec(d*x+c)*tan(d*x+c)+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*B/cos(d*x+c)^2","B"
959,1,173,92,0.596000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A}{4 d \cos \left(d x +c \right)^{4}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a B \sin \left(d x +c \right)}{8 d}-\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a B}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a*A/cos(d*x+c)^4+1/4/d*a*B*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a*B*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a*B*sin(d*x+c)/d-1/8/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a*A*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a*A*sec(d*x+c)*tan(d*x+c)+3/8/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a*B/cos(d*x+c)^4","A"
960,1,217,145,0.598000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A}{6 d \cos \left(d x +c \right)^{6}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a B \sin \left(d x +c \right)}{16 d}-\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{a A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{a B}{6 d \cos \left(d x +c \right)^{6}}"," ",0,"1/6/d*a*A/cos(d*x+c)^6+1/6/d*a*B*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*a*B*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*a*B*sin(d*x+c)^3/cos(d*x+c)^2+1/16*a*B*sin(d*x+c)/d-1/16/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a*A*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a*A*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a*A*sec(d*x+c)*tan(d*x+c)+5/16/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a*B/cos(d*x+c)^6","A"
961,1,138,126,0.505000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)-\frac{a A \left(\cos^{7}\left(d x +c \right)\right)}{7}-\frac{a B \left(\cos^{7}\left(d x +c \right)\right)}{7}+a A \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)}{d}"," ",0,"1/d*(a*B*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)-1/7*a*A*cos(d*x+c)^7-1/7*a*B*cos(d*x+c)^7+a*A*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c))","A"
962,1,118,101,0.493000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)-\frac{a A \left(\cos^{5}\left(d x +c \right)\right)}{5}-\frac{a B \left(\cos^{5}\left(d x +c \right)\right)}{5}+a A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)}{d}"," ",0,"1/d*(a*B*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)-1/5*a*A*cos(d*x+c)^5-1/5*a*B*cos(d*x+c)^5+a*A*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c))","A"
963,1,96,76,0.359000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a B \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)-\frac{a A \left(\cos^{3}\left(d x +c \right)\right)}{3}-\frac{a B \left(\cos^{3}\left(d x +c \right)\right)}{3}+a A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)}{d}"," ",0,"1/d*(a*B*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)-1/3*a*A*cos(d*x+c)^3-1/3*a*B*cos(d*x+c)^3+a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
964,1,54,29,0.461000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a A}{\cos \left(d x +c \right)}+a B \left(\tan \left(d x +c \right)-d x -c \right)+a A \tan \left(d x +c \right)+\frac{a B}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a*A/cos(d*x+c)+a*B*(tan(d*x+c)-d*x-c)+a*A*tan(d*x+c)+a*B/cos(d*x+c))","A"
965,1,72,46,0.519000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a A}{3 \cos \left(d x +c \right)^{3}}+\frac{a B \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}-a A \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{a B}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(1/3*a*A/cos(d*x+c)^3+1/3*a*B*sin(d*x+c)^3/cos(d*x+c)^3-a*A*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/3*a*B/cos(d*x+c)^3)","A"
966,1,102,67,0.547000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a A}{5 \cos \left(d x +c \right)^{5}}+a B \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)-a A \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{a B}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(1/5*a*A/cos(d*x+c)^5+a*B*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)-a*A*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/5*a*B/cos(d*x+c)^5)","A"
967,1,130,88,0.603000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a A}{7 \cos \left(d x +c \right)^{7}}+a B \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)-a A \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{a B}{7 \cos \left(d x +c \right)^{7}}}{d}"," ",0,"1/d*(1/7*a*A/cos(d*x+c)^7+a*B*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)-a*A*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+1/7*a*B/cos(d*x+c)^7)","A"
968,1,158,109,0.632000," ","int(sec(d*x+c)^10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{a A}{9 \cos \left(d x +c \right)^{9}}+a B \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)-a A \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)+\frac{a B}{9 \cos \left(d x +c \right)^{9}}}{d}"," ",0,"1/d*(1/9*a*A/cos(d*x+c)^9+a*B*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)-a*A*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c)+1/9*a*B/cos(d*x+c)^9)","A"
969,1,231,124,0.475000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)-\frac{a^{2} A \left(\cos^{8}\left(d x +c \right)\right)}{4}+2 B \,a^{2} \left(-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+\frac{a^{2} A \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}-\frac{B \,a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{8}}{d}"," ",0,"1/d*(a^2*A*(-1/9*cos(d*x+c)^8*sin(d*x+c)+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+B*a^2*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)-1/4*a^2*A*cos(d*x+c)^8+2*B*a^2*(-1/9*cos(d*x+c)^8*sin(d*x+c)+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+1/7*a^2*A*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)-1/8*B*a^2*cos(d*x+c)^8)","A"
970,1,201,97,0.473000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)-\frac{a^{2} A \left(\cos^{6}\left(d x +c \right)\right)}{3}+2 B \,a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+\frac{a^{2} A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}-\frac{B \,a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a^2*A*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+B*a^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)-1/3*a^2*A*cos(d*x+c)^6+2*B*a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+1/5*a^2*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)-1/6*B*a^2*cos(d*x+c)^6)","B"
971,1,171,72,0.485000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)-\frac{a^{2} A \left(\cos^{4}\left(d x +c \right)\right)}{2}+2 B \,a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+\frac{a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}-\frac{B \,a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4}}{d}"," ",0,"1/d*(a^2*A*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+B*a^2*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)-1/2*a^2*A*cos(d*x+c)^4+2*B*a^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)-1/4*B*a^2*cos(d*x+c)^4)","B"
972,1,75,47,0.240000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{B \,a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(a^{2} A +2 B \,a^{2}\right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(2 a^{2} A +B \,a^{2}\right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+a^{2} A \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/4*B*a^2*sin(d*x+c)^4+1/3*(A*a^2+2*B*a^2)*sin(d*x+c)^3+1/2*(2*A*a^2+B*a^2)*sin(d*x+c)^2+a^2*A*sin(d*x+c))","A"
973,1,127,58,0.368000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","-\frac{a^{2} A \sin \left(d x +c \right)}{d}+\frac{2 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{B \,a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{2 B \,a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 a^{2} A \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 B \,a^{2} \sin \left(d x +c \right)}{d}+\frac{2 B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a^2*A*sin(d*x+c)+2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))-1/2/d*B*a^2*sin(d*x+c)^2-2/d*B*a^2*ln(cos(d*x+c))-2/d*a^2*A*ln(cos(d*x+c))-2/d*B*a^2*sin(d*x+c)+2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))","B"
974,1,189,43,0.600000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} A \sin \left(d x +c \right)}{2 d}+\frac{B \,a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{B \,a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a^{2} A}{d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{2} \sin \left(d x +c \right)}{d}-\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,a^{2}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"1/2/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^2+1/2/d*a^2*A*sin(d*x+c)+1/2/d*B*a^2*tan(d*x+c)^2+1/d*B*a^2*ln(cos(d*x+c))+1/d*a^2*A/cos(d*x+c)^2+1/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/d*B*a^2*sin(d*x+c)-1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a^2*A*sec(d*x+c)*tan(d*x+c)+1/2/d*B*a^2/cos(d*x+c)^2","B"
975,1,281,71,0.569000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} A \sin \left(d x +c \right)}{8 d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{B \,a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} A}{2 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{2} \sin \left(d x +c \right)}{4 d}-\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{a^{2} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{B \,a^{2}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^2+1/8/d*a^2*A*sin(d*x+c)+1/4/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*B*a^2*sin(d*x+c)^4/cos(d*x+c)^4+1/2/d*a^2*A/cos(d*x+c)^4+1/2/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/4/d*B*a^2*sin(d*x+c)-1/4/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a^2*A*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^2*A*sec(d*x+c)*tan(d*x+c)+1/4/d*B*a^2/cos(d*x+c)^4","B"
976,1,379,122,0.734000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} A \sin \left(d x +c \right)}{16 d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{B \,a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} A}{3 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{2} \sin \left(d x +c \right)}{8 d}-\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{2} A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{2} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{B \,a^{2}}{6 d \cos \left(d x +c \right)^{6}}"," ",0,"1/6/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*a^2*A*sin(d*x+c)^3/cos(d*x+c)^2+1/16/d*a^2*A*sin(d*x+c)+1/4/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*B*a^2*sin(d*x+c)^4/cos(d*x+c)^6+1/12/d*B*a^2*sin(d*x+c)^4/cos(d*x+c)^4+1/3/d*a^2*A/cos(d*x+c)^6+1/3/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^6+1/4/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*B*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8/d*B*a^2*sin(d*x+c)-1/8/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a^2*A*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a^2*A*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a^2*A*sec(d*x+c)*tan(d*x+c)+1/6/d*B*a^2/cos(d*x+c)^6","B"
977,1,245,182,0.500000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-\frac{2 a^{2} A \left(\cos^{7}\left(d x +c \right)\right)}{7}+2 B \,a^{2} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+a^{2} A \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)-\frac{B \,a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7}}{d}"," ",0,"1/d*(a^2*A*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+B*a^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-2/7*a^2*A*cos(d*x+c)^7+2*B*a^2*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+a^2*A*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)-1/7*B*a^2*cos(d*x+c)^7)","A"
978,1,215,153,0.490000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)-\frac{2 a^{2} A \left(\cos^{5}\left(d x +c \right)\right)}{5}+2 B \,a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+a^{2} A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{B \,a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(a^2*A*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+B*a^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)-2/5*a^2*A*cos(d*x+c)^5+2*B*a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+a^2*A*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)-1/5*B*a^2*cos(d*x+c)^5)","A"
979,1,182,124,0.388000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+B \,a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)-\frac{2 a^{2} A \left(\cos^{3}\left(d x +c \right)\right)}{3}+2 B \,a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+a^{2} A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{B \,a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(a^2*A*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+B*a^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)-2/3*a^2*A*cos(d*x+c)^3+2*B*a^2*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/3*B*a^2*cos(d*x+c)^3)","A"
980,1,123,55,0.611000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\tan \left(d x +c \right)-d x -c \right)+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+\frac{2 a^{2} A}{\cos \left(d x +c \right)}+2 B \,a^{2} \left(\tan \left(d x +c \right)-d x -c \right)+a^{2} A \tan \left(d x +c \right)+\frac{B \,a^{2}}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a^2*A*(tan(d*x+c)-d*x-c)+B*a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+2*a^2*A/cos(d*x+c)+2*B*a^2*(tan(d*x+c)-d*x-c)+a^2*A*tan(d*x+c)+B*a^2/cos(d*x+c))","B"
981,1,162,67,0.655000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{a^{2} A \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{2 a^{2} A}{3 \cos \left(d x +c \right)^{3}}+\frac{2 B \,a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{3 \cos \left(d x +c \right)^{3}}-a^{2} A \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{B \,a^{2}}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(1/3*a^2*A*sin(d*x+c)^3/cos(d*x+c)^3+B*a^2*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+2/3*a^2*A/cos(d*x+c)^3+2/3*B*a^2*sin(d*x+c)^3/cos(d*x+c)^3-a^2*A*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/3*B*a^2/cos(d*x+c)^3)","B"
982,1,231,96,0.639000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)+\frac{2 a^{2} A}{5 \cos \left(d x +c \right)^{5}}+2 B \,a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)-a^{2} A \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{B \,a^{2}}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^2*A*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+B*a^2*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c))+2/5*a^2*A/cos(d*x+c)^5+2*B*a^2*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)-a^2*A*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/5*B*a^2/cos(d*x+c)^5)","B"
983,1,295,119,0.713000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)+\frac{2 a^{2} A}{7 \cos \left(d x +c \right)^{7}}+2 B \,a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)-a^{2} A \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{B \,a^{2}}{7 \cos \left(d x +c \right)^{7}}}{d}"," ",0,"1/d*(a^2*A*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+B*a^2*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c))+2/7*a^2*A/cos(d*x+c)^7+2*B*a^2*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)-a^2*A*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+1/7*B*a^2/cos(d*x+c)^7)","B"
984,1,359,142,0.712000," ","int(sec(d*x+c)^10*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{63}\right)+\frac{2 a^{2} A}{9 \cos \left(d x +c \right)^{9}}+2 B \,a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)-a^{2} A \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)+\frac{B \,a^{2}}{9 \cos \left(d x +c \right)^{9}}}{d}"," ",0,"1/d*(a^2*A*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+B*a^2*(1/9*sin(d*x+c)^4/cos(d*x+c)^9+5/63*sin(d*x+c)^4/cos(d*x+c)^7+1/21*sin(d*x+c)^4/cos(d*x+c)^5+1/63*sin(d*x+c)^4/cos(d*x+c)^3-1/63*sin(d*x+c)^4/cos(d*x+c)-1/63*(2+sin(d*x+c)^2)*cos(d*x+c))+2/9*a^2*A/cos(d*x+c)^9+2*B*a^2*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)-a^2*A*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c)+1/9*B*a^2/cos(d*x+c)^9)","B"
985,1,423,165,0.808000," ","int(sec(d*x+c)^12*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \left(\frac{\sin^{3}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{9}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{231 \cos \left(d x +c \right)^{7}}+\frac{64 \left(\sin^{3}\left(d x +c \right)\right)}{1155 \cos \left(d x +c \right)^{5}}+\frac{128 \left(\sin^{3}\left(d x +c \right)\right)}{3465 \cos \left(d x +c \right)^{3}}\right)+B \,a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{7 \left(\sin^{4}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{33 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{99 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{99 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{99}\right)+\frac{2 a^{2} A}{11 \cos \left(d x +c \right)^{11}}+2 B \,a^{2} \left(\frac{\sin^{3}\left(d x +c \right)}{11 \cos \left(d x +c \right)^{11}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{99 \cos \left(d x +c \right)^{9}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{231 \cos \left(d x +c \right)^{7}}+\frac{64 \left(\sin^{3}\left(d x +c \right)\right)}{1155 \cos \left(d x +c \right)^{5}}+\frac{128 \left(\sin^{3}\left(d x +c \right)\right)}{3465 \cos \left(d x +c \right)^{3}}\right)-a^{2} A \left(-\frac{256}{693}-\frac{\left(\sec^{10}\left(d x +c \right)\right)}{11}-\frac{10 \left(\sec^{8}\left(d x +c \right)\right)}{99}-\frac{80 \left(\sec^{6}\left(d x +c \right)\right)}{693}-\frac{32 \left(\sec^{4}\left(d x +c \right)\right)}{231}-\frac{128 \left(\sec^{2}\left(d x +c \right)\right)}{693}\right) \tan \left(d x +c \right)+\frac{B \,a^{2}}{11 \cos \left(d x +c \right)^{11}}}{d}"," ",0,"1/d*(a^2*A*(1/11*sin(d*x+c)^3/cos(d*x+c)^11+8/99*sin(d*x+c)^3/cos(d*x+c)^9+16/231*sin(d*x+c)^3/cos(d*x+c)^7+64/1155*sin(d*x+c)^3/cos(d*x+c)^5+128/3465*sin(d*x+c)^3/cos(d*x+c)^3)+B*a^2*(1/11*sin(d*x+c)^4/cos(d*x+c)^11+7/99*sin(d*x+c)^4/cos(d*x+c)^9+5/99*sin(d*x+c)^4/cos(d*x+c)^7+1/33*sin(d*x+c)^4/cos(d*x+c)^5+1/99*sin(d*x+c)^4/cos(d*x+c)^3-1/99*sin(d*x+c)^4/cos(d*x+c)-1/99*(2+sin(d*x+c)^2)*cos(d*x+c))+2/11*a^2*A/cos(d*x+c)^11+2*B*a^2*(1/11*sin(d*x+c)^3/cos(d*x+c)^11+8/99*sin(d*x+c)^3/cos(d*x+c)^9+16/231*sin(d*x+c)^3/cos(d*x+c)^7+64/1155*sin(d*x+c)^3/cos(d*x+c)^5+128/3465*sin(d*x+c)^3/cos(d*x+c)^3)-a^2*A*(-256/693-1/11*sec(d*x+c)^10-10/99*sec(d*x+c)^8-80/693*sec(d*x+c)^6-32/231*sec(d*x+c)^4-128/693*sec(d*x+c)^2)*tan(d*x+c)+1/11*B*a^2/cos(d*x+c)^11)","B"
986,1,345,124,0.489000," ","int(cos(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{11}-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{33}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{231}\right)+3 a^{3} A \left(-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)-\frac{3 a^{3} A \left(\cos^{8}\left(d x +c \right)\right)}{8}+3 B \,a^{3} \left(-\frac{\left(\cos^{8}\left(d x +c \right)\right) \sin \left(d x +c \right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+\frac{a^{3} A \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}-\frac{B \,a^{3} \left(\cos^{8}\left(d x +c \right)\right)}{8}}{d}"," ",0,"1/d*(a^3*A*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)+B*a^3*(-1/11*sin(d*x+c)^3*cos(d*x+c)^8-1/33*cos(d*x+c)^8*sin(d*x+c)+1/231*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+3*a^3*A*(-1/9*cos(d*x+c)^8*sin(d*x+c)+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+3*B*a^3*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8)-3/8*a^3*A*cos(d*x+c)^8+3*B*a^3*(-1/9*cos(d*x+c)^8*sin(d*x+c)+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+1/7*a^3*A*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)-1/8*B*a^3*cos(d*x+c)^8)","B"
987,1,305,97,0.488000," ","int(cos(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+3 a^{3} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)-\frac{a^{3} A \left(\cos^{6}\left(d x +c \right)\right)}{2}+3 B \,a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+\frac{a^{3} A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}-\frac{B \,a^{3} \left(\cos^{6}\left(d x +c \right)\right)}{6}}{d}"," ",0,"1/d*(a^3*A*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+B*a^3*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+3*a^3*A*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+3*B*a^3*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)-1/2*a^3*A*cos(d*x+c)^6+3*B*a^3*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+1/5*a^3*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)-1/6*B*a^3*cos(d*x+c)^6)","B"
988,1,265,72,0.484000," ","int(cos(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{7}-\frac{3 \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{35}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{35}\right)+3 a^{3} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)-\frac{3 a^{3} A \left(\cos^{4}\left(d x +c \right)\right)}{4}+3 B \,a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+\frac{a^{3} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}-\frac{B \,a^{3} \left(\cos^{4}\left(d x +c \right)\right)}{4}}{d}"," ",0,"1/d*(a^3*A*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)+B*a^3*(-1/7*sin(d*x+c)^3*cos(d*x+c)^4-3/35*sin(d*x+c)*cos(d*x+c)^4+1/35*(2+cos(d*x+c)^2)*sin(d*x+c))+3*a^3*A*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+3*B*a^3*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4)-3/4*a^3*A*cos(d*x+c)^4+3*B*a^3*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+1/3*a^3*A*(2+cos(d*x+c)^2)*sin(d*x+c)-1/4*B*a^3*cos(d*x+c)^4)","B"
989,1,98,47,0.227000," ","int(cos(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(a^{3} A +3 B \,a^{3}\right) \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(3 a^{3} A +3 B \,a^{3}\right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(3 a^{3} A +B \,a^{3}\right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+a^{3} A \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*B*a^3*sin(d*x+c)^5+1/4*(A*a^3+3*B*a^3)*sin(d*x+c)^4+1/3*(3*A*a^3+3*B*a^3)*sin(d*x+c)^3+1/2*(3*A*a^3+B*a^3)*sin(d*x+c)^2+a^3*A*sin(d*x+c))","B"
990,1,161,77,0.363000," ","int(sec(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","-\frac{a^{3} A \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 a^{3} A \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3 d}-\frac{4 a^{3} B \sin \left(d x +c \right)}{d}+\frac{4 B \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 a^{3} A \sin \left(d x +c \right)}{d}+\frac{4 a^{3} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{3 B \,a^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{4 B \,a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^3*A*sin(d*x+c)^2-4/d*a^3*A*ln(cos(d*x+c))-1/3/d*B*a^3*sin(d*x+c)^3-4*a^3*B*sin(d*x+c)/d+4/d*B*a^3*ln(sec(d*x+c)+tan(d*x+c))-3/d*a^3*A*sin(d*x+c)+4/d*a^3*A*ln(sec(d*x+c)+tan(d*x+c))-3/2/d*B*a^3*sin(d*x+c)^2-4/d*B*a^3*ln(cos(d*x+c))","B"
991,1,290,62,0.575000," ","int(sec(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{3} A \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} B \sin \left(d x +c \right)}{d}-\frac{3 B \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} A \sin \left(d x +c \right)}{2 d}-\frac{a^{3} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 B \,a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{3 B \,a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{3} A}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,a^{3}}{2 d \cos \left(d x +c \right)^{2}}"," ",0,"1/2/d*a^3*A*tan(d*x+c)^2+1/d*a^3*A*ln(cos(d*x+c))+1/2/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*B*a^3*sin(d*x+c)^3+3*a^3*B*sin(d*x+c)/d-3/d*B*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^2+3/2/d*a^3*A*sin(d*x+c)-1/d*a^3*A*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*B*a^3*tan(d*x+c)^2+3/d*B*a^3*ln(cos(d*x+c))+3/2/d*a^3*A/cos(d*x+c)^2+3/2/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/2/d*a^3*A*sec(d*x+c)*tan(d*x+c)+1/2/d*B*a^3/cos(d*x+c)^2","B"
992,1,312,41,0.583000," ","int(sec(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{3} A \sin \left(d x +c \right)}{8 d}+\frac{3 B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} A}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{B \,a^{3}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^2-1/8/d*B*a^3*sin(d*x+c)^3+3/4/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^2+3/8/d*a^3*A*sin(d*x+c)+3/4/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^4+3/4/d*a^3*A/cos(d*x+c)^4+3/4/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/4/d*a^3*A*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^3*A*sec(d*x+c)*tan(d*x+c)+1/4/d*B*a^3/cos(d*x+c)^4","B"
993,1,521,97,0.573000," ","int(sec(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{3 a^{3} A \sin \left(d x +c \right)}{16 d}+\frac{a^{3} A}{2 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{3}}{6 d \cos \left(d x +c \right)^{6}}-\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{48 d}+\frac{a^{3} B \sin \left(d x +c \right)}{8 d}-\frac{B \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}-\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{6}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{3} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a^{3} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"3/16/d*a^3*A*sin(d*x+c)+1/2/d*a^3*A/cos(d*x+c)^6+1/6/d*B*a^3/cos(d*x+c)^6-1/48/d*B*a^3*sin(d*x+c)^3+1/8*a^3*B*sin(d*x+c)/d-1/8/d*B*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^6+1/6/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^6+1/24/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^4-1/48/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^2+1/2/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^6+3/8/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^4+3/16/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^2+1/2/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^6+1/2/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^6+3/8/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^4+3/16/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/6/d*a^3*A*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a^3*A*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a^3*A*sec(d*x+c)*tan(d*x+c)+1/12/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^4+1/8/d*a^3*A*ln(sec(d*x+c)+tan(d*x+c))","B"
994,1,669,150,0.648000," ","int(sec(d*x+c)^9*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","-\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{128 d}-\frac{3 B \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{32 d}+\frac{15 a^{3} A \sin \left(d x +c \right)}{128 d}+\frac{5 a^{3} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{32 d}+\frac{B \,a^{3}}{8 d \cos \left(d x +c \right)^{8}}+\frac{3 a^{3} A}{8 d \cos \left(d x +c \right)^{8}}+\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{3 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{6}}+\frac{5 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}-\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{35 a^{3} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{128 d}+\frac{35 a^{3} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{192 d}+\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{6}}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{15 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{15 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{64 d \cos \left(d x +c \right)^{4}}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}+\frac{5 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{6}}+\frac{7 a^{3} A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{48 d}+\frac{3 a^{3} B \sin \left(d x +c \right)}{32 d}+\frac{a^{3} A \left(\sin^{4}\left(d x +c \right)\right)}{24 d \cos \left(d x +c \right)^{4}}+\frac{15 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{15 B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{128 d \cos \left(d x +c \right)^{2}}+\frac{3 B \,a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{a^{3} A \tan \left(d x +c \right) \left(\sec^{7}\left(d x +c \right)\right)}{8 d}+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}+\frac{3 a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{8}}"," ",0,"1/64/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^4+15/64/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^4+15/64/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^4+35/192/d*a^3*A*tan(d*x+c)*sec(d*x+c)^3-1/128/d*B*a^3*sin(d*x+c)^3-3/32/d*B*a^3*ln(sec(d*x+c)+tan(d*x+c))+15/128/d*a^3*A*sin(d*x+c)+5/32/d*a^3*A*ln(sec(d*x+c)+tan(d*x+c))+1/16/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^6+5/16/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^6+1/4/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^6+5/16/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^6+7/48/d*a^3*A*tan(d*x+c)*sec(d*x+c)^5+1/8/d*B*a^3/cos(d*x+c)^8+3/8/d*a^3*A/cos(d*x+c)^8-1/128/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^2+15/128/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^2+15/128/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^2+35/128/d*a^3*A*sec(d*x+c)*tan(d*x+c)+1/24/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^4+1/8/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^8+3/8/d*B*a^3*sin(d*x+c)^3/cos(d*x+c)^8+1/8/d*a^3*A*tan(d*x+c)*sec(d*x+c)^7+1/8/d*B*a^3*sin(d*x+c)^5/cos(d*x+c)^8+3/8/d*a^3*A*sin(d*x+c)^3/cos(d*x+c)^8+3/8/d*B*a^3*sin(d*x+c)^4/cos(d*x+c)^8+1/12/d*a^3*A*sin(d*x+c)^4/cos(d*x+c)^6+3/32*a^3*B*sin(d*x+c)/d","B"
995,1,363,215,0.464000," ","int(cos(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+3 a^{3} A \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)-\frac{3 a^{3} A \left(\cos^{7}\left(d x +c \right)\right)}{7}+3 B \,a^{3} \left(-\frac{\left(\cos^{7}\left(d x +c \right)\right) \sin \left(d x +c \right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+a^{3} A \left(\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{6}+\frac{5 d x}{16}+\frac{5 c}{16}\right)-\frac{B \,a^{3} \left(\cos^{7}\left(d x +c \right)\right)}{7}}{d}"," ",0,"1/d*(a^3*A*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+B*a^3*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*cos(d*x+c)^7*sin(d*x+c)+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+3*a^3*A*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+3*B*a^3*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)-3/7*a^3*A*cos(d*x+c)^7+3*B*a^3*(-1/8*cos(d*x+c)^7*sin(d*x+c)+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+a^3*A*(1/6*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/16*d*x+5/16*c)-1/7*B*a^3*cos(d*x+c)^7)","A"
996,1,323,186,0.454000," ","int(cos(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+3 a^{3} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)-\frac{3 a^{3} A \left(\cos^{5}\left(d x +c \right)\right)}{5}+3 B \,a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+a^{3} A \left(\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{4}+\frac{3 d x}{8}+\frac{3 c}{8}\right)-\frac{B \,a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5}}{d}"," ",0,"1/d*(a^3*A*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+B*a^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+3*a^3*A*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+3*B*a^3*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)-3/5*a^3*A*cos(d*x+c)^5+3*B*a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+a^3*A*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)-1/5*B*a^3*cos(d*x+c)^5)","A"
997,1,279,147,0.348000," ","int(cos(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+B \,a^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+3 a^{3} A \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+3 B \,a^{3} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)-a^{3} A \left(\cos^{3}\left(d x +c \right)\right)+3 B \,a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+a^{3} A \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)-\frac{B \,a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3}}{d}"," ",0,"1/d*(a^3*A*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+B*a^3*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*sin(d*x+c)*cos(d*x+c)^3+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+3*a^3*A*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+3*B*a^3*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)-a^3*A*cos(d*x+c)^3+3*B*a^3*(-1/4*sin(d*x+c)*cos(d*x+c)^3+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+a^3*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)-1/3*B*a^3*cos(d*x+c)^3)","A"
998,1,219,87,0.681000," ","int(sec(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+B \,a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+3 a^{3} A \left(\tan \left(d x +c \right)-d x -c \right)+3 B \,a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+\frac{3 a^{3} A}{\cos \left(d x +c \right)}+3 B \,a^{3} \left(\tan \left(d x +c \right)-d x -c \right)+a^{3} A \tan \left(d x +c \right)+\frac{B \,a^{3}}{\cos \left(d x +c \right)}}{d}"," ",0,"1/d*(a^3*A*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+B*a^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+3*a^3*A*(tan(d*x+c)-d*x-c)+3*B*a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^3*A/cos(d*x+c)+3*B*a^3*(tan(d*x+c)-d*x-c)+a^3*A*tan(d*x+c)+B*a^3/cos(d*x+c))","B"
999,1,248,67,0.670000," ","int(sec(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+B \,a^{3} \left(\frac{\left(\tan^{3}\left(d x +c \right)\right)}{3}-\tan \left(d x +c \right)+d x +c \right)+\frac{a^{3} A \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}+3 B \,a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{3 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{3}\right)+\frac{a^{3} A}{\cos \left(d x +c \right)^{3}}+\frac{B \,a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{\cos \left(d x +c \right)^{3}}-a^{3} A \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(d x +c \right)\right)}{3}\right) \tan \left(d x +c \right)+\frac{B \,a^{3}}{3 \cos \left(d x +c \right)^{3}}}{d}"," ",0,"1/d*(a^3*A*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+B*a^3*(1/3*tan(d*x+c)^3-tan(d*x+c)+d*x+c)+a^3*A*sin(d*x+c)^3/cos(d*x+c)^3+3*B*a^3*(1/3*sin(d*x+c)^4/cos(d*x+c)^3-1/3*sin(d*x+c)^4/cos(d*x+c)-1/3*(2+sin(d*x+c)^2)*cos(d*x+c))+a^3*A/cos(d*x+c)^3+B*a^3*sin(d*x+c)^3/cos(d*x+c)^3-a^3*A*(-2/3-1/3*sec(d*x+c)^2)*tan(d*x+c)+1/3*B*a^3/cos(d*x+c)^3)","B"
1000,1,333,101,0.657000," ","int(sec(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)+\frac{B \,a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{5 \cos \left(d x +c \right)^{5}}+3 a^{3} A \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)+3 B \,a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{15 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{15}\right)+\frac{3 a^{3} A}{5 \cos \left(d x +c \right)^{5}}+3 B \,a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{5 \cos \left(d x +c \right)^{5}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{15 \cos \left(d x +c \right)^{3}}\right)-a^{3} A \left(-\frac{8}{15}-\frac{\left(\sec^{4}\left(d x +c \right)\right)}{5}-\frac{4 \left(\sec^{2}\left(d x +c \right)\right)}{15}\right) \tan \left(d x +c \right)+\frac{B \,a^{3}}{5 \cos \left(d x +c \right)^{5}}}{d}"," ",0,"1/d*(a^3*A*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c))+1/5*B*a^3*sin(d*x+c)^5/cos(d*x+c)^5+3*a^3*A*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)+3*B*a^3*(1/5*sin(d*x+c)^4/cos(d*x+c)^5+1/15*sin(d*x+c)^4/cos(d*x+c)^3-1/15*sin(d*x+c)^4/cos(d*x+c)-1/15*(2+sin(d*x+c)^2)*cos(d*x+c))+3/5*a^3*A/cos(d*x+c)^5+3*B*a^3*(1/5*sin(d*x+c)^3/cos(d*x+c)^5+2/15*sin(d*x+c)^3/cos(d*x+c)^3)-a^3*A*(-8/15-1/5*sec(d*x+c)^4-4/15*sec(d*x+c)^2)*tan(d*x+c)+1/5*B*a^3/cos(d*x+c)^5)","B"
1001,1,435,107,0.674000," ","int(sec(d*x+c)^8*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)+B \,a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}\right)+3 a^{3} A \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)+3 B \,a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{35 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{35}\right)+\frac{3 a^{3} A}{7 \cos \left(d x +c \right)^{7}}+3 B \,a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{7 \cos \left(d x +c \right)^{7}}+\frac{4 \left(\sin^{3}\left(d x +c \right)\right)}{35 \cos \left(d x +c \right)^{5}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{3}}\right)-a^{3} A \left(-\frac{16}{35}-\frac{\left(\sec^{6}\left(d x +c \right)\right)}{7}-\frac{6 \left(\sec^{4}\left(d x +c \right)\right)}{35}-\frac{8 \left(\sec^{2}\left(d x +c \right)\right)}{35}\right) \tan \left(d x +c \right)+\frac{B \,a^{3}}{7 \cos \left(d x +c \right)^{7}}}{d}"," ",0,"1/d*(a^3*A*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c))+B*a^3*(1/7*sin(d*x+c)^5/cos(d*x+c)^7+2/35*sin(d*x+c)^5/cos(d*x+c)^5)+3*a^3*A*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)+3*B*a^3*(1/7*sin(d*x+c)^4/cos(d*x+c)^7+3/35*sin(d*x+c)^4/cos(d*x+c)^5+1/35*sin(d*x+c)^4/cos(d*x+c)^3-1/35*sin(d*x+c)^4/cos(d*x+c)-1/35*(2+sin(d*x+c)^2)*cos(d*x+c))+3/7*a^3*A/cos(d*x+c)^7+3*B*a^3*(1/7*sin(d*x+c)^3/cos(d*x+c)^7+4/35*sin(d*x+c)^3/cos(d*x+c)^5+8/105*sin(d*x+c)^3/cos(d*x+c)^3)-a^3*A*(-16/35-1/7*sec(d*x+c)^6-6/35*sec(d*x+c)^4-8/35*sec(d*x+c)^2)*tan(d*x+c)+1/7*B*a^3/cos(d*x+c)^7)","B"
1002,1,535,130,0.693000," ","int(sec(d*x+c)^10*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x)","\frac{a^{3} A \left(\frac{\sin^{4}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{63}\right)+B \,a^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{4 \left(\sin^{5}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{5}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{5}}\right)+3 a^{3} A \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)+3 B \,a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{5 \left(\sin^{4}\left(d x +c \right)\right)}{63 \cos \left(d x +c \right)^{7}}+\frac{\sin^{4}\left(d x +c \right)}{21 \cos \left(d x +c \right)^{5}}+\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)^{3}}-\frac{\sin^{4}\left(d x +c \right)}{63 \cos \left(d x +c \right)}-\frac{\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)}{63}\right)+\frac{a^{3} A}{3 \cos \left(d x +c \right)^{9}}+3 B \,a^{3} \left(\frac{\sin^{3}\left(d x +c \right)}{9 \cos \left(d x +c \right)^{9}}+\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{21 \cos \left(d x +c \right)^{7}}+\frac{8 \left(\sin^{3}\left(d x +c \right)\right)}{105 \cos \left(d x +c \right)^{5}}+\frac{16 \left(\sin^{3}\left(d x +c \right)\right)}{315 \cos \left(d x +c \right)^{3}}\right)-a^{3} A \left(-\frac{128}{315}-\frac{\left(\sec^{8}\left(d x +c \right)\right)}{9}-\frac{8 \left(\sec^{6}\left(d x +c \right)\right)}{63}-\frac{16 \left(\sec^{4}\left(d x +c \right)\right)}{105}-\frac{64 \left(\sec^{2}\left(d x +c \right)\right)}{315}\right) \tan \left(d x +c \right)+\frac{B \,a^{3}}{9 \cos \left(d x +c \right)^{9}}}{d}"," ",0,"1/d*(a^3*A*(1/9*sin(d*x+c)^4/cos(d*x+c)^9+5/63*sin(d*x+c)^4/cos(d*x+c)^7+1/21*sin(d*x+c)^4/cos(d*x+c)^5+1/63*sin(d*x+c)^4/cos(d*x+c)^3-1/63*sin(d*x+c)^4/cos(d*x+c)-1/63*(2+sin(d*x+c)^2)*cos(d*x+c))+B*a^3*(1/9*sin(d*x+c)^5/cos(d*x+c)^9+4/63*sin(d*x+c)^5/cos(d*x+c)^7+8/315*sin(d*x+c)^5/cos(d*x+c)^5)+3*a^3*A*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)+3*B*a^3*(1/9*sin(d*x+c)^4/cos(d*x+c)^9+5/63*sin(d*x+c)^4/cos(d*x+c)^7+1/21*sin(d*x+c)^4/cos(d*x+c)^5+1/63*sin(d*x+c)^4/cos(d*x+c)^3-1/63*sin(d*x+c)^4/cos(d*x+c)-1/63*(2+sin(d*x+c)^2)*cos(d*x+c))+1/3*a^3*A/cos(d*x+c)^9+3*B*a^3*(1/9*sin(d*x+c)^3/cos(d*x+c)^9+2/21*sin(d*x+c)^3/cos(d*x+c)^7+8/105*sin(d*x+c)^3/cos(d*x+c)^5+16/315*sin(d*x+c)^3/cos(d*x+c)^3)-a^3*A*(-128/315-1/9*sec(d*x+c)^8-8/63*sec(d*x+c)^6-16/105*sec(d*x+c)^4-64/315*sec(d*x+c)^2)*tan(d*x+c)+1/9*B*a^3/cos(d*x+c)^9)","B"
1003,1,107,99,0.559000," ","int(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{-\frac{B \left(\sin^{7}\left(d x +c \right)\right)}{7}+\frac{\left(-A +B \right) \left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{\left(A +2 B \right) \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(2 A -2 B \right) \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(-2 A -B \right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(-A +B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*(-1/7*B*sin(d*x+c)^7+1/6*(-A+B)*sin(d*x+c)^6+1/5*(A+2*B)*sin(d*x+c)^5+1/4*(2*A-2*B)*sin(d*x+c)^4+1/3*(-2*A-B)*sin(d*x+c)^3+1/2*(-A+B)*sin(d*x+c)^2+A*sin(d*x+c))","A"
1004,1,75,73,0.449000," ","int(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{\frac{B \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{\left(A -B \right) \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(-A -B \right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(-A +B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*(1/5*B*sin(d*x+c)^5+1/4*(A-B)*sin(d*x+c)^4+1/3*(-A-B)*sin(d*x+c)^3+1/2*(-A+B)*sin(d*x+c)^2+A*sin(d*x+c))","A"
1005,1,43,53,0.436000," ","int(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{-\frac{B \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(-A +B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*(-1/3*B*sin(d*x+c)^3+1/2*(-A+B)*sin(d*x+c)^2+A*sin(d*x+c))","A"
1006,1,51,36,0.257000," ","int(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{d a}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{d a}+\frac{B \sin \left(d x +c \right)}{d a}"," ",0,"1/d/a*ln(1+sin(d*x+c))*A-1/d/a*ln(1+sin(d*x+c))*B+B*sin(d*x+c)/d/a","A"
1007,1,112,41,0.456000," ","int(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A}{4 a d}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{4 a d}-\frac{A}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{B}{2 a d \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{4 d a}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{4 d a}"," ",0,"-1/4/a/d*ln(sin(d*x+c)-1)*A-1/4/a/d*ln(sin(d*x+c)-1)*B-1/2/a/d/(1+sin(d*x+c))*A+1/2/a/d/(1+sin(d*x+c))*B+1/4/d/a*ln(1+sin(d*x+c))*B+1/4/d/a*ln(1+sin(d*x+c))*A","B"
1008,1,169,83,0.556000," ","int(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) A}{16 a d}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{16 a d}-\frac{A}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{B}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{A}{4 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{A}{8 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{8 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) A}{16 d a}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{16 d a}"," ",0,"-3/16/a/d*ln(sin(d*x+c)-1)*A-1/16/a/d*ln(sin(d*x+c)-1)*B-1/8/a/d/(sin(d*x+c)-1)*A-1/8/a/d/(sin(d*x+c)-1)*B-1/4/a/d/(1+sin(d*x+c))*A-1/8/a/d/(1+sin(d*x+c))^2*A+1/8/a/d/(1+sin(d*x+c))^2*B+3/16/d/a*ln(1+sin(d*x+c))*A+1/16/d/a*ln(1+sin(d*x+c))*B","B"
1009,1,245,134,0.530000," ","int(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) A}{32 a d}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{32 a d}+\frac{A}{32 a d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{B}{32 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{A}{8 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{B}{16 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{3 A}{16 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{A}{24 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{24 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{3 A}{32 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{32 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) A}{32 d a}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{32 d a}"," ",0,"-5/32/a/d*ln(sin(d*x+c)-1)*A-1/32/a/d*ln(sin(d*x+c)-1)*B+1/32/a/d/(sin(d*x+c)-1)^2*A+1/32/a/d/(sin(d*x+c)-1)^2*B-1/8/a/d/(sin(d*x+c)-1)*A-1/16/a/d/(sin(d*x+c)-1)*B-3/16/a/d/(1+sin(d*x+c))*A-1/24/a/d/(1+sin(d*x+c))^3*A+1/24/a/d/(1+sin(d*x+c))^3*B-3/32/a/d/(1+sin(d*x+c))^2*A+1/32/a/d/(1+sin(d*x+c))^2*B+5/32/d/a*ln(1+sin(d*x+c))*A+1/32/d/a*ln(1+sin(d*x+c))*B","A"
1010,1,321,189,0.498000," ","int(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","-\frac{35 \ln \left(\sin \left(d x +c \right)-1\right) A}{256 a d}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) B}{256 a d}+\frac{5 A}{128 a d \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3 B}{128 a d \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{A}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{B}{96 a d \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{15 A}{128 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 B}{128 a d \left(\sin \left(d x +c \right)-1\right)}-\frac{5 A}{32 a d \left(1+\sin \left(d x +c \right)\right)}-\frac{A}{64 a d \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{B}{64 a d \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{A}{24 a d \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{48 a d \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5 A}{64 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{64 a d \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{35 \ln \left(1+\sin \left(d x +c \right)\right) A}{256 d a}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) B}{256 d a}"," ",0,"-35/256/a/d*ln(sin(d*x+c)-1)*A-5/256/a/d*ln(sin(d*x+c)-1)*B+5/128/a/d/(sin(d*x+c)-1)^2*A+3/128/a/d/(sin(d*x+c)-1)^2*B-1/96/a/d/(sin(d*x+c)-1)^3*A-1/96/a/d/(sin(d*x+c)-1)^3*B-15/128/a/d/(sin(d*x+c)-1)*A-5/128/a/d/(sin(d*x+c)-1)*B-5/32/a/d/(1+sin(d*x+c))*A-1/64/a/d/(1+sin(d*x+c))^4*A+1/64/a/d/(1+sin(d*x+c))^4*B-1/24/a/d/(1+sin(d*x+c))^3*A+1/48/a/d/(1+sin(d*x+c))^3*B-5/64/a/d/(1+sin(d*x+c))^2*A+1/64/a/d/(1+sin(d*x+c))^2*B+35/256/d/a*ln(1+sin(d*x+c))*A+5/256/d/a*ln(1+sin(d*x+c))*B","A"
1011,1,82,73,0.608000," ","int(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","\frac{-\frac{B \left(\sin^{6}\left(d x +c \right)\right)}{6}+\frac{\left(-A +2 B \right) \left(\sin^{5}\left(d x +c \right)\right)}{5}+\frac{A \left(\sin^{4}\left(d x +c \right)\right)}{2}-\frac{2 B \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(-2 A +B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right)}{d \,a^{2}}"," ",0,"1/d/a^2*(-1/6*B*sin(d*x+c)^6+1/5*(-A+2*B)*sin(d*x+c)^5+1/2*A*sin(d*x+c)^4-2/3*B*sin(d*x+c)^3+1/2*(-2*A+B)*sin(d*x+c)^2+A*sin(d*x+c))","A"
1012,1,58,47,0.594000," ","int(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","\frac{\frac{B \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(A -2 B \right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(-2 A +B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right)}{d \,a^{2}}"," ",0,"1/d/a^2*(1/4*B*sin(d*x+c)^4+1/3*(A-2*B)*sin(d*x+c)^3+1/2*(-2*A+B)*sin(d*x+c)^2+A*sin(d*x+c))","A"
1013,1,85,64,0.609000," ","int(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","-\frac{B \left(\sin^{2}\left(d x +c \right)\right)}{2 d \,a^{2}}-\frac{A \sin \left(d x +c \right)}{d \,a^{2}}+\frac{2 B \sin \left(d x +c \right)}{d \,a^{2}}+\frac{2 \ln \left(1+\sin \left(d x +c \right)\right) A}{d \,a^{2}}-\frac{2 B \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-1/2/d/a^2*B*sin(d*x+c)^2-1/d/a^2*A*sin(d*x+c)+2/d/a^2*B*sin(d*x+c)+2/d/a^2*ln(1+sin(d*x+c))*A-2*B*ln(1+sin(d*x+c))/a^2/d","A"
1014,1,56,43,0.448000," ","int(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","\frac{B \ln \left(1+\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{A}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{B}{d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"B*ln(1+sin(d*x+c))/a^2/d-1/d/a^2/(1+sin(d*x+c))*A+1/d/a^2/(1+sin(d*x+c))*B","A"
1015,1,150,69,0.625000," ","int(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A}{8 d \,a^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{8 d \,a^{2}}-\frac{A}{4 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{4 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{A}{4 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{B}{4 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{8 d \,a^{2}}+\frac{B \ln \left(1+\sin \left(d x +c \right)\right)}{8 a^{2} d}"," ",0,"-1/8/d/a^2*ln(sin(d*x+c)-1)*A-1/8/d/a^2*ln(sin(d*x+c)-1)*B-1/4/d/a^2/(1+sin(d*x+c))^2*A+1/4/d/a^2/(1+sin(d*x+c))^2*B-1/4/d/a^2/(1+sin(d*x+c))*A-1/4/d/a^2/(1+sin(d*x+c))*B+1/8/d/a^2*ln(1+sin(d*x+c))*A+1/8*B*ln(1+sin(d*x+c))/a^2/d","B"
1016,1,207,115,0.757000," ","int(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A}{8 d \,a^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{16 d \,a^{2}}-\frac{A}{16 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{B}{16 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{A}{8 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{A}{12 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{12 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{8 d \,a^{2}}+\frac{B \ln \left(1+\sin \left(d x +c \right)\right)}{16 a^{2} d}-\frac{3 A}{16 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{B}{16 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"-1/8/d/a^2*ln(sin(d*x+c)-1)*A-1/16/d/a^2*ln(sin(d*x+c)-1)*B-1/16/d/a^2/(sin(d*x+c)-1)*A-1/16/d/a^2/(sin(d*x+c)-1)*B-1/8/d/a^2/(1+sin(d*x+c))^2*A-1/12/d/a^2/(1+sin(d*x+c))^3*A+1/12/d/a^2/(1+sin(d*x+c))^3*B+1/8/d/a^2*ln(1+sin(d*x+c))*A+1/16*B*ln(1+sin(d*x+c))/a^2/d-3/16/d/a^2/(1+sin(d*x+c))*A-1/16/d/a^2/(1+sin(d*x+c))*B","A"
1017,1,283,167,0.757000," ","int(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) A}{128 d \,a^{2}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) B}{128 d \,a^{2}}+\frac{A}{64 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{B}{64 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5 A}{64 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 B}{64 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 A}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{A}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{B}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{A}{16 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{48 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}-\frac{5 A}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{B}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) A}{128 d \,a^{2}}+\frac{5 B \ln \left(1+\sin \left(d x +c \right)\right)}{128 a^{2} d}"," ",0,"-15/128/d/a^2*ln(sin(d*x+c)-1)*A-5/128/d/a^2*ln(sin(d*x+c)-1)*B+1/64/d/a^2/(sin(d*x+c)-1)^2*A+1/64/d/a^2/(sin(d*x+c)-1)^2*B-5/64/d/a^2/(sin(d*x+c)-1)*A-3/64/d/a^2/(sin(d*x+c)-1)*B-3/32/d/a^2/(1+sin(d*x+c))^2*A-1/32/d/a^2/(1+sin(d*x+c))^4*A+1/32/d/a^2/(1+sin(d*x+c))^4*B-1/16/d/a^2/(1+sin(d*x+c))^3*A+1/48/d/a^2/(1+sin(d*x+c))^3*B-5/32/d/a^2/(1+sin(d*x+c))*A-1/32/d/a^2/(1+sin(d*x+c))*B+15/128/d/a^2*ln(1+sin(d*x+c))*A+5/128*B*ln(1+sin(d*x+c))/a^2/d","A"
1018,1,359,218,0.765000," ","int(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x)","-\frac{7 \ln \left(\sin \left(d x +c \right)-1\right) A}{64 d \,a^{2}}-\frac{7 \ln \left(\sin \left(d x +c \right)-1\right) B}{256 d \,a^{2}}+\frac{3 A}{128 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{B}{64 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{A}{192 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{B}{192 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{21 A}{256 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{9 B}{256 d \,a^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{5 A}{64 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{A}{80 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{5}}+\frac{B}{80 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{5}}-\frac{A}{32 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{4}}+\frac{B}{64 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{4}}-\frac{5 A}{96 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{96 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{7 \ln \left(1+\sin \left(d x +c \right)\right) A}{64 d \,a^{2}}+\frac{7 B \ln \left(1+\sin \left(d x +c \right)\right)}{256 a^{2} d}-\frac{35 A}{256 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{5 B}{256 d \,a^{2} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"-7/64/d/a^2*ln(sin(d*x+c)-1)*A-7/256/d/a^2*ln(sin(d*x+c)-1)*B+3/128/d/a^2/(sin(d*x+c)-1)^2*A+1/64/d/a^2/(sin(d*x+c)-1)^2*B-1/192/d/a^2/(sin(d*x+c)-1)^3*A-1/192/d/a^2/(sin(d*x+c)-1)^3*B-21/256/d/a^2/(sin(d*x+c)-1)*A-9/256/d/a^2/(sin(d*x+c)-1)*B-5/64/d/a^2/(1+sin(d*x+c))^2*A-1/80/d/a^2/(1+sin(d*x+c))^5*A+1/80/d/a^2/(1+sin(d*x+c))^5*B-1/32/d/a^2/(1+sin(d*x+c))^4*A+1/64/d/a^2/(1+sin(d*x+c))^4*B-5/96/d/a^2/(1+sin(d*x+c))^3*A+1/96/d/a^2/(1+sin(d*x+c))^3*B+7/64/d/a^2*ln(1+sin(d*x+c))*A+7/256*B*ln(1+sin(d*x+c))/a^2/d-35/256/d/a^2/(1+sin(d*x+c))*A-5/256/d/a^2/(1+sin(d*x+c))*B","A"
1019,0,0,152,7.633000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1020,0,0,159,29.033000," ","int(cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{7}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1021,0,0,123,13.371000," ","int(cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{5}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1022,0,0,93,6.831000," ","int(cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{3}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1023,0,0,59,4.703000," ","int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \cos \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1024,0,0,76,2.121000," ","int(sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \sec \left(f x +e \right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1025,0,0,96,0.746000," ","int(sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\sec^{3}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1026,0,0,100,0.850000," ","int(sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\sec^{5}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1027,0,0,115,22.621000," ","int(cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{6}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1028,0,0,115,9.508000," ","int(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1029,0,0,113,4.226000," ","int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1030,0,0,111,0.761000," ","int(sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\sec^{2}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1031,0,0,121,0.822000," ","int(sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\sec^{4}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1032,0,0,121,0.937000," ","int(sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(\sec^{6}\left(f x +e \right)\right) \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int(sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1033,0,0,239,9.041000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-4-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x)","F"
1034,0,0,168,8.198000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-3-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x)","F"
1035,0,0,102,7.814000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-2-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x)","F"
1036,0,0,139,4.136000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-1-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x)","F"
1037,0,0,135,4.821000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x)","F"
1038,0,0,146,4.061000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{1-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x)","F"
1039,0,0,147,4.137000," ","int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(A +B \sin \left(f x +e \right)\right) \left(c -c \sin \left(f x +e \right)\right)^{2-p}\, dx"," ",0,"int((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x)","F"
1040,0,0,32,10.905000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A*m-A*(1+m+p)*sin(f*x+e)),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(A m -A \left(1+m +p \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A*m-A*(1+m+p)*sin(f*x+e)),x)","F"
1041,0,0,34,10.270000," ","int((g*cos(f*x+e))^p*(a-a*sin(f*x+e))^m*(A*m+A*(1+m+p)*sin(f*x+e)),x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a -a \sin \left(f x +e \right)\right)^{m} \left(A m +A \left(1+m +p \right) \sin \left(f x +e \right)\right)\, dx"," ",0,"int((g*cos(f*x+e))^p*(a-a*sin(f*x+e))^m*(A*m+A*(1+m+p)*sin(f*x+e)),x)","F"
1042,0,0,148,5.997000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
1043,0,0,127,4.077000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
1044,0,0,125,1.538000," ","int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(g \cos \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
1045,0,0,127,0.976000," ","int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p} \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +a \sin \left(f x +e \right)}\, dx"," ",0,"int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x)","F"
1046,0,0,127,4.010000," ","int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p} \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x)","F"
1047,0,0,127,2.742000," ","int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p} \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{3}}\, dx"," ",0,"int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x)","F"
1048,0,0,127,3.396000," ","int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p} \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +a \sin \left(f x +e \right)\right)^{4}}\, dx"," ",0,"int((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x)","F"
1049,0,0,153,6.288000," ","int((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(g \sec \left(f x +e \right)\right)^{p} \left(a +a \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
1050,1,95,93,0.128000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+b*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c))","A"
1051,1,77,71,0.117000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)}{d}"," ",0,"1/d*(a*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+b*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3))","A"
1052,1,57,57,0.091000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{-\frac{\left(\cos^{3}\left(d x +c \right)\right) a}{3}+b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)}{d}"," ",0,"1/d*(-1/3*cos(d*x+c)^3*a+b*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c))","A"
1053,1,63,47,0.277000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b x}{2}+\frac{b c}{2 d}"," ",0,"a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/2*b*cos(d*x+c)*sin(d*x+c)/d+1/2*b*x+1/2*b*c/d","A"
1054,1,57,41,0.240000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c)),x)","-a x -\frac{a \cot \left(d x +c \right)}{d}+\frac{b \cos \left(d x +c \right)}{d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{c a}{d}"," ",0,"-a*x-a*cot(d*x+c)/d+b*cos(d*x+c)/d+1/d*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*c*a","A"
1055,1,81,48,0.328000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{2 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-b x -\frac{b \cot \left(d x +c \right)}{d}-\frac{b c}{d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/2*a*cos(d*x+c)/d-1/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-b*x-b*cot(d*x+c)/d-b*c/d","A"
1056,1,80,46,0.404000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b \cos \left(d x +c \right)}{2 d}-\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^3-1/2/d*b/sin(d*x+c)^2*cos(d*x+c)^3-1/2*b*cos(d*x+c)/d-1/2/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1057,1,102,66,0.321000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a \cos \left(d x +c \right)}{8 d}-\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^3-1/8*a*cos(d*x+c)/d-1/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b/sin(d*x+c)^3*cos(d*x+c)^3","A"
1058,1,124,80,0.322000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{b \cos \left(d x +c \right)}{8 d}-\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^3-2/15/d*a/sin(d*x+c)^3*cos(d*x+c)^3-1/4/d*b/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*b/sin(d*x+c)^2*cos(d*x+c)^3-1/8*b*cos(d*x+c)/d-1/8/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1059,1,150,174,0.203000," ","int(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+2 a b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+b^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)}{d}"," ",0,"1/d*(a^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+2*a*b*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+b^2*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3))","A"
1060,1,141,149,0.215000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+2 a b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(a^2*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+2*a*b*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+b^2*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c))","A"
1061,1,94,96,0.186000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3}+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)}{d}"," ",0,"1/d*(-1/3*a^2*cos(d*x+c)^3+2*a*b*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+b^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3))","A"
1062,1,83,84,0.399000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a^{2} \cos \left(d x +c \right)}{d}+\frac{a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+a b x +\frac{a b c}{d}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+a^2*cos(d*x+c)/d+a*b*cos(d*x+c)*sin(d*x+c)/d+a*b*x+1/d*a*b*c-1/3*b^2*cos(d*x+c)^3/d","A"
1063,1,102,74,0.384000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-a^{2} x -\frac{a^{2} \cot \left(d x +c \right)}{d}-\frac{a^{2} c}{d}+\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{2} x}{2}+\frac{b^{2} c}{2 d}"," ",0,"-a^2*x-a^2*cot(d*x+c)/d-1/d*a^2*c+2*a*b*cos(d*x+c)/d+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/2*b^2*cos(d*x+c)*sin(d*x+c)/d+1/2*b^2*x+1/2/d*b^2*c","A"
1064,1,126,83,0.510000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \cos \left(d x +c \right)}{2 d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-2 a b x -\frac{2 a b \cot \left(d x +c \right)}{d}-\frac{2 a b c}{d}+\frac{b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-1/2*a^2*cos(d*x+c)/d-1/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2*a*b*x-2*a*b*cot(d*x+c)/d-2/d*a*b*c+b^2*cos(d*x+c)/d+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1065,1,114,90,0.422000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \cos \left(d x +c \right)}{d}-\frac{a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-b^{2} x -\frac{b^{2} \cot \left(d x +c \right)}{d}-\frac{b^{2} c}{d}"," ",0,"-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^3-a*b*cos(d*x+c)/d-1/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-b^2*x-b^2*cot(d*x+c)/d-1/d*b^2*c","A"
1066,1,173,113,0.461000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \cos \left(d x +c \right)}{8 d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \cos \left(d x +c \right)}{2 d}-\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-1/8*a^2*cos(d*x+c)/d-1/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*a*b/sin(d*x+c)^3*cos(d*x+c)^3-1/2/d*b^2/sin(d*x+c)^2*cos(d*x+c)^3-1/2*b^2*cos(d*x+c)/d-1/2/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1067,1,156,136,0.488000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}-\frac{a b \cos \left(d x +c \right)}{4 d}-\frac{a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^3-2/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^3-1/2/d*a*b/sin(d*x+c)^4*cos(d*x+c)^3-1/4/d*a*b/sin(d*x+c)^2*cos(d*x+c)^3-1/4*a*b*cos(d*x+c)/d-1/4/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b^2/sin(d*x+c)^3*cos(d*x+c)^3","A"
1068,1,244,156,0.470000," ","int(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \cos \left(d x +c \right)}{16 d}-\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{4 a b \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \cos \left(d x +c \right)}{8 d}-\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^3-1/8/d*a^2/sin(d*x+c)^4*cos(d*x+c)^3-1/16/d*a^2/sin(d*x+c)^2*cos(d*x+c)^3-1/16*a^2*cos(d*x+c)/d-1/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5/d*a*b/sin(d*x+c)^5*cos(d*x+c)^3-4/15/d*a*b/sin(d*x+c)^3*cos(d*x+c)^3-1/4/d*b^2/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*b^2/sin(d*x+c)^2*cos(d*x+c)^3-1/8*b^2*cos(d*x+c)/d-1/8/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1069,1,196,216,0.220000," ","int(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+3 a^{2} b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+3 a \,b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)+b^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{7}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{35}-\frac{8 \left(\cos^{3}\left(d x +c \right)\right)}{105}\right)}{d}"," ",0,"1/d*(a^3*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+3*a^2*b*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+3*a*b^2*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c)+b^3*(-1/7*sin(d*x+c)^4*cos(d*x+c)^3-4/35*sin(d*x+c)^2*cos(d*x+c)^3-8/105*cos(d*x+c)^3))","A"
1070,1,158,151,0.207000," ","int(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3}+3 a^{2} b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{8}+\frac{d x}{8}+\frac{c}{8}\right)+3 a \,b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{5}-\frac{2 \left(\cos^{3}\left(d x +c \right)\right)}{15}\right)+b^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{3}\left(d x +c \right)\right)}{6}-\frac{\sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{8}+\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{16}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(-1/3*a^3*cos(d*x+c)^3+3*a^2*b*(-1/4*cos(d*x+c)^3*sin(d*x+c)+1/8*cos(d*x+c)*sin(d*x+c)+1/8*d*x+1/8*c)+3*a*b^2*(-1/5*sin(d*x+c)^2*cos(d*x+c)^3-2/15*cos(d*x+c)^3)+b^3*(-1/6*sin(d*x+c)^3*cos(d*x+c)^3-1/8*cos(d*x+c)^3*sin(d*x+c)+1/16*cos(d*x+c)*sin(d*x+c)+1/16*d*x+1/16*c))","A"
1071,1,150,126,0.426000," ","int(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \cos \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} b x}{2}+\frac{3 a^{2} b c}{2 d}-\frac{a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{b^{3} x}{8}+\frac{b^{3} c}{8 d}"," ",0,"a^3*cos(d*x+c)/d+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3/2/d*a^2*b*cos(d*x+c)*sin(d*x+c)+3/2*a^2*b*x+3/2/d*a^2*b*c-a*b^2*cos(d*x+c)^3/d-1/4/d*b^3*cos(d*x+c)^3*sin(d*x+c)+1/8*b^3*cos(d*x+c)*sin(d*x+c)/d+1/8*b^3*x+1/8/d*b^3*c","A"
1072,1,125,96,0.402000," ","int(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","-a^{3} x -\frac{a^{3} \cot \left(d x +c \right)}{d}-\frac{a^{3} c}{d}+\frac{3 a^{2} b \cos \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a \,b^{2} x}{2}+\frac{3 a \,b^{2} c}{2 d}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}"," ",0,"-a^3*x-a^3*cot(d*x+c)/d-1/d*a^3*c+3*a^2*b*cos(d*x+c)/d+3/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))+3/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d+3/2*a*b^2*x+3/2/d*a*b^2*c-1/3*b^3*cos(d*x+c)^3/d","A"
1073,1,171,126,0.502000," ","int(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \cos \left(d x +c \right)}{2 d}-\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-3 a^{2} b x -\frac{3 a^{2} b \cot \left(d x +c \right)}{d}-\frac{3 a^{2} b c}{d}+\frac{3 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{b^{3} x}{2}+\frac{b^{3} c}{2 d}"," ",0,"-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-1/2*a^3*cos(d*x+c)/d-1/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3*a^2*b*x-3*a^2*b*cot(d*x+c)/d-3/d*a^2*b*c+3*a*b^2*cos(d*x+c)/d+3/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))+1/2*b^3*cos(d*x+c)*sin(d*x+c)/d+1/2*b^3*x+1/2/d*b^3*c","A"
1074,1,159,128,0.462000," ","int(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} b \cos \left(d x +c \right)}{2 d}-\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-3 a \,b^{2} x -\frac{3 a \,b^{2} \cot \left(d x +c \right)}{d}-\frac{3 a \,b^{2} c}{d}+\frac{b^{3} \cos \left(d x +c \right)}{d}+\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3-3/2/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^3-3/2*a^2*b*cos(d*x+c)/d-3/2/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-3*a*b^2*x-3*a*b^2*cot(d*x+c)/d-3/d*a*b^2*c+b^3*cos(d*x+c)/d+1/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1075,1,207,142,0.480000," ","int(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \cos \left(d x +c \right)}{8 d}-\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}-\frac{3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \cos \left(d x +c \right)}{2 d}-\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-b^{3} x -\frac{\cot \left(d x +c \right) b^{3}}{d}-\frac{b^{3} c}{d}"," ",0,"-1/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^3-1/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-1/8*a^3*cos(d*x+c)/d-1/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^2*b/sin(d*x+c)^3*cos(d*x+c)^3-3/2/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^3-3/2*a*b^2*cos(d*x+c)/d-3/2/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))-b^3*x-1/d*cot(d*x+c)*b^3-1/d*b^3*c","A"
1076,1,227,171,0.487000," ","int(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} b \cos \left(d x +c \right)}{8 d}-\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{3}}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{3} \cos \left(d x +c \right)}{2 d}-\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^3-2/15/d*a^3/sin(d*x+c)^3*cos(d*x+c)^3-3/4/d*a^2*b/sin(d*x+c)^4*cos(d*x+c)^3-3/8/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^3-3/8*a^2*b*cos(d*x+c)/d-3/8/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*a*b^2/sin(d*x+c)^3*cos(d*x+c)^3-1/2/d*b^3/sin(d*x+c)^2*cos(d*x+c)^3-1/2*b^3*cos(d*x+c)/d-1/2/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1077,1,276,198,0.481000," ","int(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \cos \left(d x +c \right)}{16 d}-\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{2 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{3}}-\frac{3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}-\frac{3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \cos \left(d x +c \right)}{8 d}-\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}"," ",0,"-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^3-1/8/d*a^3/sin(d*x+c)^4*cos(d*x+c)^3-1/16/d*a^3/sin(d*x+c)^2*cos(d*x+c)^3-1/16*a^3*cos(d*x+c)/d-1/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/5/d*a^2*b/sin(d*x+c)^5*cos(d*x+c)^3-2/5/d*a^2*b/sin(d*x+c)^3*cos(d*x+c)^3-3/4/d*a*b^2/sin(d*x+c)^4*cos(d*x+c)^3-3/8/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^3-3/8*a*b^2*cos(d*x+c)/d-3/8/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b^3/sin(d*x+c)^3*cos(d*x+c)^3","A"
1078,1,460,179,0.554000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{2 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}+\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{8 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{6 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2*tan(1/2*d*x+1/2*c)^2-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2-2/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3+8/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+2/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-8/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1079,1,353,144,0.509000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{6 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*a-6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b^2*arctan(tan(1/2*d*x+1/2*c))-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)-2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2+6/d/b^4*a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1080,1,229,101,0.454000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{2}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}"," ",0,"2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)+4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a-4/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1081,1,153,87,0.682000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/a^2*ln(tan(1/2*d*x+1/2*c))+2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b+2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1082,1,245,110,0.752000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
1083,1,307,148,0.811000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{b}{d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3*tan(1/2*d*x+1/2*c)*b-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+3/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+1/d*b/a^3/tan(1/2*d*x+1/2*c)+2/d*b^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*b^2/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+4/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*b^3/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1084,1,390,184,0.820000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \,a^{3}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{8 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^3*tan(1/2*d*x+1/2*c)^2*b-1/8/d/a^2*tan(1/2*d*x+1/2*c)+3/2/d/a^4*b^2*tan(1/2*d*x+1/2*c)-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3+1/8/d/a^2/tan(1/2*d*x+1/2*c)-3/2/d/a^4/tan(1/2*d*x+1/2*c)*b^2+1/4/d/a^3*b/tan(1/2*d*x+1/2*c)^2+1/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-4/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))-2/d*b^4/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d*b^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-6/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+8/d*b^4/a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1085,1,845,251,0.582000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}-\frac{5 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{4 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{6 a^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{7 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{10 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{19 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{16 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{6 a^{5}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{5 a^{3}}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{12 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{19 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{6 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*a-12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b^3*arctan(tan(1/2*d*x+1/2*c))-5/d*a^4/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+4/d*a^2/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-6/d*a^5/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-7/d*a^3/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+10/d*a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-19/d*a^4/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)+16/d*a^2/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)-6/d*a^5/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)+5/d*a^3/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)+12/d*a^5/b^5/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-19/d*a^3/b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a/b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1086,1,711,169,0.538000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{2}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{6 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4}}+\frac{3 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{2 a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{6 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{13 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{10 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{4 a^{4}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 a^{2}}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{9 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)+6/d/b^4*a*arctan(tan(1/2*d*x+1/2*c))+3/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2*a^4+5/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2*a^2-6/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+13/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)-10/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)+4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4/(a^2-b^2)-3/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2/(a^2-b^2)-6/d/b^4/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4+9/d/b^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-2/d/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1087,1,576,157,0.506000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}-\frac{a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{2 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a \left(a^{2}-b^{2}\right)}-\frac{7 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{4 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{2 a^{3}}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{a}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{3 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))-1/d*a^2/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-2/d*a^3/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-3/d*a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+2/d*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-7/d*a^2/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)+4/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)-2/d*a^3/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)+1/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)+2/d*a^3/b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/d*a/b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1088,1,632,145,0.721000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{3 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{4 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a \left(a^{2}-b^{2}\right)}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{5 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{2 a}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 b^{2}}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/d/a^3*ln(tan(1/2*d*x+1/2*c))+3/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+2/d*a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+1/d*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2*b^4+5/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)-8/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a/(a^2-b^2)-3/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)-3/d/a*b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^3*b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1089,1,729,191,0.735000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{5 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{6 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{4 b \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{3 b^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{10 b^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{11 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{14 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{4 b}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{5 b^{3}}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{9 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{2} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-5/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-4/d*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-3/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+10/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^5/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2-11/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)+14/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)-4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b/(a^2-b^2)+5/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)-2/d/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+9/d/a^2/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2-6/d/a^4/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1090,1,803,254,0.931000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{4}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{3 b}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{7 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{8 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{6 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a \left(a^{2}-b^{2}\right)}+\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{14 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{17 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{20 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{6 b^{2}}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}-\frac{7 b^{4}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} \left(a^{2}-b^{2}\right)}+\frac{6 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}-\frac{19 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}+\frac{12 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \left(a^{2}-b^{2}\right)^{\frac{3}{2}}}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^4*tan(1/2*d*x+1/2*c)*b-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2-1/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+6/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2+3/2/d*b/a^4/tan(1/2*d*x+1/2*c)+7/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3-8/d*b^5/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^3+6/d*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+5/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2*b^4-14/d*b^6/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)^2+17/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)-20/d*b^5/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)+6/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2/(a^2-b^2)-7/d*b^4/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/(a^2-b^2)+6/d/a*b/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-19/d/a^3*b^3/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+12/d*b^5/a^5/(a^2-b^2)^(3/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1091,1,4675,307,0.660000," ","int(cos(f*x+e)^2/(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-1/3/f*(-4*cos(f*x+e)*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b^3+4*cos(f*x+e)*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b^2-4*cos(f*x+e)*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^4+2*cos(f*x+e)*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a^2*b-4*cos(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*b^2+4*cos(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*b-4*cos(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^3+2*cos(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a^3-4*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*b^3+4*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b^2-4*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^4+2*sin(f*x+e)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a^2*b-4*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a*b^2+4*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^3*b-4*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a*b^3+2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*(-a^2+b^2)^(1/2)*a^3+2*cos(f*x+e)^2*2^(1/2)*a*b^3+cos(f*x+e)*sin(f*x+e)*2^(1/2)*a^4+cos(f*x+e)*sin(f*x+e)*2^(1/2)*a^2*b^2+2*cos(f*x+e)*2^(1/2)*a^3*b-4*sin(f*x+e)*2^(1/2)*a^2*b^2-2*2^(1/2)*a^3*b-2*2^(1/2)*a*b^3)*(a+b*sin(f*x+e))^(1/2)/(b^2*cos(f*x+e)^2-2*a*b*sin(f*x+e)-a^2-b^2)/(d*sin(f*x+e))^(1/2)*2^(1/2)/(a^2-b^2)/a^3","B"
1092,1,124,127,0.295000," ","int(cos(d*x+c)^4*sin(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+b \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)}{d}"," ",0,"1/d*(a*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+b*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5))","A"
1093,1,106,113,0.279000," ","int(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(a*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+b*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
1094,1,88,91,0.286000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)}{d}"," ",0,"1/d*(a*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+b*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5))","A"
1095,1,68,77,0.277000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5}+b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)}{d}"," ",0,"1/d*(-1/5*a*cos(d*x+c)^5+b*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c))","A"
1096,1,97,81,0.417000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cos \left(d x +c \right)}{d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{3 b \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 b x}{8}+\frac{3 b c}{8 d}"," ",0,"1/3*a*cos(d*x+c)^3/d+a*cos(d*x+c)/d+1/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/4*b*cos(d*x+c)^3*sin(d*x+c)/d+3/8*b*cos(d*x+c)*sin(d*x+c)/d+3/8*b*x+3/8*b*c/d","A"
1097,1,119,75,0.390000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 a x}{2}-\frac{3 c a}{2 d}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{b \cos \left(d x +c \right)}{d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^5-a*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a*cos(d*x+c)*sin(d*x+c)/d-3/2*a*x-3/2/d*c*a+1/3*b*cos(d*x+c)^3/d+b*cos(d*x+c)/d+1/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1098,1,143,82,0.464000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a \cos \left(d x +c \right)}{2 d}-\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 b \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b x}{2}-\frac{3 b c}{2 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a*cos(d*x+c)^3/d-3/2*a*cos(d*x+c)/d-3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/d*b/sin(d*x+c)*cos(d*x+c)^5-b*cos(d*x+c)^3*sin(d*x+c)/d-3/2*b*cos(d*x+c)*sin(d*x+c)/d-3/2*b*x-3/2*b*c/d","A"
1099,1,106,74,0.307000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a \cot \left(d x +c \right)}{d}+a x +\frac{c a}{d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 b \cos \left(d x +c \right)}{2 d}-\frac{3 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/3*a*cot(d*x+c)^3/d+a*cot(d*x+c)/d+a*x+1/d*c*a-1/2/d*b/sin(d*x+c)^2*cos(d*x+c)^5-1/2*b*cos(d*x+c)^3/d-3/2*b*cos(d*x+c)/d-3/2/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1100,1,128,80,0.339000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a \cos \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{b \cot \left(d x +c \right)}{d}+b x +\frac{b c}{d}"," ",0,"-1/4/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/8*a*cos(d*x+c)^3/d+3/8*a*cos(d*x+c)/d+3/8/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/3*b*cot(d*x+c)^3/d+b*cot(d*x+c)/d+b*x+b*c/d","A"
1101,1,116,66,0.339000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 b \cos \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^5-1/4/d*b/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*b/sin(d*x+c)^2*cos(d*x+c)^5+1/8*b*cos(d*x+c)^3/d+3/8*b*cos(d*x+c)/d+3/8/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1102,1,138,88,0.341000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{a \cos \left(d x +c \right)}{16 d}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/6/d*a/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/48*a*cos(d*x+c)^3/d+1/16*a*cos(d*x+c)/d+1/16/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*b/sin(d*x+c)^5*cos(d*x+c)^5","A"
1103,1,160,102,0.343000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{b \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{b \cos \left(d x +c \right)}{16 d}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}"," ",0,"-1/7/d*a/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*a/sin(d*x+c)^5*cos(d*x+c)^5-1/6/d*b/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*b/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*b/sin(d*x+c)^2*cos(d*x+c)^5+1/48*b*cos(d*x+c)^3/d+1/16*b*cos(d*x+c)/d+1/16/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1104,1,182,122,0.339000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{6}}-\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{4}}+\frac{a \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}+\frac{a \left(\cos^{3}\left(d x +c \right)\right)}{128 d}+\frac{3 a \cos \left(d x +c \right)}{128 d}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{b \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 b \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/8/d*a/sin(d*x+c)^8*cos(d*x+c)^5-1/16/d*a/sin(d*x+c)^6*cos(d*x+c)^5-1/64/d*a/sin(d*x+c)^4*cos(d*x+c)^5+1/128/d*a/sin(d*x+c)^2*cos(d*x+c)^5+1/128*a*cos(d*x+c)^3/d+3/128*a*cos(d*x+c)/d+3/128/d*a*ln(csc(d*x+c)-cot(d*x+c))-1/7/d*b/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*b/sin(d*x+c)^5*cos(d*x+c)^5","A"
1105,1,161,281,0.333000," ","int(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+2 a b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+b^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)}{d}"," ",0,"1/d*(a^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+2*a*b*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+b^2*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5))","A"
1106,1,163,260,0.331000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+2 a b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(a^2*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+2*a*b*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+b^2*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
1107,1,105,117,0.328000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5}+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)}{d}"," ",0,"1/d*(-1/5*a^2*cos(d*x+c)^5+2*a*b*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+b^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5))","A"
1108,1,123,106,0.545000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cos \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}+\frac{3 a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{4 d}+\frac{3 a b x}{4}+\frac{3 a b c}{4 d}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}"," ",0,"1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)/d+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+1/2*a*b*cos(d*x+c)^3*sin(d*x+c)/d+3/4*a*b*cos(d*x+c)*sin(d*x+c)/d+3/4*a*b*x+3/4/d*a*b*c-1/5*b^2*cos(d*x+c)^5/d","A"
1109,1,191,171,0.536000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 a^{2} x}{2}-\frac{3 a^{2} c}{2 d}+\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{3 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 b^{2} x}{8}+\frac{3 b^{2} c}{8 d}"," ",0,"-1/d*a^2/sin(d*x+c)*cos(d*x+c)^5-a^2*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a^2*cos(d*x+c)*sin(d*x+c)/d-3/2*a^2*x-3/2/d*a^2*c+2/3*a*b*cos(d*x+c)^3/d+2*a*b*cos(d*x+c)/d+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/4*b^2*cos(d*x+c)^3*sin(d*x+c)/d+3/8*b^2*cos(d*x+c)*sin(d*x+c)/d+3/8*b^2*x+3/8/d*b^2*c","A"
1110,1,208,177,0.652000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} \cos \left(d x +c \right)}{2 d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}-3 a b x -\frac{3 a b c}{d}+\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a^2*cos(d*x+c)^3/d-3/2*a^2*cos(d*x+c)/d-3/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/d*a*b/sin(d*x+c)*cos(d*x+c)^5-2*a*b*cos(d*x+c)^3*sin(d*x+c)/d-3*a*b*cos(d*x+c)*sin(d*x+c)/d-3*a*b*x-3/d*a*b*c+1/3*b^2*cos(d*x+c)^3/d+b^2*cos(d*x+c)/d+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1111,1,199,125,0.449000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cot \left(d x +c \right)}{d}+a^{2} x +\frac{a^{2} c}{d}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{3 a b \cos \left(d x +c \right)}{d}-\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b^{2} x}{2}-\frac{3 b^{2} c}{2 d}"," ",0,"-1/3*a^2*cot(d*x+c)^3/d+a^2*cot(d*x+c)/d+a^2*x+1/d*a^2*c-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^5-a*b*cos(d*x+c)^3/d-3*a*b*cos(d*x+c)/d-3/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*b^2/sin(d*x+c)*cos(d*x+c)^5-b^2*cos(d*x+c)^3*sin(d*x+c)/d-3/2*b^2*cos(d*x+c)*sin(d*x+c)/d-3/2*b^2*x-3/2/d*b^2*c","A"
1112,1,223,166,0.484000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} \cos \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \cot \left(d x +c \right)}{d}+2 a b x +\frac{2 a b c}{d}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{2} \cos \left(d x +c \right)}{2 d}-\frac{3 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+1/8*a^2*cos(d*x+c)^3/d+3/8*a^2*cos(d*x+c)/d+3/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3*a*b*cot(d*x+c)^3/d+2*a*b*cot(d*x+c)/d+2*a*b*x+2/d*a*b*c-1/2/d*b^2/sin(d*x+c)^2*cos(d*x+c)^5-1/2*b^2*cos(d*x+c)^3/d-3/2*b^2*cos(d*x+c)/d-3/2/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1113,1,165,197,0.503000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a b \cos \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \cot \left(d x +c \right)}{d}+b^{2} x +\frac{b^{2} c}{d}"," ",0,"-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/2/d*a*b/sin(d*x+c)^4*cos(d*x+c)^5+1/4/d*a*b/sin(d*x+c)^2*cos(d*x+c)^5+1/4*a*b*cos(d*x+c)^3/d+3/4*a*b*cos(d*x+c)/d+3/4/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/3*b^2*cot(d*x+c)^3/d+b^2*cot(d*x+c)/d+b^2*x+1/d*b^2*c","A"
1114,1,253,222,0.488000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{a^{2} \cos \left(d x +c \right)}{16 d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 b^{2} \cos \left(d x +c \right)}{8 d}+\frac{3 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*a^2/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*a^2/sin(d*x+c)^2*cos(d*x+c)^5+1/48*a^2*cos(d*x+c)^3/d+1/16*a^2*cos(d*x+c)/d+1/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5/d*a*b/sin(d*x+c)^5*cos(d*x+c)^5-1/4/d*b^2/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*b^2/sin(d*x+c)^2*cos(d*x+c)^5+1/8*b^2*cos(d*x+c)^3/d+3/8*b^2*cos(d*x+c)/d+3/8/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1115,1,194,245,0.472000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{6}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{4}}+\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{2}}+\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{24 d}+\frac{a b \cos \left(d x +c \right)}{8 d}+\frac{a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/7/d*a^2/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*a^2/sin(d*x+c)^5*cos(d*x+c)^5-1/3/d*a*b/sin(d*x+c)^6*cos(d*x+c)^5-1/12/d*a*b/sin(d*x+c)^4*cos(d*x+c)^5+1/24/d*a*b/sin(d*x+c)^2*cos(d*x+c)^5+1/24*a*b*cos(d*x+c)^3/d+1/8*a*b*cos(d*x+c)/d+1/8/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*b^2/sin(d*x+c)^5*cos(d*x+c)^5","A"
1116,1,218,334,0.335000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+3 a^{2} b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+3 a \,b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)+b^{3} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{9}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{63}-\frac{8 \left(\cos^{5}\left(d x +c \right)\right)}{315}\right)}{d}"," ",0,"1/d*(a^3*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+3*a^2*b*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+3*a*b^2*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c)+b^3*(-1/9*sin(d*x+c)^4*cos(d*x+c)^5-4/63*sin(d*x+c)^2*cos(d*x+c)^5-8/315*cos(d*x+c)^5))","A"
1117,1,180,180,0.332000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5}+3 a^{2} b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{24}+\frac{d x}{16}+\frac{c}{16}\right)+3 a \,b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{7}-\frac{2 \left(\cos^{5}\left(d x +c \right)\right)}{35}\right)+b^{3} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{5}\left(d x +c \right)\right)}{8}-\frac{\sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{16}+\frac{\left(\cos^{3}\left(d x +c \right)+\frac{3 \cos \left(d x +c \right)}{2}\right) \sin \left(d x +c \right)}{64}+\frac{3 d x}{128}+\frac{3 c}{128}\right)}{d}"," ",0,"1/d*(-1/5*a^3*cos(d*x+c)^5+3*a^2*b*(-1/6*sin(d*x+c)*cos(d*x+c)^5+1/24*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+1/16*d*x+1/16*c)+3*a*b^2*(-1/7*sin(d*x+c)^2*cos(d*x+c)^5-2/35*cos(d*x+c)^5)+b^3*(-1/8*sin(d*x+c)^3*cos(d*x+c)^5-1/16*sin(d*x+c)*cos(d*x+c)^5+1/64*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/128*d*x+3/128*c))","A"
1118,1,211,236,0.575000," ","int(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cos \left(d x +c \right)}{d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a^{2} b \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{9 a^{2} b x}{8}+\frac{9 a^{2} b c}{8 d}-\frac{3 \left(\cos^{5}\left(d x +c \right)\right) a \,b^{2}}{5 d}-\frac{b^{3} \sin \left(d x +c \right) \left(\cos^{5}\left(d x +c \right)\right)}{6 d}+\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}+\frac{b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{b^{3} x}{16}+\frac{b^{3} c}{16 d}"," ",0,"1/3*a^3*cos(d*x+c)^3/d+a^3*cos(d*x+c)/d+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3/4/d*a^2*b*sin(d*x+c)*cos(d*x+c)^3+9/8/d*a^2*b*cos(d*x+c)*sin(d*x+c)+9/8*a^2*b*x+9/8/d*a^2*b*c-3/5/d*cos(d*x+c)^5*a*b^2-1/6/d*b^3*sin(d*x+c)*cos(d*x+c)^5+1/24/d*b^3*cos(d*x+c)^3*sin(d*x+c)+1/16*b^3*cos(d*x+c)*sin(d*x+c)/d+1/16*b^3*x+1/16/d*b^3*c","A"
1119,1,216,217,0.538000," ","int(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 a^{3} x}{2}-\frac{3 a^{3} c}{2 d}+\frac{a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \cos \left(d x +c \right)}{d}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{9 a \,b^{2} x}{8}+\frac{9 a \,b^{2} c}{8 d}-\frac{\left(\cos^{5}\left(d x +c \right)\right) b^{3}}{5 d}"," ",0,"-1/d*a^3/sin(d*x+c)*cos(d*x+c)^5-a^3*cos(d*x+c)^3*sin(d*x+c)/d-3/2*a^3*cos(d*x+c)*sin(d*x+c)/d-3/2*a^3*x-3/2/d*a^3*c+1/d*a^2*b*cos(d*x+c)^3+3*a^2*b*cos(d*x+c)/d+3/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))+3/4/d*a*b^2*sin(d*x+c)*cos(d*x+c)^3+9/8*a*b^2*cos(d*x+c)*sin(d*x+c)/d+9/8*a*b^2*x+9/8/d*a*b^2*c-1/5/d*cos(d*x+c)^5*b^3","A"
1120,1,279,217,0.656000," ","int(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{3} \cos \left(d x +c \right)}{2 d}-\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{3 a^{2} b \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{9 a^{2} b \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{9 a^{2} b x}{2}-\frac{9 a^{2} b c}{2 d}+\frac{a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \cos \left(d x +c \right)}{d}+\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}+\frac{3 b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 b^{3} x}{8}+\frac{3 b^{3} c}{8 d}"," ",0,"-1/2/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5-1/2*a^3*cos(d*x+c)^3/d-3/2*a^3*cos(d*x+c)/d-3/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/d*a^2*b/sin(d*x+c)*cos(d*x+c)^5-3/d*a^2*b*sin(d*x+c)*cos(d*x+c)^3-9/2/d*a^2*b*cos(d*x+c)*sin(d*x+c)-9/2*a^2*b*x-9/2/d*a^2*b*c+a*b^2*cos(d*x+c)^3/d+3*a*b^2*cos(d*x+c)/d+3/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))+1/4/d*b^3*cos(d*x+c)^3*sin(d*x+c)+3/8*b^3*cos(d*x+c)*sin(d*x+c)/d+3/8*b^3*x+3/8/d*b^3*c","A"
1121,1,264,178,0.598000," ","int(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} \cot \left(d x +c \right)}{d}+a^{3} x +\frac{a^{3} c}{d}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{9 a^{2} b \cos \left(d x +c \right)}{2 d}-\frac{9 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{3 a \,b^{2} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{d}-\frac{9 a \,b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{9 a \,b^{2} x}{2}-\frac{9 a \,b^{2} c}{2 d}+\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{3} \cos \left(d x +c \right)}{d}+\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/3*a^3*cot(d*x+c)^3/d+a^3*cot(d*x+c)/d+a^3*x+1/d*a^3*c-3/2/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^5-3/2/d*a^2*b*cos(d*x+c)^3-9/2*a^2*b*cos(d*x+c)/d-9/2/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-3/d*a*b^2/sin(d*x+c)*cos(d*x+c)^5-3/d*a*b^2*sin(d*x+c)*cos(d*x+c)^3-9/2*a*b^2*cos(d*x+c)*sin(d*x+c)/d-9/2*a*b^2*x-9/2/d*a*b^2*c+1/3*b^3*cos(d*x+c)^3/d+b^3*cos(d*x+c)/d+1/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1122,1,316,173,0.636000," ","int(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 a^{3} \cos \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a^{2} b \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 a^{2} b x +\frac{3 a^{2} b \cot \left(d x +c \right)}{d}+\frac{3 a^{2} b c}{d}-\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{9 a \,b^{2} \cos \left(d x +c \right)}{2 d}-\frac{9 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{3 b^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}-\frac{3 b^{3} x}{2}-\frac{3 b^{3} c}{2 d}"," ",0,"-1/4/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+1/8*a^3*cos(d*x+c)^3/d+3/8*a^3*cos(d*x+c)/d+3/8/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-1/d*a^2*b*cot(d*x+c)^3+3*a^2*b*x+3*a^2*b*cot(d*x+c)/d+3/d*a^2*b*c-3/2/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^5-3/2*a*b^2*cos(d*x+c)^3/d-9/2*a*b^2*cos(d*x+c)/d-9/2/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))-1/d*b^3/sin(d*x+c)*cos(d*x+c)^5-1/d*b^3*cos(d*x+c)^3*sin(d*x+c)-3/2*b^3*cos(d*x+c)*sin(d*x+c)/d-3/2*b^3*x-3/2/d*b^3*c","A"
1123,1,260,213,0.511000," ","int(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{9 a^{2} b \cos \left(d x +c \right)}{8 d}+\frac{9 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{a \,b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{d}+3 a \,b^{2} x +\frac{3 a \,b^{2} \cot \left(d x +c \right)}{d}+\frac{3 a \,b^{2} c}{d}-\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{3} \cos \left(d x +c \right)}{2 d}-\frac{3 b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/5/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-3/4/d*a^2*b/sin(d*x+c)^4*cos(d*x+c)^5+3/8/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^5+3/8/d*a^2*b*cos(d*x+c)^3+9/8*a^2*b*cos(d*x+c)/d+9/8/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-a*b^2*cot(d*x+c)^3/d+3*a*b^2*x+3*a*b^2*cot(d*x+c)/d+3/d*a*b^2*c-1/2/d*b^3/sin(d*x+c)^2*cos(d*x+c)^5-1/2*b^3*cos(d*x+c)^3/d-3/2*b^3*cos(d*x+c)/d-3/2/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1124,1,302,261,0.510000," ","int(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}+\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{2}}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}+\frac{a^{3} \cos \left(d x +c \right)}{16 d}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{9 a \,b^{2} \cos \left(d x +c \right)}{8 d}+\frac{9 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b^{3} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}+\frac{\cot \left(d x +c \right) b^{3}}{d}+b^{3} x +\frac{b^{3} c}{d}"," ",0,"-1/6/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-1/24/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+1/48/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+1/48*a^3*cos(d*x+c)^3/d+1/16*a^3*cos(d*x+c)/d+1/16/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/5/d*a^2*b/sin(d*x+c)^5*cos(d*x+c)^5-3/4/d*a*b^2/sin(d*x+c)^4*cos(d*x+c)^5+3/8/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^5+3/8*a*b^2*cos(d*x+c)^3/d+9/8*a*b^2*cos(d*x+c)/d+9/8/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b^3*cot(d*x+c)^3+1/d*cot(d*x+c)*b^3+b^3*x+1/d*b^3*c","A"
1125,1,309,287,0.498000," ","int(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{2 a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{6}}-\frac{a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}+\frac{a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}+\frac{a^{2} b \left(\cos^{3}\left(d x +c \right)\right)}{16 d}+\frac{3 a^{2} b \cos \left(d x +c \right)}{16 d}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{3 a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}-\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{b^{3} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{3 b^{3} \cos \left(d x +c \right)}{8 d}+\frac{3 b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/7/d*a^3/sin(d*x+c)^7*cos(d*x+c)^5-2/35/d*a^3/sin(d*x+c)^5*cos(d*x+c)^5-1/2/d*a^2*b/sin(d*x+c)^6*cos(d*x+c)^5-1/8/d*a^2*b/sin(d*x+c)^4*cos(d*x+c)^5+1/16/d*a^2*b/sin(d*x+c)^2*cos(d*x+c)^5+1/16/d*a^2*b*cos(d*x+c)^3+3/16*a^2*b*cos(d*x+c)/d+3/16/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))-3/5/d*a*b^2/sin(d*x+c)^5*cos(d*x+c)^5-1/4/d*b^3/sin(d*x+c)^4*cos(d*x+c)^5+1/8/d*b^3/sin(d*x+c)^2*cos(d*x+c)^5+1/8*b^3*cos(d*x+c)^3/d+3/8*b^3*cos(d*x+c)/d+3/8/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1126,1,358,316,0.501000," ","int(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{6}}-\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{4}}+\frac{a^{3} \left(\cos^{5}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}+\frac{a^{3} \left(\cos^{3}\left(d x +c \right)\right)}{128 d}+\frac{3 a^{3} \cos \left(d x +c \right)}{128 d}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{3 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{6 a^{2} b \left(\cos^{5}\left(d x +c \right)\right)}{35 d \sin \left(d x +c \right)^{5}}-\frac{a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{6}}-\frac{a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{4}}+\frac{a \,b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}+\frac{a \,b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{16 d}+\frac{3 a \,b^{2} \cos \left(d x +c \right)}{16 d}+\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{b^{3} \left(\cos^{5}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}"," ",0,"-1/8/d*a^3/sin(d*x+c)^8*cos(d*x+c)^5-1/16/d*a^3/sin(d*x+c)^6*cos(d*x+c)^5-1/64/d*a^3/sin(d*x+c)^4*cos(d*x+c)^5+1/128/d*a^3/sin(d*x+c)^2*cos(d*x+c)^5+1/128*a^3*cos(d*x+c)^3/d+3/128*a^3*cos(d*x+c)/d+3/128/d*a^3*ln(csc(d*x+c)-cot(d*x+c))-3/7/d*a^2*b/sin(d*x+c)^7*cos(d*x+c)^5-6/35/d*a^2*b/sin(d*x+c)^5*cos(d*x+c)^5-1/2/d*a*b^2/sin(d*x+c)^6*cos(d*x+c)^5-1/8/d*a*b^2/sin(d*x+c)^4*cos(d*x+c)^5+1/16/d*a*b^2/sin(d*x+c)^2*cos(d*x+c)^5+1/16*a*b^2*cos(d*x+c)^3/d+3/16*a*b^2*cos(d*x+c)/d+3/16/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))-1/5/d*b^3/sin(d*x+c)^5*cos(d*x+c)^5","A"
1127,1,1119,290,0.584000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","-\frac{8 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{3}}-\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7}}-\frac{10 a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 a^{5}}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{36 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{60 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{44 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2}{5 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}-\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{40 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{18 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{6 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}"," ",0,"-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3+2/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a+12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3-3/2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+2/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4+8/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2-12/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^5-2/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8-4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-2/5/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5-40/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4+28/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2+4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3-5/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a-2/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+12/d*a^6/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3+5/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4+12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2-40/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4+36/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2-60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4+44/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a-18/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1128,1,938,252,0.499000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{10 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}-b^{2}}}+\frac{14 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{16 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{24 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6}}-\frac{9 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{8 a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{16 a}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{24 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}"," ",0,"-10/d/b^6*a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+14/d/b^4*a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2-5/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+3/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-3/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+5/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3-16/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*a+10/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^4-9/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2+2/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^4-2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2+3/4/d/b^2*arctan(tan(1/2*d*x+1/2*c))+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3-8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2+24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3-16/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2+24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3-40/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2+2/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^3*tan(1/2*d*x+1/2*c)-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)","B"
1129,1,627,156,0.474000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{2 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{12 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{6 a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}-\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{8 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{10 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2+4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2*tan(1/2*d*x+1/2*c)^2+4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2+8/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3-8/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3+6/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a-2/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a+8/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-10/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1130,1,380,132,0.712000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{2}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)-4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+1/d/a^2*ln(tan(1/2*d*x+1/2*c))-2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a+2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+4/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1131,1,396,149,0.751000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)+2/d/b^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^3*b*ln(tan(1/2*d*x+1/2*c))+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)-2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)+2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
1132,1,339,149,0.874000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{b}{d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{6 b \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4}}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3*tan(1/2*d*x+1/2*c)*b-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2-3/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+3/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+1/d*b/a^3/tan(1/2*d*x+1/2*c)-2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*b^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d*b^2/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+6/d/a^4*b*(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1133,1,527,227,0.787000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \,a^{3}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}+\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{10 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{8 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^3*tan(1/2*d*x+1/2*c)^2*b-5/8/d/a^2*tan(1/2*d*x+1/2*c)+3/2/d/a^4*b^2*tan(1/2*d*x+1/2*c)-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3+5/8/d/a^2/tan(1/2*d*x+1/2*c)-3/2/d/a^4/tan(1/2*d*x+1/2*c)*b^2+1/4/d/a^3*b/tan(1/2*d*x+1/2*c)^2+3/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-4/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))+2/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^4+2/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^3+2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-10/d/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+8/d/a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1134,1,634,275,0.841000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{12 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}+\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{4 d \,a^{3}}-\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{4}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6}}+\frac{b}{12 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5 b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 b^{3}}{d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{14 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{10 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/64/d/a^2*tan(1/2*d*x+1/2*c)^4-1/12/d/a^3*tan(1/2*d*x+1/2*c)^3*b-1/8/d/a^2*tan(1/2*d*x+1/2*c)^2+3/8/d/a^4*b^2*tan(1/2*d*x+1/2*c)^2+5/4/d/a^3*tan(1/2*d*x+1/2*c)*b-2/d/a^5*b^3*tan(1/2*d*x+1/2*c)-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+1/8/a^2/d/tan(1/2*d*x+1/2*c)^2-3/8/d/a^4/tan(1/2*d*x+1/2*c)^2*b^2+3/8/d/a^2*ln(tan(1/2*d*x+1/2*c))-9/2/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+5/d/a^6*ln(tan(1/2*d*x+1/2*c))*b^4+1/12/d/a^3*b/tan(1/2*d*x+1/2*c)^3-5/4/d*b/a^3/tan(1/2*d*x+1/2*c)+2/d*b^3/a^5/tan(1/2*d*x+1/2*c)-2/d*b^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^6*b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d*b^2/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+14/d/a^4*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-10/d/a^6*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1135,1,1193,312,0.609000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\frac{60 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{30 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3}}+\frac{30 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{7}}-\frac{18 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}+\frac{10 a^{5}}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{20 a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{24 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{60 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{9 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{20 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{33 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{6 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{15 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{31 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{16 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 a^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}"," ",0,"15/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-10/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+31/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-16/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-30/d*a^5/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/4/d/b^3*arctan(tan(1/2*d*x+1/2*c))+10/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+10/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-5/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-5/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+3/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-3/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+5/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3-8/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*a+30/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^4-18/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2+60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3-24/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a-6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2+60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3-20/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a-6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2+9/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-4/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2+33/d*a^3/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2+20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3-12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a","B"
1136,1,880,269,0.534000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{3 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{24 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{3 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{12 a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{20 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6}}+\frac{9 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{13 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{25 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{8 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{20 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{6} \sqrt{a^{2}-b^{2}}}-\frac{19 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5-12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4-24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2*a^2+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2+3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)-12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2+8/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3-20/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^3+9/d/b^4*a*arctan(tan(1/2*d*x+1/2*c))-7/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a^3+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a-8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^4-13/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^2+6/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-25/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a^3+10/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a-8/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4+3/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2+20/d/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4-19/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1137,1,639,162,0.544000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{6 a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}+\frac{5 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{19 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{12 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{9 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*a+12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2-3/d/b^3*arctan(tan(1/2*d*x+1/2*c))+5/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+6/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+11/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+19/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-4/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+6/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-1/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a-12/d*a^3/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+9/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1138,1,600,166,0.832000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^3,x)","\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{6 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{\arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"2/d/b^3*arctan(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))+1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+4/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+2/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+7/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+6/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+7/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+8/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a+3/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-2/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/d/a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1139,1,489,173,0.789000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^4*b*ln(tan(1/2*d*x+1/2*c))+1/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-5/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-10/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-1/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-14/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-5/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-3/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
1140,1,642,205,0.907000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{4}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{3 b}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{20 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{12 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^4*tan(1/2*d*x+1/2*c)*b-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2-3/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+6/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2+3/2/d*b/a^4/tan(1/2*d*x+1/2*c)-3/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+8/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^3-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+3/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+14/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^4-5/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+20/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^3-2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+7/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2+9/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-12/d/a^5*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1141,1,780,274,0.885000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{4}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5}}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{9 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{10 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{18 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{26 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{19 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}+\frac{20 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b-5/8/d/a^3*tan(1/2*d*x+1/2*c)+3/d/a^5*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3+5/8/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^5/tan(1/2*d*x+1/2*c)*b^2+3/8/d/a^4*b/tan(1/2*d*x+1/2*c)^2+9/2/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-10/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))+5/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-10/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-1/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-18/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5+11/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-26/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4+4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3+2/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-19/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+20/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1142,1,889,321,0.892000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{15 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{4}}-\frac{9 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}-\frac{15 b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{6 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 b^{3}}{d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{6}}-\frac{3 b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{7}}+\frac{b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{11 b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{4}}+\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{5}}-\frac{1}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{30 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{7} \sqrt{a^{2}-b^{2}}}-\frac{6 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{33 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{17 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{32 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{22 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{12 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3}}"," ",0,"-6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2+15/8/d/a^4*tan(1/2*d*x+1/2*c)*b-9/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2-15/8/d*b/a^4/tan(1/2*d*x+1/2*c)+5/d*b^3/a^6/tan(1/2*d*x+1/2*c)+11/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-1/8/d/a^4*tan(1/2*d*x+1/2*c)^3*b+3/4/d/a^5*b^2*tan(1/2*d*x+1/2*c)^2-5/d/a^6*b^3*tan(1/2*d*x+1/2*c)-3/4/d/a^5/tan(1/2*d*x+1/2*c)^2*b^2+15/d/a^7*ln(tan(1/2*d*x+1/2*c))*b^4+1/8/d/a^4*b/tan(1/2*d*x+1/2*c)^3+1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+1/64/d/a^3*tan(1/2*d*x+1/2*c)^4-1/64/d/a^3/tan(1/2*d*x+1/2*c)^4+32/d/a^6*b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-30/d/a^7*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+22/d/a^7*b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+12/d/a^6*b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-6/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/8/d/a^3*ln(tan(1/2*d*x+1/2*c))-7/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^3-1/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^4-17/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^3+33/d/a^5*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-1/8/d/a^3*tan(1/2*d*x+1/2*c)^2","B"
1143,1,1619,493,2.166000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \left(160 a^{5} b^{3} \sin \left(d x +c \right)-404 a^{3} b^{5} \sin \left(d x +c \right)+1632 a \,b^{7} \sin \left(d x +c \right)+640 a^{6} b^{2}+35 a^{2} b^{6} \left(\sin^{6}\left(d x +c \right)\right)+1436 a^{4} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-640 a^{6} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-511 a^{2} b^{6} \left(\sin^{2}\left(d x +c \right)\right)-232 a^{2} b^{6} \left(\sin^{4}\left(d x +c \right)\right)+80 a^{4} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+9240 b^{8} \left(\sin^{6}\left(d x +c \right)\right)-2772 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}+2772 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}-1280 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8}-6699 b^{8} \left(\sin^{4}\left(d x +c \right)\right)+454 a^{3} b^{5} \left(\sin^{3}\left(d x +c \right)\right)-160 a^{5} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-8322 a \,b^{7} \left(\sin^{3}\left(d x +c \right)\right)+924 b^{8} \left(\sin^{2}\left(d x +c \right)\right)-3780 a \,b^{7} \left(\sin^{7}\left(d x +c \right)\right)+10470 a \,b^{7} \left(\sin^{5}\left(d x +c \right)\right)-50 a^{3} b^{5} \left(\sin^{5}\left(d x +c \right)\right)-1516 a^{4} b^{4}+708 a^{2} b^{6}-3465 b^{8} \left(\sin^{8}\left(d x +c \right)\right)+4512 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}-4296 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}-216 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{7}+4472 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}-4932 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}+1280 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b -960 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}-3512 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{3}+2484 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}+2448 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{5}\right)}{45045 b^{7} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/45045*(-50*a^3*b^5*sin(d*x+c)^5+10470*a*b^7*sin(d*x+c)^5+80*a^4*b^4*sin(d*x+c)^4-232*a^2*b^6*sin(d*x+c)^4-160*a^5*b^3*sin(d*x+c)^3+454*a^3*b^5*sin(d*x+c)^3-8322*a*b^7*sin(d*x+c)^3-640*a^6*b^2*sin(d*x+c)^2+1436*a^4*b^4*sin(d*x+c)^2-511*a^2*b^6*sin(d*x+c)^2+160*a^5*b^3*sin(d*x+c)-404*a^3*b^5*sin(d*x+c)+1632*a*b^7*sin(d*x+c)-3780*a*b^7*sin(d*x+c)^7+640*a^6*b^2+4512*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6+35*a^2*b^6*sin(d*x+c)^6-6699*b^8*sin(d*x+c)^4+924*b^8*sin(d*x+c)^2-3465*b^8*sin(d*x+c)^8+9240*b^8*sin(d*x+c)^6-1516*a^4*b^4+708*a^2*b^6-2772*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8+2772*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8-4296*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6-216*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^7+4472*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-4932*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b-960*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-3512*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^3+2484*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+2448*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^5)/b^7/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1144,1,1356,374,1.944000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(1/2),x)","\frac{-\frac{8 a \,b^{6}}{77}+\frac{128 a^{5} b^{2}}{3465}-\frac{2132 a \,b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{3465}+\frac{16 a^{3} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3465}-\frac{356 a^{3} b^{4}}{3465}+\frac{104 a^{2} b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{3465}-\frac{32 a^{4} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3465}+\frac{32 a^{4} b^{3} \sin \left(d x +c \right)}{3465}-\frac{94 a^{2} b^{5} \sin \left(d x +c \right)}{3465}+\frac{68 a^{3} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{693}-\frac{128 a^{5} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{3465}+\frac{256 a \,b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{495}-\frac{2 a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{693}-\frac{8 b^{7} \sin \left(d x +c \right)}{77}+\frac{20 a \,b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{99}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}}{77}-\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}}{3465}-\frac{40 b^{7} \left(\sin^{5}\left(d x +c \right)\right)}{77}+\frac{34 b^{7} \left(\sin^{3}\left(d x +c \right)\right)}{77}+\frac{2 b^{7} \left(\sin^{7}\left(d x +c \right)\right)}{11}-\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{1155}-\frac{808 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}}{3465}+\frac{248 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{1155}+\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{385}+\frac{304 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}}{1155}+\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b}{3465}-\frac{128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{1155}+\frac{200 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{693}-\frac{496 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{1155}}{b^{6} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/3465*(-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+350*a*b^6*sin(d*x+c)^6-180*a*b^6+64*a^5*b^2-178*a^3*b^4-5*a^2*b^5*sin(d*x+c)^5+8*a^3*b^4*sin(d*x+c)^4-1066*a*b^6*sin(d*x+c)^4-16*a^4*b^3*sin(d*x+c)^3+52*a^2*b^5*sin(d*x+c)^3-64*a^5*b^2*sin(d*x+c)^2+170*a^3*b^4*sin(d*x+c)^2+896*a*b^6*sin(d*x+c)^2+16*a^4*b^3*sin(d*x+c)-47*a^2*b^5*sin(d*x+c)+315*b^7*sin(d*x+c)^7-900*b^7*sin(d*x+c)^5+765*b^7*sin(d*x+c)^3-180*b^7*sin(d*x+c)-180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^7-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7-404*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3+372*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+288*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+456*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-192*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+500*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-744*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4)/b^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1145,1,1155,409,2.193000," ","int(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{2 b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{7}+\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b}{105}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{35}-\frac{106 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}}{105}+\frac{74 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{35}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}}{7}-\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}}{105}+\frac{118 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{105}-\frac{34 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{35}-2 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{4} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a +2 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{5} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)+\frac{12 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{35}-\frac{2 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{105}-\frac{8 b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{7}-\frac{8 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{105}-\frac{6 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5}+\frac{2 a^{2} b^{3} \sin \left(d x +c \right)}{105}+\frac{6 b^{5} \sin \left(d x +c \right)}{7}+\frac{8 a^{3} b^{2}}{105}+\frac{6 a \,b^{4}}{7}}{b^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/105*(15*b^5*sin(d*x+c)^5+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-53*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+111*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+59*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-51*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^4*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^5*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))+18*a*b^4*sin(d*x+c)^4-a^2*b^3*sin(d*x+c)^3-60*b^5*sin(d*x+c)^3-4*a^3*b^2*sin(d*x+c)^2-63*a*b^4*sin(d*x+c)^2+a^2*b^3*sin(d*x+c)+45*b^5*sin(d*x+c)+4*a^3*b^2+45*a*b^4)/b^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1146,1,656,397,1.895000," ","int(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x)","-\frac{-6 a \,b^{4} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(2 a^{3} b^{2}+21 a \,b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \left(15 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-15 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}+4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b +42 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+11 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}-57 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}-53 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+57 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}\right) \sin \left(d x +c \right)-8 a^{2} b^{3} \left(\cos^{4}\left(d x +c \right)\right)+23 a^{2} b^{3} \left(\cos^{2}\left(d x +c \right)\right)}{15 a \,b^{3} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/15*(-6*a*b^4*sin(d*x+c)*cos(d*x+c)^4+(2*a^3*b^2+21*a*b^4)*cos(d*x+c)^2*sin(d*x+c)+(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(15*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4-15*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5+4*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b+42*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+11*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3-57*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-4*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5-53*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+57*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)*sin(d*x+c)-8*a^2*b^3*cos(d*x+c)^4+23*a^2*b^3*cos(d*x+c)^2)/a/b^3/sin(d*x+c)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","A"
1147,1,1364,414,2.073000," ","int(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x)","\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-42 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+31 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{2}\left(d x +c \right)\right)+11 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{2} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{3} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{2}\left(d x +c \right)\right)+8 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+8 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+3 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-2 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-3 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-9 a^{2} b^{3} \sin \left(d x +c \right)-6 a^{3} b^{2}}{12 a^{2} b^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/12*(8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^2-42*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2+31*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^2+11*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^2-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2+36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^2*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^3*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^2+8*a^2*b^3*sin(d*x+c)^5+8*a^3*b^2*sin(d*x+c)^4+3*a*b^4*sin(d*x+c)^4+a^2*b^3*sin(d*x+c)^3-2*a^3*b^2*sin(d*x+c)^2-3*a*b^4*sin(d*x+c)^2-9*a^2*b^3*sin(d*x+c)-6*a^3*b^2)/a^2/b^2/sin(d*x+c)^2/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1148,1,1495,420,2.132000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x)","-\frac{80 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)-77 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-48 a^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{3}\left(d x +c \right)\right)-32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{3}\left(d x +c \right)\right)+78 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)-b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{3}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)+36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{3}\left(d x +c \right)\right)+32 a^{3} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+3 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)+32 a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-42 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-3 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-40 a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+10 a^{3} b^{2} \sin \left(d x +c \right)+8 a^{4} b}{24 a^{3} b \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/24*(80*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^3-77*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-48*a^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^3-32*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^3+78*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^3-b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^3+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3+36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^3+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^3+32*a^3*b^2*sin(d*x+c)^5+3*a*b^4*sin(d*x+c)^5+32*a^4*b*sin(d*x+c)^4+a^2*b^3*sin(d*x+c)^4-42*a^3*b^2*sin(d*x+c)^3-3*a*b^4*sin(d*x+c)^3-40*a^4*b*sin(d*x+c)^2-a^2*b^3*sin(d*x+c)^2+10*a^3*b^2*sin(d*x+c)+8*a^4*b)/a^3/b/sin(d*x+c)^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1149,1,1761,477,2.456000," ","int(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(1/2),x)","\frac{168 a^{5} \left(\sin^{2}\left(d x +c \right)\right)+5 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-48 a^{5}-56 a^{4} b \sin \left(d x +c \right)-5 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+66 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+2 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-120 a^{5} \left(\sin^{4}\left(d x +c \right)\right)-15 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-188 a^{4} b \left(\sin^{5}\left(d x +c \right)\right)+15 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)-68 a^{3} b^{2} \left(\sin^{6}\left(d x +c \right)\right)+244 a^{4} b \left(\sin^{3}\left(d x +c \right)\right)-196 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)-78 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)-72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+83 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+264 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{4}\left(d x +c \right)\right)-68 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)}{192 a^{4} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/192*(-196*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-78*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4-5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-72*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+72*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+83*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+264*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-48*a^5-68*a^3*b^2*sin(d*x+c)^6+15*a*b^4*sin(d*x+c)^6-188*a^4*b*sin(d*x+c)^5+244*a^4*b*sin(d*x+c)^3-56*a^4*b*sin(d*x+c)-120*a^5*sin(d*x+c)^4+168*a^5*sin(d*x+c)^2+5*a^2*b^3*sin(d*x+c)^5+66*a^3*b^2*sin(d*x+c)^4-15*a*b^4*sin(d*x+c)^4-5*a^2*b^3*sin(d*x+c)^3+2*a^3*b^2*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4-144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^4-68*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4)/a^4/sin(d*x+c)^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1150,1,2075,545,2.503000," ","int(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x)","-\frac{384 a^{6} b -105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+384 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b \left(\sin^{5}\left(d x +c \right)\right)-168 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+116 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-402 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-35 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+720 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)-8 a^{4} b^{3} \left(\sin^{2}\left(d x +c \right)\right)-1152 a^{6} b \left(\sin^{2}\left(d x +c \right)\right)-332 a^{3} b^{4} \left(\sin^{7}\left(d x +c \right)\right)-384 a^{5} b^{2} \left(\sin^{7}\left(d x +c \right)\right)+105 a \,b^{6} \left(\sin^{7}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{7} \left(\sin^{5}\left(d x +c \right)\right)-384 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} \left(\sin^{5}\left(d x +c \right)\right)+432 a^{5} b^{2} \sin \left(d x +c \right)-116 a^{4} b^{3} \left(\sin^{6}\left(d x +c \right)\right)-384 a^{6} b \left(\sin^{6}\left(d x +c \right)\right)+35 a^{2} b^{5} \left(\sin^{6}\left(d x +c \right)\right)+124 a^{4} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+1152 a^{6} b \left(\sin^{4}\left(d x +c \right)\right)-35 a^{2} b^{5} \left(\sin^{4}\left(d x +c \right)\right)+1368 a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+14 a^{3} b^{4} \left(\sin^{3}\left(d x +c \right)\right)+318 a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-1416 a^{5} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-105 a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)-720 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-360 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)+360 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+52 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+437 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{1920 a^{5} b \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/1920*(384*a^6*b-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+384*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^5-168*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5+116*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5-402*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5-35*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5-720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5-360*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5+360*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+52*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5+437*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^7*sin(d*x+c)^5-384*a^5*b^2*sin(d*x+c)^7-332*a^3*b^4*sin(d*x+c)^7+105*a*b^6*sin(d*x+c)^7-384*a^6*b*sin(d*x+c)^6-116*a^4*b^3*sin(d*x+c)^6+35*a^2*b^5*sin(d*x+c)^6+1152*a^6*b*sin(d*x+c)^4+124*a^4*b^3*sin(d*x+c)^4-35*a^2*b^5*sin(d*x+c)^4-1416*a^5*b^2*sin(d*x+c)^3+1368*a^5*b^2*sin(d*x+c)^5-105*a*b^6*sin(d*x+c)^5+318*a^3*b^4*sin(d*x+c)^5+14*a^3*b^4*sin(d*x+c)^3-1152*a^6*b*sin(d*x+c)^2-8*a^4*b^3*sin(d*x+c)^2+432*a^5*b^2*sin(d*x+c)-384*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^5)/a^5/b/sin(d*x+c)^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1151,1,1801,554,2.032000," ","int(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(-10 a^{4} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+32 a^{6} b^{3} \sin \left(d x +c \right)-112 a^{4} b^{5} \sin \left(d x +c \right)+1512 a^{2} b^{7} \sin \left(d x +c \right)+780 a \,b^{8}+128 a^{7} b^{2}+360 a^{3} b^{6}-428 a^{5} b^{4}-6699 a \,b^{8} \left(\sin^{8}\left(d x +c \right)\right)-256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{9}+780 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{9}+412 a^{5} b^{4} \left(\sin^{2}\left(d x +c \right)\right)+840 a \,b^{8} \left(\sin^{2}\left(d x +c \right)\right)-128 a^{7} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-305 a^{3} b^{6} \left(\sin^{2}\left(d x +c \right)\right)+2988 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{8}+1020 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{5}-3480 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{6}-1104 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{7}+1144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b^{2}-1704 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{4}+4584 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{6}-3768 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{8}+256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8} b -192 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b^{2}+10362 a^{2} b^{7} \left(\sin^{5}\left(d x +c \right)\right)+17682 a \,b^{8} \left(\sin^{6}\left(d x +c \right)\right)+7 a^{3} b^{6} \left(\sin^{6}\left(d x +c \right)\right)+780 b^{9} \sin \left(d x +c \right)-62 a^{3} b^{6} \left(\sin^{4}\left(d x +c \right)\right)+16 a^{5} b^{4} \left(\sin^{4}\left(d x +c \right)\right)-12603 a \,b^{8} \left(\sin^{4}\left(d x +c \right)\right)-3759 a^{2} b^{7} \left(\sin^{7}\left(d x +c \right)\right)+122 a^{4} b^{5} \left(\sin^{3}\left(d x +c \right)\right)-32 a^{6} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-8115 a^{2} b^{7} \left(\sin^{3}\left(d x +c \right)\right)+7644 b^{9} \left(\sin^{7}\left(d x +c \right)\right)-5109 b^{9} \left(\sin^{5}\left(d x +c \right)\right)-312 b^{9} \left(\sin^{3}\left(d x +c \right)\right)-3003 b^{9} \left(\sin^{9}\left(d x +c \right)\right)-952 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{3}+684 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{4}\right)}{45045 b^{7} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/45045*(7*a^3*b^6*sin(d*x+c)^6+17682*a*b^8*sin(d*x+c)^6-10*a^4*b^5*sin(d*x+c)^5+10362*a^2*b^7*sin(d*x+c)^5+16*a^5*b^4*sin(d*x+c)^4-62*a^3*b^6*sin(d*x+c)^4-12603*a*b^8*sin(d*x+c)^4-32*a^6*b^3*sin(d*x+c)^3+122*a^4*b^5*sin(d*x+c)^3-8115*a^2*b^7*sin(d*x+c)^3-128*a^7*b^2*sin(d*x+c)^2+412*a^5*b^4*sin(d*x+c)^2-305*a^3*b^6*sin(d*x+c)^2+840*a*b^8*sin(d*x+c)^2+32*a^6*b^3*sin(d*x+c)-112*a^4*b^5*sin(d*x+c)+1512*a^2*b^7*sin(d*x+c)-6699*a*b^8*sin(d*x+c)^8+780*a*b^8+128*a^7*b^2+360*a^3*b^6-428*a^5*b^4-3759*a^2*b^7*sin(d*x+c)^7-256*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^9-952*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^3-3003*b^9*sin(d*x+c)^9+7644*b^9*sin(d*x+c)^7-5109*b^9*sin(d*x+c)^5-312*b^9*sin(d*x+c)^3+780*b^9*sin(d*x+c)+684*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^4+2988*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^8+1020*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^5-3480*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^6-1104*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^7+1144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b^2+780*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^9-1704*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^4+4584*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^6-3768*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^8+256*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8*b-192*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b^2)/b^7/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1152,1,1619,432,1.956000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2),x)","\frac{\frac{32 a^{5} b^{3} \sin \left(d x +c \right)}{15015}-\frac{46 a^{3} b^{5} \sin \left(d x +c \right)}{5005}-\frac{2648 a \,b^{7} \sin \left(d x +c \right)}{15015}+\frac{128 a^{6} b^{2}}{15015}+\frac{86 a^{2} b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{429}+\frac{172 a^{4} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5005}-\frac{128 a^{6} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{15015}-\frac{3028 a^{2} b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{5005}+\frac{16 a^{4} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{15015}-\frac{16 b^{8} \left(\sin^{6}\left(d x +c \right)\right)}{39}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}}{65}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}}{65}-\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8}}{15015}+\frac{148 a^{3} b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{15015}-\frac{32 a^{5} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{15015}+\frac{12178 a \,b^{7} \left(\sin^{3}\left(d x +c \right)\right)}{15015}-\frac{2956 a \,b^{7} \left(\sin^{5}\left(d x +c \right)\right)}{3003}-\frac{8 b^{8} \left(\sin^{2}\left(d x +c \right)\right)}{195}-\frac{2 a^{3} b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{3003}+\frac{50 a \,b^{7} \left(\sin^{7}\left(d x +c \right)\right)}{143}+\frac{386 a^{2} b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{715}-\frac{76 a^{4} b^{4}}{2145}-\frac{2032 a^{2} b^{6}}{15015}+\frac{58 b^{8} \left(\sin^{4}\left(d x +c \right)\right)}{195}+\frac{80 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}}{1001}-\frac{472 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{7}}{5005}+\frac{2 b^{8} \left(\sin^{8}\left(d x +c \right)\right)}{13}+\frac{72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}}{5005}+\frac{104 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}}{1155}-\frac{632 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}}{3003}+\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b}{15015}-\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}}{5005}-\frac{232 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{3}}{3003}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}}{143}+\frac{464 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{5}}{3003}}{b^{6} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/15015*(-5*a^3*b^5*sin(d*x+c)^5-7390*a*b^7*sin(d*x+c)^5+8*a^4*b^4*sin(d*x+c)^4-4542*a^2*b^6*sin(d*x+c)^4-16*a^5*b^3*sin(d*x+c)^3+74*a^3*b^5*sin(d*x+c)^3+6089*a*b^7*sin(d*x+c)^3-64*a^6*b^2*sin(d*x+c)^2+258*a^4*b^4*sin(d*x+c)^2+4053*a^2*b^6*sin(d*x+c)^2+16*a^5*b^3*sin(d*x+c)-69*a^3*b^5*sin(d*x+c)-1324*a*b^7*sin(d*x+c)+2625*a*b^7*sin(d*x+c)^7+64*a^6*b^2+108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6+1505*a^2*b^6*sin(d*x+c)^6+2233*b^8*sin(d*x+c)^4-308*b^8*sin(d*x+c)^2+1155*b^8*sin(d*x+c)^8-3080*b^8*sin(d*x+c)^6-266*a^4*b^4-1016*a^2*b^6+924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8+600*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6-708*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^7+676*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-1580*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-580*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^3+420*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+1160*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^5)/b^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1153,1,1405,457,1.918000," ","int(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2),x)","\frac{-\frac{32 b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{45}+\frac{2 a^{3} b^{3} \sin \left(d x +c \right)}{315}+\frac{482 a \,b^{5} \sin \left(d x +c \right)}{315}+\frac{2 b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{9}+2 a \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{5} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)+\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b}{315}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{105}-\frac{38 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}}{63}-\frac{152 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}}{105}+\frac{202 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{315}-\frac{118 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{105}+\frac{22 b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{45}-\frac{652 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{315}-\frac{62 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{45}-\frac{2 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{315}-\frac{8 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{315}+\frac{106 a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{315}+\frac{34 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{63}+\frac{8 a^{4} b^{2}}{315}+\frac{328 a^{2} b^{4}}{315}-2 a^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{4} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)+\frac{18 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{7}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}}{315}}{b^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(35*b^6*sin(d*x+c)^6-112*b^6*sin(d*x+c)^4+77*b^6*sin(d*x+c)^2+85*a*b^5*sin(d*x+c)^5-315*a^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^4*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))+53*a^2*b^4*sin(d*x+c)^4-a^3*b^3*sin(d*x+c)^3-326*a*b^5*sin(d*x+c)^3-4*a^4*b^2*sin(d*x+c)^2-217*a^2*b^4*sin(d*x+c)^2+a^3*b^3*sin(d*x+c)+241*a*b^5*sin(d*x+c)+405*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+315*a*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^5*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-95*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3-228*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5+101*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+4*a^4*b^2+164*a^2*b^4-177*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6)/b^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1154,1,726,443,1.774000," ","int(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x)","-\frac{-26 a \,b^{4} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(2 a^{3} b^{2}+31 a \,b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \left(105 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-105 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}-163 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+167 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b +102 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+61 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}-207 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+40 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}\right) \sin \left(d x +c \right)+10 b^{5} \left(\cos^{6}\left(d x +c \right)\right)+\left(-18 a^{2} b^{3}+10 b^{5}\right) \left(\cos^{4}\left(d x +c \right)\right)+\left(53 a^{2} b^{3}-20 b^{5}\right) \left(\cos^{2}\left(d x +c \right)\right)}{35 \sin \left(d x +c \right) b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/35*(-26*a*b^4*sin(d*x+c)*cos(d*x+c)^4+(2*a^3*b^2+31*a*b^4)*cos(d*x+c)^2*sin(d*x+c)+(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(105*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4-105*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5-4*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5-163*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+167*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+4*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b+102*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+61*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3-207*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+40*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5)*sin(d*x+c)+10*b^5*cos(d*x+c)^6+(-18*a^2*b^3+10*b^5)*cos(d*x+c)^4+(53*a^2*b^3-20*b^5)*cos(d*x+c)^2)/sin(d*x+c)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","A"
1155,1,1379,448,2.087000," ","int(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x)","\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-126 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+37 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+81 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{2}\left(d x +c \right)\right)+89 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-81 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+60 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{2} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-60 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{3} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{2}\left(d x +c \right)\right)+8 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)+24 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+16 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+17 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+11 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-6 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-25 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-35 a^{2} b^{3} \sin \left(d x +c \right)-10 a^{3} b^{2}}{20 a \,b^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/20*(8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^2-126*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2+37*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+81*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^2+89*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^2-81*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2+60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^2*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2-60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^3*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^2+8*a*b^4*sin(d*x+c)^6+24*a^2*b^3*sin(d*x+c)^5+16*a^3*b^2*sin(d*x+c)^4+17*a*b^4*sin(d*x+c)^4+11*a^2*b^3*sin(d*x+c)^3-6*a^3*b^2*sin(d*x+c)^2-25*a*b^4*sin(d*x+c)^2-35*a^2*b^3*sin(d*x+c)-10*a^3*b^2)/a/b^2/sin(d*x+c)^2/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1156,1,1511,451,2.159000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x)","\frac{48 a^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{3}\left(d x +c \right)\right)+48 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{3}\left(d x +c \right)\right)-162 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)+63 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{3}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-96 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)+99 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+108 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-108 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{3}\left(d x +c \right)\right)+16 a^{2} b^{3} \left(\sin^{6}\left(d x +c \right)\right)-16 a^{3} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+3 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)-32 a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+38 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-3 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+40 a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-17 a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)-22 a^{3} b^{2} \sin \left(d x +c \right)-8 a^{4} b}{24 a^{2} b \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/24*(48*a^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^3+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^3-162*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^3+63*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^3+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^3+99*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3+108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^3+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^3+16*a^2*b^3*sin(d*x+c)^6-16*a^3*b^2*sin(d*x+c)^5+3*a*b^4*sin(d*x+c)^5-32*a^4*b*sin(d*x+c)^4+a^2*b^3*sin(d*x+c)^4+38*a^3*b^2*sin(d*x+c)^3-3*a*b^4*sin(d*x+c)^3+40*a^4*b*sin(d*x+c)^2-17*a^2*b^3*sin(d*x+c)^2-22*a^3*b^2*sin(d*x+c)-8*a^4*b)/a^2/b/sin(d*x+c)^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1157,1,1760,473,2.352000," ","int(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2),x)","-\frac{108 a^{3} b^{2} \left(\sin^{6}\left(d x +c \right)\right)+a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+16 a^{5}+40 a^{4} b \sin \left(d x +c \right)-134 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-188 a^{4} b \left(\sin^{3}\left(d x +c \right)\right)+26 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+40 a^{5} \left(\sin^{4}\left(d x +c \right)\right)-3 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+148 a^{4} b \left(\sin^{5}\left(d x +c \right)\right)+3 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)-216 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)+48 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{4}\left(d x +c \right)\right)+236 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-20 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+234 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-56 a^{5} \left(\sin^{2}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-48 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+72 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-233 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{64 a^{3} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/64*(-20*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4+234*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4-((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4-48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-72*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+72*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4-233*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4-216*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4+16*a^5+108*a^3*b^2*sin(d*x+c)^6+3*a*b^4*sin(d*x+c)^6+148*a^4*b*sin(d*x+c)^5-188*a^4*b*sin(d*x+c)^3+40*a^4*b*sin(d*x+c)+40*a^5*sin(d*x+c)^4-56*a^5*sin(d*x+c)^2+a^2*b^3*sin(d*x+c)^5-134*a^3*b^2*sin(d*x+c)^4-3*a*b^4*sin(d*x+c)^4-a^2*b^3*sin(d*x+c)^3+26*a^3*b^2*sin(d*x+c)^2-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^4+236*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4)/a^3/sin(d*x+c)^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1158,1,2075,545,2.401000," ","int(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x)","-\frac{128 a^{6} b -772 a^{4} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-120 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+244 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)-131 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)-384 a^{6} b \left(\sin^{2}\left(d x +c \right)\right)+5 a^{2} b^{5} \left(\sin^{4}\left(d x +c \right)\right)-128 a^{5} b^{2} \left(\sin^{7}\left(d x +c \right)\right)-15 a \,b^{6} \left(\sin^{7}\left(d x +c \right)\right)+184 a^{4} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+304 a^{5} b^{2} \sin \left(d x +c \right)+116 a^{3} b^{4} \left(\sin^{7}\left(d x +c \right)\right)+588 a^{4} b^{3} \left(\sin^{6}\left(d x +c \right)\right)-128 a^{6} b \left(\sin^{6}\left(d x +c \right)\right)-5 a^{2} b^{5} \left(\sin^{6}\left(d x +c \right)\right)+15 a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)-2 a^{3} b^{4} \left(\sin^{3}\left(d x +c \right)\right)-114 a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-1032 a^{5} b^{2} \left(\sin^{3}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{7} \left(\sin^{5}\left(d x +c \right)\right)-128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} \left(\sin^{5}\left(d x +c \right)\right)+384 a^{6} b \left(\sin^{4}\left(d x +c \right)\right)+856 a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b \left(\sin^{5}\left(d x +c \right)\right)-936 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+692 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+126 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+720 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)-720 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+120 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{640 a^{4} b \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/640*(128*a^6*b+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^5-936*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5+692*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5+126*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5+5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5-720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5+120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5-120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5+244*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5-131*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^7*sin(d*x+c)^5-128*a^5*b^2*sin(d*x+c)^7+116*a^3*b^4*sin(d*x+c)^7-15*a*b^6*sin(d*x+c)^7-128*a^6*b*sin(d*x+c)^6+588*a^4*b^3*sin(d*x+c)^6-5*a^2*b^5*sin(d*x+c)^6+384*a^6*b*sin(d*x+c)^4-772*a^4*b^3*sin(d*x+c)^4+5*a^2*b^5*sin(d*x+c)^4-1032*a^5*b^2*sin(d*x+c)^3+856*a^5*b^2*sin(d*x+c)^5+15*a*b^6*sin(d*x+c)^5-114*a^3*b^4*sin(d*x+c)^5-2*a^3*b^4*sin(d*x+c)^3-384*a^6*b*sin(d*x+c)^2+184*a^4*b^3*sin(d*x+c)^2+304*a^5*b^2*sin(d*x+c)-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^5)/a^4/b/sin(d*x+c)^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1159,1,2458,608,3.029000," ","int(cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-1/7680*(-960*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^6+2160*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6-2160*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^6-540*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6+540*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^6+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6+1552*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6+617*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6+2544*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^6-1728*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6-105*a*b^6*sin(d*x+c)^6-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^7*sin(d*x+c)^6-35*a^2*b^5*sin(d*x+c)^5+14*a^3*b^4*sin(d*x+c)^4-8*a^4*b^3*sin(d*x+c)^3+1712*a^5*b^2*sin(d*x+c)^2+1280*a^7-2064*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6-480*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6+960*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6-2064*a^5*b^2*sin(d*x+c)^8-512*a^3*b^4*sin(d*x+c)^8+105*a*b^6*sin(d*x+c)^8-2544*a^6*b*sin(d*x+c)^7-176*a^4*b^3*sin(d*x+c)^7+184*a^4*b^3*sin(d*x+c)^5+498*a^3*b^4*sin(d*x+c)^6+5888*a^5*b^2*sin(d*x+c)^6+35*a^2*b^5*sin(d*x+c)^7+8272*a^6*b*sin(d*x+c)^5-5536*a^5*b^2*sin(d*x+c)^4-8672*a^6*b*sin(d*x+c)^3+2944*a^6*b*sin(d*x+c)-480*a^7*sin(d*x+c)^6+2720*a^7*sin(d*x+c)^4-3520*a^7*sin(d*x+c)^2+176*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^6-582*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6-35*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^6+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6)/a^5/sin(d*x+c)^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1160,1,1801,485,1.865000," ","int(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 a^{4} b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{9009}+\frac{32 a^{6} b^{3} \sin \left(d x +c \right)}{45045}-\frac{38 a^{4} b^{5} \sin \left(d x +c \right)}{9009}-\frac{3656 a^{2} b^{7} \sin \left(d x +c \right)}{15015}-\frac{8 a \,b^{8}}{231}+\frac{128 a^{7} b^{2}}{45045}-\frac{2272 a^{3} b^{6}}{15015}-\frac{148 a^{5} b^{4}}{9009}+\frac{88 a \,b^{8} \left(\sin^{8}\left(d x +c \right)\right)}{195}-\frac{32 a^{6} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{45045}+\frac{17588 a^{2} b^{7} \left(\sin^{3}\left(d x +c \right)\right)}{15015}+\frac{12868 a \,b^{8} \left(\sin^{4}\left(d x +c \right)\right)}{15015}+\frac{724 a^{5} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{45045}-\frac{56 a \,b^{8} \left(\sin^{2}\left(d x +c \right)\right)}{715}-\frac{128 a^{7} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{45045}+\frac{24928 a^{3} b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{45045}-\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{8}}{1001}+\frac{328 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{5}}{3003}+\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{6}}{273}-\frac{136 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{7}}{3003}+\frac{136 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b^{2}}{3465}-\frac{184 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{4}}{1365}-\frac{568 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{6}}{3003}+\frac{872 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{8}}{3003}-\frac{2564 a \,b^{8} \left(\sin^{6}\left(d x +c \right)\right)}{2145}-\frac{8 b^{9} \sin \left(d x +c \right)}{231}+\frac{1288 a^{3} b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{6435}-\frac{21688 a^{2} b^{7} \left(\sin^{5}\left(d x +c \right)\right)}{15015}-\frac{27128 a^{3} b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{45045}+\frac{16 a^{5} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{45045}+\frac{1108 a^{2} b^{7} \left(\sin^{7}\left(d x +c \right)\right)}{2145}+\frac{40 a^{4} b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{9009}+\frac{16 b^{9} \left(\sin^{3}\left(d x +c \right)\right)}{1155}-\frac{56 b^{9} \left(\sin^{7}\left(d x +c \right)\right)}{165}+\frac{262 b^{9} \left(\sin^{5}\left(d x +c \right)\right)}{1155}+\frac{2 b^{9} \left(\sin^{9}\left(d x +c \right)\right)}{15}-\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{9}}{45045}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{9}}{231}-\frac{1576 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{3}}{45045}+\frac{128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{4}}{5005}+\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8} b}{45045}-\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b^{2}}{15015}}{b^{6} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/45045*(4508*a^3*b^6*sin(d*x+c)^6-26922*a*b^8*sin(d*x+c)^6-5*a^4*b^5*sin(d*x+c)^5-32532*a^2*b^7*sin(d*x+c)^5+8*a^5*b^4*sin(d*x+c)^4-13564*a^3*b^6*sin(d*x+c)^4+19302*a*b^8*sin(d*x+c)^4-16*a^6*b^3*sin(d*x+c)^3+100*a^4*b^5*sin(d*x+c)^3+26382*a^2*b^7*sin(d*x+c)^3-64*a^7*b^2*sin(d*x+c)^2+362*a^5*b^4*sin(d*x+c)^2+12464*a^3*b^6*sin(d*x+c)^2-1764*a*b^8*sin(d*x+c)^2+16*a^6*b^3*sin(d*x+c)-95*a^4*b^5*sin(d*x+c)-5484*a^2*b^7*sin(d*x+c)+10164*a*b^8*sin(d*x+c)^8-780*a*b^8+64*a^7*b^2-3408*a^3*b^6-370*a^5*b^4+11634*a^2*b^7*sin(d*x+c)^7-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^9-788*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^3+3003*b^9*sin(d*x+c)^9-7644*b^9*sin(d*x+c)^7+5109*b^9*sin(d*x+c)^5+312*b^9*sin(d*x+c)^3-780*b^9*sin(d*x+c)+576*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^4-5760*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^8+2460*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^5+5280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^6-1020*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^7+884*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b^2-780*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^9-3036*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^4-4260*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^6+6540*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^8+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8*b-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b^2)/b^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1161,1,1573,510,2.042000," ","int(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)","\frac{\frac{34 b^{7} \left(\sin^{3}\left(d x +c \right)\right)}{77}-\frac{2 a^{4} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{693}-\frac{8 a \,b^{6}}{77}+\frac{8 a^{5} b^{2}}{693}+\frac{232 a^{3} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{693}-\frac{2056 a^{2} b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{693}+\frac{778 a^{3} b^{4}}{693}+\frac{64 a \,b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{99}-\frac{1412 a \,b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{693}+\frac{548 a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{693}+\frac{2 a^{4} b^{3} \sin \left(d x +c \right)}{693}+\frac{1508 a^{2} b^{5} \sin \left(d x +c \right)}{693}-\frac{8 a^{5} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{693}-\frac{8 b^{7} \sin \left(d x +c \right)}{77}-\frac{1010 a^{3} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{693}+\frac{148 a \,b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{99}+\frac{2 b^{7} \left(\sin^{7}\left(d x +c \right)\right)}{11}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}}{77}-\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}}{693}-\frac{40 b^{7} \left(\sin^{5}\left(d x +c \right)\right)}{77}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{231}+\frac{310 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{693}-2 a^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{4} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)-\frac{298 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}}{693}+\frac{296 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{231}+\frac{246 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{77}-\frac{344 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}}{231}+\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b}{693}-\frac{272 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{231}-\frac{394 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{231}+2 a^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{5} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{b^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/693*(-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+224*a*b^6*sin(d*x+c)^6-36*a*b^6+4*a^5*b^2-693*a^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^4*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))+389*a^3*b^4+274*a^2*b^5*sin(d*x+c)^5+116*a^3*b^4*sin(d*x+c)^4-706*a*b^6*sin(d*x+c)^4-a^4*b^3*sin(d*x+c)^3-1028*a^2*b^5*sin(d*x+c)^3-4*a^5*b^2*sin(d*x+c)^2-505*a^3*b^4*sin(d*x+c)^2+518*a*b^6*sin(d*x+c)^2+a^4*b^3*sin(d*x+c)+754*a^2*b^5*sin(d*x+c)+63*b^7*sin(d*x+c)^7-180*b^7*sin(d*x+c)^5+153*b^7*sin(d*x+c)^3-36*b^7*sin(d*x+c)-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^7-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7-149*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3+444*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+1107*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4-516*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-408*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+155*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-591*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+693*a^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^5*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2)))/b^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1162,1,865,491,1.953000," ","int(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x)","-\frac{70 b^{6} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)+\left(-340 a^{2} b^{4}+14 b^{6}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+\left(10 a^{4} b^{2}+57 a^{2} b^{4}-84 b^{6}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \left(20 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}+1669 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-1857 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+168 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}-1575 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+1575 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}-20 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b -930 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-739 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}+2673 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}-816 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}-168 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}\right) \sin \left(d x +c \right)+260 a \,b^{5} \left(\cos^{6}\left(d x +c \right)\right)+\left(-160 a^{3} b^{3}+232 a \,b^{5}\right) \left(\cos^{4}\left(d x +c \right)\right)+\left(475 a^{3} b^{3}-492 a \,b^{5}\right) \left(\cos^{2}\left(d x +c \right)\right)}{315 \sin \left(d x +c \right) b^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/315*(70*b^6*sin(d*x+c)*cos(d*x+c)^6+(-340*a^2*b^4+14*b^6)*cos(d*x+c)^4*sin(d*x+c)+(10*a^4*b^2+57*a^2*b^4-84*b^6)*cos(d*x+c)^2*sin(d*x+c)-(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(20*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+1669*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-1857*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+168*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-1575*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4+1575*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5-20*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-930*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-739*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3+2673*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4-816*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-168*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6)*sin(d*x+c)+260*a*b^5*cos(d*x+c)^6+(-160*a^3*b^3+232*a*b^5)*cos(d*x+c)^4+(475*a^3*b^3-492*a*b^5)*cos(d*x+c)^2)/sin(d*x+c)/b^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","A"
1163,1,1520,491,2.238000," ","int(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x)","\frac{8 b^{5} \left(\sin^{7}\left(d x +c \right)\right)+8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-258 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+3 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+279 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-32 b^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{2}\left(d x +c \right)\right)-8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{2}\left(d x +c \right)\right)+255 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-247 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+84 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{2} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-84 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{3} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{2}\left(d x +c \right)\right)+32 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)+48 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-32 b^{5} \left(\sin^{5}\left(d x +c \right)\right)+24 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+7 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+29 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+24 b^{5} \left(\sin^{3}\left(d x +c \right)\right)-10 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-39 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-77 a^{2} b^{3} \sin \left(d x +c \right)-14 a^{3} b^{2}}{28 b^{2} \sin \left(d x +c \right)^{2} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/28*(8*b^5*sin(d*x+c)^7+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^2-258*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2+3*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+279*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-32*b^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^2-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^2+255*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^2-247*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2+84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^2*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2-84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^3*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^2+32*a*b^4*sin(d*x+c)^6+48*a^2*b^3*sin(d*x+c)^5-32*b^5*sin(d*x+c)^5+24*a^3*b^2*sin(d*x+c)^4+7*a*b^4*sin(d*x+c)^4+29*a^2*b^3*sin(d*x+c)^3+24*b^5*sin(d*x+c)^3-10*a^3*b^2*sin(d*x+c)^2-39*a*b^4*sin(d*x+c)^2-77*a^2*b^3*sin(d*x+c)-14*a^3*b^2)/b^2/sin(d*x+c)^2/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1164,1,1526,490,2.065000," ","int(cot(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x)","\frac{240 a^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{3}\left(d x +c \right)\right)+288 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{3}\left(d x +c \right)\right)-1566 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)+537 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{3}\left(d x +c \right)\right)+501 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-528 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)+1029 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-501 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+900 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-900 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-75 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+75 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{3}\left(d x +c \right)\right)+48 a \,b^{4} \left(\sin^{7}\left(d x +c \right)\right)+224 a^{2} b^{3} \left(\sin^{6}\left(d x +c \right)\right)+16 a^{3} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+117 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)-160 a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+71 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+154 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-165 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+200 a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-295 a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)-170 a^{3} b^{2} \sin \left(d x +c \right)-40 a^{4} b}{120 a b \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/120*(240*a^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^3+288*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^3-1566*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^3+537*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^3+501*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-528*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^3+1029*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-501*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3+900*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-900*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^3-75*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3+75*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^3+48*a*b^4*sin(d*x+c)^7+224*a^2*b^3*sin(d*x+c)^6+16*a^3*b^2*sin(d*x+c)^5+117*a*b^4*sin(d*x+c)^5-160*a^4*b*sin(d*x+c)^4+71*a^2*b^3*sin(d*x+c)^4+154*a^3*b^2*sin(d*x+c)^3-165*a*b^4*sin(d*x+c)^3+200*a^4*b*sin(d*x+c)^2-295*a^2*b^3*sin(d*x+c)^2-170*a^3*b^2*sin(d*x+c)-40*a^4*b)/a/b/sin(d*x+c)^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1165,1,1777,510,2.086000," ","int(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2),x)","\frac{884 a^{4} b \left(\sin^{3}\left(d x +c \right)\right)+15 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)-48 a^{5}+1491 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-1998 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+1080 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-1080 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-184 a^{4} b \sin \left(d x +c \right)-254 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-133 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+706 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-452 a^{3} b^{2} \left(\sin^{6}\left(d x +c \right)\right)-120 a^{5} \left(\sin^{4}\left(d x +c \right)\right)-700 a^{4} b \left(\sin^{5}\left(d x +c \right)\right)-15 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+5 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+128 a^{2} b^{3} \left(\sin^{7}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{4}\left(d x +c \right)\right)+444 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+507 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+1032 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-1476 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)+168 a^{5} \left(\sin^{2}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{192 a^{2} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/192*(444*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-1998*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+507*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4+1080*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4-1080*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+1491*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+1032*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-48*a^5-452*a^3*b^2*sin(d*x+c)^6+15*a*b^4*sin(d*x+c)^6-700*a^4*b*sin(d*x+c)^5+884*a^4*b*sin(d*x+c)^3-184*a^4*b*sin(d*x+c)-120*a^5*sin(d*x+c)^4+168*a^5*sin(d*x+c)^2+128*a^2*b^3*sin(d*x+c)^7+5*a^2*b^3*sin(d*x+c)^5+706*a^3*b^2*sin(d*x+c)^4-15*a*b^4*sin(d*x+c)^4-133*a^2*b^3*sin(d*x+c)^3-254*a^3*b^2*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4-144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^4-1476*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4)/a^2/sin(d*x+c)^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1166,1,2075,543,2.418000," ","int(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x)","\frac{-128 a^{6} b +2652 a^{4} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+384 a^{6} b \left(\sin^{2}\left(d x +c \right)\right)+128 a^{5} b^{2} \left(\sin^{7}\left(d x +c \right)\right)-384 a^{6} b \left(\sin^{4}\left(d x +c \right)\right)+5 a^{2} b^{5} \left(\sin^{4}\left(d x +c \right)\right)-15 a \,b^{6} \left(\sin^{7}\left(d x +c \right)\right)-584 a^{4} b^{3} \left(\sin^{2}\left(d x +c \right)\right)-464 a^{5} b^{2} \sin \left(d x +c \right)-1196 a^{3} b^{4} \left(\sin^{7}\left(d x +c \right)\right)-258 a^{3} b^{4} \left(\sin^{3}\left(d x +c \right)\right)-2068 a^{4} b^{3} \left(\sin^{6}\left(d x +c \right)\right)+128 a^{6} b \left(\sin^{6}\left(d x +c \right)\right)+15 a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+1454 a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-5 a^{2} b^{5} \left(\sin^{6}\left(d x +c \right)\right)+1592 a^{5} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-1256 a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)-128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b \left(\sin^{5}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6} \left(\sin^{5}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{7} \left(\sin^{5}\left(d x +c \right)\right)+128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} \left(\sin^{5}\left(d x +c \right)\right)+3096 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)-492 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-2466 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-1200 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+1200 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3} \left(\sin^{5}\left(d x +c \right)\right)+600 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)-600 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)-2604 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+2461 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4} \left(\sin^{5}\left(d x +c \right)\right)}{640 a^{3} b \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/640*(-128*a^6*b+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^5+3096*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5-492*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5-2466*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5+5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5-1200*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5+1200*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^5+600*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5-600*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^5-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^5-2604*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^5+2461*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^5+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^7*sin(d*x+c)^5+128*a^5*b^2*sin(d*x+c)^7-1196*a^3*b^4*sin(d*x+c)^7-15*a*b^6*sin(d*x+c)^7+128*a^6*b*sin(d*x+c)^6-2068*a^4*b^3*sin(d*x+c)^6-5*a^2*b^5*sin(d*x+c)^6-384*a^6*b*sin(d*x+c)^4+2652*a^4*b^3*sin(d*x+c)^4+5*a^2*b^5*sin(d*x+c)^4+1592*a^5*b^2*sin(d*x+c)^3-1256*a^5*b^2*sin(d*x+c)^5+15*a*b^6*sin(d*x+c)^5+1454*a^3*b^4*sin(d*x+c)^5-258*a^3*b^4*sin(d*x+c)^3+384*a^6*b*sin(d*x+c)^2-584*a^4*b^3*sin(d*x+c)^2-464*a^5*b^2*sin(d*x+c)+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^5)/a^3/b/sin(d*x+c)^5/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1167,1,2458,608,2.848000," ","int(cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"1/1536*(192*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^6-2160*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6+2160*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^6-180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6+180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^6+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6-896*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6+191*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6-816*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b*sin(d*x+c)^6+2592*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2*sin(d*x+c)^6-15*a*b^6*sin(d*x+c)^6-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^7*sin(d*x+c)^6-5*a^2*b^5*sin(d*x+c)^5+2*a^3*b^4*sin(d*x+c)^4-440*a^4*b^3*sin(d*x+c)^3-1072*a^5*b^2*sin(d*x+c)^2-256*a^7+720*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6+96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6-192*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^7*sin(d*x+c)^6+720*a^5*b^2*sin(d*x+c)^8-176*a^3*b^4*sin(d*x+c)^8+15*a*b^6*sin(d*x+c)^8+816*a^6*b*sin(d*x+c)^7-1376*a^4*b^3*sin(d*x+c)^7+1816*a^4*b^3*sin(d*x+c)^5+174*a^3*b^4*sin(d*x+c)^6-3232*a^5*b^2*sin(d*x+c)^6+5*a^2*b^5*sin(d*x+c)^7-2576*a^6*b*sin(d*x+c)^5+3584*a^5*b^2*sin(d*x+c)^4+2656*a^6*b*sin(d*x+c)^3-896*a^6*b*sin(d*x+c)+96*a^7*sin(d*x+c)^6-544*a^7*sin(d*x+c)^4+704*a^7*sin(d*x+c)^2-1696*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3*sin(d*x+c)^6-186*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4*sin(d*x+c)^6-5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5*sin(d*x+c)^6+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6*sin(d*x+c)^6)/a^4/sin(d*x+c)^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1168,1,1619,501,1.753000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{256 a^{5} b^{3} \sin \left(d x +c \right)}{3003}-\frac{696 a^{3} b^{5} \sin \left(d x +c \right)}{5005}+\frac{472 a \,b^{7} \sin \left(d x +c \right)}{15015}+\frac{1024 a^{6} b^{2}}{3003}+\frac{8 a^{2} b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{429}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}}{65}-\frac{2048 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{8}}{3003}+\frac{2304 a^{4} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5005}-\frac{1024 a^{6} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{3003}-\frac{2 a \,b^{7} \left(\sin^{7}\left(d x +c \right)\right)}{143}-\frac{8 b^{8} \left(\sin^{2}\left(d x +c \right)\right)}{195}+\frac{2488 a^{3} b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{15015}-\frac{256 a^{5} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{3003}-\frac{16 b^{8} \left(\sin^{6}\left(d x +c \right)\right)}{39}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{8}}{65}-\frac{80 a^{3} b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{3003}+\frac{164 a \,b^{7} \left(\sin^{5}\left(d x +c \right)\right)}{3003}-\frac{1082 a \,b^{7} \left(\sin^{3}\left(d x +c \right)\right)}{15015}-\frac{18944 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{3}}{15015}+\frac{4336 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}}{5005}+\frac{200 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{5}}{429}-\frac{428 a^{2} b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{5005}+\frac{128 a^{4} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{3003}-\frac{4 a^{2} b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{715}-\frac{7552 a^{4} b^{4}}{15015}+\frac{1088 a^{2} b^{6}}{15015}+\frac{2 b^{8} \left(\sin^{8}\left(d x +c \right)\right)}{13}+\frac{592 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}}{5005}+\frac{58 b^{8} \left(\sin^{4}\left(d x +c \right)\right)}{195}-\frac{232 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{6}}{1001}+\frac{568 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{7}}{5005}+\frac{2048 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}}{1155}-\frac{20008 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{4}}{15015}+\frac{2048 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7} b}{3003}-\frac{512 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b^{2}}{1001}}{b^{8} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/15015*(-200*a^3*b^5*sin(d*x+c)^5+410*a*b^7*sin(d*x+c)^5+320*a^4*b^4*sin(d*x+c)^4-642*a^2*b^6*sin(d*x+c)^4-640*a^5*b^3*sin(d*x+c)^3+1244*a^3*b^5*sin(d*x+c)^3-541*a*b^7*sin(d*x+c)^3-2560*a^6*b^2*sin(d*x+c)^2+3456*a^4*b^4*sin(d*x+c)^2-42*a^2*b^6*sin(d*x+c)^2+640*a^5*b^3*sin(d*x+c)-1044*a^3*b^5*sin(d*x+c)+236*a*b^7*sin(d*x+c)-105*a*b^7*sin(d*x+c)^7+2560*a^6*b^2+888*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6+140*a^2*b^6*sin(d*x+c)^6+2233*b^8*sin(d*x+c)^4-308*b^8*sin(d*x+c)^2+1155*b^8*sin(d*x+c)^8-3080*b^8*sin(d*x+c)^6-3776*a^4*b^4+544*a^2*b^6+924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-924*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^8-5120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^8-1740*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^6+852*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^7+13312*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-10004*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+5120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7*b-3840*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b^2-9472*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^3+6504*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^4+3500*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^5)/b^8/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1169,1,1356,439,1.705000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x)","-\frac{2 \left(-765 b^{7} \left(\sin^{3}\left(d x +c \right)\right)-160 a^{4} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+180 a \,b^{6}+640 a^{5} b^{2}+80 a^{3} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+322 a^{2} b^{5} \left(\sin^{3}\left(d x +c \right)\right)+180 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}-1280 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}-988 a^{3} b^{4}+35 a \,b^{6} \left(\sin^{6}\left(d x +c \right)\right)-166 a \,b^{6} \left(\sin^{4}\left(d x +c \right)\right)-50 a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+160 a^{4} b^{3} \sin \left(d x +c \right)-272 a^{2} b^{5} \sin \left(d x +c \right)-640 a^{5} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+908 a^{3} b^{4} \left(\sin^{2}\left(d x +c \right)\right)+180 b^{7} \sin \left(d x +c \right)-49 a \,b^{6} \left(\sin^{2}\left(d x +c \right)\right)-315 b^{7} \left(\sin^{7}\left(d x +c \right)\right)+996 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}+1280 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b -2688 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}+900 b^{7} \left(\sin^{5}\left(d x +c \right)\right)-960 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}+3416 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}-2456 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}+552 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}+1692 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}-732 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}\right)}{3465 b^{7} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/3465*(-960*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+35*a*b^6*sin(d*x+c)^6+180*a*b^6+640*a^5*b^2-988*a^3*b^4-50*a^2*b^5*sin(d*x+c)^5+80*a^3*b^4*sin(d*x+c)^4-166*a*b^6*sin(d*x+c)^4-160*a^4*b^3*sin(d*x+c)^3+322*a^2*b^5*sin(d*x+c)^3-640*a^5*b^2*sin(d*x+c)^2+908*a^3*b^4*sin(d*x+c)^2-49*a*b^6*sin(d*x+c)^2+160*a^4*b^3*sin(d*x+c)-272*a^2*b^5*sin(d*x+c)-315*b^7*sin(d*x+c)^7+900*b^7*sin(d*x+c)^5-765*b^7*sin(d*x+c)^3+180*b^7*sin(d*x+c)+180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^7-1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7-2456*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3+552*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+1692*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+996*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-732*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+3416*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-2688*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4)/b^7/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1170,1,1190,329,1.623000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{2 b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{9}-\frac{2 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{63}+\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b}{315}-\frac{64 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{105}-\frac{104 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}}{63}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{7}+\frac{88 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}}{105}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{256 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}}{315}+\frac{712 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{315}-\frac{208 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{105}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}+\frac{16 a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{315}-\frac{32 b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{45}-\frac{32 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{315}+\frac{68 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{315}-\frac{128 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{315}+\frac{28 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{45}+\frac{22 b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{45}+\frac{32 a^{3} b^{3} \sin \left(d x +c \right)}{315}-\frac{58 a \,b^{5} \sin \left(d x +c \right)}{315}+\frac{128 a^{4} b^{2}}{315}-\frac{212 a^{2} b^{4}}{315}}{b^{6} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(35*b^6*sin(d*x+c)^6-5*a*b^5*sin(d*x+c)^5+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-260*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3+180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+132*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+356*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-312*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6+8*a^2*b^4*sin(d*x+c)^4-112*b^6*sin(d*x+c)^4-16*a^3*b^3*sin(d*x+c)^3+34*a*b^5*sin(d*x+c)^3-64*a^4*b^2*sin(d*x+c)^2+98*a^2*b^4*sin(d*x+c)^2+77*b^6*sin(d*x+c)^2+16*a^3*b^3*sin(d*x+c)-29*a*b^5*sin(d*x+c)+64*a^4*b^2-106*a^2*b^4)/b^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1171,1,1018,363,1.860000," ","int(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(1/2),x)","\frac{\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b}{15}-\frac{4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{5}-\frac{46 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}}{15}+\frac{14 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{5}-\frac{16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}}{15}+\frac{58 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{15}-\frac{14 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{5}-2 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{4} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a +2 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{5} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)+\frac{2 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{5}-\frac{2 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{15}-\frac{8 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{15}-\frac{2 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{5}+\frac{2 a^{2} b^{3} \sin \left(d x +c \right)}{15}+\frac{8 a^{3} b^{2}}{15}}{a \,b^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/15*(8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-23*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+21*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+29*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-21*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^4*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^5*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))+3*a*b^4*sin(d*x+c)^4-a^2*b^3*sin(d*x+c)^3-4*a^3*b^2*sin(d*x+c)^2-3*a*b^4*sin(d*x+c)^2+a^2*b^3*sin(d*x+c)+4*a^3*b^2)/a/b^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1172,1,704,361,3.085000," ","int(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(\left(-2 a^{3} b^{2}-3 a \,b^{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \left(3 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a b -b^{2}}{a b}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-3 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a b -b^{2}}{a b}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -6 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+7 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}-\EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-3 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}\right) \sin \left(d x +c \right)+2 a^{2} b^{3} \left(\cos^{4}\left(d x +c \right)\right)-5 a^{2} b^{3} \left(\cos^{2}\left(d x +c \right)\right)\right)}{3 b^{3} \sqrt{\left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) b +\left(\cos^{2}\left(d x +c \right)\right) a}\, a^{2} \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/3*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-2*a^3*b^2-3*a*b^4)*sin(d*x+c)*cos(d*x+c)^2+(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(3*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a*b-b^2)/a/b,((a-b)/(a+b))^(1/2))*a*b^4-3*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a*b-b^2)/a/b,((a-b)/(a+b))^(1/2))*b^5-4*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-6*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+7*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+3*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+4*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5-EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-3*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)*sin(d*x+c)+2*a^2*b^3*cos(d*x+c)^4-5*a^2*b^3*cos(d*x+c)^2)/b^3/(cos(d*x+c)^2*sin(d*x+c)*b+cos(d*x+c)^2*a)^(1/2)/a^2/sin(d*x+c)/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","A"
1173,1,913,380,3.310000," ","int(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(\frac{2 \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{4 \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, b \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, a}-\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}{2 a \sin \left(d x +c \right)^{2}}+\frac{3 b \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}{4 a^{2} \sin \left(d x +c \right)}+\frac{b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{2 a \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{3 b^{2} \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{4 a^{2} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}-\frac{\left(4 a^{2}+3 b^{2}\right) \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, b \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{4 a^{3} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}\right)}{\cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*(2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))+4*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/a*b*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2))-1/2/a*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/sin(d*x+c)^2+3/4/a^2*b*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/sin(d*x+c)+1/2/a*b*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+3/4*b^2/a^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))-1/4*(4*a^2+3*b^2)/a^3*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*b*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2)))/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1174,1,1496,422,2.134000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x)","\frac{48 a^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{3}\left(d x +c \right)\right)-16 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{3}\left(d x +c \right)\right)-42 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)-5 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{3}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)+47 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)+36 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{3}\left(d x +c \right)\right)-32 a^{3} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+15 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)-32 a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+5 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+30 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-15 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+40 a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-5 a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+2 a^{3} b^{2} \sin \left(d x +c \right)-8 a^{4} b}{24 a^{4} \sin \left(d x +c \right)^{3} b \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/24*(48*a^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^3-16*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^3-42*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^3-5*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^3+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-32*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^3+47*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3+36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^3+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^3-32*a^3*b^2*sin(d*x+c)^5+15*a*b^4*sin(d*x+c)^5-32*a^4*b*sin(d*x+c)^4+5*a^2*b^3*sin(d*x+c)^4+30*a^3*b^2*sin(d*x+c)^3-15*a*b^4*sin(d*x+c)^3+40*a^4*b*sin(d*x+c)^2-5*a^2*b^3*sin(d*x+c)^2+2*a^3*b^2*sin(d*x+c)-8*a^4*b)/a^4/sin(d*x+c)^3/b/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1175,1,1761,477,2.342000," ","int(cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^(1/2),x)","-\frac{76 a^{4} b \left(\sin^{3}\left(d x +c \right)\right)+105 a \,b^{4} \left(\sin^{6}\left(d x +c \right)\right)+48 a^{5}+293 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-258 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)-216 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+216 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-8 a^{4} b \sin \left(d x +c \right)+14 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-35 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+174 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)-188 a^{3} b^{2} \left(\sin^{6}\left(d x +c \right)\right)+120 a^{5} \left(\sin^{4}\left(d x +c \right)\right)-68 a^{4} b \left(\sin^{5}\left(d x +c \right)\right)-105 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+35 a^{2} b^{3} \left(\sin^{5}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{4}\left(d x +c \right)\right)+68 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{4}\left(d x +c \right)\right)-35 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+120 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)+144 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-188 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{4}\left(d x +c \right)\right)-168 a^{5} \left(\sin^{2}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{192 a^{5} \sin \left(d x +c \right)^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/192*(68*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-258*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4-35*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4-144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^4-216*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+216*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^4+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+293*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^4+120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4+48*a^5-188*a^3*b^2*sin(d*x+c)^6+105*a*b^4*sin(d*x+c)^6-68*a^4*b*sin(d*x+c)^5+76*a^4*b*sin(d*x+c)^3-8*a^4*b*sin(d*x+c)+120*a^5*sin(d*x+c)^4-168*a^5*sin(d*x+c)^2+35*a^2*b^3*sin(d*x+c)^5+174*a^3*b^2*sin(d*x+c)^4-105*a*b^4*sin(d*x+c)^4-35*a^2*b^3*sin(d*x+c)^3+14*a^3*b^2*sin(d*x+c)^2-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^4+144*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^4-188*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^4)/a^5/sin(d*x+c)^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1176,1,1356,498,1.923000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(-255 b^{7} \left(\sin^{3}\left(d x +c \right)\right)-640 a^{4} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+60 a \,b^{6}+2560 a^{5} b^{2}+320 a^{3} b^{4} \left(\sin^{4}\left(d x +c \right)\right)+892 a^{2} b^{5} \left(\sin^{3}\left(d x +c \right)\right)+60 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{7}-2368 a^{3} b^{4}-552 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}-5868 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}+140 a \,b^{6} \left(\sin^{6}\left(d x +c \right)\right)-466 a \,b^{6} \left(\sin^{4}\left(d x +c \right)\right)-200 a^{2} b^{5} \left(\sin^{5}\left(d x +c \right)\right)+640 a^{4} b^{3} \sin \left(d x +c \right)-692 a^{2} b^{5} \sin \left(d x +c \right)-2560 a^{5} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+2048 a^{3} b^{4} \left(\sin^{2}\left(d x +c \right)\right)+60 b^{7} \sin \left(d x +c \right)+300 b^{7} \left(\sin^{5}\left(d x +c \right)\right)+266 a \,b^{6} \left(\sin^{2}\left(d x +c \right)\right)-105 b^{7} \left(\sin^{7}\left(d x +c \right)\right)+1476 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}+5120 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b -3840 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}+10496 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}-5120 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}+492 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}-6656 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}+4392 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}\right)}{1155 b^{8} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/1155*(-3840*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2+140*a*b^6*sin(d*x+c)^6+60*a*b^6+2560*a^5*b^2-2368*a^3*b^4-200*a^2*b^5*sin(d*x+c)^5+320*a^3*b^4*sin(d*x+c)^4-466*a*b^6*sin(d*x+c)^4-640*a^4*b^3*sin(d*x+c)^3+892*a^2*b^5*sin(d*x+c)^3-2560*a^5*b^2*sin(d*x+c)^2+2048*a^3*b^4*sin(d*x+c)^2+266*a*b^6*sin(d*x+c)^2+640*a^4*b^3*sin(d*x+c)-692*a^2*b^5*sin(d*x+c)-105*b^7*sin(d*x+c)^7+300*b^7*sin(d*x+c)^5-255*b^7*sin(d*x+c)^3+60*b^7*sin(d*x+c)+60*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^7-5120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7-6656*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3+492*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+4392*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+1476*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5+5120*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-552*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+10496*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-5868*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4)/b^8/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1177,1,1190,437,1.854000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x)","\frac{\frac{2 b^{6} \left(\sin^{6}\left(d x +c \right)\right)}{9}-\frac{20 a \,b^{5} \left(\sin^{5}\left(d x +c \right)\right)}{63}+\frac{512 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b}{63}-\frac{128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{21}-\frac{3184 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}}{315}+\frac{232 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{35}+\frac{208 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}}{105}-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}-\frac{512 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}}{63}+\frac{5104 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}}{315}-\frac{904 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}}{105}+\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}}{15}+\frac{32 a^{2} b^{4} \left(\sin^{4}\left(d x +c \right)\right)}{63}-\frac{32 b^{6} \left(\sin^{4}\left(d x +c \right)\right)}{45}-\frac{64 a^{3} b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{63}+\frac{428 a \,b^{5} \left(\sin^{3}\left(d x +c \right)\right)}{315}-\frac{256 a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{63}+\frac{136 a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)}{45}+\frac{22 b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{45}+\frac{64 a^{3} b^{3} \sin \left(d x +c \right)}{63}-\frac{328 a \,b^{5} \sin \left(d x +c \right)}{315}+\frac{256 a^{4} b^{2}}{63}-\frac{1112 a^{2} b^{4}}{315}}{b^{7} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"2/315*(35*b^6*sin(d*x+c)^6-50*a*b^5*sin(d*x+c)^5+1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-960*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-1592*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3+1044*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+312*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-1280*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+2552*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-1356*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+84*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6+80*a^2*b^4*sin(d*x+c)^4-112*b^6*sin(d*x+c)^4-160*a^3*b^3*sin(d*x+c)^3+214*a*b^5*sin(d*x+c)^3-640*a^4*b^2*sin(d*x+c)^2+476*a^2*b^4*sin(d*x+c)^2+77*b^6*sin(d*x+c)^2+160*a^3*b^3*sin(d*x+c)-164*a*b^5*sin(d*x+c)+640*a^4*b^2-556*a^2*b^4)/b^7/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1178,1,943,307,1.651000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(-5 b^{5} \left(\sin^{5}\left(d x +c \right)\right)+128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -96 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-148 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+96 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+20 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-128 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+244 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-116 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+8 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)-16 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+20 b^{5} \left(\sin^{3}\left(d x +c \right)\right)-64 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+42 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+16 a^{2} b^{3} \sin \left(d x +c \right)-15 b^{5} \sin \left(d x +c \right)+64 a^{3} b^{2}-50 a \,b^{4}\right)}{35 b^{6} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/35*(-5*b^5*sin(d*x+c)^5+128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-148*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+20*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5-128*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+244*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-116*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+8*a*b^4*sin(d*x+c)^4-16*a^2*b^3*sin(d*x+c)^3+20*b^5*sin(d*x+c)^3-64*a^3*b^2*sin(d*x+c)^2+42*a*b^4*sin(d*x+c)^2+16*a^2*b^3*sin(d*x+c)-15*b^5*sin(d*x+c)+64*a^3*b^2-50*a*b^4)/b^6/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1179,1,1010,373,1.875000," ","int(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(3/2),x)","-\frac{2 \left(8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -6 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+11 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{4} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a -3 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{5} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right)-a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)-4 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+3 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)+a^{2} b^{3} \sin \left(d x +c \right)+4 a^{3} b^{2}-3 a \,b^{4}\right)}{3 a^{2} b^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-2/3*(8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+11*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^4*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a-3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^5*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))-a^2*b^3*sin(d*x+c)^3-4*a^3*b^2*sin(d*x+c)^2+3*a*b^4*sin(d*x+c)^2+a^2*b^3*sin(d*x+c)+4*a^3*b^2-3*a*b^4)/a^2/b^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1180,1,618,377,1.690000," ","int(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x)","-\frac{\left(-2 a^{3} b^{2}+3 a \,b^{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \left(4 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}-7 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+3 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}-3 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+3 \EllipticPi \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-4 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b +6 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}+\EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}-3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}\right) \sin \left(d x +c \right)+a^{2} b^{3} \left(\cos^{2}\left(d x +c \right)\right)}{b^{3} \sin \left(d x +c \right) a^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-((-2*a^3*b^2+3*a*b^4)*sin(d*x+c)*cos(d*x+c)^2+(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(4*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5-7*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+3*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-3*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4+3*EllipticPi((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5-4*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b+6*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2+EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3-3*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)*sin(d*x+c)+a^2*b^3*cos(d*x+c)^2)/b^3/sin(d*x+c)/a^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","A"
1181,1,1349,435,2.016000," ","int(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x)","-\frac{8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-18 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)-5 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-8 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{2}\left(d x +c \right)\right)+23 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{2} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{2}\left(d x +c \right)\right)+12 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, b^{3} \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{2}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{2}\left(d x +c \right)\right)-8 a^{3} b^{2} \left(\sin^{4}\left(d x +c \right)\right)+15 a \,b^{4} \left(\sin^{4}\left(d x +c \right)\right)+5 a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+6 a^{3} b^{2} \left(\sin^{2}\left(d x +c \right)\right)-15 a \,b^{4} \left(\sin^{2}\left(d x +c \right)\right)-5 a^{2} b^{3} \sin \left(d x +c \right)+2 a^{3} b^{2}}{4 b^{2} \sin \left(d x +c \right)^{2} a^{4} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"-1/4*(8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^2-18*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2-5*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^2+23*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^2*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^2+12*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*b^3*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^2+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^2-8*a^3*b^2*sin(d*x+c)^4+15*a*b^4*sin(d*x+c)^4+5*a^2*b^3*sin(d*x+c)^3+6*a^3*b^2*sin(d*x+c)^2-15*a*b^4*sin(d*x+c)^2-5*a^2*b^3*sin(d*x+c)+2*a^3*b^2)/b^2/sin(d*x+c)^2/a^4/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1182,1,1496,481,2.180000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x)","\frac{48 a^{5} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) \left(\sin^{3}\left(d x +c \right)\right)+32 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b \left(\sin^{3}\left(d x +c \right)\right)-150 b^{2} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} \left(\sin^{3}\left(d x +c \right)\right)-35 b^{3} \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \left(\sin^{3}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-80 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} \left(\sin^{3}\left(d x +c \right)\right)+185 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-108 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)+108 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3} \left(\sin^{3}\left(d x +c \right)\right)+105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)-105 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{5} \left(\sin^{3}\left(d x +c \right)\right)-80 a^{3} b^{2} \left(\sin^{5}\left(d x +c \right)\right)+105 a \,b^{4} \left(\sin^{5}\left(d x +c \right)\right)-32 a^{4} b \left(\sin^{4}\left(d x +c \right)\right)+35 a^{2} b^{3} \left(\sin^{4}\left(d x +c \right)\right)+66 a^{3} b^{2} \left(\sin^{3}\left(d x +c \right)\right)-105 a \,b^{4} \left(\sin^{3}\left(d x +c \right)\right)+40 a^{4} b \left(\sin^{2}\left(d x +c \right)\right)-35 a^{2} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+14 a^{3} b^{2} \sin \left(d x +c \right)-8 a^{4} b}{24 b \,a^{5} \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"1/24*(48*a^5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*sin(d*x+c)^3+32*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b*sin(d*x+c)^3-150*b^2*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)^3-35*b^3*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)^3+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-80*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*sin(d*x+c)^3+185*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^2*sin(d*x+c)^3+108*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^3*sin(d*x+c)^3+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^4*sin(d*x+c)^3-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^5*sin(d*x+c)^3-80*a^3*b^2*sin(d*x+c)^5+105*a*b^4*sin(d*x+c)^5-32*a^4*b*sin(d*x+c)^4+35*a^2*b^3*sin(d*x+c)^4+66*a^3*b^2*sin(d*x+c)^3-105*a*b^4*sin(d*x+c)^3+40*a^4*b*sin(d*x+c)^2-35*a^2*b^3*sin(d*x+c)^2+14*a^3*b^2*sin(d*x+c)-8*a^4*b)/b/a^5/sin(d*x+c)^3/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1183,1,2033,499,2.103000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x)","\frac{-\frac{2 b^{7} \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{9}+\frac{2 \left(120 a^{2} b^{5}-7 b^{7}\right) \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)}{315}+\frac{2 \left(3200 a^{4} b^{3}-1740 a^{2} b^{5}+42 b^{7}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{315}-\frac{8 \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, b \left(1280 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}-2048 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}+789 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}-21 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}-1280 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b +960 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}+1088 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}-666 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}-123 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}+21 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{6}\right) \sin \left(d x +c \right)}{315}+\frac{8 a \,b^{6} \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{2 \left(-320 a^{3} b^{4}+102 a \,b^{6}\right) \left(\cos^{4}\left(d x +c \right)\right)}{315}+\frac{2 \left(2560 a^{5} b^{2}-896 a^{3} b^{4}-162 a \,b^{6}\right) \left(\cos^{2}\left(d x +c \right)\right)}{315}-\frac{2048 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{7}}{63}+\frac{16384 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{315}-\frac{2104 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{105}+\frac{8 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{15}+\frac{2048 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} b}{63}-\frac{512 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b^{2}}{21}-\frac{8704 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{3}}{315}+\frac{592 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{4}}{35}+\frac{328 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{5}}{105}-\frac{8 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{6}}{15}}{\left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{8} \cos \left(d x +c \right) d}"," ",0,"2/315*(-35*b^7*sin(d*x+c)*cos(d*x+c)^6+(120*a^2*b^5-7*b^7)*cos(d*x+c)^4*sin(d*x+c)+(3200*a^4*b^3-1740*a^2*b^5+42*b^7)*cos(d*x+c)^2*sin(d*x+c)-4*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*b*(1280*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6-2048*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+789*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4-21*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6-1280*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b+960*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2+1088*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3-666*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4-123*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5+21*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^6)*sin(d*x+c)+60*a*b^6*cos(d*x+c)^6+(-320*a^3*b^4+102*a*b^6)*cos(d*x+c)^4+(2560*a^5*b^2-896*a^3*b^4-162*a*b^6)*cos(d*x+c)^2-5120*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^7+8192*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-3156*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+84*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6+5120*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*b-3840*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b^2-4352*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^3+2664*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^4+492*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^5-84*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^6)/(a+b*sin(d*x+c))^(3/2)/b^8/cos(d*x+c)/d","B"
1184,1,1642,445,1.903000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 \left(6 a \,b^{5} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)+\left(160 a^{3} b^{3}-66 a \,b^{5}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+4 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b \left(64 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b -48 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-46 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}+27 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}+3 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{5}-64 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}+94 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}-30 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}\right) \sin \left(d x +c \right)+3 b^{6} \left(\cos^{6}\left(d x +c \right)\right)+\left(-16 a^{2} b^{4}+3 b^{6}\right) \left(\cos^{4}\left(d x +c \right)\right)+\left(128 a^{4} b^{2}-28 a^{2} b^{4}-6 b^{6}\right) \left(\cos^{2}\left(d x +c \right)\right)+256 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b -192 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-184 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3}+108 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}+12 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5}-256 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6}+376 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2}-120 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4}\right)}{21 \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{7} \cos \left(d x +c \right) d}"," ",0,"-2/21*(6*a*b^5*sin(d*x+c)*cos(d*x+c)^4+(160*a^3*b^3-66*a*b^5)*cos(d*x+c)^2*sin(d*x+c)+4*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b*(64*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-48*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-46*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+27*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4+3*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^5-64*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+94*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-30*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)*sin(d*x+c)+3*b^6*cos(d*x+c)^6+(-16*a^2*b^4+3*b^6)*cos(d*x+c)^4+(128*a^4*b^2-28*a^2*b^4-6*b^6)*cos(d*x+c)^2+256*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b-192*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-184*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3+108*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4+12*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5-256*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6+376*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2-120*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4)/(a+b*sin(d*x+c))^(3/2)/b^7/cos(d*x+c)/d","B"
1185,1,1430,300,1.921000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(5/2),x)","\frac{\frac{2 b^{5} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{2 \left(80 a^{2} b^{3}-18 b^{5}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}+\frac{8 \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, b \left(32 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b -24 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}-17 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{3}+9 \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}-32 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4}+41 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{2}-9 \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) b^{4}\right) \sin \left(d x +c \right)}{15}-\frac{16 a \,b^{4} \left(\cos^{4}\left(d x +c \right)\right)}{15}+\frac{2 \left(64 a^{3} b^{2}-2 a \,b^{4}\right) \left(\cos^{2}\left(d x +c \right)\right)}{15}+\frac{256 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b}{15}-\frac{64 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{5}-\frac{136 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{3}}{15}+\frac{24 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticF \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{5}-\frac{256 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5}}{15}+\frac{328 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{2}}{15}-\frac{24 \sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a +b}+\frac{b}{a +b}}\, \sqrt{-\frac{b \sin \left(d x +c \right)}{a -b}-\frac{b}{a -b}}\, \EllipticE \left(\sqrt{\frac{b \sin \left(d x +c \right)}{a -b}+\frac{a}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{4}}{5}}{\left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{6} \cos \left(d x +c \right) d}"," ",0,"2/15*(3*b^5*sin(d*x+c)*cos(d*x+c)^4+(80*a^2*b^3-18*b^5)*cos(d*x+c)^2*sin(d*x+c)+4*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*b*(32*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b-24*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^2-17*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^3+9*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4-32*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4+41*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^2-9*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*b^4)*sin(d*x+c)-8*a*b^4*cos(d*x+c)^4+(64*a^3*b^2-2*a*b^4)*cos(d*x+c)^2+128*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b-96*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-68*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^3+36*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticF((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4-128*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5+164*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^2-36*(b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2)*(-b/(a+b)*sin(d*x+c)+b/(a+b))^(1/2)*(-b/(a-b)*sin(d*x+c)-b/(a-b))^(1/2)*EllipticE((b/(a-b)*sin(d*x+c)+a/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^4)/(a+b*sin(d*x+c))^(3/2)/b^6/cos(d*x+c)/d","B"
1186,1,1375,388,6.696000," ","int(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(5/2),x)","\frac{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}\, \left(\frac{\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}-\frac{4 a \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}}{b^{3}}+\frac{\left(3 a^{4}-2 a^{2} b^{2}-b^{4}\right) \left(\frac{2 b \left(\cos^{2}\left(d x +c \right)\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 a \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{\left(a^{2}-b^{2}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}\right)}{b^{3} a^{2}}-\frac{2 \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, b \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, -\frac{\left(-\frac{a}{b}+1\right) b}{a}, \sqrt{\frac{a -b}{a +b}}\right)}{a^{3} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{\left(-a^{4}+2 a^{2} b^{2}-b^{4}\right) \left(\frac{2 \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}{3 b \left(a^{2}-b^{2}\right) \left(\sin \left(d x +c \right)+\frac{a}{b}\right)^{2}}+\frac{8 b \left(\cos^{2}\left(d x +c \right)\right) a}{3 \left(a^{2}-b^{2}\right)^{2} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{2 \left(3 a^{2}+b^{2}\right) \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)}{\left(3 a^{4}-6 a^{2} b^{2}+3 b^{4}\right) \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}+\frac{8 a b \left(\frac{a}{b}-1\right) \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{\frac{b \left(1-\sin \left(d x +c \right)\right)}{a +b}}\, \sqrt{\frac{\left(-1-\sin \left(d x +c \right)\right) b}{a -b}}\, \left(\left(-\frac{a}{b}-1\right) \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)+\EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{3 \left(a^{2}-b^{2}\right)^{2} \sqrt{-\left(-a -b \sin \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right)}}\right)}{a \,b^{3}}\right)}{\cos \left(d x +c \right) \sqrt{a +b \sin \left(d x +c \right)}\, d}"," ",0,"(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*(1/b^3*(2*b*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))-4*a*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))+1/b^3*(3*a^4-2*a^2*b^2-b^4)/a^2*(2*b*cos(d*x+c)^2/(a^2-b^2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*a/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+2*b/(a^2-b^2)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))))-2/a^3*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*b*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),-(-a/b+1)/a*b,((a-b)/(a+b))^(1/2))+(-a^4+2*a^2*b^2-b^4)/a/b^3*(2/3/b/(a^2-b^2)*(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)/(sin(d*x+c)+a/b)^2+8/3*b*cos(d*x+c)^2/(a^2-b^2)^2*a/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)+2*(3*a^2+b^2)/(3*a^4-6*a^2*b^2+3*b^4)*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+8/3*a*b/(a^2-b^2)^2*(a/b-1)*((a+b*sin(d*x+c))/(a-b))^(1/2)*(b*(1-sin(d*x+c))/(a+b))^(1/2)*((-1-sin(d*x+c))*b/(a-b))^(1/2)/(-(-a-b*sin(d*x+c))*cos(d*x+c)^2)^(1/2)*((-a/b-1)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))+EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2)))))/cos(d*x+c)/(a+b*sin(d*x+c))^(1/2)/d","B"
1187,1,2112,419,2.187000," ","int(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x)","-\frac{2 a^{4} b^{2} \sin \left(d x +c \right)+4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b \sin \left(d x +c \right)+6 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2} \sin \left(d x +c \right)+5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3} \sin \left(d x +c \right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4} \sin \left(d x +c \right)-2 a^{4} b^{2} \left(\sin^{3}\left(d x +c \right)\right)+a^{3} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+20 a^{2} b^{4} \sin \left(d x +c \right)+6 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+5 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4} \left(\sin^{2}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5} \left(\sin^{2}\left(d x +c \right)\right)-4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{5} b \left(\sin^{2}\left(d x +c \right)\right)-11 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{3} b^{3} \left(\sin^{2}\left(d x +c \right)\right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5} \left(\sin^{2}\left(d x +c \right)\right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5} \left(\sin^{2}\left(d x +c \right)\right)+4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticF \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2} \left(\sin^{2}\left(d x +c \right)\right)+3 a^{3} b^{3}+15 a \,b^{5} \left(\sin^{2}\left(d x +c \right)\right)-20 a^{2} b^{4} \left(\sin^{3}\left(d x +c \right)\right)-15 a \,b^{5} \left(\sin^{4}\left(d x +c \right)\right)-4 a^{3} b^{3} \left(\sin^{4}\left(d x +c \right)\right)-4 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{6} \sin \left(d x +c \right)-11 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{4} b^{2} \sin \left(d x +c \right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticE \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4} \sin \left(d x +c \right)-15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} b^{4} \sin \left(d x +c \right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) a \,b^{5} \sin \left(d x +c \right)+15 \sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}\, \sqrt{-\frac{\left(\sin \left(d x +c \right)-1\right) b}{a +b}}\, \sqrt{-\frac{\left(1+\sin \left(d x +c \right)\right) b}{a -b}}\, \EllipticPi \left(\sqrt{\frac{a +b \sin \left(d x +c \right)}{a -b}}, \frac{a -b}{a}, \sqrt{\frac{a -b}{a +b}}\right) b^{6} \left(\sin^{2}\left(d x +c \right)\right)}{3 a^{4} \sin \left(d x +c \right) \left(a +b \sin \left(d x +c \right)\right)^{\frac{3}{2}} b^{3} \cos \left(d x +c \right) d}"," ",0,"-1/3*(15*a*b^5*sin(d*x+c)^2-4*a^3*b^3*sin(d*x+c)^4-15*a*b^5*sin(d*x+c)^4-2*a^4*b^2*sin(d*x+c)^3-20*a^2*b^4*sin(d*x+c)^3+a^3*b^3*sin(d*x+c)^2+2*a^4*b^2*sin(d*x+c)+6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^2+5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^2-4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^2-11*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^2+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^2+20*a^2*b^4*sin(d*x+c)+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^6*sin(d*x+c)^2-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^2+4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)+6*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)+5*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)-11*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)-15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)+15*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)+4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^2+3*a^3*b^3-4*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*sin(d*x+c))/a^4/sin(d*x+c)/(a+b*sin(d*x+c))^(3/2)/b^3/cos(d*x+c)/d","B"
1188,1,2617,472,2.429000," ","int(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/12*(-35*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^2+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^2+105*a*b^5*sin(d*x+c)^5-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*sin(d*x+c)^2-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^2-78*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^2-21*a^3*b^3*sin(d*x+c)+140*a^2*b^4*sin(d*x+c)^4+29*a^3*b^3*sin(d*x+c)^3-105*a*b^5*sin(d*x+c)^3+10*a^4*b^2*sin(d*x+c)^2-140*a^2*b^4*sin(d*x+c)^2-8*a^3*b^3*sin(d*x+c)^5-16*a^4*b^2*sin(d*x+c)^4+6*a^4*b^2-78*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^3-35*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^3+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^3-8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^3+113*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^3-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^3-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^3+36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^3+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^3+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^2+113*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^2-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^2-36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^2+36*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^2-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^6*sin(d*x+c)^3+105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^2+8*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^3)/a^5/sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2)/b^2/cos(d*x+c)/d","B"
1189,1,2870,519,2.438000," ","int(cot(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"1/24*(159*a^3*b^3*sin(d*x+c)^4-315*a*b^5*sin(d*x+c)^4+126*a^4*b^2*sin(d*x+c)^3-420*a^2*b^4*sin(d*x+c)^3-63*a^3*b^3*sin(d*x+c)^2+18*a^4*b^2*sin(d*x+c)+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*sin(d*x+c)^3+411*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^4-315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^4-180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^4-8*a^5*b-96*a^3*b^3*sin(d*x+c)^6+315*a*b^5*sin(d*x+c)^6-144*a^4*b^2*sin(d*x+c)^5+420*a^2*b^4*sin(d*x+c)^5-32*a^5*b*sin(d*x+c)^4+40*a^5*b*sin(d*x+c)^2+180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^4+315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^4+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^3+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^4+411*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^3-315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^3-180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^3+48*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^4-306*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^4-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^4+315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^4-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^5*b*sin(d*x+c)^4-105*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^3+315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^3+180*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^3*b^3*sin(d*x+c)^3+315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a^2*b^4*sin(d*x+c)^3-315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*a*b^5*sin(d*x+c)^3-306*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticF(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^4*b^2*sin(d*x+c)^3-315*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticPi(((a+b*sin(d*x+c))/(a-b))^(1/2),(a-b)/a,((a-b)/(a+b))^(1/2))*b^6*sin(d*x+c)^4-96*((a+b*sin(d*x+c))/(a-b))^(1/2)*(-(sin(d*x+c)-1)*b/(a+b))^(1/2)*(-(1+sin(d*x+c))*b/(a-b))^(1/2)*EllipticE(((a+b*sin(d*x+c))/(a-b))^(1/2),((a-b)/(a+b))^(1/2))*a^6*sin(d*x+c)^3)/sin(d*x+c)^3/a^6/(a+b*sin(d*x+c))^(3/2)/b/cos(d*x+c)/d","B"
1190,1,24365,458,1.160000," ","int(cos(f*x+e)^4/(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1191,0,0,31,0.938000," ","int(cos(d*x+c)^4*sin(d*x+c)^(1/3)/(a+b*sin(d*x+c))^(1/2),x)","\int \frac{\left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{\frac{1}{3}}\left(d x +c \right)\right)}{\sqrt{a +b \sin \left(d x +c \right)}}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^(1/3)/(a+b*sin(d*x+c))^(1/2),x)","F"
1192,0,0,31,1.063000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{p}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x)","F"
1193,0,0,35,1.596000," ","int(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{-3-p}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{p}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x)","F"
1194,0,0,35,1.397000," ","int(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{-4-p}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{p}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x)","F"
1195,0,0,611,28.104000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x)","F"
1196,0,0,475,17.906000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","F"
1197,0,0,117,7.331000," ","int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","\int \left(\cos^{4}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","F"
1198,1,138,85,0.265000," ","int(cos(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)+b \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{11}-\frac{5 \left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{99}-\frac{5 \sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{231}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)}{d}"," ",0,"1/d*(a*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6)+b*(-1/11*sin(d*x+c)^5*cos(d*x+c)^6-5/99*sin(d*x+c)^3*cos(d*x+c)^6-5/231*sin(d*x+c)*cos(d*x+c)^6+1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1199,1,120,85,0.267000," ","int(cos(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+b \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{10}-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{20}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{60}\right)}{d}"," ",0,"1/d*(a*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+b*(-1/10*sin(d*x+c)^4*cos(d*x+c)^6-1/20*sin(d*x+c)^2*cos(d*x+c)^6-1/60*cos(d*x+c)^6))","A"
1200,1,102,71,0.265000," ","int(cos(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)}{d}"," ",0,"1/d*(a*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+b*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1201,1,84,71,0.267000," ","int(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(a*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+b*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6))","A"
1202,1,64,57,0.271000," ","int(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6}+b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(-1/6*a*cos(d*x+c)^6+b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1203,1,94,80,0.384000," ","int(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{8 b \sin \left(d x +c \right)}{15 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{5 d}+\frac{4 b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/4*a*cos(d*x+c)^4/d+1/2*a*cos(d*x+c)^2/d+a*ln(sin(d*x+c))/d+8/15*b*sin(d*x+c)/d+1/5/d*cos(d*x+c)^4*sin(d*x+c)*b+4/15/d*b*sin(d*x+c)*cos(d*x+c)^2","A"
1204,1,116,79,0.344000," ","int(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 a \sin \left(d x +c \right)}{3 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}-\frac{4 a \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}+\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/d*a/sin(d*x+c)*cos(d*x+c)^6-8/3*a*sin(d*x+c)/d-1/d*cos(d*x+c)^4*sin(d*x+c)*a-4/3/d*a*sin(d*x+c)*cos(d*x+c)^2+1/4*b*cos(d*x+c)^4/d+1/2*b*cos(d*x+c)^2/d+b*ln(sin(d*x+c))/d","A"
1205,1,139,80,0.385000," ","int(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{a \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 b \sin \left(d x +c \right)}{3 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{d}-\frac{4 b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/2/d*a/sin(d*x+c)^2*cos(d*x+c)^6-1/2*a*cos(d*x+c)^4/d-a*cos(d*x+c)^2/d-2*a*ln(sin(d*x+c))/d-1/d*b/sin(d*x+c)*cos(d*x+c)^6-8/3*b*sin(d*x+c)/d-1/d*cos(d*x+c)^4*sin(d*x+c)*b-4/3/d*b*sin(d*x+c)*cos(d*x+c)^2","A"
1206,1,159,79,0.385000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{d}+\frac{4 a \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{b \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a/sin(d*x+c)^3*cos(d*x+c)^6+1/d*a/sin(d*x+c)*cos(d*x+c)^6+8/3*a*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*a+4/3/d*a*sin(d*x+c)*cos(d*x+c)^2-1/2/d*b/sin(d*x+c)^2*cos(d*x+c)^6-1/2*b*cos(d*x+c)^4/d-b*cos(d*x+c)^2/d-2*b*ln(sin(d*x+c))/d","A"
1207,1,136,77,0.408000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 b \sin \left(d x +c \right)}{3 d}+\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) b}{d}+\frac{4 b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/4/d*a*cot(d*x+c)^4+1/2*a*cot(d*x+c)^2/d+a*ln(sin(d*x+c))/d-1/3/d*b/sin(d*x+c)^3*cos(d*x+c)^6+1/d*b/sin(d*x+c)*cos(d*x+c)^6+8/3*b*sin(d*x+c)/d+1/d*cos(d*x+c)^4*sin(d*x+c)*b+4/3/d*b*sin(d*x+c)*cos(d*x+c)^2","A"
1208,1,160,80,0.404000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c)),x)","-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}-\frac{8 a \sin \left(d x +c \right)}{15 d}-\frac{\left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right) a}{5 d}-\frac{4 a \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{b \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{b \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{b \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/5/d*a/sin(d*x+c)^5*cos(d*x+c)^6+1/15/d*a/sin(d*x+c)^3*cos(d*x+c)^6-1/5/d*a/sin(d*x+c)*cos(d*x+c)^6-8/15*a*sin(d*x+c)/d-1/5/d*cos(d*x+c)^4*sin(d*x+c)*a-4/15/d*a*sin(d*x+c)*cos(d*x+c)^2-1/4/d*b*cot(d*x+c)^4+1/2*b*cot(d*x+c)^2/d+b*ln(sin(d*x+c))/d","A"
1209,1,110,55,0.434000," ","int(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c)),x)","\frac{-\frac{a \left(\cos^{6}\left(d x +c \right)\right)}{6 \sin \left(d x +c \right)^{6}}+b \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}\right)}{d}"," ",0,"1/d*(-1/6*a/sin(d*x+c)^6*cos(d*x+c)^6+b*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1210,1,128,57,0.451000," ","int(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{b \left(\cos^{6}\left(d x +c \right)\right)}{6 \sin \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(a*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*b/sin(d*x+c)^6*cos(d*x+c)^6)","B"
1211,1,148,71,0.346000," ","int(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{8 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{24 \sin \left(d x +c \right)^{6}}\right)+b \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)}{d}"," ",0,"1/d*(a*(-1/8/sin(d*x+c)^8*cos(d*x+c)^6-1/24/sin(d*x+c)^6*cos(d*x+c)^6)+b*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
1212,1,166,71,0.460000," ","int(cos(d*x+c)^5*csc(d*x+c)^10*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{6}\left(d x +c \right)}{21 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)+b \left(-\frac{\cos^{6}\left(d x +c \right)}{8 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{24 \sin \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(a*(-1/9/sin(d*x+c)^9*cos(d*x+c)^6-1/21/sin(d*x+c)^7*cos(d*x+c)^6-1/105/sin(d*x+c)^5*cos(d*x+c)^6+1/315/sin(d*x+c)^3*cos(d*x+c)^6-1/105/sin(d*x+c)*cos(d*x+c)^6-1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+b*(-1/8/sin(d*x+c)^8*cos(d*x+c)^6-1/24/sin(d*x+c)^6*cos(d*x+c)^6))","B"
1213,1,184,85,0.331000," ","int(cos(d*x+c)^5*csc(d*x+c)^11*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{6}\left(d x +c \right)}{20 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{60 \sin \left(d x +c \right)^{6}}\right)+b \left(-\frac{\cos^{6}\left(d x +c \right)}{9 \sin \left(d x +c \right)^{9}}-\frac{\cos^{6}\left(d x +c \right)}{21 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{315 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)}{d}"," ",0,"1/d*(a*(-1/10/sin(d*x+c)^10*cos(d*x+c)^6-1/20/sin(d*x+c)^8*cos(d*x+c)^6-1/60/sin(d*x+c)^6*cos(d*x+c)^6)+b*(-1/9/sin(d*x+c)^9*cos(d*x+c)^6-1/21/sin(d*x+c)^7*cos(d*x+c)^6-1/105/sin(d*x+c)^5*cos(d*x+c)^6+1/315/sin(d*x+c)^3*cos(d*x+c)^6-1/105/sin(d*x+c)*cos(d*x+c)^6-1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","B"
1214,1,202,85,0.439000," ","int(cos(d*x+c)^5*csc(d*x+c)^12*(a+b*sin(d*x+c)),x)","\frac{a \left(-\frac{\cos^{6}\left(d x +c \right)}{11 \sin \left(d x +c \right)^{11}}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right)}{99 \sin \left(d x +c \right)^{9}}-\frac{5 \left(\cos^{6}\left(d x +c \right)\right)}{231 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{231 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{693 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{231 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{231}\right)+b \left(-\frac{\cos^{6}\left(d x +c \right)}{10 \sin \left(d x +c \right)^{10}}-\frac{\cos^{6}\left(d x +c \right)}{20 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{60 \sin \left(d x +c \right)^{6}}\right)}{d}"," ",0,"1/d*(a*(-1/11/sin(d*x+c)^11*cos(d*x+c)^6-5/99/sin(d*x+c)^9*cos(d*x+c)^6-5/231/sin(d*x+c)^7*cos(d*x+c)^6-1/231/sin(d*x+c)^5*cos(d*x+c)^6+1/693/sin(d*x+c)^3*cos(d*x+c)^6-1/231/sin(d*x+c)*cos(d*x+c)^6-1/231*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+b*(-1/10/sin(d*x+c)^10*cos(d*x+c)^6-1/20/sin(d*x+c)^8*cos(d*x+c)^6-1/60/sin(d*x+c)^6*cos(d*x+c)^6))","B"
1215,1,155,124,0.311000," ","int(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+2 a b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)+b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{9}-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{21}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{105}\right)}{d}"," ",0,"1/d*(a^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+2*a*b*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6)+b^2*(-1/9*sin(d*x+c)^3*cos(d*x+c)^6-1/21*sin(d*x+c)*cos(d*x+c)^6+1/105*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1216,1,101,124,0.311000," ","int(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6}+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(-1/6*a^2*cos(d*x+c)^6+2*a*b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+b^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6))","A"
1217,1,119,120,0.532000," ","int(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{16 a b \sin \left(d x +c \right)}{15 d}+\frac{2 a b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}+\frac{8 a b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{\left(\cos^{6}\left(d x +c \right)\right) b^{2}}{6 d}"," ",0,"1/4/d*a^2*cos(d*x+c)^4+1/2/d*a^2*cos(d*x+c)^2+a^2*ln(sin(d*x+c))/d+16/15*a*b*sin(d*x+c)/d+2/5/d*a*b*sin(d*x+c)*cos(d*x+c)^4+8/15/d*a*b*sin(d*x+c)*cos(d*x+c)^2-1/6/d*cos(d*x+c)^6*b^2","A"
1218,1,185,119,0.451000," ","int(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 a^{2} \sin \left(d x +c \right)}{3 d}-\frac{a^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{4 a^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}+\frac{a b \left(\cos^{4}\left(d x +c \right)\right)}{2 d}+\frac{a b \left(\cos^{2}\left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\sin \left(d x +c \right)\right)}{d}+\frac{8 b^{2} \sin \left(d x +c \right)}{15 d}+\frac{\sin \left(d x +c \right) b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 \sin \left(d x +c \right) b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"-1/d*a^2/sin(d*x+c)*cos(d*x+c)^6-8/3*a^2*sin(d*x+c)/d-1/d*a^2*sin(d*x+c)*cos(d*x+c)^4-4/3/d*a^2*sin(d*x+c)*cos(d*x+c)^2+1/2/d*a*b*cos(d*x+c)^4+1/d*a*b*cos(d*x+c)^2+2*a*b*ln(sin(d*x+c))/d+8/15*b^2*sin(d*x+c)/d+1/5/d*sin(d*x+c)*b^2*cos(d*x+c)^4+4/15/d*sin(d*x+c)*b^2*cos(d*x+c)^2","A"
1219,1,197,119,0.535000," ","int(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{16 a b \sin \left(d x +c \right)}{3 d}-\frac{2 a b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{8 a b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^6-1/2/d*a^2*cos(d*x+c)^4-1/d*a^2*cos(d*x+c)^2-2*a^2*ln(sin(d*x+c))/d-2/d*a*b/sin(d*x+c)*cos(d*x+c)^6-16/3*a*b*sin(d*x+c)/d-2/d*a*b*sin(d*x+c)*cos(d*x+c)^4-8/3/d*a*b*sin(d*x+c)*cos(d*x+c)^2+1/4/d*b^2*cos(d*x+c)^4+1/2/d*b^2*cos(d*x+c)^2+b^2*ln(sin(d*x+c))/d","A"
1220,1,255,116,0.503000," ","int(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 a^{2} \sin \left(d x +c \right)}{3 d}+\frac{a^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{4 a^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}-\frac{a b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{4 a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{8 b^{2} \sin \left(d x +c \right)}{3 d}-\frac{\sin \left(d x +c \right) b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{d}-\frac{4 \sin \left(d x +c \right) b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6+1/d*a^2/sin(d*x+c)*cos(d*x+c)^6+8/3*a^2*sin(d*x+c)/d+1/d*a^2*sin(d*x+c)*cos(d*x+c)^4+4/3/d*a^2*sin(d*x+c)*cos(d*x+c)^2-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^6-1/d*a*b*cos(d*x+c)^4-2/d*a*b*cos(d*x+c)^2-4*a*b*ln(sin(d*x+c))/d-1/d*b^2/sin(d*x+c)*cos(d*x+c)^6-8/3*b^2*sin(d*x+c)/d-1/d*sin(d*x+c)*b^2*cos(d*x+c)^4-4/3/d*sin(d*x+c)*b^2*cos(d*x+c)^2","B"
1221,1,220,118,0.534000," ","int(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{a^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{a^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{16 a b \sin \left(d x +c \right)}{3 d}+\frac{2 a b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{8 a b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{d}-\frac{2 b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/4/d*a^2*cot(d*x+c)^4+1/2/d*a^2*cot(d*x+c)^2+a^2*ln(sin(d*x+c))/d-2/3/d*a*b/sin(d*x+c)^3*cos(d*x+c)^6+2/d*a*b/sin(d*x+c)*cos(d*x+c)^6+16/3*a*b*sin(d*x+c)/d+2/d*a*b*sin(d*x+c)*cos(d*x+c)^4+8/3/d*a*b*sin(d*x+c)*cos(d*x+c)^2-1/2/d*b^2/sin(d*x+c)^2*cos(d*x+c)^6-1/2/d*b^2*cos(d*x+c)^4-1/d*b^2*cos(d*x+c)^2-2*b^2*ln(sin(d*x+c))/d","A"
1222,1,279,118,0.541000," ","int(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}-\frac{8 a^{2} \sin \left(d x +c \right)}{15 d}-\frac{a^{2} \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{4 a^{2} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{a b \left(\cot^{4}\left(d x +c \right)\right)}{2 d}+\frac{a b \left(\cot^{2}\left(d x +c \right)\right)}{d}+\frac{2 a b \ln \left(\sin \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}+\frac{8 b^{2} \sin \left(d x +c \right)}{3 d}+\frac{\sin \left(d x +c \right) b^{2} \left(\cos^{4}\left(d x +c \right)\right)}{d}+\frac{4 \sin \left(d x +c \right) b^{2} \left(\cos^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"-1/5/d*a^2/sin(d*x+c)^5*cos(d*x+c)^6+1/15/d*a^2/sin(d*x+c)^3*cos(d*x+c)^6-1/5/d*a^2/sin(d*x+c)*cos(d*x+c)^6-8/15*a^2*sin(d*x+c)/d-1/5/d*a^2*sin(d*x+c)*cos(d*x+c)^4-4/15/d*a^2*sin(d*x+c)*cos(d*x+c)^2-1/2/d*a*b*cot(d*x+c)^4+1/d*a*b*cot(d*x+c)^2+2*a*b*ln(sin(d*x+c))/d-1/3/d*b^2/sin(d*x+c)^3*cos(d*x+c)^6+1/d*b^2/sin(d*x+c)*cos(d*x+c)^6+8/3*b^2*sin(d*x+c)/d+1/d*sin(d*x+c)*b^2*cos(d*x+c)^4+4/3/d*sin(d*x+c)*b^2*cos(d*x+c)^2","B"
1223,1,196,120,0.565000," ","int(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}-\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{5}}+\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)^{3}}-\frac{2 a b \left(\cos^{6}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)}-\frac{16 a b \sin \left(d x +c \right)}{15 d}-\frac{2 a b \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5 d}-\frac{8 a b \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)}{15 d}-\frac{b^{2} \left(\cot^{4}\left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\cot^{2}\left(d x +c \right)\right)}{2 d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{d}"," ",0,"-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^6-2/5/d*a*b/sin(d*x+c)^5*cos(d*x+c)^6+2/15/d*a*b/sin(d*x+c)^3*cos(d*x+c)^6-2/5/d*a*b/sin(d*x+c)*cos(d*x+c)^6-16/15*a*b*sin(d*x+c)/d-2/5/d*a*b*sin(d*x+c)*cos(d*x+c)^4-8/15/d*a*b*sin(d*x+c)*cos(d*x+c)^2-1/4/d*b^2*cot(d*x+c)^4+1/2/d*b^2*cot(d*x+c)^2+b^2*ln(sin(d*x+c))/d","A"
1224,1,218,121,0.557000," ","int(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{a b \left(\cos^{6}\left(d x +c \right)\right)}{3 \sin \left(d x +c \right)^{6}}+b^{2} \left(-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{15 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{5 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}\right)}{d}"," ",0,"1/d*(a^2*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/3*a*b/sin(d*x+c)^6*cos(d*x+c)^6+b^2*(-1/5/sin(d*x+c)^5*cos(d*x+c)^6+1/15/sin(d*x+c)^3*cos(d*x+c)^6-1/5/sin(d*x+c)*cos(d*x+c)^6-1/5*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)))","A"
1225,1,173,124,0.562000," ","int(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\cos^{6}\left(d x +c \right)}{8 \sin \left(d x +c \right)^{8}}-\frac{\cos^{6}\left(d x +c \right)}{24 \sin \left(d x +c \right)^{6}}\right)+2 a b \left(-\frac{\cos^{6}\left(d x +c \right)}{7 \sin \left(d x +c \right)^{7}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)^{5}}+\frac{\cos^{6}\left(d x +c \right)}{105 \sin \left(d x +c \right)^{3}}-\frac{\cos^{6}\left(d x +c \right)}{35 \sin \left(d x +c \right)}-\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{b^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6 \sin \left(d x +c \right)^{6}}}{d}"," ",0,"1/d*(a^2*(-1/8/sin(d*x+c)^8*cos(d*x+c)^6-1/24/sin(d*x+c)^6*cos(d*x+c)^6)+2*a*b*(-1/7/sin(d*x+c)^7*cos(d*x+c)^6-1/35/sin(d*x+c)^5*cos(d*x+c)^6+1/105/sin(d*x+c)^3*cos(d*x+c)^6-1/35/sin(d*x+c)*cos(d*x+c)^6-1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*b^2/sin(d*x+c)^6*cos(d*x+c)^6)","A"
1226,1,342,225,0.546000," ","int(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{\sin^{6}\left(d x +c \right)}{6 b^{2} d}-\frac{2 a \left(\sin^{5}\left(d x +c \right)\right)}{5 b^{3} d}+\frac{3 \left(\sin^{4}\left(d x +c \right)\right) a^{2}}{4 d \,b^{4}}-\frac{\sin^{4}\left(d x +c \right)}{2 b^{2} d}-\frac{4 \left(\sin^{3}\left(d x +c \right)\right) a^{3}}{3 d \,b^{5}}+\frac{4 a \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{3} d}+\frac{5 \left(\sin^{2}\left(d x +c \right)\right) a^{4}}{2 d \,b^{6}}-\frac{3 \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{d \,b^{4}}+\frac{\sin^{2}\left(d x +c \right)}{2 b^{2} d}-\frac{6 a^{5} \sin \left(d x +c \right)}{d \,b^{7}}+\frac{8 a^{3} \sin \left(d x +c \right)}{d \,b^{5}}-\frac{2 a \sin \left(d x +c \right)}{b^{3} d}+\frac{7 a^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{8}}-\frac{10 a^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{6}}+\frac{3 a^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{4}}+\frac{a^{7}}{d \,b^{8} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 a^{5}}{d \,b^{6} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"1/6*sin(d*x+c)^6/b^2/d-2/5*a*sin(d*x+c)^5/b^3/d+3/4/d/b^4*sin(d*x+c)^4*a^2-1/2*sin(d*x+c)^4/b^2/d-4/3/d/b^5*sin(d*x+c)^3*a^3+4/3*a*sin(d*x+c)^3/b^3/d+5/2/d/b^6*sin(d*x+c)^2*a^4-3/d/b^4*sin(d*x+c)^2*a^2+1/2*sin(d*x+c)^2/b^2/d-6/d/b^7*a^5*sin(d*x+c)+8/d/b^5*a^3*sin(d*x+c)-2*a*sin(d*x+c)/b^3/d+7/d*a^6/b^8*ln(a+b*sin(d*x+c))-10/d*a^4/b^6*ln(a+b*sin(d*x+c))+3/d*a^2/b^4*ln(a+b*sin(d*x+c))+1/d*a^7/b^8/(a+b*sin(d*x+c))-2/d*a^5/b^6/(a+b*sin(d*x+c))+1/d*a^3/b^4/(a+b*sin(d*x+c))","A"
1227,1,285,187,0.522000," ","int(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\sin^{5}\left(d x +c \right)}{5 b^{2} d}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{2 b^{3} d}+\frac{\left(\sin^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{4}}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{2} d}-\frac{2 \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{d \,b^{5}}+\frac{2 a \left(\sin^{2}\left(d x +c \right)\right)}{b^{3} d}+\frac{5 a^{4} \sin \left(d x +c \right)}{d \,b^{6}}-\frac{6 \sin \left(d x +c \right) a^{2}}{d \,b^{4}}+\frac{\sin \left(d x +c \right)}{b^{2} d}-\frac{6 a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{7}}+\frac{8 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{5}}-\frac{2 a \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}-\frac{a^{6}}{d \,b^{7} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 a^{4}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"1/5*sin(d*x+c)^5/b^2/d-1/2*a*sin(d*x+c)^4/b^3/d+1/d/b^4*sin(d*x+c)^3*a^2-2/3*sin(d*x+c)^3/b^2/d-2/d/b^5*sin(d*x+c)^2*a^3+2*a*sin(d*x+c)^2/b^3/d+5/d/b^6*a^4*sin(d*x+c)-6/d/b^4*sin(d*x+c)*a^2+sin(d*x+c)/b^2/d-6/d*a^5/b^7*ln(a+b*sin(d*x+c))+8/d*a^3/b^5*ln(a+b*sin(d*x+c))-2*a*ln(a+b*sin(d*x+c))/b^3/d-1/d*a^6/b^7/(a+b*sin(d*x+c))+2/d*a^4/b^5/(a+b*sin(d*x+c))-1/d*a^2/b^3/(a+b*sin(d*x+c))","A"
1228,1,229,151,0.550000," ","int(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{\sin^{4}\left(d x +c \right)}{4 b^{2} d}-\frac{2 a \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{3} d}+\frac{3 \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{4}}-\frac{\sin^{2}\left(d x +c \right)}{b^{2} d}-\frac{4 a^{3} \sin \left(d x +c \right)}{d \,b^{5}}+\frac{4 a \sin \left(d x +c \right)}{b^{3} d}+\frac{5 a^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{6}}-\frac{6 a^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{4}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}+\frac{a^{5}}{d \,b^{6} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"1/4*sin(d*x+c)^4/b^2/d-2/3*a*sin(d*x+c)^3/b^3/d+3/2/d/b^4*sin(d*x+c)^2*a^2-sin(d*x+c)^2/b^2/d-4/d/b^5*a^3*sin(d*x+c)+4*a*sin(d*x+c)/b^3/d+5/d*a^4/b^6*ln(a+b*sin(d*x+c))-6/d*a^2/b^4*ln(a+b*sin(d*x+c))+1/d/b^2*ln(a+b*sin(d*x+c))+1/d*a^5/b^6/(a+b*sin(d*x+c))-2/d*a^3/b^4/(a+b*sin(d*x+c))+1/d*a/b^2/(a+b*sin(d*x+c))","A"
1229,1,169,118,0.757000," ","int(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{\sin^{2}\left(d x +c \right)}{2 b^{2} d}-\frac{2 a \sin \left(d x +c \right)}{b^{3} d}+\frac{a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 a}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{1}{a d \left(a +b \sin \left(d x +c \right)\right)}+\frac{3 a^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{4}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/2*sin(d*x+c)^2/b^2/d-2*a*sin(d*x+c)/b^3/d+1/d*a^3/b^4/(a+b*sin(d*x+c))-2/d*a/b^2/(a+b*sin(d*x+c))+1/a/d/(a+b*sin(d*x+c))+3/d*a^2/b^4*ln(a+b*sin(d*x+c))-2/d/b^2*ln(a+b*sin(d*x+c))-ln(a+b*sin(d*x+c))/a^2/d+ln(sin(d*x+c))/a^2/d","A"
1230,1,151,109,0.796000," ","int(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\sin \left(d x +c \right)}{b^{2} d}-\frac{2 a \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{3} d}+\frac{2 b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3}}-\frac{a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2}{b d \left(a +b \sin \left(d x +c \right)\right)}-\frac{b}{d \,a^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{d \,a^{2} \sin \left(d x +c \right)}-\frac{2 b \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}"," ",0,"sin(d*x+c)/b^2/d-2*a*ln(a+b*sin(d*x+c))/b^3/d+2/d/a^3*b*ln(a+b*sin(d*x+c))-1/d*a^2/b^3/(a+b*sin(d*x+c))+2/b/d/(a+b*sin(d*x+c))-1/d*b/a^2/(a+b*sin(d*x+c))-1/d/a^2/sin(d*x+c)-2*b*ln(sin(d*x+c))/a^3/d","A"
1231,1,189,129,0.884000," ","int(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{a}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2}{a d \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{2}}{d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}-\frac{3 b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{4}}-\frac{1}{2 d \,a^{2} \sin \left(d x +c \right)^{2}}-\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{3 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{2 b}{d \,a^{3} \sin \left(d x +c \right)}"," ",0,"1/d*a/b^2/(a+b*sin(d*x+c))-2/a/d/(a+b*sin(d*x+c))+1/d/a^3*b^2/(a+b*sin(d*x+c))+1/d/b^2*ln(a+b*sin(d*x+c))+2*ln(a+b*sin(d*x+c))/a^2/d-3/d/a^4*b^2*ln(a+b*sin(d*x+c))-1/2/d/a^2/sin(d*x+c)^2-2*ln(sin(d*x+c))/a^2/d+3/d/a^4*ln(sin(d*x+c))*b^2+2/d/a^3*b/sin(d*x+c)","A"
1232,1,209,145,0.839000," ","int(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","-\frac{1}{b d \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 b}{d \,a^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{b^{3}}{d \,a^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{4 b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3}}+\frac{4 b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{5}}-\frac{1}{3 d \,a^{2} \sin \left(d x +c \right)^{3}}+\frac{2}{d \,a^{2} \sin \left(d x +c \right)}-\frac{3 b^{2}}{d \,a^{4} \sin \left(d x +c \right)}+\frac{b}{d \,a^{3} \sin \left(d x +c \right)^{2}}+\frac{4 b \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{4 b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{5}}"," ",0,"-1/b/d/(a+b*sin(d*x+c))+2/d*b/a^2/(a+b*sin(d*x+c))-1/d/a^4*b^3/(a+b*sin(d*x+c))-4/d/a^3*b*ln(a+b*sin(d*x+c))+4/d*b^3/a^5*ln(a+b*sin(d*x+c))-1/3/d/a^2/sin(d*x+c)^3+2/d/a^2/sin(d*x+c)-3/d/a^4/sin(d*x+c)*b^2+1/d/a^3*b/sin(d*x+c)^2+4*b*ln(sin(d*x+c))/a^3/d-4/d*b^3/a^5*ln(sin(d*x+c))","A"
1233,1,282,182,0.882000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}+\frac{6 b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{4}}-\frac{5 \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{6}}+\frac{1}{a d \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 b^{2}}{d \,a^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{4}}{d \,a^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{1}{4 d \,a^{2} \sin \left(d x +c \right)^{4}}+\frac{1}{d \,a^{2} \sin \left(d x +c \right)^{2}}-\frac{3 b^{2}}{2 d \,a^{4} \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{6 \ln \left(\sin \left(d x +c \right)\right) b^{2}}{d \,a^{4}}+\frac{5 \ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{6}}+\frac{2 b}{3 d \,a^{3} \sin \left(d x +c \right)^{3}}-\frac{4 b}{d \,a^{3} \sin \left(d x +c \right)}+\frac{4 b^{3}}{d \,a^{5} \sin \left(d x +c \right)}"," ",0,"-ln(a+b*sin(d*x+c))/a^2/d+6/d/a^4*b^2*ln(a+b*sin(d*x+c))-5/d/a^6*ln(a+b*sin(d*x+c))*b^4+1/a/d/(a+b*sin(d*x+c))-2/d/a^3*b^2/(a+b*sin(d*x+c))+1/d/a^5/(a+b*sin(d*x+c))*b^4-1/4/d/a^2/sin(d*x+c)^4+1/d/a^2/sin(d*x+c)^2-3/2/d/a^4/sin(d*x+c)^2*b^2+ln(sin(d*x+c))/a^2/d-6/d/a^4*ln(sin(d*x+c))*b^2+5/d/a^6*ln(sin(d*x+c))*b^4+2/3/d/a^3*b/sin(d*x+c)^3-4/d/a^3*b/sin(d*x+c)+4/d*b^3/a^5/sin(d*x+c)","A"
1234,1,343,220,0.903000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x)","-\frac{b}{d \,a^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 b^{3}}{d \,a^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{b^{5}}{d \,a^{6} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3}}-\frac{8 b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{5}}+\frac{6 b^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{7}}-\frac{1}{5 d \,a^{2} \sin \left(d x +c \right)^{5}}+\frac{2}{3 d \,a^{2} \sin \left(d x +c \right)^{3}}-\frac{b^{2}}{d \,a^{4} \sin \left(d x +c \right)^{3}}-\frac{1}{d \,a^{2} \sin \left(d x +c \right)}+\frac{6 b^{2}}{d \,a^{4} \sin \left(d x +c \right)}-\frac{5 b^{4}}{d \,a^{6} \sin \left(d x +c \right)}+\frac{b}{2 d \,a^{3} \sin \left(d x +c \right)^{4}}-\frac{2 b}{d \,a^{3} \sin \left(d x +c \right)^{2}}+\frac{2 b^{3}}{d \,a^{5} \sin \left(d x +c \right)^{2}}-\frac{2 b \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{8 b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{5}}-\frac{6 b^{5} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{7}}"," ",0,"-1/d*b/a^2/(a+b*sin(d*x+c))+2/d/a^4*b^3/(a+b*sin(d*x+c))-1/d*b^5/a^6/(a+b*sin(d*x+c))+2/d/a^3*b*ln(a+b*sin(d*x+c))-8/d*b^3/a^5*ln(a+b*sin(d*x+c))+6/d*b^5/a^7*ln(a+b*sin(d*x+c))-1/5/d/a^2/sin(d*x+c)^5+2/3/d/a^2/sin(d*x+c)^3-1/d/a^4/sin(d*x+c)^3*b^2-1/d/a^2/sin(d*x+c)+6/d/a^4/sin(d*x+c)*b^2-5/d/a^6/sin(d*x+c)*b^4+1/2/d/a^3*b/sin(d*x+c)^4-2/d/a^3*b/sin(d*x+c)^2+2/d*b^3/a^5/sin(d*x+c)^2-2*b*ln(sin(d*x+c))/a^3/d+8/d*b^3/a^5*ln(sin(d*x+c))-6/d*b^5/a^7*ln(sin(d*x+c))","A"
1235,0,0,170,26.341000," ","int(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","F"
1236,0,0,123,11.377000," ","int(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","\int \left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","F"
1237,0,0,169,3.267000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x)","F"
1238,0,0,193,8.674000," ","int(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x)","\int \frac{\left(\cos^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{\left(a +b \sin \left(d x +c \right)\right)^{2}}\, dx"," ",0,"int(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x)","F"
1239,1,225,216,0.326000," ","int(cos(d*x+c)^6*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+2 a b \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)+b^{2} \left(-\frac{\left(\sin^{6}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{13}-\frac{6 \left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{143}-\frac{8 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{429}-\frac{16 \left(\cos^{7}\left(d x +c \right)\right)}{3003}\right)}{d}"," ",0,"1/d*(a^2*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+2*a*b*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*sin(d*x+c)*cos(d*x+c)^7+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c)+b^2*(-1/13*sin(d*x+c)^6*cos(d*x+c)^7-6/143*sin(d*x+c)^4*cos(d*x+c)^7-8/429*sin(d*x+c)^2*cos(d*x+c)^7-16/3003*cos(d*x+c)^7))","A"
1240,1,237,230,0.327000," ","int(cos(d*x+c)^6*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+2 a b \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)+b^{2} \left(-\frac{\left(\sin^{5}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{12}-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{24}-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{64}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{384}+\frac{5 d x}{1024}+\frac{5 c}{1024}\right)}{d}"," ",0,"1/d*(a^2*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+2*a*b*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7)+b^2*(-1/12*sin(d*x+c)^5*cos(d*x+c)^7-1/24*sin(d*x+c)^3*cos(d*x+c)^7-1/64*sin(d*x+c)*cos(d*x+c)^7+1/384*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/1024*d*x+5/1024*c))","A"
1241,1,171,169,0.326000," ","int(cos(d*x+c)^6*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+2 a b \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)+b^{2} \left(-\frac{\left(\sin^{4}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{11}-\frac{4 \left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{99}-\frac{8 \left(\cos^{7}\left(d x +c \right)\right)}{693}\right)}{d}"," ",0,"1/d*(a^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+2*a*b*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c)+b^2*(-1/11*sin(d*x+c)^4*cos(d*x+c)^7-4/99*sin(d*x+c)^2*cos(d*x+c)^7-8/693*cos(d*x+c)^7))","A"
1242,1,183,185,0.326000," ","int(cos(d*x+c)^6*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+2 a b \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)+b^{2} \left(-\frac{\left(\sin^{3}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{10}-\frac{3 \sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{80}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{160}+\frac{3 d x}{256}+\frac{3 c}{256}\right)}{d}"," ",0,"1/d*(a^2*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+2*a*b*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7)+b^2*(-1/10*sin(d*x+c)^3*cos(d*x+c)^7-3/80*sin(d*x+c)*cos(d*x+c)^7+1/160*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+3/256*d*x+3/256*c))","A"
1243,1,115,138,0.325000," ","int(cos(d*x+c)^6*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7}+2 a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{7}\left(d x +c \right)\right)}{8}+\frac{\left(\cos^{5}\left(d x +c \right)+\frac{5 \left(\cos^{3}\left(d x +c \right)\right)}{4}+\frac{15 \cos \left(d x +c \right)}{8}\right) \sin \left(d x +c \right)}{48}+\frac{5 d x}{128}+\frac{5 c}{128}\right)+b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{7}\left(d x +c \right)\right)}{9}-\frac{2 \left(\cos^{7}\left(d x +c \right)\right)}{63}\right)}{d}"," ",0,"1/d*(-1/7*a^2*cos(d*x+c)^7+2*a*b*(-1/8*sin(d*x+c)*cos(d*x+c)^7+1/48*(cos(d*x+c)^5+5/4*cos(d*x+c)^3+15/8*cos(d*x+c))*sin(d*x+c)+5/128*d*x+5/128*c)+b^2*(-1/9*sin(d*x+c)^2*cos(d*x+c)^7-2/63*cos(d*x+c)^7))","A"
1244,1,160,143,0.549000," ","int(cos(d*x+c)^6*csc(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} \cos \left(d x +c \right)}{d}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{a b \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{12 d}+\frac{5 a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{5 a b x}{8}+\frac{5 a b c}{8 d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d}"," ",0,"1/5*a^2*cos(d*x+c)^5/d+1/3*a^2*cos(d*x+c)^3/d+a^2*cos(d*x+c)/d+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+1/3*a*b*cos(d*x+c)^5*sin(d*x+c)/d+5/12*a*b*cos(d*x+c)^3*sin(d*x+c)/d+5/8*a*b*cos(d*x+c)*sin(d*x+c)/d+5/8*a*b*x+5/8/d*a*b*c-1/7*b^2*cos(d*x+c)^7/d","A"
1245,1,250,166,0.460000," ","int(cos(d*x+c)^6*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{15 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 a^{2} x}{8}-\frac{15 a^{2} c}{8 d}+\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{2 a b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{2 a b \cos \left(d x +c \right)}{d}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{6 d}+\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{24 d}+\frac{5 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{16 d}+\frac{5 b^{2} x}{16}+\frac{5 b^{2} c}{16 d}"," ",0,"-1/d*a^2/sin(d*x+c)*cos(d*x+c)^7-a^2*cos(d*x+c)^5*sin(d*x+c)/d-5/4*a^2*cos(d*x+c)^3*sin(d*x+c)/d-15/8*a^2*cos(d*x+c)*sin(d*x+c)/d-15/8*a^2*x-15/8/d*a^2*c+2/5*a*b*cos(d*x+c)^5/d+2/3*a*b*cos(d*x+c)^3/d+2*a*b*cos(d*x+c)/d+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/6*b^2*cos(d*x+c)^5*sin(d*x+c)/d+5/24*b^2*cos(d*x+c)^3*sin(d*x+c)/d+5/16*b^2*cos(d*x+c)*sin(d*x+c)/d+5/16*b^2*x+5/16/d*b^2*c","A"
1246,1,261,164,0.548000," ","int(cos(d*x+c)^6*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{2 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{2 a b \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{2 d}-\frac{15 a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{4 d}-\frac{15 a b x}{4}-\frac{15 a b c}{4 d}+\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{5 d}+\frac{b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} \cos \left(d x +c \right)}{d}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/2*a^2*cos(d*x+c)^5/d-5/6*a^2*cos(d*x+c)^3/d-5/2*a^2*cos(d*x+c)/d-5/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/d*a*b/sin(d*x+c)*cos(d*x+c)^7-2*a*b*cos(d*x+c)^5*sin(d*x+c)/d-5/2*a*b*cos(d*x+c)^3*sin(d*x+c)/d-15/4*a*b*cos(d*x+c)*sin(d*x+c)/d-15/4*a*b*x-15/4/d*a*b*c+1/5*b^2*cos(d*x+c)^5/d+1/3*b^2*cos(d*x+c)^3/d+b^2*cos(d*x+c)/d+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1247,1,321,167,0.516000," ","int(cos(d*x+c)^6*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 a^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a^{2} x}{2}+\frac{5 a^{2} c}{2 d}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{d}-\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right)}{3 d}-\frac{5 a b \cos \left(d x +c \right)}{d}-\frac{5 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{d \sin \left(d x +c \right)}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{d}-\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{4 d}-\frac{15 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}-\frac{15 b^{2} x}{8}-\frac{15 b^{2} c}{8 d}"," ",0,"-1/3/d*a^2/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*a^2/sin(d*x+c)*cos(d*x+c)^7+4/3*a^2*cos(d*x+c)^5*sin(d*x+c)/d+5/3*a^2*cos(d*x+c)^3*sin(d*x+c)/d+5/2*a^2*cos(d*x+c)*sin(d*x+c)/d+5/2*a^2*x+5/2/d*a^2*c-1/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7-a*b*cos(d*x+c)^5/d-5/3*a*b*cos(d*x+c)^3/d-5*a*b*cos(d*x+c)/d-5/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/d*b^2/sin(d*x+c)*cos(d*x+c)^7-b^2*cos(d*x+c)^5*sin(d*x+c)/d-5/4*b^2*cos(d*x+c)^3*sin(d*x+c)/d-15/8*b^2*cos(d*x+c)*sin(d*x+c)/d-15/8*b^2*x-15/8/d*b^2*c","A"
1248,1,334,164,0.540000," ","int(cos(d*x+c)^6*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 a^{2} \cos \left(d x +c \right)}{8 d}+\frac{15 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{8 a b \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{8 a b \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{10 a b \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 a b \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+5 a b x +\frac{5 a b c}{d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{2 d}-\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{6 d}-\frac{5 b^{2} \cos \left(d x +c \right)}{2 d}-\frac{5 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}"," ",0,"-1/4/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7+3/8*a^2*cos(d*x+c)^5/d+5/8*a^2*cos(d*x+c)^3/d+15/8*a^2*cos(d*x+c)/d+15/8/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/3/d*a*b/sin(d*x+c)^3*cos(d*x+c)^7+8/3/d*a*b/sin(d*x+c)*cos(d*x+c)^7+8/3*a*b*cos(d*x+c)^5*sin(d*x+c)/d+10/3*a*b*cos(d*x+c)^3*sin(d*x+c)/d+5*a*b*cos(d*x+c)*sin(d*x+c)/d+5*a*b*x+5/d*a*b*c-1/2/d*b^2/sin(d*x+c)^2*cos(d*x+c)^7-1/2*b^2*cos(d*x+c)^5/d-5/6*b^2*cos(d*x+c)^3/d-5/2*b^2*cos(d*x+c)/d-5/2/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","B"
1249,1,302,182,0.558000," ","int(cos(d*x+c)^6*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{a^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{a^{2} \cot \left(d x +c \right)}{d}-a^{2} x -\frac{a^{2} c}{d}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{4}}+\frac{3 a b \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{2}}+\frac{3 a b \left(\cos^{5}\left(d x +c \right)\right)}{4 d}+\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{15 a b \cos \left(d x +c \right)}{4 d}+\frac{15 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{3}}+\frac{4 b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)}+\frac{4 b^{2} \left(\cos^{5}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3 d}+\frac{5 b^{2} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 b^{2} x}{2}+\frac{5 b^{2} c}{2 d}"," ",0,"-1/5*a^2*cot(d*x+c)^5/d+1/3*a^2*cot(d*x+c)^3/d-a^2*cot(d*x+c)/d-a^2*x-1/d*a^2*c-1/2/d*a*b/sin(d*x+c)^4*cos(d*x+c)^7+3/4/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7+3/4*a*b*cos(d*x+c)^5/d+5/4*a*b*cos(d*x+c)^3/d+15/4*a*b*cos(d*x+c)/d+15/4/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/3/d*b^2/sin(d*x+c)^3*cos(d*x+c)^7+4/3/d*b^2/sin(d*x+c)*cos(d*x+c)^7+4/3*b^2*cos(d*x+c)^5*sin(d*x+c)/d+5/3*b^2*cos(d*x+c)^3*sin(d*x+c)/d+5/2*b^2*cos(d*x+c)*sin(d*x+c)/d+5/2*b^2*x+5/2/d*b^2*c","A"
1250,1,318,163,0.456000," ","int(cos(d*x+c)^6*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{16 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}-\frac{2 a b \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{2 a b \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{2 a b \cot \left(d x +c \right)}{d}-2 a b x -\frac{2 a b c}{d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{4}}+\frac{3 b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}+\frac{3 b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{8 d}+\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{8 d}+\frac{15 b^{2} \cos \left(d x +c \right)}{8 d}+\frac{15 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}"," ",0,"-1/6/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/24/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-1/16/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/16*a^2*cos(d*x+c)^5/d-5/48*a^2*cos(d*x+c)^3/d-5/16*a^2*cos(d*x+c)/d-5/16/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/5*a*b*cot(d*x+c)^5/d+2/3*a*b*cot(d*x+c)^3/d-2*a*b*cot(d*x+c)/d-2*a*b*x-2/d*a*b*c-1/4/d*b^2/sin(d*x+c)^4*cos(d*x+c)^7+3/8/d*b^2/sin(d*x+c)^2*cos(d*x+c)^7+3/8*b^2*cos(d*x+c)^5/d+5/8*b^2*cos(d*x+c)^3/d+15/8*b^2*cos(d*x+c)/d+15/8/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1251,1,222,144,0.459000," ","int(cos(d*x+c)^6*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{3 d \sin \left(d x +c \right)^{6}}+\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{12 d \sin \left(d x +c \right)^{4}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right)}{24 d}-\frac{5 a b \cos \left(d x +c \right)}{8 d}-\frac{5 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{8 d}-\frac{b^{2} \left(\cot^{5}\left(d x +c \right)\right)}{5 d}+\frac{b^{2} \left(\cot^{3}\left(d x +c \right)\right)}{3 d}-\frac{b^{2} \cot \left(d x +c \right)}{d}-b^{2} x -\frac{b^{2} c}{d}"," ",0,"-1/7/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/3/d*a*b/sin(d*x+c)^6*cos(d*x+c)^7+1/12/d*a*b/sin(d*x+c)^4*cos(d*x+c)^7-1/8/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7-1/8*a*b*cos(d*x+c)^5/d-5/24*a*b*cos(d*x+c)^3/d-5/8*a*b*cos(d*x+c)/d-5/8/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/5*b^2*cot(d*x+c)^5/d+1/3*b^2*cot(d*x+c)^3/d-b^2*cot(d*x+c)/d-b^2*x-1/d*b^2*c","A"
1252,1,333,147,0.455000," ","int(cos(d*x+c)^6*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{5 a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{5 a^{2} \cos \left(d x +c \right)}{128 d}-\frac{5 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{6 d \sin \left(d x +c \right)^{6}}+\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{4}}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{16 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{16 d}-\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{48 d}-\frac{5 b^{2} \cos \left(d x +c \right)}{16 d}-\frac{5 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{16 d}"," ",0,"-1/8/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-1/48/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/192/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-1/128/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-1/128*a^2*cos(d*x+c)^5/d-5/384*a^2*cos(d*x+c)^3/d-5/128*a^2*cos(d*x+c)/d-5/128/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/7/d*a*b/sin(d*x+c)^7*cos(d*x+c)^7-1/6/d*b^2/sin(d*x+c)^6*cos(d*x+c)^7+1/24/d*b^2/sin(d*x+c)^4*cos(d*x+c)^7-1/16/d*b^2/sin(d*x+c)^2*cos(d*x+c)^7-1/16*b^2*cos(d*x+c)^5/d-5/48*b^2*cos(d*x+c)^3/d-5/16*b^2*cos(d*x+c)/d-5/16/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","B"
1253,1,232,137,0.465000," ","int(cos(d*x+c)^6*csc(d*x+c)^10*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{2 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{4 d \sin \left(d x +c \right)^{8}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{24 d \sin \left(d x +c \right)^{6}}+\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{96 d \sin \left(d x +c \right)^{4}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{64 d \sin \left(d x +c \right)^{2}}-\frac{a b \left(\cos^{5}\left(d x +c \right)\right)}{64 d}-\frac{5 a b \left(\cos^{3}\left(d x +c \right)\right)}{192 d}-\frac{5 a b \cos \left(d x +c \right)}{64 d}-\frac{5 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{64 d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{7 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/9/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7-2/63/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/4/d*a*b/sin(d*x+c)^8*cos(d*x+c)^7-1/24/d*a*b/sin(d*x+c)^6*cos(d*x+c)^7+1/96/d*a*b/sin(d*x+c)^4*cos(d*x+c)^7-1/64/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7-1/64*a*b*cos(d*x+c)^5/d-5/192*a*b*cos(d*x+c)^3/d-5/64*a*b*cos(d*x+c)/d-5/64/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/7/d*b^2/sin(d*x+c)^7*cos(d*x+c)^7","A"
1254,1,404,194,0.462000," ","int(cos(d*x+c)^6*csc(d*x+c)^11*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{10 d \sin \left(d x +c \right)^{10}}-\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{8}}-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{160 d \sin \left(d x +c \right)^{6}}+\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{1280 d \sin \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\cos^{5}\left(d x +c \right)\right)}{1280 d}-\frac{a^{2} \left(\cos^{3}\left(d x +c \right)\right)}{256 d}-\frac{3 a^{2} \cos \left(d x +c \right)}{256 d}-\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{256 d}-\frac{2 a b \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{4 a b \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{8}}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{48 d \sin \left(d x +c \right)^{6}}+\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{192 d \sin \left(d x +c \right)^{4}}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{128 d \sin \left(d x +c \right)^{2}}-\frac{b^{2} \left(\cos^{5}\left(d x +c \right)\right)}{128 d}-\frac{5 b^{2} \left(\cos^{3}\left(d x +c \right)\right)}{384 d}-\frac{5 b^{2} \cos \left(d x +c \right)}{128 d}-\frac{5 b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}"," ",0,"-1/10/d*a^2/sin(d*x+c)^10*cos(d*x+c)^7-3/80/d*a^2/sin(d*x+c)^8*cos(d*x+c)^7-1/160/d*a^2/sin(d*x+c)^6*cos(d*x+c)^7+1/640/d*a^2/sin(d*x+c)^4*cos(d*x+c)^7-3/1280/d*a^2/sin(d*x+c)^2*cos(d*x+c)^7-3/1280*a^2*cos(d*x+c)^5/d-1/256*a^2*cos(d*x+c)^3/d-3/256*a^2*cos(d*x+c)/d-3/256/d*a^2*ln(csc(d*x+c)-cot(d*x+c))-2/9/d*a*b/sin(d*x+c)^9*cos(d*x+c)^7-4/63/d*a*b/sin(d*x+c)^7*cos(d*x+c)^7-1/8/d*b^2/sin(d*x+c)^8*cos(d*x+c)^7-1/48/d*b^2/sin(d*x+c)^6*cos(d*x+c)^7+1/192/d*b^2/sin(d*x+c)^4*cos(d*x+c)^7-1/128/d*b^2/sin(d*x+c)^2*cos(d*x+c)^7-1/128*b^2*cos(d*x+c)^5/d-5/384*b^2*cos(d*x+c)^3/d-5/128*b^2*cos(d*x+c)/d-5/128/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","B"
1255,1,303,180,0.456000," ","int(cos(d*x+c)^6*csc(d*x+c)^12*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{11 d \sin \left(d x +c \right)^{11}}-\frac{4 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{99 d \sin \left(d x +c \right)^{9}}-\frac{8 a^{2} \left(\cos^{7}\left(d x +c \right)\right)}{693 d \sin \left(d x +c \right)^{7}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{5 d \sin \left(d x +c \right)^{10}}-\frac{3 a b \left(\cos^{7}\left(d x +c \right)\right)}{40 d \sin \left(d x +c \right)^{8}}-\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{80 d \sin \left(d x +c \right)^{6}}+\frac{a b \left(\cos^{7}\left(d x +c \right)\right)}{320 d \sin \left(d x +c \right)^{4}}-\frac{3 a b \left(\cos^{7}\left(d x +c \right)\right)}{640 d \sin \left(d x +c \right)^{2}}-\frac{3 a b \left(\cos^{5}\left(d x +c \right)\right)}{640 d}-\frac{a b \left(\cos^{3}\left(d x +c \right)\right)}{128 d}-\frac{3 a b \cos \left(d x +c \right)}{128 d}-\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{128 d}-\frac{b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{9 d \sin \left(d x +c \right)^{9}}-\frac{2 b^{2} \left(\cos^{7}\left(d x +c \right)\right)}{63 d \sin \left(d x +c \right)^{7}}"," ",0,"-1/11/d*a^2/sin(d*x+c)^11*cos(d*x+c)^7-4/99/d*a^2/sin(d*x+c)^9*cos(d*x+c)^7-8/693/d*a^2/sin(d*x+c)^7*cos(d*x+c)^7-1/5/d*a*b/sin(d*x+c)^10*cos(d*x+c)^7-3/40/d*a*b/sin(d*x+c)^8*cos(d*x+c)^7-1/80/d*a*b/sin(d*x+c)^6*cos(d*x+c)^7+1/320/d*a*b/sin(d*x+c)^4*cos(d*x+c)^7-3/640/d*a*b/sin(d*x+c)^2*cos(d*x+c)^7-3/640*a*b*cos(d*x+c)^5/d-1/128*a*b*cos(d*x+c)^3/d-3/128*a*b*cos(d*x+c)/d-3/128/d*a*b*ln(csc(d*x+c)-cot(d*x+c))-1/9/d*b^2/sin(d*x+c)^9*cos(d*x+c)^7-2/63/d*b^2/sin(d*x+c)^7*cos(d*x+c)^7","A"
1256,1,2076,498,0.568000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\text{Expression too large to display}"," ",0,"15/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3-5/4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+2/d*a^7/b^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-30/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^5+14/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*a^6-70/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*a^4+46/5/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*a^2-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12-10/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8-6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4+16/d/b^9*arctan(tan(1/2*d*x+1/2*c))*a^7-2/7/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7-28/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+28/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a^3+210/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^6-1090/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^4+146/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^2+280/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^6-1360/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^4+84/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^6-29/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a^3-30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a^5+29/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a^3-85/12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a+210/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^6+2/d*a^6/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-4/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+176/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^2-7/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a+84/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^6-400/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^4-160/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^4-16/d*a^8/b^9/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+38/d*a^6/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a^5-9/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a^3+11/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a+14/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^6-30/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^4+18/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^2+24/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a^5-28/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a^3+232/5/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^2-11/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a+7/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a^5-330/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^4-6/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a^5+9/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a^3+606/5/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^2-24/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a^5+85/12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a+72/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^2","B"
1257,1,1817,446,0.542000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{560 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{184 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{57 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{60 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{88 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{124 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{5 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{27 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{12 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{56 a^{3}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{92 a}{15 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{6}}{d \,b^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{14 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{8}}-\frac{12 a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{25 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6}}-\frac{45 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{4}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,b^{2}}-\frac{120 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{176 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{56 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{27 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{57 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{10 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{24 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{12 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{104 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{36 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{120 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{60 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{32 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}-b^{2}}}+\frac{22 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{14 a^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{8} \sqrt{a^{2}-b^{2}}}"," ",0,"10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^4-12/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*a^5-11/8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+5/24/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-15/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+15/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-5/24/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+11/8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+56/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*a^3-92/15/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*a-14/d/b^8*arctan(tan(1/2*d*x+1/2*c))*a^6+25/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^4-45/4/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2+4/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^4-2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2-2/d*a^6/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+5/8/d/b^2*arctan(tan(1/2*d*x+1/2*c))-60/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^5+104/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^3-36/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a-5/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^4-120/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^5+176/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^3-56/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a-32/d/b^6*a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+22/d/b^4*a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^3*tan(1/2*d*x+1/2*c)+14/d*a^7/b^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+27/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^2-15/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^4+57/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^2-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^4+15/2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^2-120/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^5+560/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^3-184/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a-15/2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^2+15/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^4-57/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^2-60/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^5+88/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^3-124/5/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a+5/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^4-27/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^2-12/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^5+24/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^3-12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a-2/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)","B"
1258,1,1321,214,0.466000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{60 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{60 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{80 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{18 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{20 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{3}}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{7}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}+\frac{2 a^{5}}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{56 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{10 a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{14 a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{46}{15 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{9 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{40 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{52 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{26 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{16 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{40 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{12 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}"," ",0,"-4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3+9/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a+4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3-20/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3+15/2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+2/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+12/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^5+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a+2/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8+12/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+56/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+28/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4-14/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2+2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+46/15/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5-9/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a+10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4-18/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3-5/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a+40/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4-60/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2+60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4-80/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3+5/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a+40/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4-52/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2+26/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-16/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-4/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-12/d*a^6/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1259,1,778,254,0.698000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^2,x)","\frac{2 a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 a^{2}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{5}}-\frac{10 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{8 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{14 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2-6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2*a^2-8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2-14/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3+8/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^3-10/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a+1/d/a^2*ln(tan(1/2*d*x+1/2*c))+2/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-4/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a+2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-8/d*a^4/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+14/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1260,1,680,240,0.770000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 a}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{4}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{6 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}-\frac{8 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{4 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*a-6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^2+5/d/b^2*arctan(tan(1/2*d*x+1/2*c))-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a*tan(1/2*d*x+1/2*c)+4/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)-2/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a^2+4/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+6/d/b^4*a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-8/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3*b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1261,1,618,237,0.809000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}+\frac{2}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{3}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{b}{d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}+\frac{8 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3*tan(1/2*d*x+1/2*c)*b+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)+4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2-5/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+3/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+1/d*b/a^3/tan(1/2*d*x+1/2*c)+2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-4/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a-4/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d*a^2/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+8/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^4*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1262,1,678,275,0.771000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \,a^{3}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{2}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{24 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{9}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{4 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right) a}+\frac{4 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{14 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}+\frac{8 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^2*tan(1/2*d*x+1/2*c)^3-1/4/d/a^3*tan(1/2*d*x+1/2*c)^2*b-9/8/d/a^2*tan(1/2*d*x+1/2*c)+3/2/d/a^4*b^2*tan(1/2*d*x+1/2*c)-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))-1/24/a^2/d/tan(1/2*d*x+1/2*c)^3+9/8/d/a^2/tan(1/2*d*x+1/2*c)-3/2/d/a^4/tan(1/2*d*x+1/2*c)*b^2+1/4/d/a^3*b/tan(1/2*d*x+1/2*c)^2+5/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-4/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)/a*tan(1/2*d*x+1/2*c)+4/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+4/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/b^2*a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-14/d/a^3*b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+8/d/a^5*b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1263,1,718,286,0.808000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 a^{2} d}-\frac{b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{12 d \,a^{3}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a^{2} d}+\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{4 d \,a^{3}}-\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5}}-\frac{1}{64 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{4 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{4}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{6}}+\frac{b}{12 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{9 b}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 b^{3}}{d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{10 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{20 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{10 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/64/d/a^2*tan(1/2*d*x+1/2*c)^4-1/12/d/a^3*b*tan(1/2*d*x+1/2*c)^3-1/4/d/a^2*tan(1/2*d*x+1/2*c)^2+3/8/d/a^4*b^2*tan(1/2*d*x+1/2*c)^2+9/4/d/a^3*tan(1/2*d*x+1/2*c)*b-2/d/a^5*b^3*tan(1/2*d*x+1/2*c)-1/64/a^2/d/tan(1/2*d*x+1/2*c)^4+1/4/a^2/d/tan(1/2*d*x+1/2*c)^2-3/8/d/a^4/tan(1/2*d*x+1/2*c)^2*b^2+15/8/d/a^2*ln(tan(1/2*d*x+1/2*c))-15/2/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+5/d/a^6*ln(tan(1/2*d*x+1/2*c))*b^4+1/12/d/a^3*b/tan(1/2*d*x+1/2*c)^3-9/4/d*b/a^3/tan(1/2*d*x+1/2*c)+2/d*b^3/a^5/tan(1/2*d*x+1/2*c)+2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-4/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^5+2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-4/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^4-10/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+20/d/a^4*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-10/d/a^6*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1264,1,897,401,0.823000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x)","-\frac{2 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{1}{160 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 a^{2} d}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{2}}-\frac{11}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{2}}-\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{7}{96 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{27 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{27 b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{10 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5}}-\frac{5 b^{4}}{2 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{32 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{b^{3}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{2 d \,a^{3}}+\frac{5 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{6}}+\frac{4 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{16 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{7}}+\frac{12 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{7} \sqrt{a^{2}-b^{2}}}-\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{32 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{8 d \,a^{4}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{2 d \,a^{5}}-\frac{2 b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{b^{2}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{26 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}"," ",0,"-1/160/a^2/d/tan(1/2*d*x+1/2*c)^5+11/16/d/a^2*tan(1/2*d*x+1/2*c)-11/16/d/a^2/tan(1/2*d*x+1/2*c)-15/4/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-2/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-2/d/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+7/96/a^2/d/tan(1/2*d*x+1/2*c)^3-7/96/d/a^2*tan(1/2*d*x+1/2*c)^3+1/160/d/a^2*tan(1/2*d*x+1/2*c)^5+1/2/d/a^3*tan(1/2*d*x+1/2*c)^2*b-27/8/d/a^4*b^2*tan(1/2*d*x+1/2*c)+27/8/d/a^4/tan(1/2*d*x+1/2*c)*b^2-1/2/d/a^3*b/tan(1/2*d*x+1/2*c)^2+10/d/a^5*b^3*ln(tan(1/2*d*x+1/2*c))+4/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-5/2/d/a^6/tan(1/2*d*x+1/2*c)*b^4+1/32/d/a^3*b/tan(1/2*d*x+1/2*c)^4+1/2/d/a^5*b^3/tan(1/2*d*x+1/2*c)^2-1/32/d/a^3*tan(1/2*d*x+1/2*c)^4*b+1/8/d/a^4*tan(1/2*d*x+1/2*c)^3*b^2-1/2/d/a^5*tan(1/2*d*x+1/2*c)^2*b^3+5/2/d/a^6*b^4*tan(1/2*d*x+1/2*c)-2/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^5-2/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+16/d/a^3*b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^7*b^5*ln(tan(1/2*d*x+1/2*c))+12/d/a^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6-2/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^6-1/8/d/a^4/tan(1/2*d*x+1/2*c)^3*b^2+4/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-26/d/a^5*b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1265,1,1048,455,0.816000," ","int(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c))^2,x)","\frac{2 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{6 d \,a^{5}}+\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{8 d \,a^{6}}+\frac{2 b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{4 b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{3}}+\frac{45 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{8 d \,a^{4}}+\frac{11 b}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2}}-\frac{1}{384 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{3}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{3 b^{2}}{4 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}-\frac{25 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{2 d \,a^{6}}-\frac{7 b}{48 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{9 b^{3}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{80 d \,a^{3}}+\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{64 d \,a^{4}}+\frac{32 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d \,a^{2}}-\frac{15}{128 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{b^{3}}{6 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{3 b^{5}}{d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{7}}-\frac{3 b^{2}}{64 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{5 b^{4}}{8 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{8}}+\frac{b}{80 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a^{2} d}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{4}}+\frac{7 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{48 d \,a^{3}}-\frac{22 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{14 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{8} \sqrt{a^{2}-b^{2}}}+\frac{2 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{8} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{9 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{5}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}"," ",0,"-11/8/d/a^3*tan(1/2*d*x+1/2*c)*b+45/8/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+11/8/d*b/a^3/tan(1/2*d*x+1/2*c)+2/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-5/16/d/a^2*ln(tan(1/2*d*x+1/2*c))-1/384/d/a^2/tan(1/2*d*x+1/2*c)^6+1/384/d/a^2*tan(1/2*d*x+1/2*c)^6-3/128/d/a^2*tan(1/2*d*x+1/2*c)^4+3/128/a^2/d/tan(1/2*d*x+1/2*c)^4+3/4/d/a^4/tan(1/2*d*x+1/2*c)^2*b^2-25/2/d/a^6*ln(tan(1/2*d*x+1/2*c))*b^4-7/48/d/a^3*b/tan(1/2*d*x+1/2*c)^3-9/2/d*b^3/a^5/tan(1/2*d*x+1/2*c)+15/128/d/a^2*tan(1/2*d*x+1/2*c)^2+32/d/a^6*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-15/128/a^2/d/tan(1/2*d*x+1/2*c)^2+1/6/d/a^5*b^3/tan(1/2*d*x+1/2*c)^3+3/d*b^5/a^7/tan(1/2*d*x+1/2*c)-1/80/d/a^3*b*tan(1/2*d*x+1/2*c)^5+3/64/d/a^4*tan(1/2*d*x+1/2*c)^4*b^2-1/6/d/a^5*tan(1/2*d*x+1/2*c)^3*b^3+5/8/d/a^6*tan(1/2*d*x+1/2*c)^2*b^4-3/d/a^7*b^5*tan(1/2*d*x+1/2*c)+2/d/a^7*b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-3/64/d/a^4/tan(1/2*d*x+1/2*c)^4*b^2-5/8/d/a^6/tan(1/2*d*x+1/2*c)^2*b^4+7/d/a^8*ln(tan(1/2*d*x+1/2*c))*b^6+1/80/d/a^3*b/tan(1/2*d*x+1/2*c)^5-4/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^4-4/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b^5+4/d/a^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-22/d/a^4*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-14/d/a^8*b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+7/48/d/a^3*b*tan(1/2*d*x+1/2*c)^3-3/4/d/a^4*b^2*tan(1/2*d*x+1/2*c)^2+9/2/d/a^5*b^3*tan(1/2*d*x+1/2*c)+2/d/a^8*b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)","B"
1266,1,2174,509,0.586000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-84/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a-10/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+5/8/d/b^3*arctan(tan(1/2*d*x+1/2*c))-42/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*a^5+140/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*a^3-46/5/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*a+11/8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-11/8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+5/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-15/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+15/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-5/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+75/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^4-45/2/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2-56/d/b^9*arctan(tan(1/2*d*x+1/2*c))*a^6-14/d*a^7/b^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+19/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-5/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+45/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^4-57/2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^2-210/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^5+220/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^3-186/5/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a+15/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^4-27/2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^2-42/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^5+60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^3-6/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+440/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^3-15/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^4+27/2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^2-45/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^4+57/2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^2-16/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-9/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+33/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-43/d*a^6/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+59/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^4+15/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^2-420/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^5+1400/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^3-92/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^4-15/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^2-13/d*a^6/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+17/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-4/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-14/d*a^7/b^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+56/d*a^7/b^9/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-103/d*a^5/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+53/d*a^3/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-18/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a-210/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^5+260/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^3-54/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a-420/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^5","B"
1267,1,1676,460,0.645000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{46}{15 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{15 a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{30 a^{4}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{56 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{6 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{28 a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{3 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{12 a^{6}}{d \,b^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{27 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{30 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{27 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{120 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d 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a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{15 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{20 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{36 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{42 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{6}}{d \,b^{8} \sqrt{a^{2}-b^{2}}}+\frac{71 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{4}}{d \,b^{6} \sqrt{a^{2}-b^{2}}}-\frac{31 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{45 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{4 d \,b^{4}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{50 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6}}"," ",0,"-36/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2+46/15/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5+20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3-15/2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a+120/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4-120/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2+180/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4-160/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2-20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3+15/2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a-13/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a^3+2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a+10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3-27/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a+42/d/b^8*arctan(tan(1/2*d*x+1/2*c))*a^5-15/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^4+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4+28/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+56/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4+6/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8+12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6-28/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2+3/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2-42/d/b^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^6+71/d/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^4-31/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+11/d/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a^5+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4+12/d/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^6+9/d/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^4-27/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^2+37/d/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a^5-47/d/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a^3+10/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a+120/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4-104/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3+27/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a+45/4/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a+6/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+12/d/b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^6+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-50/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^3","B"
1268,1,1325,224,0.571000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20 a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{14 a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{60 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{38 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{9 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3}}+\frac{18 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{21 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 a^{5}}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{30 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{7}}+\frac{30 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}-\frac{6 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{35 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 a^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{60 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{42 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{15 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{9 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{31 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{30 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}-\frac{45 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"-6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2-20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3+18/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a-6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2-60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3+42/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a+21/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-15/4/d/b^3*arctan(tan(1/2*d*x+1/2*c))-1/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a-2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2-4/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+9/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+1/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-1/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-9/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3+14/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*a-30/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^4+30/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2-10/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+11/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2+6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2-60/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3+38/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a+15/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+35/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-10/d*a^5/b^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-9/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-31/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-9/d*a^4/b^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+9/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+30/d*a^5/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-45/d*a^3/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1269,1,988,376,0.802000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{6 a}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{5}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{5 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{6 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{19 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 a^{3}}{d \,b^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{12 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{11 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{\arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^2*a-12/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^2+5/d/b^3*arctan(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))-5/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+4/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-6/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-9/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+9/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+6/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-19/d*a^2/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+11/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+8/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-6/d*a^3/b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+3/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a+3/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+12/d*a^3/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-11/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/d/a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1270,1,903,300,0.816000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{2}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{4}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{13 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 a^{2}}{d \,b^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{1}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{3 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{3 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/d/a^3*tan(1/2*d*x+1/2*c)+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)+6/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^4*b*ln(tan(1/2*d*x+1/2*c))+3/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a+3/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-6/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2+4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*a^2+9/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-3/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-10/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3+13/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a+1/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-14/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2+4/d/b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2+1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-5/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-6/d/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+3/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","B"
1271,1,943,372,0.870000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{3 b}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{8 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 b^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{13 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{20 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 a}{d \,b^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{\arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a b \sqrt{a^{2}-b^{2}}}+\frac{11 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{12 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^4*tan(1/2*d*x+1/2*c)*b-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2-5/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+6/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2+3/2/d*b/a^4/tan(1/2*d*x+1/2*c)-1/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-7/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+8/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-2/d*a/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-9/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2-3/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+14/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-7/d/b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-13/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+20/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-2/d/b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a-5/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+7/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+2/d*a/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/d/a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+11/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-12/d/a^5*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1272,1,873,310,0.856000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d \,a^{3}}-\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{4}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{3 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{5}}-\frac{1}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{9}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b^{2}}{d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{10 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{18 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{25 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{26 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{25 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}+\frac{20 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a^3*tan(1/2*d*x+1/2*c)^3-3/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b-9/8/d/a^3*tan(1/2*d*x+1/2*c)+3/d/a^5*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3+9/8/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^5/tan(1/2*d*x+1/2*c)*b^2+3/8/d/a^4*b/tan(1/2*d*x+1/2*c)^2+15/2/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-10/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))-1/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+11/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-10/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+9/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b+9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-18/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5+1/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+25/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-26/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4+9/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3+5/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-25/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+20/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1273,1,1070,334,0.906000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x)","-\frac{5 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{6}}-\frac{3 b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{7}}+\frac{b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{13 b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{1}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{2}{d a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d \,a^{3}}+\frac{3 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{9 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{27 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{4}}-\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}-\frac{27 b}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{15 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{15 b^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{1}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{15 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{11 b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{5}}+\frac{5 b^{3}}{d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}-\frac{37 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{30 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{7} \sqrt{a^{2}-b^{2}}}+\frac{32 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{22 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{12 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{45 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"-5/d/a^6*b^3*tan(1/2*d*x+1/2*c)-3/4/d/a^5/tan(1/2*d*x+1/2*c)^2*b^2+15/d/a^7*ln(tan(1/2*d*x+1/2*c))*b^4+1/8/d/a^4*b/tan(1/2*d*x+1/2*c)^3+1/64/d/a^3*tan(1/2*d*x+1/2*c)^4-1/64/d/a^3/tan(1/2*d*x+1/2*c)^4+2/d/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+2/d/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+27/8/d/a^4*tan(1/2*d*x+1/2*c)*b-15/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2-27/8/d*b/a^4/tan(1/2*d*x+1/2*c)-13/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-1/4/d/a^3*tan(1/2*d*x+1/2*c)^2+1/4/d/a^3/tan(1/2*d*x+1/2*c)^2-15/d/a^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+5/d*b^3/a^6/tan(1/2*d*x+1/2*c)-1/8/d/a^4*b*tan(1/2*d*x+1/2*c)^3+11/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^4+15/8/d/a^3*ln(tan(1/2*d*x+1/2*c))-9/d/a^3*b^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+5/d/a^2*b/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+3/4/d/a^5*b^2*tan(1/2*d*x+1/2*c)^2-15/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-15/d/a^5*b^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-37/d/a^4*b^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+32/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^5+22/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^6-30/d/a^7*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+12/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^5+45/d/a^5*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1274,1,1252,467,0.902000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^3,x)","\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}-\frac{27 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{5}}-\frac{4 b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{7}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{11}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{45 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{5 b^{3}}{4 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{21 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{8}}-\frac{15 b^{4}}{2 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{3 b}{64 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{15 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{7}}+\frac{19 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{21 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{4 d \,a^{6}}-\frac{13 b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{64 d \,a^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{4 d \,a^{5}}+\frac{25 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d \,a^{3}}+\frac{3 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \,a^{4}}+\frac{17 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{3}}-\frac{3 b}{4 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{71 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}+\frac{31 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}+\frac{27 b^{2}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{49 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{26 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{7}}{d \,a^{8} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{38 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \,a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{42 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{8} \sqrt{a^{2}-b^{2}}}"," ",0,"11/16/d/a^3*tan(1/2*d*x+1/2*c)-27/4/d/a^5*b^2*tan(1/2*d*x+1/2*c)-7/96/d/a^3*tan(1/2*d*x+1/2*c)^3+7/96/d/a^3/tan(1/2*d*x+1/2*c)^3+1/160/d/a^3*tan(1/2*d*x+1/2*c)^5-1/160/d/a^3/tan(1/2*d*x+1/2*c)^5+17/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3-11/16/d/a^3/tan(1/2*d*x+1/2*c)-45/8/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-2/d/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+5/4/d/a^6*b^3/tan(1/2*d*x+1/2*c)^2-21/d/a^8*b^5*ln(tan(1/2*d*x+1/2*c))-15/2/d/a^7/tan(1/2*d*x+1/2*c)*b^4+3/64/d/a^4*b/tan(1/2*d*x+1/2*c)^4-1/4/d/a^5/tan(1/2*d*x+1/2*c)^3*b^2-5/4/d/a^6*tan(1/2*d*x+1/2*c)^2*b^3+15/2/d/a^7*b^4*tan(1/2*d*x+1/2*c)-13/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^5-3/64/d/a^4*tan(1/2*d*x+1/2*c)^4*b+1/4/d/a^5*tan(1/2*d*x+1/2*c)^3*b^2+25/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))-3/4/d/a^4*b/tan(1/2*d*x+1/2*c)^2+19/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+21/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5+49/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4-71/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4-5/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-4/d/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b+9/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-11/d/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2+31/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2+27/4/d/a^5/tan(1/2*d*x+1/2*c)*b^2+3/4/d/a^4*tan(1/2*d*x+1/2*c)^2*b-14/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^6-26/d/a^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^7-38/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^6+42/d/a^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6","B"
1275,1,1576,571,0.923000," ","int(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c))^3,x)","-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}+\frac{33 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{5}}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 d \,a^{3}}-\frac{1}{896 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}-\frac{3}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{5}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{4}}-\frac{5 b^{3}}{2 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{105 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{8}}+\frac{135 b^{4}}{8 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{9 b}{128 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{7 b^{2}}{16 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{135 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{7}}-\frac{9 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{2 d \,a^{6}}+\frac{25 b^{5}}{d \,a^{6} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{128 d \,a^{4}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{16 d \,a^{5}}-\frac{75 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{6}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d \,a^{3}}-\frac{45 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{128 d \,a^{4}}-\frac{8 b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}-\frac{17 b^{7}}{d \,a^{8} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{b \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{80 d \,a^{5}}-\frac{5 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{32 d \,a^{6}}+\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{8 d \,a^{7}}-\frac{21 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{8 d \,a^{8}}+\frac{14 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{9}}-\frac{3 b^{2}}{80 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{5 b^{4}}{8 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{14 b^{6}}{d \,a^{9} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{128 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{5 b^{3}}{32 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{21 b^{5}}{8 d \,a^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{36 b^{7} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{10}}+\frac{45 b}{128 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{81 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{6} \sqrt{a^{2}-b^{2}}}-\frac{12 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{33 b^{2}}{8 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \,a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{23 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{4}}{d \,a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{72 b^{8} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{10} \sqrt{a^{2}-b^{2}}}+\frac{27 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{33 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{7}}{d \,a^{8} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{73 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{6}}{d \,a^{7} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{18 b^{8} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{9} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{34 b^{9} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{10} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{50 b^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{9} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{141 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{6}}{d \,a^{8} \sqrt{a^{2}-b^{2}}}"," ",0,"-5/128/d/a^3*tan(1/2*d*x+1/2*c)+33/8/d/a^5*b^2*tan(1/2*d*x+1/2*c)+1/896/d/a^3*tan(1/2*d*x+1/2*c)^7-1/896/d/a^3/tan(1/2*d*x+1/2*c)^7+3/128/d/a^3*tan(1/2*d*x+1/2*c)^3-3/128/d/a^3/tan(1/2*d*x+1/2*c)^3-1/128/d/a^3*tan(1/2*d*x+1/2*c)^5+1/128/d/a^3/tan(1/2*d*x+1/2*c)^5-8/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^3+5/128/d/a^3/tan(1/2*d*x+1/2*c)+15/16/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-5/2/d/a^6*b^3/tan(1/2*d*x+1/2*c)^2+105/2/d/a^8*b^5*ln(tan(1/2*d*x+1/2*c))+135/8/d/a^7/tan(1/2*d*x+1/2*c)*b^4-9/128/d/a^4*b/tan(1/2*d*x+1/2*c)^4+7/16/d/a^5/tan(1/2*d*x+1/2*c)^3*b^2+5/2/d/a^6*tan(1/2*d*x+1/2*c)^2*b^3-135/8/d/a^7*b^4*tan(1/2*d*x+1/2*c)+25/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^5+9/128/d/a^4*tan(1/2*d*x+1/2*c)^4*b-7/16/d/a^5*tan(1/2*d*x+1/2*c)^3*b^2-75/4/d/a^6*b^3*ln(tan(1/2*d*x+1/2*c))-17/d/a^8*b^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-1/128/d/a^4*b*tan(1/2*d*x+1/2*c)^6+3/80/d/a^5*tan(1/2*d*x+1/2*c)^5*b^2-5/32/d/a^6*tan(1/2*d*x+1/2*c)^4*b^3+5/8/d/a^7*tan(1/2*d*x+1/2*c)^3*b^4-21/8/d/a^8*tan(1/2*d*x+1/2*c)^2*b^5+14/d/a^9*b^6*tan(1/2*d*x+1/2*c)-3/80/d/a^5/tan(1/2*d*x+1/2*c)^5*b^2-5/8/d/a^7/tan(1/2*d*x+1/2*c)^3*b^4-14/d/a^9/tan(1/2*d*x+1/2*c)*b^6+1/128/d/a^4*b/tan(1/2*d*x+1/2*c)^6+5/32/d/a^6*b^3/tan(1/2*d*x+1/2*c)^4+21/8/d/a^8*b^5/tan(1/2*d*x+1/2*c)^2-36/d/a^10*b^7*ln(tan(1/2*d*x+1/2*c))+45/128/d/a^4*b/tan(1/2*d*x+1/2*c)^2-9/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^4+9/d/a^6/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5-23/d/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^4+81/d/a^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4-8/d/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-12/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2-33/8/d/a^5/tan(1/2*d*x+1/2*c)*b^2-45/128/d/a^4*tan(1/2*d*x+1/2*c)^2*b-18/d/a^9*b^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-34/d/a^10*b^9/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-50/d/a^9*b^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+72/d/a^10*b^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+27/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^6+33/d/a^8/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^7+73/d/a^7/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^6-141/d/a^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^6","B"
1276,1,56846,648,2.755000," ","int(cos(f*x+e)^6/(a+b*sin(f*x+e))^(13/2)/(d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1277,1,371,159,0.926000," ","int((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x)","\frac{\left(-2 \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) a^{2}+\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) b^{2}+2 \sqrt{2}\, \cos \left(f x +e \right) \sin \left(f x +e \right) a b +\sqrt{2}\, \cos \left(f x +e \right) a^{2}+\sqrt{2}\, \cos \left(f x +e \right) b^{2}-2 \sqrt{2}\, \sin \left(f x +e \right) a b -\sqrt{2}\, a^{2}-\sqrt{2}\, b^{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{2}}{3 f \left(-1+\cos \left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{5}{2}} \sqrt{d \sin \left(f x +e \right)}}"," ",0,"1/3/f*(-2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*sin(f*x+e)*a^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)*sin(f*x+e)*b^2+2*2^(1/2)*cos(f*x+e)*sin(f*x+e)*a*b+2^(1/2)*cos(f*x+e)*a^2+2^(1/2)*cos(f*x+e)*b^2-2*2^(1/2)*sin(f*x+e)*a*b-2^(1/2)*a^2-2^(1/2)*b^2)*cos(f*x+e)*sin(f*x+e)/(-1+cos(f*x+e))/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2)*2^(1/2)","B"
1278,1,615,192,0.928000," ","int((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(7/2)/(d*sin(f*x+e))^(1/2),x)","\frac{\left(8 \EllipticE \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(\cos^{3}\left(f x +e \right)\right) a b -4 \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{3}\left(f x +e \right)\right) a b +8 \EllipticE \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(\cos^{2}\left(f x +e \right)\right) a b -4 \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) a b -4 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{2}\, a b +4 \left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, a^{2}-\left(\cos^{2}\left(f x +e \right)\right) \sin \left(f x +e \right) \sqrt{2}\, b^{2}+2 \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, a b +\sin \left(f x +e \right) \sqrt{2}\, a^{2}+\sin \left(f x +e \right) \sqrt{2}\, b^{2}+2 a b \sqrt{2}\right) \cos \left(f x +e \right) \sqrt{2}}{5 f \left(g \cos \left(f x +e \right)\right)^{\frac{7}{2}} \sqrt{d \sin \left(f x +e \right)}}"," ",0,"1/5/f*(8*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^3*a*b-4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)^3*a*b+8*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*cos(f*x+e)^2*a*b-4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*cos(f*x+e)^2*a*b-4*cos(f*x+e)^3*2^(1/2)*a*b+4*cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*a^2-cos(f*x+e)^2*sin(f*x+e)*2^(1/2)*b^2+2*cos(f*x+e)^2*2^(1/2)*a*b+sin(f*x+e)*2^(1/2)*a^2+sin(f*x+e)*2^(1/2)*b^2+2*a*b*2^(1/2))*cos(f*x+e)/(g*cos(f*x+e))^(7/2)/(d*sin(f*x+e))^(1/2)*2^(1/2)","B"
1279,1,73,72,0.178000," ","int(cos(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}+\frac{a^{2} \sin \left(d x +c \right)}{b^{3} d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}+\frac{\sin^{3}\left(d x +c \right)}{3 b d}"," ",0,"-a^3*ln(a+b*sin(d*x+c))/b^4/d+a^2*sin(d*x+c)/b^3/d-1/2*a*sin(d*x+c)^2/b^2/d+1/3*sin(d*x+c)^3/b/d","A"
1280,1,54,53,0.176000," ","int(cos(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}-\frac{a \sin \left(d x +c \right)}{b^{2} d}+\frac{\sin^{2}\left(d x +c \right)}{2 b d}"," ",0,"1/d/b^3*ln(a+b*sin(d*x+c))*a^2-a*sin(d*x+c)/b^2/d+1/2*sin(d*x+c)^2/b/d","A"
1281,1,35,34,0.122000," ","int(cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}+\frac{\sin \left(d x +c \right)}{b d}"," ",0,"-1/d/b^2*a*ln(a+b*sin(d*x+c))+sin(d*x+c)/b/d","A"
1282,1,35,34,0.220000," ","int(cos(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}"," ",0,"ln(sin(d*x+c))/a/d-1/d/a*ln(a+b*sin(d*x+c))","A"
1283,1,35,50,0.194000," ","int(cos(d*x+c)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{\csc \left(d x +c \right)}{a d}+\frac{b \ln \left(a \csc \left(d x +c \right)+b \right)}{d \,a^{2}}"," ",0,"-csc(d*x+c)/a/d+1/d/a^2*b*ln(a*csc(d*x+c)+b)","A"
1284,1,73,70,0.250000," ","int(cos(d*x+c)*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}"," ",0,"-b^2*ln(a+b*sin(d*x+c))/a^3/d-1/2/d/a/sin(d*x+c)^2+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)","A"
1285,1,871,218,0.318000," ","int(cos(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6}}+\frac{3 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4}{15 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 a^{4} \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6}}"," ",0,"-1/4/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4-2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2+2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3-4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6+4/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-4/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4-2/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2-1/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3+2/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^5-1/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a-4/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2-1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3+1/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a+1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3-4/15/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3-3/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a-8/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2-4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4-2/d*a^4*(a^2-b^2)^(1/2)/b^6*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+3/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a+8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4+12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4","B"
1286,1,657,176,0.278000," ","int(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b}+\frac{2 a^{3} \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5}}"," ",0,"-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2+1/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2-7/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2+7/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3+2/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2-1/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3+2/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*a-2/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4+1/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+1/4/d/b*arctan(tan(1/2*d*x+1/2*c))+2/d*a^3*(a^2-b^2)^(1/2)/b^5*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1287,1,318,135,0.274000," ","int(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}-\frac{a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{2 a^{2} \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4}}"," ",0,"1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2*tan(1/2*d*x+1/2*c)^2-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2-2/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3+2/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-1/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-2/d*a^2*(a^2-b^2)^(1/2)/b^4*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1288,1,214,91,0.237000," ","int(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{2 a \sqrt{a^{2}-b^{2}}\, \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3}}"," ",0,"-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+1/d/b*arctan(tan(1/2*d*x+1/2*c))+2/d*a*(a^2-b^2)^(1/2)/b^3*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1289,1,137,70,0.426000," ","int(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/b*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))+2/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1290,1,155,75,0.437000," ","int(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1291,1,166,105,0.480000," ","int(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \sqrt{a^{2}-b^{2}}\, b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3}}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d/a^2*b/tan(1/2*d*x+1/2*c)+2/d*(a^2-b^2)^(1/2)/a^3*b*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1292,1,250,140,0.455000," ","int(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{24 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{2}}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{2 \sqrt{a^{2}-b^{2}}\, b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4}}"," ",0,"1/24/d/a*tan(1/2*d*x+1/2*c)^3-1/8/d/a^2*tan(1/2*d*x+1/2*c)^2*b-1/8/a/d*tan(1/2*d*x+1/2*c)+1/2/d/a^3*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a/tan(1/2*d*x+1/2*c)^3+1/8/a/d/tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)*b^2+1/8/d/a^2*b/tan(1/2*d*x+1/2*c)^2+1/2/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))-2/d*(a^2-b^2)^(1/2)/a^4*b^2*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1293,1,315,179,0.490000," ","int(cos(d*x+c)^2*csc(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d a}-\frac{b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2}}+\frac{b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{1}{64 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}+\frac{b}{24 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{3}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 \sqrt{a^{2}-b^{2}}\, b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5}}"," ",0,"1/64/d/a*tan(1/2*d*x+1/2*c)^4-1/24/d/a^2*b*tan(1/2*d*x+1/2*c)^3+1/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)^2+1/8/d/a^2*tan(1/2*d*x+1/2*c)*b-1/2/d/a^4*b^3*tan(1/2*d*x+1/2*c)-1/64/d/a/tan(1/2*d*x+1/2*c)^4-1/8/a/d*ln(tan(1/2*d*x+1/2*c))-1/2/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^4+1/24/d/a^2*b/tan(1/2*d*x+1/2*c)^3-1/8/d*b^2/a^3/tan(1/2*d*x+1/2*c)^2-1/8/d/a^2*b/tan(1/2*d*x+1/2*c)+1/2/d*b^3/a^4/tan(1/2*d*x+1/2*c)+2/d*(a^2-b^2)^(1/2)/a^5*b^3*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1294,1,439,221,0.495000," ","int(cos(d*x+c)^2*csc(d*x+c)^6/(a+b*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d a}-\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{64 d \,a^{2}}+\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{96 d a}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{24 d \,a^{3}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{8 d \,a^{4}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{5}}-\frac{1}{160 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{1}{96 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{2}}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{4}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{64 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{b^{3}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}+\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}-\frac{2 \sqrt{a^{2}-b^{2}}\, b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6}}"," ",0,"1/160/d/a*tan(1/2*d*x+1/2*c)^5-1/64/d/a^2*tan(1/2*d*x+1/2*c)^4*b+1/96/d/a*tan(1/2*d*x+1/2*c)^3+1/24/d/a^3*tan(1/2*d*x+1/2*c)^3*b^2-1/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b^3-1/16/a/d*tan(1/2*d*x+1/2*c)-1/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)+1/2/d/a^5*b^4*tan(1/2*d*x+1/2*c)-1/160/d/a/tan(1/2*d*x+1/2*c)^5-1/96/d/a/tan(1/2*d*x+1/2*c)^3-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3*b^2+1/16/a/d/tan(1/2*d*x+1/2*c)+1/8/d/a^3/tan(1/2*d*x+1/2*c)*b^2-1/2/d/a^5/tan(1/2*d*x+1/2*c)*b^4+1/64/d/a^2*b/tan(1/2*d*x+1/2*c)^4+1/8/d*b^3/a^4/tan(1/2*d*x+1/2*c)^2+1/8/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+1/2/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))-1/d/a^6*b^5*ln(tan(1/2*d*x+1/2*c))-2/d*(a^2-b^2)^(1/2)/a^6*b^4*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1295,1,182,141,0.296000," ","int(cos(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{\sin^{5}\left(d x +c \right)}{5 b d}+\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 b^{2} d}-\frac{\left(\sin^{3}\left(d x +c \right)\right) a^{2}}{3 d \,b^{3}}+\frac{\sin^{3}\left(d x +c \right)}{3 b d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{3}}{2 d \,b^{4}}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}-\frac{a^{4} \sin \left(d x +c \right)}{d \,b^{5}}+\frac{a^{2} \sin \left(d x +c \right)}{b^{3} d}+\frac{a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{6}}-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}"," ",0,"-1/5*sin(d*x+c)^5/b/d+1/4*a*sin(d*x+c)^4/b^2/d-1/3/d/b^3*sin(d*x+c)^3*a^2+1/3*sin(d*x+c)^3/b/d+1/2/d/b^4*sin(d*x+c)^2*a^3-1/2*a*sin(d*x+c)^2/b^2/d-1/d/b^5*a^4*sin(d*x+c)+a^2*sin(d*x+c)/b^3/d+1/d*a^5/b^6*ln(a+b*sin(d*x+c))-a^3*ln(a+b*sin(d*x+c))/b^4/d","A"
1296,1,144,113,0.294000," ","int(cos(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{\sin^{4}\left(d x +c \right)}{4 b d}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{2} d}-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d \,b^{3}}+\frac{\sin^{2}\left(d x +c \right)}{2 b d}+\frac{\sin \left(d x +c \right) a^{3}}{d \,b^{4}}-\frac{a \sin \left(d x +c \right)}{b^{2} d}-\frac{a^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{5}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}"," ",0,"-1/4*sin(d*x+c)^4/b/d+1/3*a*sin(d*x+c)^3/b^2/d-1/2/d/b^3*a^2*sin(d*x+c)^2+1/2*sin(d*x+c)^2/b/d+1/d/b^4*sin(d*x+c)*a^3-a*sin(d*x+c)/b^2/d-1/d*a^4/b^5*ln(a+b*sin(d*x+c))+1/d/b^3*ln(a+b*sin(d*x+c))*a^2","A"
1297,1,106,85,0.213000," ","int(cos(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\sin^{3}\left(d x +c \right)}{3 b d}+\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}-\frac{a^{2} \sin \left(d x +c \right)}{b^{3} d}+\frac{\sin \left(d x +c \right)}{b d}+\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}-\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}"," ",0,"-1/3*sin(d*x+c)^3/b/d+1/2*a*sin(d*x+c)^2/b^2/d-a^2*sin(d*x+c)/b^3/d+sin(d*x+c)/b/d+a^3*ln(a+b*sin(d*x+c))/b^4/d-1/d/b^2*a*ln(a+b*sin(d*x+c))","A"
1298,1,68,59,0.397000," ","int(cos(d*x+c)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\sin \left(d x +c \right)}{b d}+\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}"," ",0,"-sin(d*x+c)/b/d+1/d/b^2*a*ln(a+b*sin(d*x+c))-1/d/a*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d","A"
1299,1,72,60,0.393000," ","int(cos(d*x+c)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}+\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"-ln(a+b*sin(d*x+c))/b/d+b*ln(a+b*sin(d*x+c))/a^2/d-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d","A"
1300,1,106,82,0.454000," ","int(cos(d*x+c)^3*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}-\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}"," ",0,"1/d/a*ln(a+b*sin(d*x+c))-b^2*ln(a+b*sin(d*x+c))/a^3/d-1/2/d/a/sin(d*x+c)^2-ln(sin(d*x+c))/a/d+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)","A"
1301,1,1501,263,0.314000," ","int(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d b}-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{20 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{5 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{24 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{80 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{3 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7}}+\frac{2 a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{47 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{13 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{13 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{47 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{8 a^{3}}{3 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 a}{5 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{16 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{4 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{20 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 a^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}+\frac{4 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{10 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{3 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{7 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}"," ",0,"3/4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+1/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^2-3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^4+2/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^5+1/8/d/b*arctan(tan(1/2*d*x+1/2*c))+5/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^2-4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^3+20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^5-24/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^3-80/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^3+4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a-16/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a-2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4+2/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^6+2/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*a^5+1/8/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11-47/24/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9+13/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7-13/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5+47/24/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3-1/8/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)-8/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*a^3+2/5/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*a+7/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^2+10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^5-2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^4+3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^4-7/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^2+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^4-1/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^2+20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^5-12/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^3+2/5/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a+10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^5+4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a-5/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^2-1/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^4-2/d*a^7/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d*a^5/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^4","B"
1302,1,941,218,0.307000," ","int(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{3 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,b^{2}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{8 a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2}{5 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{12 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{4 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{2 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}-b^{2}}}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{44 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{12 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{2 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{2 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{28 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{4 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{4 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{\left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}"," ",0,"-3/4/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^4+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8*a^2-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a^3-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^8-4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4-2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*a^4+8/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*a^2+3/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-2/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^5+5/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a+28/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^2+1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a^3-5/4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)*a-1/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^9*a^3+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-2/5/d/b/(1+tan(1/2*d*x+1/2*c)^2)^5+2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a^3-1/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^3*a+44/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^2+12/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^2-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^2*a^4-4/d*a^4/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*a^6/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^7*a-8/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^6*a^4-12/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^5*tan(1/2*d*x+1/2*c)^4*a^4","B"
1303,1,760,148,0.247000," ","int(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{4 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{20 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{8 a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b}-\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}+\frac{4 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2-5/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7+2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3-4/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2+3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3-8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2-3/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3-20/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2+5/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)+2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3-8/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*a+2/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4-3/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+3/4/d/b*arctan(tan(1/2*d*x+1/2*c))-2/d*a^5/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1304,1,334,115,0.441000," ","int(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}"," ",0,"1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a+2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2-3/d/b*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))-2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1305,1,249,99,0.438000," ","int(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)-2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-4/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1306,1,286,114,0.485000," ","int(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}+\frac{4 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b+2/d/b*arctan(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2-3/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d/a^2*b/tan(1/2*d*x+1/2*c)-2/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1307,1,348,141,0.456000," ","int(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{2}}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{24 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{2}}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}-\frac{4 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a*tan(1/2*d*x+1/2*c)^3-1/8/d/a^2*tan(1/2*d*x+1/2*c)^2*b-5/8/a/d*tan(1/2*d*x+1/2*c)+1/2/d/a^3*b^2*tan(1/2*d*x+1/2*c)-1/24/d/a/tan(1/2*d*x+1/2*c)^3+5/8/a/d/tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)*b^2+1/8/d/a^2*b/tan(1/2*d*x+1/2*c)^2+3/2/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))+2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1308,1,455,183,0.486000," ","int(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d a}-\frac{b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{1}{64 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}+\frac{b}{24 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{5 b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{3}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{4 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/64/d/a*tan(1/2*d*x+1/2*c)^4-1/24/d/a^2*b*tan(1/2*d*x+1/2*c)^3-1/8/a/d*tan(1/2*d*x+1/2*c)^2+1/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)^2+5/8/d/a^2*tan(1/2*d*x+1/2*c)*b-1/2/d/a^4*b^3*tan(1/2*d*x+1/2*c)-1/64/d/a/tan(1/2*d*x+1/2*c)^4+1/8/a/d/tan(1/2*d*x+1/2*c)^2-1/8/d*b^2/a^3/tan(1/2*d*x+1/2*c)^2+3/8/a/d*ln(tan(1/2*d*x+1/2*c))-3/2/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^4+1/24/d/a^2*b/tan(1/2*d*x+1/2*c)^3-5/8/d/a^2*b/tan(1/2*d*x+1/2*c)+1/2/d*b^3/a^4/tan(1/2*d*x+1/2*c)-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^5*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1309,1,583,227,0.493000," ","int(cos(d*x+c)^4*csc(d*x+c)^6/(a+b*sin(d*x+c)),x)","\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d a}-\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{64 d \,a^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{32 d a}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{24 d \,a^{3}}+\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{8 d \,a^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{5 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{5}}-\frac{1}{160 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{1}{32 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{2}}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{1}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{4}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{64 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{b^{3}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}+\frac{3 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{4 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}+\frac{2 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}"," ",0,"1/160/d/a*tan(1/2*d*x+1/2*c)^5-1/64/d/a^2*tan(1/2*d*x+1/2*c)^4*b-1/32/d/a*tan(1/2*d*x+1/2*c)^3+1/24/d/a^3*tan(1/2*d*x+1/2*c)^3*b^2+1/8/d/a^2*tan(1/2*d*x+1/2*c)^2*b-1/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b^3+1/16/a/d*tan(1/2*d*x+1/2*c)-5/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)+1/2/d/a^5*b^4*tan(1/2*d*x+1/2*c)-1/160/d/a/tan(1/2*d*x+1/2*c)^5+1/32/d/a/tan(1/2*d*x+1/2*c)^3-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3*b^2-1/16/a/d/tan(1/2*d*x+1/2*c)+5/8/d/a^3/tan(1/2*d*x+1/2*c)*b^2-1/2/d/a^5/tan(1/2*d*x+1/2*c)*b^4+1/64/d/a^2*b/tan(1/2*d*x+1/2*c)^4-1/8/d/a^2*b/tan(1/2*d*x+1/2*c)^2+1/8/d*b^3/a^4/tan(1/2*d*x+1/2*c)^2-3/8/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+3/2/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))-1/d/a^6*b^5*ln(tan(1/2*d*x+1/2*c))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4+2/d/a^6*b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1310,1,329,200,0.296000," ","int(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\sin^{7}\left(d x +c \right)}{7 b d}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{6 b^{2} d}+\frac{\left(\sin^{5}\left(d x +c \right)\right) a^{2}}{5 d \,b^{3}}-\frac{2 \left(\sin^{5}\left(d x +c \right)\right)}{5 b d}-\frac{\left(\sin^{4}\left(d x +c \right)\right) a^{3}}{4 d \,b^{4}}+\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{2 b^{2} d}+\frac{a^{4} \left(\sin^{3}\left(d x +c \right)\right)}{3 d \,b^{5}}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right) a^{2}}{3 d \,b^{3}}+\frac{\sin^{3}\left(d x +c \right)}{3 b d}-\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{5}}{2 d \,b^{6}}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{3}}{d \,b^{4}}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}+\frac{\sin \left(d x +c \right) a^{6}}{d \,b^{7}}-\frac{2 a^{4} \sin \left(d x +c \right)}{d \,b^{5}}+\frac{a^{2} \sin \left(d x +c \right)}{b^{3} d}-\frac{a^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{8}}+\frac{2 a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{6}}-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}"," ",0,"1/7*sin(d*x+c)^7/b/d-1/6*a*sin(d*x+c)^6/b^2/d+1/5/d/b^3*sin(d*x+c)^5*a^2-2/5*sin(d*x+c)^5/b/d-1/4/d/b^4*sin(d*x+c)^4*a^3+1/2*a*sin(d*x+c)^4/b^2/d+1/3/d/b^5*a^4*sin(d*x+c)^3-2/3/d/b^3*sin(d*x+c)^3*a^2+1/3*sin(d*x+c)^3/b/d-1/2/d/b^6*sin(d*x+c)^2*a^5+1/d/b^4*sin(d*x+c)^2*a^3-1/2*a*sin(d*x+c)^2/b^2/d+1/d/b^7*sin(d*x+c)*a^6-2/d/b^5*a^4*sin(d*x+c)+a^2*sin(d*x+c)/b^3/d-1/d*a^7/b^8*ln(a+b*sin(d*x+c))+2/d*a^5/b^6*ln(a+b*sin(d*x+c))-a^3*ln(a+b*sin(d*x+c))/b^4/d","A"
1311,1,273,170,0.294000," ","int(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\sin^{6}\left(d x +c \right)}{6 b d}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{5 b^{2} d}+\frac{\left(\sin^{4}\left(d x +c \right)\right) a^{2}}{4 d \,b^{3}}-\frac{\sin^{4}\left(d x +c \right)}{2 b d}-\frac{\left(\sin^{3}\left(d x +c \right)\right) a^{3}}{3 d \,b^{4}}+\frac{2 a \left(\sin^{3}\left(d x +c \right)\right)}{3 b^{2} d}+\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{4}}{2 d \,b^{5}}-\frac{a^{2} \left(\sin^{2}\left(d x +c \right)\right)}{d \,b^{3}}+\frac{\sin^{2}\left(d x +c \right)}{2 b d}-\frac{\sin \left(d x +c \right) a^{5}}{d \,b^{6}}+\frac{2 \sin \left(d x +c \right) a^{3}}{d \,b^{4}}-\frac{a \sin \left(d x +c \right)}{b^{2} d}+\frac{a^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{7}}-\frac{2 a^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{5}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}"," ",0,"1/6*sin(d*x+c)^6/b/d-1/5*a*sin(d*x+c)^5/b^2/d+1/4/d/b^3*sin(d*x+c)^4*a^2-1/2*sin(d*x+c)^4/b/d-1/3/d/b^4*sin(d*x+c)^3*a^3+2/3*a*sin(d*x+c)^3/b^2/d+1/2/d/b^5*sin(d*x+c)^2*a^4-1/d/b^3*a^2*sin(d*x+c)^2+1/2*sin(d*x+c)^2/b/d-1/d/b^6*sin(d*x+c)*a^5+2/d/b^4*sin(d*x+c)*a^3-a*sin(d*x+c)/b^2/d+1/d*a^6/b^7*ln(a+b*sin(d*x+c))-2/d*a^4/b^5*ln(a+b*sin(d*x+c))+1/d/b^3*ln(a+b*sin(d*x+c))*a^2","A"
1312,1,215,140,0.223000," ","int(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\sin^{5}\left(d x +c \right)}{5 b d}-\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 b^{2} d}+\frac{\left(\sin^{3}\left(d x +c \right)\right) a^{2}}{3 d \,b^{3}}-\frac{2 \left(\sin^{3}\left(d x +c \right)\right)}{3 b d}-\frac{\left(\sin^{2}\left(d x +c \right)\right) a^{3}}{2 d \,b^{4}}+\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{b^{2} d}+\frac{a^{4} \sin \left(d x +c \right)}{d \,b^{5}}-\frac{2 a^{2} \sin \left(d x +c \right)}{b^{3} d}+\frac{\sin \left(d x +c \right)}{b d}-\frac{a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{6}}+\frac{2 a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}-\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}"," ",0,"1/5*sin(d*x+c)^5/b/d-1/4*a*sin(d*x+c)^4/b^2/d+1/3/d/b^3*sin(d*x+c)^3*a^2-2/3*sin(d*x+c)^3/b/d-1/2/d/b^4*sin(d*x+c)^2*a^3+a*sin(d*x+c)^2/b^2/d+1/d/b^5*a^4*sin(d*x+c)-2*a^2*sin(d*x+c)/b^3/d+sin(d*x+c)/b/d-1/d*a^5/b^6*ln(a+b*sin(d*x+c))+2*a^3*ln(a+b*sin(d*x+c))/b^4/d-1/d/b^2*a*ln(a+b*sin(d*x+c))","A"
1313,1,140,103,0.425000," ","int(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{\sin^{3}\left(d x +c \right)}{3 b d}-\frac{a \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}+\frac{a^{2} \sin \left(d x +c \right)}{b^{3} d}-\frac{2 \sin \left(d x +c \right)}{b d}-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{4} d}+\frac{2 a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}"," ",0,"1/3*sin(d*x+c)^3/b/d-1/2*a*sin(d*x+c)^2/b^2/d+a^2*sin(d*x+c)/b^3/d-2*sin(d*x+c)/b/d-a^3*ln(a+b*sin(d*x+c))/b^4/d+2/d/b^2*a*ln(a+b*sin(d*x+c))-1/d/a*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d","A"
1314,1,124,94,0.423000," ","int(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\sin^{2}\left(d x +c \right)}{2 b d}-\frac{a \sin \left(d x +c \right)}{b^{2} d}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a^{2}}{d \,b^{3}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{b d}+\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}"," ",0,"1/2*sin(d*x+c)^2/b/d-a*sin(d*x+c)/b^2/d+1/d/b^3*ln(a+b*sin(d*x+c))*a^2-2*ln(a+b*sin(d*x+c))/b/d+b*ln(a+b*sin(d*x+c))/a^2/d-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d","A"
1315,1,140,103,0.483000," ","int(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\sin \left(d x +c \right)}{b d}-\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2}}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right)}{d a}-\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}-\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}"," ",0,"sin(d*x+c)/b/d-1/d/b^2*a*ln(a+b*sin(d*x+c))+2/d/a*ln(a+b*sin(d*x+c))-b^2*ln(a+b*sin(d*x+c))/a^3/d-1/2/d/a/sin(d*x+c)^2-2*ln(sin(d*x+c))/a/d+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)","A"
1316,1,163,116,0.447000," ","int(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{b d}-\frac{2 b \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}+\frac{b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{4}}-\frac{1}{3 d a \sin \left(d x +c \right)^{3}}+\frac{2}{d a \sin \left(d x +c \right)}-\frac{b^{2}}{d \,a^{3} \sin \left(d x +c \right)}+\frac{2 b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{4}}+\frac{b}{2 d \,a^{2} \sin \left(d x +c \right)^{2}}"," ",0,"ln(a+b*sin(d*x+c))/b/d-2*b*ln(a+b*sin(d*x+c))/a^2/d+1/d/a^4*b^3*ln(a+b*sin(d*x+c))-1/3/d/a/sin(d*x+c)^3+2/d/a/sin(d*x+c)-1/d/a^3/sin(d*x+c)*b^2+2*b*ln(sin(d*x+c))/a^2/d-1/d/a^4*b^3*ln(sin(d*x+c))+1/2/d/a^2*b/sin(d*x+c)^2","A"
1317,1,216,142,0.481000," ","int(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(a +b \sin \left(d x +c \right)\right)}{d a}+\frac{2 b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}-\frac{1}{4 d a \sin \left(d x +c \right)^{4}}+\frac{1}{d a \sin \left(d x +c \right)^{2}}-\frac{b^{2}}{2 d \,a^{3} \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{2 b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{\ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}-\frac{2 b}{d \,a^{2} \sin \left(d x +c \right)}+\frac{b^{3}}{d \,a^{4} \sin \left(d x +c \right)}+\frac{b}{3 d \,a^{2} \sin \left(d x +c \right)^{3}}"," ",0,"-1/d/a*ln(a+b*sin(d*x+c))+2*b^2*ln(a+b*sin(d*x+c))/a^3/d-1/d/a^5*ln(a+b*sin(d*x+c))*b^4-1/4/d/a/sin(d*x+c)^4+1/d/a/sin(d*x+c)^2-1/2/d/a^3/sin(d*x+c)^2*b^2+ln(sin(d*x+c))/a/d-2*b^2*ln(sin(d*x+c))/a^3/d+1/d/a^5*ln(sin(d*x+c))*b^4-2/d/a^2*b/sin(d*x+c)+1/d/a^4*b^3/sin(d*x+c)+1/3/d/a^2*b/sin(d*x+c)^3","A"
1318,1,274,171,0.487000," ","int(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c)),x)","\frac{b \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{2} d}-\frac{2 b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{4}}+\frac{b^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{6}}-\frac{1}{5 d a \sin \left(d x +c \right)^{5}}+\frac{2}{3 d a \sin \left(d x +c \right)^{3}}-\frac{b^{2}}{3 d \,a^{3} \sin \left(d x +c \right)^{3}}-\frac{1}{d a \sin \left(d x +c \right)}+\frac{2 b^{2}}{d \,a^{3} \sin \left(d x +c \right)}-\frac{b^{4}}{d \,a^{5} \sin \left(d x +c \right)}-\frac{b}{d \,a^{2} \sin \left(d x +c \right)^{2}}+\frac{b^{3}}{2 d \,a^{4} \sin \left(d x +c \right)^{2}}+\frac{b}{4 d \,a^{2} \sin \left(d x +c \right)^{4}}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{2 b^{3} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{4}}-\frac{b^{5} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{6}}"," ",0,"b*ln(a+b*sin(d*x+c))/a^2/d-2/d/a^4*b^3*ln(a+b*sin(d*x+c))+1/d/a^6*b^5*ln(a+b*sin(d*x+c))-1/5/d/a/sin(d*x+c)^5+2/3/d/a/sin(d*x+c)^3-1/3/d/a^3/sin(d*x+c)^3*b^2-1/d/a/sin(d*x+c)+2/d/a^3/sin(d*x+c)*b^2-1/d/a^5/sin(d*x+c)*b^4-1/d/a^2*b/sin(d*x+c)^2+1/2/d/a^4*b^3/sin(d*x+c)^2+1/4/d/a^2*b/sin(d*x+c)^4-b*ln(sin(d*x+c))/a^2/d+2/d/a^4*b^3*ln(sin(d*x+c))-1/d/a^6*b^5*ln(sin(d*x+c))","A"
1319,1,330,202,0.554000," ","int(cos(d*x+c)^5*csc(d*x+c)^7/(a+b*sin(d*x+c)),x)","-\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{a^{3} d}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}-\frac{b^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{7}}-\frac{1}{6 d a \sin \left(d x +c \right)^{6}}+\frac{1}{2 d a \sin \left(d x +c \right)^{4}}-\frac{b^{2}}{4 d \,a^{3} \sin \left(d x +c \right)^{4}}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}+\frac{b^{2}}{d \,a^{3} \sin \left(d x +c \right)^{2}}-\frac{b^{4}}{2 d \,a^{5} \sin \left(d x +c \right)^{2}}-\frac{2 b}{3 d \,a^{2} \sin \left(d x +c \right)^{3}}+\frac{b^{3}}{3 d \,a^{4} \sin \left(d x +c \right)^{3}}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}-\frac{2 \ln \left(\sin \left(d x +c \right)\right) b^{4}}{d \,a^{5}}+\frac{b^{6} \ln \left(\sin \left(d x +c \right)\right)}{d \,a^{7}}+\frac{b}{5 d \,a^{2} \sin \left(d x +c \right)^{5}}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}-\frac{2 b^{3}}{d \,a^{4} \sin \left(d x +c \right)}+\frac{b^{5}}{d \,a^{6} \sin \left(d x +c \right)}"," ",0,"-b^2*ln(a+b*sin(d*x+c))/a^3/d+2/d/a^5*ln(a+b*sin(d*x+c))*b^4-1/d/a^7*b^6*ln(a+b*sin(d*x+c))-1/6/d/a/sin(d*x+c)^6+1/2/d/a/sin(d*x+c)^4-1/4/d/a^3/sin(d*x+c)^4*b^2-1/2/d/a/sin(d*x+c)^2+1/d/a^3/sin(d*x+c)^2*b^2-1/2/d/a^5/sin(d*x+c)^2*b^4-2/3/d/a^2*b/sin(d*x+c)^3+1/3/d/a^4*b^3/sin(d*x+c)^3+b^2*ln(sin(d*x+c))/a^3/d-2/d/a^5*ln(sin(d*x+c))*b^4+1/d/a^7*b^6*ln(sin(d*x+c))+1/5/d/a^2*b/sin(d*x+c)^5+1/d/a^2*b/sin(d*x+c)-2/d/a^4*b^3/sin(d*x+c)+1/d/a^6*b^5/sin(d*x+c)","A"
1320,1,2587,440,0.317000," ","int(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\text{Expression too large to display}"," ",0,"5/8/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+5/64/d/b*arctan(tan(1/2*d*x+1/2*c))+29/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9*a^4-14/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12*a^7+38/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12*a^5-30/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12*a^3+11/8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)*a^2-14/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2*a^7-2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-15/4/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4+5/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^6-2/d/b^9*arctan(tan(1/2*d*x+1/2*c))*a^8-1765/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9+895/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11-397/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13+5/64/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15-46/15/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*a^3+2/7/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*a-2/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*a^7+14/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*a^5-5/64/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)+397/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3-895/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5+1765/192/d/b/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7+113/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5*a^2-70/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6*a^7+61/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3*a^2+94/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2*a^5-85/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9*a^2-42/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10*a^7+314/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10*a^5-218/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10*a^3+10/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^10*a+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^12*a-9/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)*a^4-278/15/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2*a^3+6/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^14*a^5-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^14*a^3+2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^14*a+2/7/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^2*a+490/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8*a^5-70/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8*a^7-42/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4*a^7-1486/15/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6*a^3+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6*a+5/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7*a^6-29/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7*a^4+85/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^7*a^2+2/d/b^9*a^9/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-322/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8*a^3+10/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^8*a+1/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)*a^6+9/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5*a^6-6/d*a^7/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a^5/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-11/8/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15*a^2+5/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3*a^6-37/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^3*a^4-5/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^9*a^6-57/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^5*a^4-2/d/b^8/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^14*a^7+470/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^6*a^5-61/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13*a^2-1/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15*a^6+9/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^15*a^4-5/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13*a^6+37/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^13*a^4+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4*a+278/3/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4*a^5-838/15/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^4*a^3-9/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11*a^6+57/4/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11*a^4-113/24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^8*tan(1/2*d*x+1/2*c)^11*a^2","B"
1321,1,1808,383,0.301000," ","int(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{5 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,b^{2}}-\frac{85 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{24 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{2}{7 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{29 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{218 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{6 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{6 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{272 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{176 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{4 d \,b^{4}}-\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6}}-\frac{2 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{7}}{d \,b^{8}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{40 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{2 a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{14 a^{4}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{46 a^{2}}{15 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{4 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{6 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{6 a^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{6} \sqrt{a^{2}-b^{2}}}-\frac{2 a^{8} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{8} \sqrt{a^{2}-b^{2}}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{6 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{80 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{3 d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{232 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{15 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{12 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{7 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{7 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{6 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{\left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{9 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{146 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{3 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{29 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{85 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{24 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{30 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{32 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{24 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{11 \left(\tan^{13}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{8 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{202 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{5 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{30 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{66 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{3}}{4 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a}{8 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}+\frac{2 \left(\tan^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{7}}"," ",0,"-5/8/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-2/7/d/b/(1+tan(1/2*d*x+1/2*c)^2)^7+202/5/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^2-1/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a^5+1/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a^5-9/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a^3+146/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^2+40/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^6-272/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^4+176/3/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^6*a^2-5/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a^5+29/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a^3-218/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^4-4/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a^5+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^6-66/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4*a^4+9/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a^3-11/8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)*a+2/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^6-6/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^4+6/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12*a^2-7/6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a+12/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^6-80/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^4+232/15/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^2*a^2+12/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^6+15/4/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-5/d/b^6*arctan(tan(1/2*d*x+1/2*c))*a^5+46/15/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*a^2-10/d/b/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8+2/d/b^8*arctan(tan(1/2*d*x+1/2*c))*a^7-6/d/b/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^4-2/d/b/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^12+2/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*a^6-14/3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*a^4+2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+4/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a^5-7/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a^3+7/6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^11*a+5/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a^5-29/4/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a^3+85/24/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^9*a+30/d/b^7/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^8*a^6+7/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^3*a^3-6/d*a^4/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a^6/b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-32/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^4+24/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^10*a^2-2/d*a^8/b^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+11/8/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^13*a-85/24/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^7*tan(1/2*d*x+1/2*c)^5*a","B"
1322,1,1551,215,0.255000," ","int(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d b}-\frac{92 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{26 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{10 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{3 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{20 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{10 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{6 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{6 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{20 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{44 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{140 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{3 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{6}}{d \,b^{7}}-\frac{11 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{5 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{15 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{15 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{14 a^{3}}{3 d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{46 a}{15 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{9 \left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{28 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{6 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{18 \left(\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{19 \left(\tan^{9}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{22 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{2 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{2 \left(\tan^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{5}}{d \,b^{6} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}+\frac{2 a^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{7} \sqrt{a^{2}-b^{2}}}-\frac{6 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{62 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{5 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{19 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{4 d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}-\frac{\left(\tan^{11}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{6}}"," ",0,"-15/4/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2-5/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^2+3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^4-2/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^5+5/8/d/b*arctan(tan(1/2*d*x+1/2*c))-9/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^2+6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a^3-20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^5+44/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a^3+140/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^3-92/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a+26/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^3-18/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a+6/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+5/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4-2/d/b^7*arctan(tan(1/2*d*x+1/2*c))*a^6-2/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*a^5-11/8/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11+5/24/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9-15/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7+15/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5-5/24/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3+11/8/d/b/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)+14/3/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*a^3-46/15/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*a-19/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^3*a^2-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^5+2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^5*a^4-3/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^4+19/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^9*a^2-2/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^4+5/2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^7*a^2-20/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^6*a^5+22/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a^3-62/5/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^2*a-10/d/b^6/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^8*a^5-28/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^4*a-6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^10*a+9/4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^2+1/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)*a^4+2/d*a^7/b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*a^5/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-1/d/b^5/(1+tan(1/2*d*x+1/2*c)^2)^6*tan(1/2*d*x+1/2*c)^11*a^4","B"
1323,1,827,235,0.446000," ","int(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{9 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{6 \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{14 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{38 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 a^{3}}{d \,b^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{14 a}{3 d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{4}}{d \,b^{5}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}-\frac{15 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{5} \sqrt{a^{2}-b^{2}}}-\frac{6 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}+\frac{6 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*a^2+9/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a^3+6/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^6*a-1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*a^2+1/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a^3+14/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^4*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*a^2-1/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3-6/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a^3+38/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^2*a+1/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*a^2-9/4/d/b/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)-2/d/b^4/(1+tan(1/2*d*x+1/2*c)^2)^4*a^3+14/3/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^4*a-2/d/b^5*arctan(tan(1/2*d*x+1/2*c))*a^4+5/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2-15/4/d/b*arctan(tan(1/2*d*x+1/2*c))+1/a/d*ln(tan(1/2*d*x+1/2*c))+2/d*a^5/b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1324,1,557,172,0.437000," ","int(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}+\frac{a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{6 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 a^{2}}{d \,b^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14}{3 d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{3}}{d \,b^{4}}-\frac{5 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{4} \sqrt{a^{2}-b^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"1/2/a/d*tan(1/2*d*x+1/2*c)+1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)^5+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4*a^2-6/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^4+4/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2*tan(1/2*d*x+1/2*c)^2-8/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^2-1/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^3*a*tan(1/2*d*x+1/2*c)+2/d/b^3/(1+tan(1/2*d*x+1/2*c)^2)^3*a^2-14/3/d/b/(1+tan(1/2*d*x+1/2*c)^2)^3+2/d/b^4*arctan(tan(1/2*d*x+1/2*c))*a^3-5/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-2/d*a^4/b^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2-6/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1325,1,483,161,0.483000," ","int(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}+\frac{5 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{3} \sqrt{a^{2}-b^{2}}}-\frac{6 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}+\frac{6 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2+5/d/b*arctan(tan(1/2*d*x+1/2*c))-1/8/a/d/tan(1/2*d*x+1/2*c)^2-5/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d/a^2*b/tan(1/2*d*x+1/2*c)+2/d*a^3/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1326,1,442,186,0.463000," ","int(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{24 d a}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{8 d \,a^{2}}-\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}+\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}+\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{24 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{9}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{2}}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}-\frac{b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) a^{2}}{d \,b^{2} \sqrt{a^{2}-b^{2}}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}-\frac{6 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"1/24/d/a*tan(1/2*d*x+1/2*c)^3-1/8/d/a^2*tan(1/2*d*x+1/2*c)^2*b-9/8/a/d*tan(1/2*d*x+1/2*c)+1/2/d/a^3*b^2*tan(1/2*d*x+1/2*c)+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-1/24/d/a/tan(1/2*d*x+1/2*c)^3+9/8/a/d/tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)*b^2+1/8/d/a^2*b/tan(1/2*d*x+1/2*c)^2+5/2/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))-2/d/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*a^2+6/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1327,1,523,182,0.490000," ","int(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{64 d a}-\frac{b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{2}}-\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{4 a d}+\frac{b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{3}}+\frac{9 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{8 d \,a^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{4}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}-\frac{1}{64 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{1}{4 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 a d}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{2 d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \,a^{5}}+\frac{b}{24 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{9 b}{8 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{3}}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{2 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d b \sqrt{a^{2}-b^{2}}}-\frac{6 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}+\frac{6 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"1/64/d/a*tan(1/2*d*x+1/2*c)^4-1/24/d/a^2*b*tan(1/2*d*x+1/2*c)^3-1/4/a/d*tan(1/2*d*x+1/2*c)^2+1/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)^2+9/8/d/a^2*tan(1/2*d*x+1/2*c)*b-1/2/d/a^4*b^3*tan(1/2*d*x+1/2*c)-2/d/b*arctan(tan(1/2*d*x+1/2*c))-1/64/d/a/tan(1/2*d*x+1/2*c)^4+1/4/a/d/tan(1/2*d*x+1/2*c)^2-1/8/d*b^2/a^3/tan(1/2*d*x+1/2*c)^2+15/8/a/d*ln(tan(1/2*d*x+1/2*c))-5/2/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^4+1/24/d/a^2*b/tan(1/2*d*x+1/2*c)^3-9/8/d/a^2*b/tan(1/2*d*x+1/2*c)+1/2/d*b^3/a^4/tan(1/2*d*x+1/2*c)+2/d*a/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^5*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1328,1,629,224,0.492000," ","int(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c)),x)","-\frac{1}{160 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \sqrt{a^{2}-b^{2}}}+\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 a d}-\frac{11}{16 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{9 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}+\frac{9 b^{2}}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{5}}-\frac{b^{2}}{24 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{4}}{2 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b}{64 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{b^{3}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{7}{96 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{15 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{2}}-\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{64 d \,a^{2}}-\frac{b}{4 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{4}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{8 d \,a^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{24 d \,a^{3}}+\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{4 d \,a^{2}}-\frac{b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{6}}+\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{160 d a}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d a}+\frac{6 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}-\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/160/d/a/tan(1/2*d*x+1/2*c)^5-2/d/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+11/16/a/d*tan(1/2*d*x+1/2*c)-11/16/a/d/tan(1/2*d*x+1/2*c)+1/4/d/a^2*tan(1/2*d*x+1/2*c)^2*b-9/8/d/a^3*b^2*tan(1/2*d*x+1/2*c)+9/8/d/a^3/tan(1/2*d*x+1/2*c)*b^2-1/8/d/a^4*tan(1/2*d*x+1/2*c)^2*b^3+1/2/d/a^5*b^4*tan(1/2*d*x+1/2*c)-1/24/d/a^3/tan(1/2*d*x+1/2*c)^3*b^2-1/2/d/a^5/tan(1/2*d*x+1/2*c)*b^4+1/64/d/a^2*b/tan(1/2*d*x+1/2*c)^4+1/8/d*b^3/a^4/tan(1/2*d*x+1/2*c)^2+7/96/d/a/tan(1/2*d*x+1/2*c)^3-15/8/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/4/d/a^2*b/tan(1/2*d*x+1/2*c)^2+5/2/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))+1/160/d/a*tan(1/2*d*x+1/2*c)^5-1/d/a^6*b^5*ln(tan(1/2*d*x+1/2*c))-1/64/d/a^2*tan(1/2*d*x+1/2*c)^4*b+1/24/d/a^3*tan(1/2*d*x+1/2*c)^3*b^2-7/96/d/a*tan(1/2*d*x+1/2*c)^3+6/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^6*b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1329,1,780,340,0.506000," ","int(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c)),x)","-\frac{b^{2}}{64 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{d \,a^{7}}+\frac{b}{160 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{b^{5}}{2 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{3}}{24 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{b^{4}}{8 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \sqrt{a^{2}-b^{2}}}-\frac{15}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{6 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 a d}-\frac{b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{160 d \,a^{2}}+\frac{9 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{7 b}{96 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{b^{2}}{4 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{9 b^{3}}{8 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{64 d \,a^{3}}+\frac{7 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{96 d \,a^{2}}-\frac{11 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{16 d \,a^{2}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{8 d \,a^{3}}+\frac{11 b}{16 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{8 d \,a^{5}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{2 d \,a^{5}}-\frac{b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d \,a^{3}}-\frac{b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{6}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{24 d \,a^{4}}+\frac{3}{128 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}+\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d a}+\frac{6 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d a}-\frac{2 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{7} \sqrt{a^{2}-b^{2}}}+\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}-\frac{1}{384 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}"," ",0,"-1/64/d/a^3/tan(1/2*d*x+1/2*c)^4*b^2+1/d/a^7*ln(tan(1/2*d*x+1/2*c))*b^6+1/160/d/a^2*b/tan(1/2*d*x+1/2*c)^5+1/2/d*b^5/a^6/tan(1/2*d*x+1/2*c)+1/24/d/a^4*b^3/tan(1/2*d*x+1/2*c)^3-1/8/d/a^5/tan(1/2*d*x+1/2*c)^2*b^4-1/160/d/a^2*b*tan(1/2*d*x+1/2*c)^5+1/64/d/a^3*tan(1/2*d*x+1/2*c)^4*b^2+1/8/d/a^5*tan(1/2*d*x+1/2*c)^2*b^4-1/24/d/a^4*tan(1/2*d*x+1/2*c)^3*b^3+2/d*b/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+15/128/a/d*tan(1/2*d*x+1/2*c)^2-15/128/a/d/tan(1/2*d*x+1/2*c)^2-6/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-5/16/a/d*ln(tan(1/2*d*x+1/2*c))+9/8/d/a^4*b^3*tan(1/2*d*x+1/2*c)-7/96/d/a^2*b/tan(1/2*d*x+1/2*c)^3+1/4/d*b^2/a^3/tan(1/2*d*x+1/2*c)^2-9/8/d*b^3/a^4/tan(1/2*d*x+1/2*c)-11/16/d/a^2*tan(1/2*d*x+1/2*c)*b+15/8/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+11/16/d/a^2*b/tan(1/2*d*x+1/2*c)+7/96/d/a^2*b*tan(1/2*d*x+1/2*c)^3-1/4/d/a^3*b^2*tan(1/2*d*x+1/2*c)^2-5/2/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^4-1/2/d/a^6*b^5*tan(1/2*d*x+1/2*c)+3/128/d/a/tan(1/2*d*x+1/2*c)^4+6/d/a^5*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d/a^7*b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/128/d/a*tan(1/2*d*x+1/2*c)^4+1/384/d/a*tan(1/2*d*x+1/2*c)^6-1/384/d/a/tan(1/2*d*x+1/2*c)^6","B"
1330,1,952,392,0.519000," ","int(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c)),x)","\frac{1}{128 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{b}{384 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 d a}-\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{5}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{11 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{3}}-\frac{11 b^{2}}{16 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{9 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{5}}+\frac{7 b^{2}}{96 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{9 b^{4}}{8 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{b^{3}}{4 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3}{128 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{5 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{16 d \,a^{2}}+\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{128 d \,a^{2}}+\frac{15 b}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{15 b^{3} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{4 d \,a^{4}}-\frac{15 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{128 d \,a^{2}}+\frac{5 b^{5} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{6}}-\frac{1}{896 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{7}}+\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d a}-\frac{b^{7} \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{8}}+\frac{\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)}{896 d a}-\frac{b^{6}}{2 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{b^{5}}{8 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{b^{2}}{160 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{b^{4}}{24 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{b^{3}}{64 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{2 b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{6} \sqrt{a^{2}-b^{2}}}+\frac{2 b^{8} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{8} \sqrt{a^{2}-b^{2}}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{24 d \,a^{5}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{160 d \,a^{3}}+\frac{6 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \,a^{4} \sqrt{a^{2}-b^{2}}}-\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{64 d \,a^{4}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{96 d \,a^{3}}-\frac{b \left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{384 d \,a^{2}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{8 d \,a^{6}}"," ",0,"1/128/d/a/tan(1/2*d*x+1/2*c)^5+1/384/d/a^2*b/tan(1/2*d*x+1/2*c)^6-5/128/a/d*tan(1/2*d*x+1/2*c)+5/128/a/d/tan(1/2*d*x+1/2*c)-15/128/d/a^2*tan(1/2*d*x+1/2*c)^2*b+11/16/d/a^3*b^2*tan(1/2*d*x+1/2*c)-11/16/d/a^3/tan(1/2*d*x+1/2*c)*b^2+1/24/d/a^5*tan(1/2*d*x+1/2*c)^3*b^4+1/4/d/a^4*tan(1/2*d*x+1/2*c)^2*b^3-9/8/d/a^5*b^4*tan(1/2*d*x+1/2*c)+7/96/d/a^3/tan(1/2*d*x+1/2*c)^3*b^2+9/8/d/a^5/tan(1/2*d*x+1/2*c)*b^4-3/128/d/a^2*b/tan(1/2*d*x+1/2*c)^4-1/4/d*b^3/a^4/tan(1/2*d*x+1/2*c)^2-3/128/d/a/tan(1/2*d*x+1/2*c)^3+5/16/d/a^2*b*ln(tan(1/2*d*x+1/2*c))+15/128/d/a^2*b/tan(1/2*d*x+1/2*c)^2-15/8/d/a^4*b^3*ln(tan(1/2*d*x+1/2*c))-1/128/d/a*tan(1/2*d*x+1/2*c)^5+1/160/d/a^3*tan(1/2*d*x+1/2*c)^5*b^2-1/64/d/a^4*tan(1/2*d*x+1/2*c)^4*b^3+5/2/d/a^6*b^5*ln(tan(1/2*d*x+1/2*c))+3/128/d/a^2*tan(1/2*d*x+1/2*c)^4*b-7/96/d/a^3*tan(1/2*d*x+1/2*c)^3*b^2-1/384/d/a^2*b*tan(1/2*d*x+1/2*c)^6+1/896/d/a*tan(1/2*d*x+1/2*c)^7-1/896/d/a/tan(1/2*d*x+1/2*c)^7+3/128/d/a*tan(1/2*d*x+1/2*c)^3+1/2/d/a^7*b^6*tan(1/2*d*x+1/2*c)-1/8/d/a^6*tan(1/2*d*x+1/2*c)^2*b^5-1/d/a^8*b^7*ln(tan(1/2*d*x+1/2*c))-1/2/d/a^7/tan(1/2*d*x+1/2*c)*b^6+1/8/d/a^6*b^5/tan(1/2*d*x+1/2*c)^2-1/160/d/a^3/tan(1/2*d*x+1/2*c)^5*b^2-1/24/d/a^5/tan(1/2*d*x+1/2*c)^3*b^4+1/64/d/a^4*b^3/tan(1/2*d*x+1/2*c)^4-2/d*b^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^6*b^6/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d/a^8*b^8/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/a^4/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1331,1,1143,449,0.506000," ","int(cos(d*x+c)^6*csc(d*x+c)^9/(a+b*sin(d*x+c)),x)","\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{8 d \,a^{7}}+\frac{3 b^{2}}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{6}}{2 d \,a^{7}}-\frac{b}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}-\frac{9 b^{5}}{8 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{7 b^{3}}{96 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{b^{4}}{4 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{1}{2048 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{8}}-\frac{1}{128 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \sqrt{a^{2}-b^{2}}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 a d}+\frac{b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}-\frac{11 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{16 d \,a^{4}}+\frac{3 b}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}-\frac{15 b^{2}}{128 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{11 b^{3}}{16 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 \left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{128 d \,a^{3}}-\frac{b^{2}}{384 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}-\frac{b^{4}}{64 d \,a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{b^{6}}{8 d \,a^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{3 b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{2}}+\frac{5 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{128 d \,a^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{16 d \,a^{3}}-\frac{5 b}{128 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b^{9} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{9} \sqrt{a^{2}-b^{2}}}-\frac{\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{4 d \,a^{5}}+\frac{15 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{8 d \,a^{5}}-\frac{\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)}{384 d a}+\frac{15 b^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{128 d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{8}}{d \,a^{9}}+\frac{b}{896 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{7}}+\frac{b^{3}}{160 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{5}}+\frac{b^{5}}{24 d \,a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{3}}+\frac{b^{7}}{2 d \,a^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{8}}+\frac{\left(\tan^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{384 d \,a^{3}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{160 d \,a^{4}}+\frac{\left(\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{64 d \,a^{5}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{24 d \,a^{6}}+\frac{9 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{6}}+\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{96 d \,a^{4}}-\frac{1}{256 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{4}}-\frac{6 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{5} \sqrt{a^{2}-b^{2}}}+\frac{\tan^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)}{256 d a}-\frac{b \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{896 d \,a^{2}}+\frac{6 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{7} \sqrt{a^{2}-b^{2}}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{128 a d}+\frac{1}{384 d a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{6}}+\frac{\tan^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)}{2048 d a}"," ",0,"3/128/d/a^3/tan(1/2*d*x+1/2*c)^4*b^2-5/2/d/a^7*ln(tan(1/2*d*x+1/2*c))*b^6-1/128/d/a^2*b/tan(1/2*d*x+1/2*c)^5-9/8/d*b^5/a^6/tan(1/2*d*x+1/2*c)-7/96/d/a^4*b^3/tan(1/2*d*x+1/2*c)^3+1/4/d/a^5/tan(1/2*d*x+1/2*c)^2*b^4+1/128/d/a^2*b*tan(1/2*d*x+1/2*c)^5-3/128/d/a^3*tan(1/2*d*x+1/2*c)^4*b^2-1/4/d/a^5*tan(1/2*d*x+1/2*c)^2*b^4+7/96/d/a^4*tan(1/2*d*x+1/2*c)^3*b^3+1/2048/d/a*tan(1/2*d*x+1/2*c)^8-1/2048/d/a/tan(1/2*d*x+1/2*c)^8+1/128/a/d*tan(1/2*d*x+1/2*c)^2-1/128/a/d/tan(1/2*d*x+1/2*c)^2+2/d/a^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-5/128/a/d*ln(tan(1/2*d*x+1/2*c))-11/16/d/a^4*b^3*tan(1/2*d*x+1/2*c)+3/128/d/a^2*b/tan(1/2*d*x+1/2*c)^3-15/128/d*b^2/a^3/tan(1/2*d*x+1/2*c)^2+11/16/d*b^3/a^4/tan(1/2*d*x+1/2*c)-1/384/d/a^3/tan(1/2*d*x+1/2*c)^6*b^2-1/64/d/a^5/tan(1/2*d*x+1/2*c)^4*b^4-1/8/d/a^7/tan(1/2*d*x+1/2*c)^2*b^6+5/128/d/a^2*tan(1/2*d*x+1/2*c)*b-5/16/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2-5/128/d/a^2*b/tan(1/2*d*x+1/2*c)-2/d/a^9*b^9/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-3/128/d/a^2*b*tan(1/2*d*x+1/2*c)^3+15/128/d/a^3*b^2*tan(1/2*d*x+1/2*c)^2+15/8/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^4+1/d/a^9*ln(tan(1/2*d*x+1/2*c))*b^8+1/896/d/a^2*b/tan(1/2*d*x+1/2*c)^7+1/160/d/a^4*b^3/tan(1/2*d*x+1/2*c)^5+1/24/d/a^6*b^5/tan(1/2*d*x+1/2*c)^3+1/2/d*b^7/a^8/tan(1/2*d*x+1/2*c)-1/896/d/a^2*b*tan(1/2*d*x+1/2*c)^7+1/384/d/a^3*tan(1/2*d*x+1/2*c)^6*b^2-1/160/d/a^4*tan(1/2*d*x+1/2*c)^5*b^3+1/64/d/a^5*tan(1/2*d*x+1/2*c)^4*b^4-1/24/d/a^6*tan(1/2*d*x+1/2*c)^3*b^5+1/8/d/a^7*tan(1/2*d*x+1/2*c)^2*b^6-1/2/d/a^8*b^7*tan(1/2*d*x+1/2*c)+9/8/d/a^6*b^5*tan(1/2*d*x+1/2*c)-1/256/d/a/tan(1/2*d*x+1/2*c)^4-6/d/a^5*b^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d/a^7*b^7/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+1/256/d/a*tan(1/2*d*x+1/2*c)^4-1/384/d/a*tan(1/2*d*x+1/2*c)^6+1/384/d/a/tan(1/2*d*x+1/2*c)^6","B"
1332,1,95,89,0.367000," ","int(sec(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{\sin \left(d x +c \right)}{b d}-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2} \left(a +b \right) \left(a -b \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-sin(d*x+c)/b/d-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)+1/d/b^2*a^3/(a+b)/(a-b)*ln(a+b*sin(d*x+c))-1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1333,1,81,76,0.358000," ","int(sec(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{a^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right) b}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)-1/d*a^2/(a+b)/(a-b)/b*ln(a+b*sin(d*x+c))+1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1334,1,76,70,0.293000," ","int(sec(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{a \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right) \left(a -b \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)+1/d*a/(a+b)/(a-b)*ln(a+b*sin(d*x+c))-1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1335,1,95,89,0.400000," ","int(csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d a \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)+1/d*b^2/a/(a+b)/(a-b)*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d-1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1336,1,113,106,0.416000," ","int(csc(d*x+c)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}-\frac{b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{2} \left(a +b \right) \left(a -b \right)}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}+\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)-1/d*b^3/a^2/(a+b)/(a-b)*ln(a+b*sin(d*x+c))-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d+1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1337,1,144,126,0.480000," ","int(csc(d*x+c)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right)}{d \left(2 a +2 b \right)}+\frac{b^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3} \left(a +b \right) \left(a -b \right)}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right)}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)+1/d*b^4/a^3/(a+b)/(a-b)*ln(a+b*sin(d*x+c))-1/2/d/a/sin(d*x+c)^2+ln(sin(d*x+c))/a/d+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)-1/d/(2*a-2*b)*ln(1+sin(d*x+c))","A"
1338,1,283,253,0.428000," ","int(sec(d*x+c)^2*sin(d*x+c)^5/(a+b*sin(d*x+c)),x)","-\frac{64}{d \left(64 a +64 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 a}{d \,b^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) a^{2}}{d \,b^{3}}-\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{64}{d \left(64 a -64 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) b^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-64/d/(64*a+64*b)/(tan(1/2*d*x+1/2*c)-1)-1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^2*a+1/d/b/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)-2/d/b^2/(1+tan(1/2*d*x+1/2*c)^2)^2*a-2/d/b^3*arctan(tan(1/2*d*x+1/2*c))*a^2-3/d/b*arctan(tan(1/2*d*x+1/2*c))+64/d/(64*a-64*b)/(tan(1/2*d*x+1/2*c)+1)+2/d/(a-b)/(a+b)*a^5/b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1339,1,162,178,0.369000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{32}{d \left(32 a +32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2}{d b \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{32}{d \left(32 a -32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) b^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-32/d/(32*a+32*b)/(tan(1/2*d*x+1/2*c)-1)+2/d/b/(1+tan(1/2*d*x+1/2*c)^2)+2/d/b^2*a*arctan(tan(1/2*d*x+1/2*c))-32/d/(32*a-32*b)/(tan(1/2*d*x+1/2*c)+1)-2/d/(a-b)/(a+b)*a^4/b^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1340,1,138,128,0.405000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{16}{d \left(16 a +16 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d b}+\frac{16}{d \left(16 a -16 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) b \sqrt{a^{2}-b^{2}}}"," ",0,"-16/d/(16*a+16*b)/(tan(1/2*d*x+1/2*c)-1)-2/d/b*arctan(tan(1/2*d*x+1/2*c))+16/d/(16*a-16*b)/(tan(1/2*d*x+1/2*c)+1)+2/d/(a-b)/(a+b)*a^3/b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1341,1,117,91,0.378000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{8}{d \left(8 a +8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{d \left(8 a -8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-8/d/(8*a+8*b)/(tan(1/2*d*x+1/2*c)-1)-8/d/(8*a-8*b)/(tan(1/2*d*x+1/2*c)+1)-2/d*a^2/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1342,1,116,77,0.303000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{4}{d \left(4 a +4 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{4}{d \left(4 a -4 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-4/d/(4*a+4*b)/(tan(1/2*d*x+1/2*c)-1)+4/d/(4*a-4*b)/(tan(1/2*d*x+1/2*c)+1)+2/d*a*b/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1343,1,130,113,0.439000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{1}{d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right) \left(a +b \right) a \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)+2/d*b^3/(a-b)/(a+b)/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1344,1,169,123,0.440000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{1}{d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)+1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-1/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)-2/d/a^2*b^4/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1345,1,227,170,0.501000," ","int(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{1}{d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)+1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/8/a/d/tan(1/2*d*x+1/2*c)^2+3/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d/a^2*b/tan(1/2*d*x+1/2*c)+1/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)+2/d/a^3*b^5/(a-b)/(a+b)/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1346,1,164,120,0.407000," ","int(sec(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{2}}-\frac{a^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}-\frac{b \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)+1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*a+1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*b-1/d*a^3/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))+1/d/(4*a-4*b)/(1+sin(d*x+c))+1/2*a*ln(1+sin(d*x+c))/(a-b)^2/d-1/4*b*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1347,1,123,110,0.435000," ","int(sec(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{2}}+\frac{a^{2} b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}-\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)+1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*a+1/d*a^2/(a+b)^2*b/(a-b)^2*ln(a+b*sin(d*x+c))-1/d/(4*a-4*b)/(1+sin(d*x+c))-1/4*a*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1348,1,123,111,0.355000," ","int(sec(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{2}}-\frac{a \,b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{b \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*b-1/d*a*b^2/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))+1/d/(4*a-4*b)/(1+sin(d*x+c))+1/4*b*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1349,1,181,148,0.494000," ","int(csc(d*x+c)*sec(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{2 d \left(a +b \right)^{2}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{2}}-\frac{b^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d a \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}-\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{2 \left(a -b \right)^{2} d}+\frac{3 b \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*a-3/4/d/(a+b)^2*ln(sin(d*x+c)-1)*b-1/d/a*b^4/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d+1/d/(4*a-4*b)/(1+sin(d*x+c))-1/2*a*ln(1+sin(d*x+c))/(a-b)^2/d+3/4*b*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1350,1,199,163,0.494000," ","int(csc(d*x+c)^2*sec(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a}{4 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b}{d \left(a +b \right)^{2}}+\frac{b^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{2} \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{3 a \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}-\frac{b \ln \left(1+\sin \left(d x +c \right)\right)}{\left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-3/4/d/(a+b)^2*ln(sin(d*x+c)-1)*a-1/d/(a+b)^2*ln(sin(d*x+c)-1)*b+1/d*b^5/a^2/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d-1/d/(4*a-4*b)/(1+sin(d*x+c))+3/4*a*ln(1+sin(d*x+c))/(a-b)^2/d-b*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1351,1,231,187,0.541000," ","int(csc(d*x+c)^3*sec(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{1}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a}{d \left(a +b \right)^{2}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) b}{4 d \left(a +b \right)^{2}}-\frac{b^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3} \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}+\frac{2 \ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}+\frac{1}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}-\frac{a \ln \left(1+\sin \left(d x +c \right)\right)}{\left(a -b \right)^{2} d}+\frac{5 b \ln \left(1+\sin \left(d x +c \right)\right)}{4 \left(a -b \right)^{2} d}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)-1/d/(a+b)^2*ln(sin(d*x+c)-1)*a-5/4/d/(a+b)^2*ln(sin(d*x+c)-1)*b-1/d/a^3*b^6/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))-1/2/d/a/sin(d*x+c)^2+2*ln(sin(d*x+c))/a/d+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)+1/d/(4*a-4*b)/(1+sin(d*x+c))-a*ln(1+sin(d*x+c))/(a-b)^2/d+5/4*b*ln(1+sin(d*x+c))/(a-b)^2/d","A"
1352,1,269,168,0.392000," ","int(sec(d*x+c)^4*sin(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{32}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(32 a +32 b \right)}-\frac{16}{d \left(32 a +32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{32}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(32 a -32 b \right)}+\frac{16}{d \left(32 a -32 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{a}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-32/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(32*a+32*b)-16/d/(32*a+32*b)/(tan(1/2*d*x+1/2*c)-1)^2+1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a+1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-32/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(32*a-32*b)+16/d/(32*a-32*b)/(tan(1/2*d*x+1/2*c)+1)^2+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b+2/d*a^4/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1353,1,222,133,0.418000," ","int(sec(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","-\frac{16}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(16 a +16 b \right)}-\frac{8}{d \left(16 a +16 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{a}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{d \left(16 a -16 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{16}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(16 a -16 b \right)}-\frac{a}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a^{3} b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-16/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(16*a+16*b)-8/d/(16*a+16*b)/(tan(1/2*d*x+1/2*c)-1)^2+1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-8/d/(16*a-16*b)/(tan(1/2*d*x+1/2*c)+1)^2+16/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(16*a-16*b)-1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-2/d*a^3*b/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1354,1,224,156,0.413000," ","int(sec(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","-\frac{8}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(8 a +8 b \right)}-\frac{4}{d \left(8 a +8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{8}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(8 a -8 b \right)}+\frac{4}{d \left(8 a -8 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{2} b^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-8/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(8*a+8*b)-4/d/(8*a+8*b)/(tan(1/2*d*x+1/2*c)-1)^2-1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-8/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(8*a-8*b)+4/d/(8*a-8*b)/(tan(1/2*d*x+1/2*c)+1)^2+1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b+2/d*a^2*b^2/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1355,1,272,129,0.353000," ","int(sec(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x)","-\frac{4}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3} \left(4 a +4 b \right)}-\frac{2}{d \left(4 a +4 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{a}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{b}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2}{d \left(4 a -4 b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{4}{3 d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3} \left(4 a -4 b \right)}+\frac{a}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{b}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a \,b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-4/3/d/(tan(1/2*d*x+1/2*c)-1)^3/(4*a+4*b)-2/d/(4*a+4*b)/(tan(1/2*d*x+1/2*c)-1)^2-1/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-2/d/(4*a-4*b)/(tan(1/2*d*x+1/2*c)+1)^2+4/3/d/(tan(1/2*d*x+1/2*c)+1)^3/(4*a-4*b)+1/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b-2/d*a*b^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1356,1,279,183,0.489000," ","int(csc(d*x+c)*sec(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{1}{3 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 a}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 b}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{1}{2 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{1}{3 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{3 a}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} a \sqrt{a^{2}-b^{2}}}"," ",0,"-1/3/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^2-3/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b+1/a/d*ln(tan(1/2*d*x+1/2*c))-1/2/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^2+1/3/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^3+3/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b-2/d*b^5/(a-b)^2/(a+b)^2/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1357,1,317,209,0.484000," ","int(csc(d*x+c)^2*sec(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{2 a}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{5 b}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 a d}-\frac{1}{2 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}-\frac{2 a}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 b}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{1}{3 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}+\frac{1}{2 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{2 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-5/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-1/3/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^2+1/2/a/d*tan(1/2*d*x+1/2*c)-1/2/a/d/tan(1/2*d*x+1/2*c)-1/d/a^2*b*ln(tan(1/2*d*x+1/2*c))-2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a+5/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b-1/3/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^3+1/2/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^2+2/d/a^2*b^6/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1358,1,376,311,0.552000," ","int(csc(d*x+c)^3*sec(d*x+c)^4/(a+b*sin(d*x+c)),x)","-\frac{5 a}{2 d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 b}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{3 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{1}{2 d \left(a +b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{2}}-\frac{1}{8 a d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{3}}+\frac{b}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{5 a}{2 d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 b}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{1}{3 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{1}{2 d \left(a -b \right) \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{2 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-5/2/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*a-3/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)*b-1/3/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^3-1/2/d/(a+b)/(tan(1/2*d*x+1/2*c)-1)^2+1/8/a/d*tan(1/2*d*x+1/2*c)^2-1/2/d/a^2*tan(1/2*d*x+1/2*c)*b-1/8/a/d/tan(1/2*d*x+1/2*c)^2+5/2/a/d*ln(tan(1/2*d*x+1/2*c))+1/d/a^3*ln(tan(1/2*d*x+1/2*c))*b^2+1/2/d/a^2*b/tan(1/2*d*x+1/2*c)+5/2/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*a-3/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)*b+1/3/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^3-1/2/d/(a-b)/(tan(1/2*d*x+1/2*c)+1)^2-2/d/a^3*b^7/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1359,1,338,230,0.487000," ","int(sec(d*x+c)^5*sin(d*x+c)^8/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{13 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{11 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{35 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}-\frac{57 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{2 d \left(a +b \right)^{3}}-\frac{\sin^{2}\left(d x +c \right)}{2 b d}+\frac{a \sin \left(d x +c \right)}{b^{2} d}-\frac{a^{8} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{3} \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{13 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{11 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{35 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{57 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+13/16/d/(a+b)^2/(sin(d*x+c)-1)*a+11/16/d/(a+b)^2/(sin(d*x+c)-1)*b-35/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-57/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-3/2/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2-1/2*sin(d*x+c)^2/b/d+a*sin(d*x+c)/b^2/d-1/d/b^3*a^8/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+13/16/d/(a-b)^2/(1+sin(d*x+c))*a-11/16/d/(a-b)^2/(1+sin(d*x+c))*b+35/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-57/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+3/2/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1360,1,321,213,0.487000," ","int(sec(d*x+c)^5*sin(d*x+c)^7/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{11 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{9 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{3}}-\frac{37 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}-\frac{\sin \left(d x +c \right)}{b d}+\frac{a^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,b^{2} \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{11 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{9 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}+\frac{37 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+11/16/d/(a+b)^2/(sin(d*x+c)-1)*a+9/16/d/(a+b)^2/(sin(d*x+c)-1)*b-3/2/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-37/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-15/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2-sin(d*x+c)/b/d+1/d/b^2*a^7/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-11/16/d/(a-b)^2/(1+sin(d*x+c))*a+9/16/d/(a-b)^2/(1+sin(d*x+c))*b-3/2/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+37/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-15/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1361,1,308,200,0.484000," ","int(sec(d*x+c)^5*sin(d*x+c)^6/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{9 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{7 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}-\frac{21 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{2 d \left(a +b \right)^{3}}-\frac{a^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3} b}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{9 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{7 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{21 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+9/16/d/(a+b)^2/(sin(d*x+c)-1)*a+7/16/d/(a+b)^2/(sin(d*x+c)-1)*b-15/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-21/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2-1/d*a^6/(a+b)^3/(a-b)^3/b*ln(a+b*sin(d*x+c))-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+9/16/d/(a-b)^2/(1+sin(d*x+c))*a-7/16/d/(a-b)^2/(1+sin(d*x+c))*b+15/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-21/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+1/2/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1362,1,304,196,0.451000," ","int(sec(d*x+c)^5*sin(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{7 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{5 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{3}}-\frac{9 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{a^{5} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{7 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{5 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}+\frac{9 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+7/16/d/(a+b)^2/(sin(d*x+c)-1)*a+5/16/d/(a+b)^2/(sin(d*x+c)-1)*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-9/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d*a^5/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-7/16/d/(a-b)^2/(1+sin(d*x+c))*a+5/16/d/(a-b)^2/(1+sin(d*x+c))*b-1/2/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+9/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-3/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1363,1,260,182,0.398000," ","int(sec(d*x+c)^5*sin(d*x+c)^4/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{5 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{3 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{a^{4} b \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+5/16/d/(a+b)^2/(sin(d*x+c)-1)*a+3/16/d/(a+b)^2/(sin(d*x+c)-1)*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-1/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-1/d*a^4*b/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+5/16/d/(a-b)^2/(1+sin(d*x+c))*a-3/16/d/(a-b)^2/(1+sin(d*x+c))*b+3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-1/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b","A"
1364,1,261,174,0.415000," ","int(sec(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{a^{3} b^{2} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+3/16/d/(a+b)^2/(sin(d*x+c)-1)*a+1/16/d/(a+b)^2/(sin(d*x+c)-1)*b+3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b+1/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d*a^3/(a+b)^3*b^2/(a-b)^3*ln(a+b*sin(d*x+c))+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-3/16/d/(a-b)^2/(1+sin(d*x+c))*a+1/16/d/(a-b)^2/(1+sin(d*x+c))*b-3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+1/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1365,1,262,170,0.409000," ","int(sec(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}+\frac{\ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}+\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{a^{2} b^{3} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2+1/16/d/(a+b)^2/(sin(d*x+c)-1)*a-1/16/d/(a+b)^2/(sin(d*x+c)-1)*b+1/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2+3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-1/d*a^2*b^3/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+1/16/d/(a-b)^2/(1+sin(d*x+c))*a+1/16/d/(a-b)^2/(1+sin(d*x+c))*b-1/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b","A"
1366,1,259,169,0.350000," ","int(sec(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{a \,b^{4} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2-1/16/d/(a+b)^2/(sin(d*x+c)-1)*a-3/16/d/(a+b)^2/(sin(d*x+c)-1)*b-1/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d*a*b^4/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+1/16/d/(a-b)^2/(1+sin(d*x+c))*a-3/16/d/(a-b)^2/(1+sin(d*x+c))*b+1/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-3/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1367,1,321,221,0.454000," ","int(csc(d*x+c)*sec(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{7 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{3}}-\frac{21 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{b^{6} \ln \left(a +b \sin \left(d x +c \right)\right)}{d a \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{\ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{5 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{7 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}+\frac{21 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2-5/16/d/(a+b)^2/(sin(d*x+c)-1)*a-7/16/d/(a+b)^2/(sin(d*x+c)-1)*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-21/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-15/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d/a*b^6/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))+ln(sin(d*x+c))/a/d+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+5/16/d/(a-b)^2/(1+sin(d*x+c))*a-7/16/d/(a-b)^2/(1+sin(d*x+c))*b-1/2/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+21/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-15/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1368,1,340,238,0.475000," ","int(csc(d*x+c)^2*sec(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{7 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{9 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{16 d \left(a +b \right)^{3}}-\frac{37 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{2 d \left(a +b \right)^{3}}-\frac{b^{7} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{2} \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{d a \sin \left(d x +c \right)}-\frac{b \ln \left(\sin \left(d x +c \right)\right)}{a^{2} d}-\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{7 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{9 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{16 d \left(a -b \right)^{3}}-\frac{37 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{2 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2-7/16/d/(a+b)^2/(sin(d*x+c)-1)*a-9/16/d/(a+b)^2/(sin(d*x+c)-1)*b-15/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-37/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-3/2/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2-1/d*b^7/a^2/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/d/a/sin(d*x+c)-b*ln(sin(d*x+c))/a^2/d-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2-7/16/d/(a-b)^2/(1+sin(d*x+c))*a+9/16/d/(a-b)^2/(1+sin(d*x+c))*b+15/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2-37/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b+3/2/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1369,1,371,260,0.551000," ","int(csc(d*x+c)^3*sec(d*x+c)^5/(a+b*sin(d*x+c)),x)","\frac{1}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{9 a}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{11 b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2}}{2 d \left(a +b \right)^{3}}-\frac{57 \ln \left(\sin \left(d x +c \right)-1\right) a b}{16 d \left(a +b \right)^{3}}-\frac{35 \ln \left(\sin \left(d x +c \right)-1\right) b^{2}}{16 d \left(a +b \right)^{3}}+\frac{b^{8} \ln \left(a +b \sin \left(d x +c \right)\right)}{d \,a^{3} \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{1}{2 d a \sin \left(d x +c \right)^{2}}+\frac{3 \ln \left(\sin \left(d x +c \right)\right)}{a d}+\frac{b^{2} \ln \left(\sin \left(d x +c \right)\right)}{a^{3} d}+\frac{b}{d \,a^{2} \sin \left(d x +c \right)}+\frac{1}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{9 a}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{11 b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2}}{2 d \left(a -b \right)^{3}}+\frac{57 \ln \left(1+\sin \left(d x +c \right)\right) a b}{16 d \left(a -b \right)^{3}}-\frac{35 \ln \left(1+\sin \left(d x +c \right)\right) b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2-9/16/d/(a+b)^2/(sin(d*x+c)-1)*a-11/16/d/(a+b)^2/(sin(d*x+c)-1)*b-3/2/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2-57/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a*b-35/16/d/(a+b)^3*ln(sin(d*x+c)-1)*b^2+1/d/a^3*b^8/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))-1/2/d/a/sin(d*x+c)^2+3*ln(sin(d*x+c))/a/d+b^2*ln(sin(d*x+c))/a^3/d+1/d/a^2*b/sin(d*x+c)+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2+9/16/d/(a-b)^2/(1+sin(d*x+c))*a-11/16/d/(a-b)^2/(1+sin(d*x+c))*b-3/2/d/(a-b)^3*ln(1+sin(d*x+c))*a^2+57/16/d/(a-b)^3*ln(1+sin(d*x+c))*a*b-35/16/d/(a-b)^3*ln(1+sin(d*x+c))*b^2","A"
1370,1,1674,534,6.597000," ","int(sin(f*x+e)^4*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{16 \left(\cos^{6}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{7 f b}-\frac{24 \left(\cos^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{7 f b}+\frac{8 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{21 f b}+\frac{8 \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{21 f b}-\frac{4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}\, a^{2}}{3 f \,b^{3}}-\frac{4 \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}\, a^{2}}{3 f \,b^{3}}+\frac{2 a^{2} \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f \,b^{3}}+\frac{g \,a^{4} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{2 f \,b^{3}}+\frac{16 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a g \left(\sin^{5}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{5 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{16 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a g \left(\sin^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{5 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a g \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{5 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} g \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,b^{4} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a g \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{5 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} g \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \sqrt{2}\, \left(-16 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{4} b^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-9 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-7 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+3 b^{2}\right)}{2 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \left(4 a^{2}-3 b^{2}\right)}\right) \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}{8 f \,b^{6} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"16/7/f/b*cos(1/2*f*x+1/2*e)^6*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-24/7/f/b*cos(1/2*f*x+1/2*e)^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+8/21/f/b*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+8/21/f/b*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-4/3/f/b^3*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)*a^2-4/3/f/b^3*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)*a^2+2/f/b^3*a^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f*g/b^3*a^4*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+16/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)^5/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)-16/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+4/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3*g/b^4/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-4/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3*g/b^6/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)","C"
1371,1,2363,490,7.479000," ","int(sin(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"4/3/f*a/b^2*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+4/3/f*a/b^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-2/f*a/b^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-1/2/f*g*a^3/b^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5-16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*a^2+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*a^2-4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)-1/4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b^5/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((2*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2-sin(1/2*f*x+1/2*e)^2*a^2-2*b^2*_alpha^2+a^2)/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1372,1,924,395,6.204000," ","int(sin(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","-\frac{4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{3 f b}-\frac{4 \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{3 f b}+\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f b}+\frac{g \,a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{2 f b}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, g a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, g a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right)}{8 f \,b^{4} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"-4/3/f/b*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-4/3/f/b*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+2/f/b*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f*g/b*a^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g*a/b^4/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1373,1,884,371,6.866000," ","int(sin(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","-\frac{g a \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{2 f}-\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, g \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f b \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, g \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f b \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, g \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}+2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-a^{2}\right) \left(\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{4 f \,b^{3} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"-1/2/f*g*a*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+1/4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g/b^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((-2*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+sin(1/2*f*x+1/2*e)^2*a^2+2*b^2*_alpha^2-a^2)/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1374,1,188,351,2.938000," ","int(csc(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","-\frac{\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{2 a f}-\frac{\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{2 a f}-\frac{g \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{a \sqrt{-g}\, f}"," ",0,"-1/2/a/f*g^(1/2)*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))-1/2/a/f*g^(1/2)*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))-1/a/(-g)^(1/2)/f*g*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))","A"
1375,1,1266,449,13.133000," ","int(csc(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{4 \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} b \left(\left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right) \left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right)}{\textit{\_R} \left(\textit{\_R}^{6} b^{2}-3 \textit{\_R}^{4} b^{2} g +8 \textit{\_R}^{2} a^{2} g^{2}-5 \textit{\_R}^{2} b^{2} g^{2}-b^{2} g^{3}\right)}\right) \sqrt{-g}\, b^{2} g +\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}+\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}+2 g \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)\right)+\left(-8 \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) a g -\frac{\sqrt{-g}\, g^{3} \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \sqrt{2}\, \left(-16 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{4} b^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-9 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-7 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+3 b^{2}\right)}{2 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \left(4 a^{2}-3 b^{2}\right)}\right) \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}\right)}{a}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-16 \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} a g \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+16 \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} a g \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-4 \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} a g}{8 a^{2} \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, f}"," ",0,"1/8*(4*cos(1/2*f*x+1/2*e)*sin(1/2*f*x+1/2*e)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*b*(sum(1/_R/(_R^6*b^2-3*_R^4*b^2*g+8*_R^2*a^2*g^2-5*_R^2*b^2*g^2-b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R)*(_R^6-_R^4*g-_R^2*g^2+g^3),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))*(-g)^(1/2)*b^2*g+g^(1/2)*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)+g^(1/2)*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)+2*g*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g)))+(-8*(-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*a*g-(-g)^(1/2)*g^3*sin(1/2*f*x+1/2*e)^4*(2*sin(1/2*f*x+1/2*e)^2-1)^2/a*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2)))*cos(1/2*f*x+1/2*e)-16*(-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*a*g*sin(1/2*f*x+1/2*e)^4+16*(-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*a*g*sin(1/2*f*x+1/2*e)^2-4*(-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*a*g)/a^2/(-g)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)/f","C"
1376,1,307,540,3.251000," ","int(csc(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{8 f a}+\frac{\sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{8 f a \cos \left(\frac{f x}{2}+\frac{e}{2}\right)^{2}}-\frac{g \ln \left(\frac{-2 g +2 \sqrt{-g}\, \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{4 f a \sqrt{-g}}-\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}-\frac{\sqrt{g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{8 a f}"," ",0,"1/16/f/a/(-1+cos(1/2*f*x+1/2*e))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/8/f*g^(1/2)/a*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))+1/8/f/a/cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-1/4/f*g/a/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))-1/16/f/a/(cos(1/2*f*x+1/2*e)+1)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/8/f*g^(1/2)/a*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))","A"
1377,1,3600,673,10.475000," ","int((g*cos(f*x+e))^(3/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"8/5/f*g*a/b^2*cos(1/2*f*x+1/2*e)^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-8/5/f*g*a/b^2*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-8/5/f*g*a/b^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-2/f*g*a^3/b^4*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*g*a/b^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*g^3*a^5/b^4*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-2/f*g^3*a^3/b^2*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-32/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)^7/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+272/15/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)^5/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-16/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*a^2+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*a^2-12/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+64/15/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*a^2-4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*a^2+12/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^5*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^4*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^5/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^4*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1378,1,1778,554,8.438000," ","int((g*cos(f*x+e))^(3/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x)","-\frac{8 g \left(\cos^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b}+\frac{8 g \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b}+\frac{8 g \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b}+\frac{2 g \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, a^{2}}{f \,b^{3}}-\frac{2 g \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f b}-\frac{2 g^{3} a^{4} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f \,b^{3}}+\frac{2 g^{3} a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f b}+\frac{8 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \,g^{2} \left(\sin^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{3 f \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}-\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{3 f \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} g^{2} \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}{f \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}+\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \,g^{2} \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}{3 f \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{5} g^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 f \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{6}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} g^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 f \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{4}}"," ",0,"-8/5/f*g/b*cos(1/2*f*x+1/2*e)^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+8/5/f*g/b*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+8/5/f*g/b*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+2/f*g/b^3*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2-2/f*g/b*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-2/f*g^3/b^3*a^4*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+2/f*g^3/b*a^2*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g^2*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^4/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^5*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^6*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^4*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1379,1,2432,450,7.276000," ","int((g*cos(f*x+e))^(3/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-2/f*g*a/b^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*g^3*a^3/b^2*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-2/f*g^3*a*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/b/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1380,1,216,457,2.939000," ","int((g*cos(f*x+e))^(3/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x)","-\frac{g^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{2 a f}-\frac{g^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{2 a f}+\frac{2 g \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{a f}+\frac{g^{2} \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{a \sqrt{-g}\, f}"," ",0,"-1/2/a/f*g^(3/2)*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))-1/2/a/f*g^(3/2)*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))+2/a/f*g*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/a/(-g)^(1/2)/f*g^2*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))","A"
1381,1,2324,485,13.642000," ","int((g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"1/2/f*g^(3/2)*b/a^2*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))-2/f*g^3*b*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+2/f*g^3*b^3/a^2*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/f*g^2*b/a^2/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))+1/2/f*g^(3/2)*b/a^2*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))-1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g^2*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a*g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)","C"
1382,1,312,570,3.247000," ","int((g*cos(f*x+e))^(3/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x)","\frac{g^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{8 a f}+\frac{g \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}-\frac{g^{2} \ln \left(\frac{-2 g +2 \sqrt{-g}\, \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{4 f a \sqrt{-g}}+\frac{g^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{8 f a}-\frac{g \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{8 f a \cos \left(\frac{f x}{2}+\frac{e}{2}\right)^{2}}-\frac{g \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"1/8/f*g^(3/2)/a*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))+1/16/f*g/a/(-1+cos(1/2*f*x+1/2*e))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/4/f*g^2/a/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))+1/8/f*g^(3/2)/a*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))-1/8/f*g/a/cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-1/16/f*g/a/(cos(1/2*f*x+1/2*e)+1)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)","A"
1383,1,4548,660,8.449000," ","int((g*cos(f*x+e))^(5/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"20/21/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)+12/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)-20/21/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)-12/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)+1216/105/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5-1216/105/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5-40/7/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+40/7/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+152/105/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)-152/105/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+64/7/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^9-64/7/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^9-576/35/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^7+576/35/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^7-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3*a^2-8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)*a^2+8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)*a^2-16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5*a^2+16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5*a^2+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3*a^2+1/4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^7/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((sin(1/2*f*x+1/2*e)^2*(2*_alpha^2*a^2*b^2-2*_alpha^2*b^4-a^4+a^2*b^2)-2*_alpha^2*a^2*b^2+2*_alpha^2*b^4+a^4-a^2*b^2)/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2+16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2-16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2-4/3/f*g^2*a^3/b^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+2/f*g^2*a^3/b^4*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-2/f*g^2*a/b^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-1/2/f*g^3*a^3/b^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/2/f*g^3*a^5/b^4*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+12/7/f*g^2*a/b^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+16/7/f*g^2*a/b^2*cos(1/2*f*x+1/2*e)^6*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-24/7/f*g^2*a/b^2*cos(1/2*f*x+1/2*e)^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+12/7/f*g^2*a/b^2*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-4/3/f*g^2*a^3/b^4*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^5/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^4-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^5/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^4","C"
1384,1,1937,539,6.956000," ","int((g*cos(f*x+e))^(5/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-16/7/f*g^2/b*cos(1/2*f*x+1/2*e)^6*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+24/7/f*g^2/b*cos(1/2*f*x+1/2*e)^4*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-12/7/f*g^2/b*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-12/7/f*g^2/b*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+4/3/f*g^2/b^3*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)*a^2+4/3/f*g^2/b^3*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)*a^2-2/f*g^2/b^3*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2+2/f*g^2/b*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-1/2/f*g^3/b^3*a^4*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/2/f*g^3/b*a^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+16/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^7-32/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a^3/b^4/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-6/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-4/5/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3*a/b^6/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((a^2-b^2)/_alpha*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1385,1,2612,437,7.894000," ","int((g*cos(f*x+e))^(5/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-4/3/f*g^2*a/b^2*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-4/3/f*g^2*a/b^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+2/f*g^2*a/b^2*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f*g^3*a^3/b^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/2/f*g^3*a*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5+16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^5+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2-16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3-8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*a^2+16/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)+8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+1/4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/b^5/a^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((sin(1/2*f*x+1/2*e)^2*(2*_alpha^2*a^2*b^2-2*_alpha^2*b^4-a^4+a^2*b^2)-2*_alpha^2*a^2*b^2+2*_alpha^2*b^4+a^4-a^2*b^2)/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1386,1,259,443,3.168000," ","int((g*cos(f*x+e))^(5/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x)","-\frac{g^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{2 a f}-\frac{g^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{2 a f}-\frac{4 \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, g^{2} \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{3 a f}+\frac{2 g^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{3 a f}-\frac{g^{3} \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{a \sqrt{-g}\, f}"," ",0,"-1/2/a/f*g^(5/2)*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))-1/2/a/f*g^(5/2)*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))-4/3/a/f*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)*g^2*sin(1/2*f*x+1/2*e)^2+2/3/a/f*g^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/a/(-g)^(1/2)/f*g^3*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))","A"
1387,1,1987,478,14.199000," ","int((g*cos(f*x+e))^(5/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"1/2/f*g^(5/2)*b/a^2*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))-1/2/f*g^3*b*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/2/f*g^3*b^3/a^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/f*g^3*b/a^2/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))+1/2/f*g^(5/2)*b/a^2*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))-1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/a/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/a/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/a/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^2/a/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/a/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2*sum((-a^2+b^2)/_alpha*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/a*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/a/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/a/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*g^3/a*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)","C"
1388,1,318,553,3.071000," ","int((g*cos(f*x+e))^(5/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x)","\frac{3 g^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{8 f a}+\frac{g^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{3 g^{3} \ln \left(\frac{-2 g +2 \sqrt{-g}\, \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{4 f a \sqrt{-g}}+\frac{3 g^{\frac{5}{2}} \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{8 a f}+\frac{g^{2} \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{8 f a \cos \left(\frac{f x}{2}+\frac{e}{2}\right)^{2}}-\frac{g^{2} \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"3/8/f*g^(5/2)/a*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))+1/16/f*g^2/a/(-1+cos(1/2*f*x+1/2*e))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+3/4/f*g^3/a/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))+3/8/f*g^(5/2)/a*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))+1/8/f*g^2/a/cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-1/16/f*g^2/a/(cos(1/2*f*x+1/2*e)+1)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)","A"
1389,1,1455,547,6.867000," ","int(sin(f*x+e)^4/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\frac{8 \left(\cos^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b g}-\frac{8 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b g}-\frac{8 \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{5 f b g}-\frac{2 a^{2} \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f \,b^{3} g}+\frac{2 a^{4} g \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f \,b^{3}}-\frac{8 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \left(\sin^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{3 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{3 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}{f \,b^{4} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}{3 f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \sqrt{2}\, \left(-16 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{4} b^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-9 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-7 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+3 b^{2}\right)}{2 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \left(4 a^{2}-3 b^{2}\right)}\right) \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}{8 f \,b^{6} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"8/5/f/b*cos(1/2*f*x+1/2*e)^4/g*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-8/5/f/b*cos(1/2*f*x+1/2*e)^2/g*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-8/5/f/b/g*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-2/f/b^3*a^2/g*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*a^4/b^3*g*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-8/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3/b^4/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3/b^6/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha/(2*_alpha^2-1)*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)","C"
1390,1,2015,501,7.313000," ","int(sin(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"2/f*a/b^2/g*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-2/f*a^3/b^2*g*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/(2*_alpha^2-1)*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*_alpha^4*b^2-8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*_alpha^2*b^2+2^(1/2)*a^2*_alpha*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b^3/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/(2*_alpha^2-1)*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*_alpha^4*b^2-8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*_alpha^2*b^2+2^(1/2)*a^2*_alpha*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)","C"
1391,1,855,408,6.547000," ","int(sin(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f b g}+\frac{2 a^{2} g \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f b}+\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right)}{8 f \,b^{4} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"-2/f/b/g*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*a^2/b*g*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/b^2/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/b^4/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1392,1,1181,382,6.053000," ","int(sin(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","-\frac{2 a g \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(8 \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right)}{2 f b \,a^{2} \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\underline{\hspace{1.25 ex}}\alpha  \left(8 \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\right)}{\left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right)}{2 f b \,a^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"-2/f*a*g*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b*sum(_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))/a^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b*sum(_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))/a^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)","C"
1393,1,186,365,3.056000," ","int(csc(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\frac{\ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{a \sqrt{-g}\, f}-\frac{\ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{2 a \sqrt{g}\, f}-\frac{\ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{2 a \sqrt{g}\, f}"," ",0,"1/a/(-g)^(1/2)/f*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))-1/2/a/g^(1/2)/f*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))-1/2/a/g^(1/2)/f*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))","A"
1394,1,1217,464,13.885000," ","int(csc(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\frac{-4 \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} g^{\frac{3}{2}} \sqrt{-g}\, a +8 \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} g^{\frac{3}{2}} \sqrt{-g}\, a \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+\left(-8 g^{\frac{3}{2}} \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right) \sqrt{-g}\, a -\frac{g^{\frac{7}{2}} \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \frac{-4 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+4 b^{2}}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \sqrt{2}\, \left(-16 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{4} b^{2}+12 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-9 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) b^{2}+4 \underline{\hspace{1.25 ex}}\alpha^{2} a^{2}-7 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+3 b^{2}\right)}{2 \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \left(4 a^{2}-3 b^{2}\right)}\right) \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right)}}\right) \sqrt{-g}}{a}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right)+4 \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} b \left(4 \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\textit{\_R} \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right) \left(\textit{\_R}^{2}+g \right)}{\textit{\_R}^{6} b^{2}-3 \textit{\_R}^{4} b^{2} g +8 \textit{\_R}^{2} a^{2} g^{2}-5 \textit{\_R}^{2} b^{2} g^{2}-b^{2} g^{3}}\right) g^{\frac{5}{2}} \sqrt{-g}\, b^{2}-2 g^{\frac{3}{2}} \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)+\ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g +\sqrt{-g}\, \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) g \right)}{8 a^{2} g^{\frac{3}{2}} \sqrt{-g}\, \left(-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \right)^{\frac{3}{2}} \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, f}"," ",0,"1/8*(-4*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*g^(3/2)*(-g)^(1/2)*a+8*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*g^(3/2)*(-g)^(1/2)*a*sin(1/2*f*x+1/2*e)^2+(-8*g^(3/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(-g)^(1/2)*a-g^(7/2)*sin(1/2*f*x+1/2*e)^4*(2*sin(1/2*f*x+1/2*e)^2-1)^2/a*sum(1/_alpha/(2*_alpha^2-1)*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(-g)^(1/2))*cos(1/2*f*x+1/2*e)+4*cos(1/2*f*x+1/2*e)*sin(1/2*f*x+1/2*e)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*b*(4*sum(1/(_R^6*b^2-3*_R^4*b^2*g+8*_R^2*a^2*g^2-5*_R^2*b^2*g^2-b^2*g^3)*_R*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R)*(_R^2+g),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))*g^(5/2)*(-g)^(1/2)*b^2-2*g^(3/2)*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))+ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g+(-g)^(1/2)*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*g))/a^2/g^(3/2)/(-g)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)/f","C"
1395,1,315,553,3.456000," ","int(csc(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","-\frac{3 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{8 a \sqrt{g}\, f}+\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a g \left(-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)\right)}+\frac{3 \ln \left(\frac{-2 g +2 \sqrt{-g}\, \sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right)}{4 f a \sqrt{-g}}-\frac{3 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right)}{8 a \sqrt{g}\, f}-\frac{\sqrt{2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g -g}}{8 f a g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)^{2}}-\frac{\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{16 f a g \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1\right)}"," ",0,"-3/8/f/a/g^(1/2)*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))+1/16/f/a/g/(-1+cos(1/2*f*x+1/2*e))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+3/4/f/a/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))-3/8/f/a/g^(1/2)*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))-1/8/f/a/g/cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-1/16/f/a/g/(cos(1/2*f*x+1/2*e)+1)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)","A"
1396,1,1990,624,8.634000," ","int(sin(f*x+e)^4/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"4/3/f/g^2/b*cos(1/2*f*x+1/2*e)^2*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)+4/3/f/g^2/b*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2)-2/f/g^2/b*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f/g^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/2/f/g/b*a^4/(a-b)/(a+b)*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/2/f/g^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2/f/g*a^3/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/b^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-4/f/g*a/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-1/4/f*a^3/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/b^4*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+4/f/g*a/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+1/8/f*a^3/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/b^4*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1397,1,1613,557,11.944000," ","int(sin(f*x+e)^3/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","-\frac{a \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{2 f \,g^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)}+\frac{a^{3} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{2 f g \left(a -b \right) \left(a +b \right)}+\frac{a \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{2 f \,g^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f b g \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}-\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f b g \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}-\frac{8 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, b \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}}{f \,g^{2} \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}+\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, b \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}+\frac{8 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, b \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}-\frac{4 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, b \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right)^{3} \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1}}-\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{2} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\left(-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) \underline{\hspace{1.25 ex}}\alpha^{2} b^{2}+\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}+2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-a^{2}\right) \left(\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right)}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{4 f \,b^{3} g \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a -b \right) \left(a +b \right)}"," ",0,"-1/2/f/g^2*a/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/2/f/g*a^3/(a-b)/(a+b)*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/2/f/g^2*a/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/g*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/g/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*cos(1/2*f*x+1/2*e)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-1/4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b^3/g/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2/(a-b)/(a+b)*sum((-2*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+sin(1/2*f*x+1/2*e)^2*a^2+2*b^2*_alpha^2-a^2)/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))","C"
1398,1,1105,479,8.012000," ","int(sin(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{2 f \,g^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)}-\frac{b \,a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{6}-\textit{\_R}^{4} g -\textit{\_R}^{2} g^{2}+g^{3}\right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{2 f g \left(a -b \right) \left(a +b \right)}-\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{2 f \,g^{2} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)}-\frac{4 a \left(\cos^{3}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}{f g \left(a +b \right) \left(a -b \right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}-\frac{2 a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, \EllipticE \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f g \left(a +b \right) \left(a -b \right) \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}\, \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{4 a \cos \left(\frac{f x}{2}+\frac{e}{2}\right)}{f g \left(a +b \right) \left(a -b \right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}+\frac{a \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{8 \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \underline{\hspace{1.25 ex}}\alpha^{3} b^{2}-8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}+\sqrt{2}\, a^{2} \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right) \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{\underline{\hspace{1.25 ex}}\alpha  \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}}{8 f g \,b^{2} \left(a +b \right) \left(a -b \right) \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}"," ",0,"1/2/f/g^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/2/f/g*b*a^2/(a-b)/(a+b)*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/2/f/g^2*b/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-4/f/g*a/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3-2/f/g*a/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+4/f/g*a/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+1/8/f/g*a/b^2/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)","C"
1399,1,1938,441,9.045000," ","int(sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/2/f/g^2*a/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/2/f/g*a*b^2/(a-b)/(a+b)*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/2/f/g^2*a/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-8/f/g*b/(a+b)/(a-b)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3-4/f/g*b/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)+8/f/g*b/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)^3+8/f/g*b/(a+b)/(a-b)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+4/f/g*b/(a+b)/(a-b)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)-8/f/g*b/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*cos(1/2*f*x+1/2*e)+1/4/f/g/b/a^2/(a+b)/(a-b)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*sum((2*_alpha^2*b^2-a^2)/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/4/f/g/b/a^2/(a+b)/(a-b)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum((2*_alpha^2*b^2-a^2)/_alpha/(2*_alpha^2-1)*(8*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))*(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)","C"
1400,1,425,521,4.584000," ","int(csc(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\frac{-\left(4 \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) g^{\frac{5}{2}}+2 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g^{2}+2 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}\, g^{2}\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+2 \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) g^{\frac{5}{2}}-4 \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, g^{\frac{3}{2}} \sqrt{-g}+\ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g^{2}+\ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}\, g^{2}}{2 g^{\frac{7}{2}} \sqrt{-g}\, a \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) f}"," ",0,"1/2*(-(4*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))*g^(5/2)+2*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^2+2*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^2)*sin(1/2*f*x+1/2*e)^2+2*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))*g^(5/2)-4*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)*g^(3/2)*(-g)^(1/2)+ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^2+ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^2)/g^(7/2)/(-g)^(1/2)/a/(2*sin(1/2*f*x+1/2*e)^2-1)/f","A"
1401,1,3469,659,17.192000," ","int(csc(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"-1/f/g^(3/2)*b/(2+2^(1/2))/(2^(1/2)-2)/a^2*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))-1/f/g^2*b/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/2/f/g*b^5/(a-b)/(a+b)/a^2*sum((_R^6-_R^4*g-_R^2*g^2+g^3)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/f/g*b/a^2/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))-1/f/g^(3/2)*b/(2+2^(1/2))/(2^(1/2)-2)/a^2*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))+1/f/g^2*b/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)*2^(1/2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3*a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)^5/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3/a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)^5/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*b^2-6/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3*a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)+2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3/a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*b^2+6/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3*a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)^3/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3/a/cos(1/2*f*x+1/2*e)/sin(1/2*f*x+1/2*e)^3/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*b^2-3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3*a/sin(1/2*f*x+1/2*e)^5/(2*sin(1/2*f*x+1/2*e)^2-1)^(3/2)/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)+1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g^3/a/sin(1/2*f*x+1/2*e)^5/(2*sin(1/2*f*x+1/2*e)^2-1)^(3/2)/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))*(sin(1/2*f*x+1/2*e)^2)^(1/2)*b^2+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g/a^3*sin(1/2*f*x+1/2*e)^3/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*b^2-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g/a^3*sin(1/2*f*x+1/2*e)/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*b^2+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/g/a^3/sin(1/2*f*x+1/2*e)/(2*sin(1/2*f*x+1/2*e)^2-1)^2/(a^2-b^2)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*b^2","C"
1402,1,1268,639,11.508000," ","int(sin(f*x+e)^4/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}{f \,g^{3} b}-\frac{2 a^{4} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f g b \left(a -b \right) \left(a +b \right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)^{2}}+\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)^{2}}-\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, b^{2} \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{5} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a -b \right) \left(a +b \right) b^{4}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}{3 f \,g^{3} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{3 f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}"," ",0,"2/f/g^3/b*(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-2/f/g/b*a^4/(a-b)/(a+b)*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/12/f/g^3*b/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*b/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/b^2*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^5/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a-b)/(a+b)/b^4*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))","C"
1403,1,2331,570,13.090000," ","int(sin(f*x+e)^3/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"2/f/g*a^3/(a-b)/(a+b)*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/12/f/g^3*a/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*a*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*a/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*a*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*cos(1/2*f*x+1/2*e)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2/(a-b)/(a+b)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*a^2/(a-b)/(a+b)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))","C"
1404,1,1089,488,10.387000," ","int(sin(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","-\frac{2 b \,a^{2} \left(\munderset{\textit{\_R} =\RootOf \left(b^{2} \textit{\_Z}^{8}-4 b^{2} g \,\textit{\_Z}^{6}+\left(16 a^{2} g^{2}-10 b^{2} g^{2}\right) \textit{\_Z}^{4}-4 b^{2} g^{3} \textit{\_Z}^{2}+b^{2} g^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{4}+\textit{\_R}^{2} g \right) \ln \left(\sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-\cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g}\, \sqrt{2}-\textit{\_R} \right)}{\textit{\_R}^{7} b^{2}-3 \textit{\_R}^{5} b^{2} g +8 \textit{\_R}^{3} a^{2} g^{2}-5 \textit{\_R}^{3} b^{2} g^{2}-\textit{\_R} \,b^{2} g^{3}}\right)}{f g \left(a -b \right) \left(a +b \right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)^{2}}-\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+\frac{\sqrt{2}}{2}\right)}-\frac{b \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)^{2}}+\frac{b \sqrt{2}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}}{12 f \,g^{3} \left(a^{2}-b^{2}\right) \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{\sqrt{2}}{2}\right)}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a^{3} \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(4 b^{2} \textit{\_Z}^{4}-4 \textit{\_Z}^{2} b^{2}+a^{2}\right)}{\sum}\frac{\frac{\sqrt{2}\, \arctanh \left(\frac{g \left(4 \underline{\hspace{1.25 ex}}\alpha^{2}-3\right) \left(4 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) a^{2}-3 b^{2} \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}-3 a^{2}+2 b^{2}\right) \sqrt{2}}{2 \left(4 a^{2}-3 b^{2}\right) \sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}\, \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}\right)}{\sqrt{\frac{g \left(2 b^{2} \underline{\hspace{1.25 ex}}\alpha^{2}+a^{2}-2 b^{2}\right)}{b^{2}}}}+\frac{8 b^{2} \underline{\hspace{1.25 ex}}\alpha  \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right) \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), -\frac{4 b^{2} \left(\underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}{a^{2}}, \sqrt{2}\right)}{a^{2} \sqrt{-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g \left(2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}}}{\underline{\hspace{1.25 ex}}\alpha  \left(2 \underline{\hspace{1.25 ex}}\alpha^{2}-1\right)}\right)}{8 f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a -b \right) \left(a +b \right) b^{2}}+\frac{\sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \cos \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}{3 f \,g^{3} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)}\, a \sqrt{\frac{1}{2}-\frac{\cos \left(f x +e \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{f x}{2}+\frac{e}{2}\right), \sqrt{2}\right)}{3 f \,g^{2} \sin \left(\frac{f x}{2}+\frac{e}{2}\right) \sqrt{g \left(2 \left(\cos^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-1\right)}\, \left(a^{2}-b^{2}\right) \sqrt{-g \left(2 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-\left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)\right)}}"," ",0,"-2/f/g*b*a^2/(a-b)/(a+b)*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/12/f/g^3*b/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*b/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*b*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a^3/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a-b)/(a+b)/b^2*sum(1/_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+1/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))","C"
1405,1,2322,456,13.246000," ","int(sin(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"2/f/g*a*b^2/(a-b)/(a+b)*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))+1/12/f/g^3*a/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*a*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/12/f/g^3*a/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/12/f/g^3*a*2^(1/2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*cos(1/2*f*x+1/2*e)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)+8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*cos(1/2*f*x+1/2*e)+4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))-4/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)/(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)*EllipticE(cos(1/2*f*x+1/2*e),2^(1/2))+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a-b)/(a+b)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a-b)/(a+b)*sum(_alpha/(2*_alpha^2-1)*(2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*arctanh(1/2*g*(4*_alpha^2-3)/(4*a^2-3*b^2)*(4*cos(1/2*f*x+1/2*e)^2*a^2-3*b^2*cos(1/2*f*x+1/2*e)^2+b^2*_alpha^2-3*a^2+2*b^2)*2^(1/2)/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2))+8*b^2/a^2*_alpha*(_alpha^2-1)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-sin(1/2*f*x+1/2*e)^2*g*(2*sin(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),-4*b^2/a^2*(_alpha^2-1),2^(1/2))),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))+2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-2/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^3/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*cos(1/2*f*x+1/2*e)*(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)/(cos(1/2*f*x+1/2*e)^2-1/2)^2-4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))+4/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*b/g^2/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)/(a^2-b^2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(-2*cos(1/2*f*x+1/2*e)^2+1)^(1/2)/(-g*(2*sin(1/2*f*x+1/2*e)^4-sin(1/2*f*x+1/2*e)^2))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))","C"
1406,1,627,535,5.241000," ","int(csc(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\frac{\left(24 \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) g^{\frac{7}{2}}-12 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g^{3}-12 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}\, g^{3}\right) \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+\left(-24 \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) g^{\frac{7}{2}}+12 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g^{3}+12 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}\, g^{3}\right) \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+6 \ln \left(\frac{2 \sqrt{-g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) g^{\frac{7}{2}}+4 \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}\, \sqrt{-g}\, g^{\frac{5}{2}}-3 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}+4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{-1+\cos \left(\frac{f x}{2}+\frac{e}{2}\right)}\right) \sqrt{-g}\, g^{3}-3 \ln \left(\frac{2 \sqrt{g}\, \sqrt{-2 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right) g +g}-4 g \cos \left(\frac{f x}{2}+\frac{e}{2}\right)-2 g}{\cos \left(\frac{f x}{2}+\frac{e}{2}\right)+1}\right) \sqrt{-g}\, g^{3}}{6 \sqrt{-g}\, g^{\frac{11}{2}} a \left(4 \left(\sin^{4}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{f x}{2}+\frac{e}{2}\right)\right)+1\right) f}"," ",0,"1/6*((24*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))*g^(7/2)-12*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3-12*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3)*sin(1/2*f*x+1/2*e)^4+(-24*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))*g^(7/2)+12*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3+12*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3)*sin(1/2*f*x+1/2*e)^2+6*ln(2/cos(1/2*f*x+1/2*e)*((-g)^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-g))*g^(7/2)+4*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)*(-g)^(1/2)*g^(5/2)-3*ln(2/(-1+cos(1/2*f*x+1/2*e))*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3-3*ln(2/(cos(1/2*f*x+1/2*e)+1)*(g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g*cos(1/2*f*x+1/2*e)-g))*(-g)^(1/2)*g^3)/(-g)^(1/2)/g^(11/2)/a/(4*sin(1/2*f*x+1/2*e)^4-4*sin(1/2*f*x+1/2*e)^2+1)/f","A"
1407,1,2312,673,19.530000," ","int(csc(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"2/f/g^(5/2)*b/(2+2^(1/2))^2/(2^(1/2)-2)^2/a^2*ln((4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(-1+cos(1/2*f*x+1/2*e)))-2/f/g*b^5/(a-b)/(a+b)/a^2*sum((_R^4+_R^2*g)/(_R^7*b^2-3*_R^5*b^2*g+8*_R^3*a^2*g^2-5*_R^3*b^2*g^2-_R*b^2*g^3)*ln((-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-cos(1/2*f*x+1/2*e)*g^(1/2)*2^(1/2)-_R),_R=RootOf(b^2*_Z^8-4*b^2*g*_Z^6+(16*a^2*g^2-10*b^2*g^2)*_Z^4-4*b^2*g^3*_Z^2+b^2*g^4))-1/f/g^2*b/a^2/(-g)^(1/2)*ln((-2*g+2*(-g)^(1/2)*(2*cos(1/2*f*x+1/2*e)^2*g-g)^(1/2))/cos(1/2*f*x+1/2*e))+1/6/f/g^3*b/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/6/f/g^3*b*2^(1/2)/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)+1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+1/6/f/g^3*b/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))^2*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-1/6/f/g^3*b*2^(1/2)/(2+2^(1/2))/(2^(1/2)-2)/(a^2-b^2)/(cos(1/2*f*x+1/2*e)-1/2*2^(1/2))*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)+2/f/g^(5/2)*b/(2+2^(1/2))^2/(2^(1/2)-2)^2/a^2*ln((-4*g*cos(1/2*f*x+1/2*e)+2*g^(1/2)*(-2*sin(1/2*f*x+1/2*e)^2*g+g)^(1/2)-2*g)/(cos(1/2*f*x+1/2*e)+1))+5/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(2*sin(1/2*f*x+1/2*e)^2-1)^(3/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)-1/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a/g/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*EllipticF(cos(1/2*f*x+1/2*e),2^(1/2))*(2*sin(1/2*f*x+1/2*e)^2-1)^(3/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*b^2-10/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)^5/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)^5/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*b^2+1/8/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a^3/g^2/(a^2-b^2)/sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*sum(1/_alpha/(2*_alpha^2-1)*(8*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*_alpha^3*b^2-8*b^2*_alpha*(sin(1/2*f*x+1/2*e)^2)^(1/2)*(2*sin(1/2*f*x+1/2*e)^2-1)^(1/2)*EllipticPi(cos(1/2*f*x+1/2*e),(-4*_alpha^2*b^2+4*b^2)/a^2,2^(1/2))*(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)+2^(1/2)*a^2*arctanh(1/2/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(1/2)/(4*a^2-3*b^2)*g*2^(1/2)*(-16*sin(1/2*f*x+1/2*e)^2*_alpha^2*a^2+12*sin(1/2*f*x+1/2*e)^2*_alpha^2*b^2+4*_alpha^4*b^2+12*sin(1/2*f*x+1/2*e)^2*a^2-9*sin(1/2*f*x+1/2*e)^2*b^2+4*_alpha^2*a^2-7*b^2*_alpha^2-3*a^2+3*b^2))*(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2))/(g*(2*_alpha^2*b^2+a^2-2*b^2)/b^2)^(1/2)/(sin(1/2*f*x+1/2*e)^2*g*(-2*sin(1/2*f*x+1/2*e)^2+1))^(1/2),_alpha=RootOf(4*_Z^4*b^2-4*_Z^2*b^2+a^2))*b^2+10/3/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)-2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)^3/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*b^2-1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)*a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)+1/2/f*(g*(2*cos(1/2*f*x+1/2*e)^2-1)*sin(1/2*f*x+1/2*e)^2)^(1/2)/a/g/cos(1/2*f*x+1/2*e)/(-2*sin(1/2*f*x+1/2*e)^4*g+sin(1/2*f*x+1/2*e)^2*g)^(3/2)/(a^2-b^2)*sin(1/2*f*x+1/2*e)/(g*(2*cos(1/2*f*x+1/2*e)^2-1))^(1/2)*b^2","C"
1408,1,4649,745,1.004000," ","int((d*sin(f*x+e))^(5/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/4/f*(a-b)*(I*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+4*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3-4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-8*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-4*I*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-I*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+4*I*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b+4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-4*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3+2*sin(f*x+e)*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*b^2-4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3+4*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3-4*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b-8*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-4*I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+4*I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2+2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-4*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b+4*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b+I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2)*(d*sin(f*x+e))^(5/2)*(g*cos(f*x+e))^(1/2)/sin(f*x+e)^3/cos(f*x+e)*2^(1/2)*a/b^3/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1409,1,3290,482,0.839000," ","int((d*sin(f*x+e))^(3/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/f*(a-b)*(-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+(-a^2+b^2)^(1/2)*cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a+(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+I*(-a^2+b^2)^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a+I*(-a^2+b^2)^(1/2)*cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a-I*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+(-a^2+b^2)^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b)*(d*sin(f*x+e))^(3/2)*(g*cos(f*x+e))^(1/2)/sin(f*x+e)^2/cos(f*x+e)*2^(1/2)*a/b^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1410,1,744,393,0.856000," ","int((d*sin(f*x+e))^(1/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{\left(a -b \right) \left(i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}-i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)+b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}-a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)-b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{d \sin \left(f x +e \right)}\, \sqrt{g \cos \left(f x +e \right)}\, \sin \left(f x +e \right) \sqrt{2}\, a}{f \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) b \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"1/f*(a-b)*(I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)-I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))+b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)-a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))-b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2)))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(d*sin(f*x+e))^(1/2)*(g*cos(f*x+e))^(1/2)*sin(f*x+e)/cos(f*x+e)/(-1+cos(f*x+e))*2^(1/2)*a/b/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","A"
1411,1,590,164,0.665000," ","int((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","-\frac{\sqrt{g \cos \left(f x +e \right)}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(a -b \right) \left(2 \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)+b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}-a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)-b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)\right) \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{f \sqrt{d \sin \left(f x +e \right)}\, \cos \left(f x +e \right) \left(-1+\cos \left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"-1/f*(g*cos(f*x+e))^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(a-b)*(2*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))+b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)-a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))-b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2)))*sin(f*x+e)^2/(d*sin(f*x+e))^(1/2)/cos(f*x+e)/(-1+cos(f*x+e))*2^(1/2)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1412,1,2502,291,0.700000," ","int((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/f*(a-b)*(4*cos(f*x+e)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-2*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+4*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a)*(g*cos(f*x+e))^(1/2)*sin(f*x+e)/(d*sin(f*x+e))^(3/2)/cos(f*x+e)*2^(1/2)/a/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1413,1,2672,331,0.733000," ","int((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"1/3/f*(a-b)*(-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b+6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2-3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+12*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3-6*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b+6*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2-3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+12*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*a^2-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*2^(1/2)*a*b)*(g*cos(f*x+e))^(1/2)*sin(f*x+e)/(d*sin(f*x+e))^(5/2)/cos(f*x+e)*2^(1/2)/a^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1414,1,6208,483,0.750000," ","int((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1415,1,6593,556,0.854000," ","int((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1416,1,2547,806,0.945000," ","int((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/4/f*(a-b)*(-I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^2+I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^2-4*I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+4*I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+4*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a^2+4*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a*b-4*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^3+4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^2+4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b+4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3-4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^2-4*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b+2*sin(f*x+e)*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*b^2-4*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b-2*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*b^2+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b)*(g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(3/2)/sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)^2*2^(1/2)*a/b^3/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1417,1,1926,517,0.809000," ","int((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","-\frac{\left(a -b \right) \left(i \sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -i \sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, a -\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, b -\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a -\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b +\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) b +\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a +\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) a -\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, a^{2}+\sin \left(f x +e \right) \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, b^{2}+\sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a^{2}-\sin \left(f x +e \right) \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b^{2}+\sqrt{-a^{2}+b^{2}}\, \left(\cos^{2}\left(f x +e \right)\right) \sqrt{2}\, b -\sqrt{-a^{2}+b^{2}}\, \cos \left(f x +e \right) \sqrt{2}\, b \right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{d \sin \left(f x +e \right)}\, \sqrt{2}\, a}{f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} b^{2} \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"-1/f*(a-b)*(I*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a-I*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a-(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b-(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a-(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b+(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a+(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a-sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2+sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*b)*(g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/cos(f*x+e)^2*2^(1/2)*a/b^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1418,1,944,490,0.632000," ","int((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\frac{\left(a -b \right) \left(i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a -i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +2 \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b -\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a -\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b -a^{2} \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a -\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b +a^{2} \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b^{2}\right) \left(\sin^{2}\left(f x +e \right)\right) \left(g \cos \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}}{f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right)^{2} \sqrt{d \sin \left(f x +e \right)}\, b \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"1/f*(a-b)*(I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a-I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+2*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-a^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b+a^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2)*sin(f*x+e)^2*(g*cos(f*x+e))^(3/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/cos(f*x+e)^2/(d*sin(f*x+e))^(1/2)*2^(1/2)/b/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","A"
1419,1,2587,299,0.656000," ","int((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"1/f*(a-b)*(2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a)*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/(d*sin(f*x+e))^(3/2)/cos(f*x+e)^2*2^(1/2)/a/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1420,1,3014,424,0.646000," ","int((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/3/f*(a-b)*(3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a*b+3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b+3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b+3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a*b+3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2-6*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*2^(1/2)*a*b+2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a^2)*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/cos(f*x+e)^2/(d*sin(f*x+e))^(5/2)*2^(1/2)/a^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1421,1,5828,504,0.717000," ","int((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1422,1,6707,670,0.812000," ","int((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1423,1,6311,757,0.963000," ","int((g*cos(f*x+e))^(5/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1424,1,5224,474,0.686000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1425,1,5212,515,0.739000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1426,1,4668,324,0.677000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/3/f*(a-b)*(2*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*a^2-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b+12*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2-3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-6*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+12*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a^2+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2-3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-3*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-6*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+3*cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)*(-a^2+b^2)^(1/2)*a^2+3*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*sin(f*x+e)*(-a^2+b^2)^(1/2)*a^2+3*cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)*a^3-3*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*sin(f*x+e)*a^3+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+6*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2-3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2-3*(-a^2+b^2)^(1/2)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-6*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3-6*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*2^(1/2)*a*b+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^3-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3)*(g*cos(f*x+e))^(5/2)*sin(f*x+e)/cos(f*x+e)^3/(d*sin(f*x+e))^(5/2)*2^(1/2)/a^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1427,1,10138,489,0.758000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1428,1,10704,570,0.836000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1429,1,17102,779,0.982000," ","int((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(11/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1430,1,2344,522,0.891000," ","int((d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/f*(I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2-I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b+I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b-I*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a^2-sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^3+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b-sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b-(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b+(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3-sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b-cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+cos(f*x+e)^2*2^(1/2)*(-a^2+b^2)^(1/2)*b^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b-cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*b^2)*(d*sin(f*x+e))^(5/2)/(-1+cos(f*x+e))/sin(f*x+e)^2/(g*cos(f*x+e))^(1/2)*2^(1/2)*a/b^2/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1431,1,941,401,0.867000," ","int((d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\frac{\left(i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a -i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}-i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) b \sqrt{-a^{2}+b^{2}}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, a +a^{2} \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)-\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) a b -a^{2} \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a b \right) \left(d \sin \left(f x +e \right)\right)^{\frac{3}{2}} \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{2}\, a}{f \left(-1+\cos \left(f x +e \right)\right) \sqrt{g \cos \left(f x +e \right)}\, b \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"1/f*(I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a*(-a^2+b^2)^(1/2)-I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b*(-a^2+b^2)^(1/2)-I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a*(-a^2+b^2)^(1/2)+I*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b*(-a^2+b^2)^(1/2)-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b*(-a^2+b^2)^(1/2)-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b*(-a^2+b^2)^(1/2)+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+a^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-a^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b)*(d*sin(f*x+e))^(3/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/(g*cos(f*x+e))^(1/2)*2^(1/2)*a/b/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1432,1,527,173,0.800000," ","int((d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","-\frac{\sqrt{d \sin \left(f x +e \right)}\, \left(\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}+a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)-b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right)-a \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)+b \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sin \left(f x +e \right) \sqrt{2}\, a}{f \left(-1+\cos \left(f x +e \right)\right) \sqrt{g \cos \left(f x +e \right)}\, \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"-1/f*(d*sin(f*x+e))^(1/2)*(EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)+a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))-a*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))+b*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2)))*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)/(-1+cos(f*x+e))/(g*cos(f*x+e))^(1/2)*2^(1/2)*a/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1433,1,631,257,0.681000," ","int(1/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\frac{\left(2 \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) a \sqrt{-a^{2}+b^{2}}-2 \EllipticF \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) a b -\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) b^{2}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, \frac{a}{a -b +\sqrt{-a^{2}+b^{2}}}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b -\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) a b +\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) b^{2}+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}, -\frac{a}{b +\sqrt{-a^{2}+b^{2}}-a}, \frac{\sqrt{2}}{2}\right) \sqrt{-a^{2}+b^{2}}\, b \right) \sqrt{\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{\frac{-1+\cos \left(f x +e \right)+\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \sqrt{-\frac{-1+\cos \left(f x +e \right)-\sin \left(f x +e \right)}{\sin \left(f x +e \right)}}\, \left(\sin^{2}\left(f x +e \right)\right) \sqrt{2}}{f \sqrt{d \sin \left(f x +e \right)}\, \left(-1+\cos \left(f x +e \right)\right) \sqrt{g \cos \left(f x +e \right)}\, \sqrt{-a^{2}+b^{2}}\, \left(a -b +\sqrt{-a^{2}+b^{2}}\right) \left(b +\sqrt{-a^{2}+b^{2}}-a \right)}"," ",0,"1/f*(2*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*(-a^2+b^2)^(1/2)-2*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*sin(f*x+e)^2/(d*sin(f*x+e))^(1/2)/(-1+cos(f*x+e))/(g*cos(f*x+e))^(1/2)*2^(1/2)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1434,1,2286,298,0.718000," ","int(1/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/f*(2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a^2-2*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b)*sin(f*x+e)/(d*sin(f*x+e))^(3/2)/(g*cos(f*x+e))^(1/2)*2^(1/2)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)/a","B"
1435,1,2987,415,0.780000," ","int(1/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-1/3/f*(3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*b^3+3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b^3-3*cos(f*x+e)*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^4+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^3+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^4+4*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^3-4*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2*b+6*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b^2-6*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*b^3+3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b^3-3*sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^4+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^3+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^4+4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^3-4*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2*b+6*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b^2-6*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b^3+6*2^(1/2)*(-a^2+b^2)^(1/2)*cos(f*x+e)*sin(f*x+e)*a^2*b-6*cos(f*x+e)*sin(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a*b^2-2*(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*a^3+2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a^2*b)*sin(f*x+e)/(d*sin(f*x+e))^(5/2)/(g*cos(f*x+e))^(1/2)*2^(1/2)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)/a^2","B"
1436,1,4619,887,0.891000," ","int((d*sin(f*x+e))^(5/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"-1/f*(-I*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+I*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3-I*(-a^2+b^2)^(1/2)*cos(f*x+e)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*a^2-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+I*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2+4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b-2*(-a^2+b^2)^(1/2)*sin(f*x+e)*2^(1/2)*b^2-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^3+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^3-2*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+I*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2-I*(-a^2+b^2)^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*a^2+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*a^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2-1/2*I,1/2*2^(1/2))*b^2-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*a^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2+1/2*I,1/2*2^(1/2))*b^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2*b+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b)*(d*sin(f*x+e))^(5/2)*cos(f*x+e)/sin(f*x+e)^3/(g*cos(f*x+e))^(3/2)*2^(1/2)*a/(a+b)/b/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1437,1,2540,346,0.885000," ","int((d*sin(f*x+e))^(3/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/f*(-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a+2*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-4*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a+2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+2*sin(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a+2*(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*b-2*(-a^2+b^2)^(1/2)*2^(1/2)*b)*(d*sin(f*x+e))^(3/2)*cos(f*x+e)/sin(f*x+e)^2/(g*cos(f*x+e))^(3/2)*2^(1/2)*a/(a+b)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1438,1,2536,341,0.892000," ","int((d*sin(f*x+e))^(1/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/f*(cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-2*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a-2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+4*cos(f*x+e)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b+4*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a-2*sin(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*b+2*(-a^2+b^2)^(1/2)*2^(1/2)*a)*(d*sin(f*x+e))^(1/2)*cos(f*x+e)/(g*cos(f*x+e))^(3/2)/sin(f*x+e)*2^(1/2)*a/(a+b)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1439,1,2559,347,0.716000," ","int(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x)","\text{Expression too large to display}"," ",0,"-1/f*(2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+2*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-4*cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-cos(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+2*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+2*2^(1/2)*sin(f*x+e)*(-a^2+b^2)^(1/2)*a^2-2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b)*cos(f*x+e)/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)*2^(1/2)/(a+b)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1440,1,3104,546,0.721000," ","int(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/f*(-2*(-a^2+b^2)^(1/2)*2^(1/2)*a^3+4*(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*a^3-2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^2+4*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^3-cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^4+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4-(-a^2+b^2)^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^3-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3+4*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^2+2*sin(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a^2*b-(-a^2+b^2)^(1/2)*cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^3-(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3+4*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3+2*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^3-8*(-a^2+b^2)^(1/2)*cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3-cos(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b^3+cos(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^3-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^2-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^4+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4-2*(-a^2+b^2)^(1/2)*cos(f*x+e)*2^(1/2)*a*b^2+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^3-8*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3-EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b^3)*cos(f*x+e)*sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)*2^(1/2)/(a+b)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)/a","B"
1441,1,3315,637,0.778000," ","int(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x)","\text{output too large to display}"," ",0,"1/3/f*(-6*(-a^2+b^2)^(1/2)*2^(1/2)*a^4+3*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^4-6*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^4+3*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^4-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^4+24*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3*b-12*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^3-12*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3*b+6*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^3+8*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*a^4+6*(-a^2+b^2)^(1/2)*sin(f*x+e)*2^(1/2)*a^3*b-12*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a^3*b+6*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b^3+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^5-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^5+3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^5-3*cos(f*x+e)*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^5+3*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^4-6*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^4+3*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^4+3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^4-3*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^4-2*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*a^2*b^2+24*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3*b-12*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticE((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^3-12*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a^3*b+6*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b^3)*cos(f*x+e)*sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)*2^(1/2)/(a+b)/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)/a^2","B"
1442,1,3490,308,1.432000," ","int((g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2/(d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"-1/2/f*(2*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+2*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*2^(1/2)*a^2-sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a^2*b+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a^2*b-2*sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a^2-2*cos(f*x+e)*2^(1/2)*(-a^2+b^2)^(1/2)*a^2-sin(f*x+e)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*(-a^2+b^2)^(1/2)*a*b-sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-a^2+b^2)^(1/2)*a*b+2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2-2*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+2*cos(f*x+e)*(-a^2+b^2)^(1/2)*2^(1/2)*a*b+sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-sin(f*x+e)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2+2*(-a^2+b^2)^(1/2)*sin(f*x+e)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^3-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*b^2+(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2-(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*a*b^2-cos(f*x+e)^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^3+cos(f*x+e)^2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^3-2*(-a^2+b^2)^(1/2)*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*a*b+(-a^2+b^2)^(1/2)*cos(f*x+e)^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*b^2+(-a^2+b^2)^(1/2)*cos(f*x+e)^2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*b^2-2*(-a^2+b^2)^(1/2)*cos(f*x+e)^2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticF((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),1/2*2^(1/2))*b^2+cos(f*x+e)^2*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),a/(a-b+(-a^2+b^2)^(1/2)),1/2*2^(1/2))*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*a*b^2-cos(f*x+e)^2*(-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e)+sin(f*x+e))/sin(f*x+e))^(1/2)*((-1+cos(f*x+e))/sin(f*x+e))^(1/2)*EllipticPi((-(-1+cos(f*x+e)-sin(f*x+e))/sin(f*x+e))^(1/2),-a/(b+(-a^2+b^2)^(1/2)-a),1/2*2^(1/2))*a*b^2)*(g*cos(f*x+e))^(3/2)*sin(f*x+e)/(a+b*sin(f*x+e))/(-1+cos(f*x+e))/(d*sin(f*x+e))^(1/2)/cos(f*x+e)^2*2^(1/2)/a/(-a^2+b^2)^(1/2)/(a-b+(-a^2+b^2)^(1/2))/(b+(-a^2+b^2)^(1/2)-a)","B"
1443,1,104,74,0.413000," ","int(sec(d*x+c)^2*sin(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+b \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+b*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
1444,1,94,59,0.404000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+b \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+b*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","A"
1445,1,59,38,0.309000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a \left(\tan \left(d x +c \right)-d x -c \right)+b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a*(tan(d*x+c)-d*x-c)+b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
1446,1,32,27,0.172000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{\frac{a}{\cos \left(d x +c \right)}+b \left(\tan \left(d x +c \right)-d x -c \right)}{d}"," ",0,"1/d*(a/cos(d*x+c)+b*(tan(d*x+c)-d*x-c))","A"
1447,1,47,36,0.415000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a}{d \cos \left(d x +c \right)}+\frac{a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b \tan \left(d x +c \right)}{d}"," ",0,"1/d*a/cos(d*x+c)+1/d*a*ln(csc(d*x+c)-cot(d*x+c))+b*tan(d*x+c)/d","A"
1448,1,69,48,0.400000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a \cot \left(d x +c \right)}{d}+\frac{b}{d \cos \left(d x +c \right)}+\frac{b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"1/d*a/sin(d*x+c)/cos(d*x+c)-2*a*cot(d*x+c)/d+1/d*b/cos(d*x+c)+1/d*b*ln(csc(d*x+c)-cot(d*x+c))","A"
1449,1,93,69,0.457000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c)),x)","-\frac{a}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a}{2 d \cos \left(d x +c \right)}+\frac{3 a \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{b}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 b \cot \left(d x +c \right)}{d}"," ",0,"-1/2/d*a/sin(d*x+c)^2/cos(d*x+c)+3/2/d*a/cos(d*x+c)+3/2/d*a*ln(csc(d*x+c)-cot(d*x+c))+1/d*b/sin(d*x+c)/cos(d*x+c)-2*b*cot(d*x+c)/d","A"
1450,1,147,92,0.547000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+2 a b \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+b^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+2*a*b*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+b^2*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
1451,1,116,88,0.452000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\tan \left(d x +c \right)-d x -c \right)+2 a b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a^2*(tan(d*x+c)-d*x-c)+2*a*b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+b^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","A"
1452,1,75,42,0.312000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{\frac{a^{2}}{\cos \left(d x +c \right)}+2 a b \left(\tan \left(d x +c \right)-d x -c \right)+b^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^2/cos(d*x+c)+2*a*b*(tan(d*x+c)-d*x-c)+b^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c)))","A"
1453,1,68,46,0.546000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{d \cos \left(d x +c \right)}+\frac{a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{2 a b \tan \left(d x +c \right)}{d}+\frac{b^{2}}{d \cos \left(d x +c \right)}"," ",0,"1/d*a^2/cos(d*x+c)+1/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2*a*b*tan(d*x+c)/d+1/d*b^2/cos(d*x+c)","A"
1454,1,90,59,0.599000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a^{2} \cot \left(d x +c \right)}{d}+\frac{2 a b}{d \cos \left(d x +c \right)}+\frac{2 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2} \tan \left(d x +c \right)}{d}"," ",0,"1/d*a^2/sin(d*x+c)/cos(d*x+c)-2*a^2*cot(d*x+c)/d+2/d*a*b/cos(d*x+c)+2/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+b^2*tan(d*x+c)/d","A"
1455,1,140,94,0.562000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a^{2}}{2 d \cos \left(d x +c \right)}+\frac{3 a^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{2 a b}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{4 a b \cot \left(d x +c \right)}{d}+\frac{b^{2}}{d \cos \left(d x +c \right)}+\frac{b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/2/d*a^2/sin(d*x+c)^2/cos(d*x+c)+3/2/d*a^2/cos(d*x+c)+3/2/d*a^2*ln(csc(d*x+c)-cot(d*x+c))+2/d*a*b/sin(d*x+c)/cos(d*x+c)-4*a*b*cot(d*x+c)/d+1/d*b^2/cos(d*x+c)+1/d*b^2*ln(csc(d*x+c)-cot(d*x+c))","A"
1456,1,162,102,0.572000," ","int(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","-\frac{a^{2}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 a^{2}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a^{2} \cot \left(d x +c \right)}{3 d}-\frac{a b}{d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a b}{d \cos \left(d x +c \right)}+\frac{3 a b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 b^{2} \cot \left(d x +c \right)}{d}"," ",0,"-1/3/d*a^2/sin(d*x+c)^3/cos(d*x+c)+4/3/d*a^2/sin(d*x+c)/cos(d*x+c)-8/3*a^2*cot(d*x+c)/d-1/d*a*b/sin(d*x+c)^2/cos(d*x+c)+3/d*a*b/cos(d*x+c)+3/d*a*b*ln(csc(d*x+c)-cot(d*x+c))+1/d*b^2/sin(d*x+c)/cos(d*x+c)-2*b^2*cot(d*x+c)/d","A"
1457,1,214,183,0.640000," ","int(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+3 a^{2} b \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+3 a \,b^{2} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)+b^{3} \left(\frac{\sin^{7}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{5}\left(d x +c \right)+\frac{5 \left(\sin^{3}\left(d x +c \right)\right)}{4}+\frac{15 \sin \left(d x +c \right)}{8}\right) \cos \left(d x +c \right)-\frac{15 d x}{8}-\frac{15 c}{8}\right)}{d}"," ",0,"1/d*(a^3*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a^2*b*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+3*a*b^2*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c))+b^3*(sin(d*x+c)^7/cos(d*x+c)+(sin(d*x+c)^5+5/4*sin(d*x+c)^3+15/8*sin(d*x+c))*cos(d*x+c)-15/8*d*x-15/8*c))","A"
1458,1,169,138,0.552000," ","int(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\tan \left(d x +c \right)-d x -c \right)+3 a^{2} b \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+3 a \,b^{2} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)+b^{3} \left(\frac{\sin^{6}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\frac{8}{3}+\sin^{4}\left(d x +c \right)+\frac{4 \left(\sin^{2}\left(d x +c \right)\right)}{3}\right) \cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*(a^3*(tan(d*x+c)-d*x-c)+3*a^2*b*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+3*a*b^2*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c)+b^3*(sin(d*x+c)^6/cos(d*x+c)+(8/3+sin(d*x+c)^4+4/3*sin(d*x+c)^2)*cos(d*x+c)))","A"
1459,1,132,71,0.452000," ","int(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{\frac{a^{3}}{\cos \left(d x +c \right)}+3 a^{2} b \left(\tan \left(d x +c \right)-d x -c \right)+3 a \,b^{2} \left(\frac{\sin^{4}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(2+\sin^{2}\left(d x +c \right)\right) \cos \left(d x +c \right)\right)+b^{3} \left(\frac{\sin^{5}\left(d x +c \right)}{\cos \left(d x +c \right)}+\left(\sin^{3}\left(d x +c \right)+\frac{3 \sin \left(d x +c \right)}{2}\right) \cos \left(d x +c \right)-\frac{3 d x}{2}-\frac{3 c}{2}\right)}{d}"," ",0,"1/d*(a^3/cos(d*x+c)+3*a^2*b*(tan(d*x+c)-d*x-c)+3*a*b^2*(sin(d*x+c)^4/cos(d*x+c)+(2+sin(d*x+c)^2)*cos(d*x+c))+b^3*(sin(d*x+c)^5/cos(d*x+c)+(sin(d*x+c)^3+3/2*sin(d*x+c))*cos(d*x+c)-3/2*d*x-3/2*c))","A"
1460,1,100,78,0.602000," ","int(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{d \cos \left(d x +c \right)}+\frac{a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \tan \left(d x +c \right)}{d}+\frac{3 a \,b^{2}}{d \cos \left(d x +c \right)}-b^{3} x +\frac{b^{3} \tan \left(d x +c \right)}{d}-\frac{b^{3} c}{d}"," ",0,"1/d*a^3/cos(d*x+c)+1/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3*a^2*b*tan(d*x+c)/d+3/d*a*b^2/cos(d*x+c)-b^3*x+b^3*tan(d*x+c)/d-1/d*b^3*c","A"
1461,1,111,87,0.651000," ","int(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{2 a^{3} \cot \left(d x +c \right)}{d}+\frac{3 a^{2} b}{d \cos \left(d x +c \right)}+\frac{3 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{3}}{d \cos \left(d x +c \right)}"," ",0,"1/d*a^3/sin(d*x+c)/cos(d*x+c)-2*a^3*cot(d*x+c)/d+3/d*a^2*b/cos(d*x+c)+3/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))+3*a*b^2*tan(d*x+c)/d+1/d*b^3/cos(d*x+c)","A"
1462,1,161,126,0.732000," ","int(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3}}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{3 a^{3}}{2 d \cos \left(d x +c \right)}+\frac{3 a^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{3 a^{2} b}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{6 a^{2} b \cot \left(d x +c \right)}{d}+\frac{3 a \,b^{2}}{d \cos \left(d x +c \right)}+\frac{3 a \,b^{2} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}+\frac{b^{3} \tan \left(d x +c \right)}{d}"," ",0,"-1/2/d*a^3/sin(d*x+c)^2/cos(d*x+c)+3/2/d*a^3/cos(d*x+c)+3/2/d*a^3*ln(csc(d*x+c)-cot(d*x+c))+3/d*a^2*b/sin(d*x+c)/cos(d*x+c)-6*a^2*b*cot(d*x+c)/d+3/d*a*b^2/cos(d*x+c)+3/d*a*b^2*ln(csc(d*x+c)-cot(d*x+c))+b^3*tan(d*x+c)/d","A"
1463,1,209,156,0.629000," ","int(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","-\frac{a^{3}}{3 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)}+\frac{4 a^{3}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{8 a^{3} \cot \left(d x +c \right)}{3 d}-\frac{3 a^{2} b}{2 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}+\frac{9 a^{2} b}{2 d \cos \left(d x +c \right)}+\frac{9 a^{2} b \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{2 d}+\frac{3 a \,b^{2}}{d \sin \left(d x +c \right) \cos \left(d x +c \right)}-\frac{6 a \,b^{2} \cot \left(d x +c \right)}{d}+\frac{b^{3}}{d \cos \left(d x +c \right)}+\frac{b^{3} \ln \left(\csc \left(d x +c \right)-\cot \left(d x +c \right)\right)}{d}"," ",0,"-1/3/d*a^3/sin(d*x+c)^3/cos(d*x+c)+4/3/d*a^3/sin(d*x+c)/cos(d*x+c)-8/3*a^3*cot(d*x+c)/d-3/2/d*a^2*b/sin(d*x+c)^2/cos(d*x+c)+9/2/d*a^2*b/cos(d*x+c)+9/2/d*a^2*b*ln(csc(d*x+c)-cot(d*x+c))+3/d*a*b^2/sin(d*x+c)/cos(d*x+c)-6*a*b^2*cot(d*x+c)/d+1/d*b^3/cos(d*x+c)+1/d*b^3*ln(csc(d*x+c)-cot(d*x+c))","A"
1464,1,303,208,0.546000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{4}}{d b \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,b^{2} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{8 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)-2/d/b^2*arctan(tan(1/2*d*x+1/2*c))-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)-2/d*a^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d*a^4/b/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+2/d*a^5/b^2/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-8/d*a^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1465,1,219,198,0.532000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 a^{3}}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{6 a^{2} b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)+2/d*a^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)*b+2/d*a^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+6/d*a^2/(a-b)^2/(a+b)^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1466,1,282,186,0.510000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 a \,b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{2} b}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 a^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{4 a \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)-2/d*a/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b^2*tan(1/2*d*x+1/2*c)-2/d*a^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*b-2/d*a^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-4/d*a/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","A"
1467,1,280,128,0.444000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{2} a}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{4 a^{2} b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}+\frac{2 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)+2/d*b^3/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*b^2/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*a+4/d*a^2/(a-b)^2/(a+b)^2*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1468,1,304,215,0.592000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2}}+\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{4}}{d \left(a -b \right)^{2} \left(a +b \right)^{2} a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{8 b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}-\frac{2 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} a^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)+1/d/a^2*ln(tan(1/2*d*x+1/2*c))+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)+2/d*b^5/(a-b)^2/(a+b)^2/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d*b^4/(a-b)^2/(a+b)^2/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+8/d*b^3/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-2/d*b^5/(a-b)^2/(a+b)^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1469,1,346,234,0.618000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{1}{2 d \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{2 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}-\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{2 b^{5}}{d \,a^{2} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}-\frac{10 b^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d a \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}+\frac{4 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)+1/2/d/a^2*tan(1/2*d*x+1/2*c)-1/2/d/a^2/tan(1/2*d*x+1/2*c)-2/d/a^3*b*ln(tan(1/2*d*x+1/2*c))-1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)-2/d/a^3*b^6/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)-2/d/a^2*b^5/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)-10/d/a*b^4/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+4/d/a^3*b^6/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1470,1,404,277,0.656000," ","int(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x)","-\frac{1}{d \left(a +b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 a^{2} d}-\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \,a^{3}}-\frac{1}{8 a^{2} d \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{4}}+\frac{b}{d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{1}{d \left(a -b \right)^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{2 b^{6}}{d \,a^{3} \left(a -b \right)^{2} \left(a +b \right)^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)}+\frac{12 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{2} \left(a +b \right)^{2} a^{2} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \left(a -b \right)^{2} \left(a +b \right)^{2} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^2/(tan(1/2*d*x+1/2*c)-1)+1/8/d/a^2*tan(1/2*d*x+1/2*c)^2-1/d/a^3*tan(1/2*d*x+1/2*c)*b-1/8/a^2/d/tan(1/2*d*x+1/2*c)^2+3/2/d/a^2*ln(tan(1/2*d*x+1/2*c))+3/d/a^4*ln(tan(1/2*d*x+1/2*c))*b^2+1/d*b/a^3/tan(1/2*d*x+1/2*c)+1/d/(a-b)^2/(tan(1/2*d*x+1/2*c)+1)+2/d/a^4*b^7/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)*tan(1/2*d*x+1/2*c)+2/d/a^3*b^6/(a-b)^2/(a+b)^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)+12/d*b^5/(a-b)^2/(a+b)^2/a^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^4*b^7/(a-b)^2/(a+b)^2/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","A"
1471,1,590,365,0.543000," ","int(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{22 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 a^{4} b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{12 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)-1/d*a^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-6/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-7/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-14/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3+1/d*a^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-22/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-7/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-3/d*a^4/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-12/d*a^2/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2","A"
1472,1,702,343,0.551000," ","int(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a^{5} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{16 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 a^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 a^{3} b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{9 a^{3} b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}+\frac{6 a \,b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)+1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)+3/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b+4/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^3+2/d*a^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+10/d*a/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^4+9/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^2+5/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b+16/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^3+2/d*a^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+5/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2+9/d*a^3/(a-b)^3/(a+b)^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+6/d*a/(a-b)^3/(a+b)^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1473,1,766,327,0.559000," ","int(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{5 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a \,b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 a^{4} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 a^{2} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{6 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{11 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{10 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) a \,b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 a^{4} b}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 a^{2} b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{2 a^{4} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{11 a^{2} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{2 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)-5/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^2-2/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*a*b^4-4/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b-11/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^3-6/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5-11/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^2-10/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*a*b^4-4/d*a^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b-3/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a^2*b^3-2/d*a^4/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-11/d*a^2/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^2-2/d/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4","B"
1474,1,643,193,0.514000," ","int(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{7 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{13 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{2 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{17 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{3}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3} b^{2}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{b^{4} a}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 a^{3} b \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}+\frac{9 a \,b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)+1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)+7/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3*b^3+6/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^2+13/d*a/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^4+2/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+17/d*a^2/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)*b^3+4/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+6/d*a^3/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*b^2+1/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a+6/d*a^3/(a-b)^3/(a+b)^3*b/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+9/d*a/(a-b)^3/(a+b)^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1475,1,787,379,0.663000," ","int(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3}}+\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{11 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{4 b^{7} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{17 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}-\frac{6 b^{8} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{29 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{8 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 b^{4} a}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{3 b^{6}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{20 a \,b^{3} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{7 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a \sqrt{a^{2}-b^{2}}}+\frac{2 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)+1/d/a^3*ln(tan(1/2*d*x+1/2*c))+1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)+11/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-4/d*b^7/(a-b)^3/(a+b)^3/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+10/d*a/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^4+17/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2-6/d*b^8/(a-b)^3/(a+b)^3/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+29/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-8/d*b^7/(a-b)^3/(a+b)^3/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+10/d*b^4/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*a-3/d*b^6/(a-b)^3/(a+b)^3/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+20/d*a/(a-b)^3/(a+b)^3*b^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-7/d*b^5/(a-b)^3/(a+b)^3/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+2/d*b^7/(a-b)^3/(a+b)^3/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1476,1,829,401,0.674000," ","int(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{3}}-\frac{1}{2 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}-\frac{3 b \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{13 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{6 b^{8} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{3} \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{12 \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{19 b^{7} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{2} \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{10 b^{9} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{35 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 b^{8} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{3} \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{12 b^{5}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{5 b^{7}}{d \,a^{2} \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{30 \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right) b^{4}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}+\frac{21 b^{6} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{2} \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}-\frac{6 b^{8} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \,a^{4} \left(a -b \right)^{3} \left(a +b \right)^{3} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)+1/2/d/a^3*tan(1/2*d*x+1/2*c)-1/2/d/a^3/tan(1/2*d*x+1/2*c)-3/d/a^4*b*ln(tan(1/2*d*x+1/2*c))-1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)-13/d/a*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+6/d/a^3*b^8/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-12/d/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2*b^5-19/d/a^2*b^7/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+10/d/a^4*b^9/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-35/d/a*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+14/d/a^3*b^8/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-12/d*b^5/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+5/d/a^2*b^7/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-30/d/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))*b^4+21/d/a^2*b^6/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-6/d/a^4*b^8/(a-b)^3/(a+b)^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1477,1,897,443,0.727000," ","int(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x)","-\frac{1}{d \left(a +b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{3}}-\frac{3 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b}{2 d \,a^{4}}-\frac{1}{8 d \,a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2}}{d \,a^{5}}+\frac{3 b}{2 d \,a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}+\frac{1}{d \left(a -b \right)^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{15 b^{7} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{8 b^{9} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 b^{6} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2} a}+\frac{21 b^{8} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{14 b^{10} \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{5} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{41 b^{7} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{2} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{20 b^{9} \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{4} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{14 b^{6}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}-\frac{7 b^{8}}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{3} \left(\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) a +2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b +a \right)^{2}}+\frac{42 b^{5} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a \sqrt{a^{2}-b^{2}}}-\frac{39 b^{7} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{3} \sqrt{a^{2}-b^{2}}}+\frac{12 b^{9} \arctan \left(\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+2 b}{2 \sqrt{a^{2}-b^{2}}}\right)}{d \left(a -b \right)^{3} \left(a +b \right)^{3} a^{5} \sqrt{a^{2}-b^{2}}}"," ",0,"-1/d/(a+b)^3/(tan(1/2*d*x+1/2*c)-1)+1/8/d/a^3*tan(1/2*d*x+1/2*c)^2-3/2/d/a^4*tan(1/2*d*x+1/2*c)*b-1/8/d/a^3/tan(1/2*d*x+1/2*c)^2+3/2/d/a^3*ln(tan(1/2*d*x+1/2*c))+6/d/a^5*ln(tan(1/2*d*x+1/2*c))*b^2+3/2/d*b/a^4/tan(1/2*d*x+1/2*c)+1/d/(a-b)^3/(tan(1/2*d*x+1/2*c)+1)+15/d*b^7/(a-b)^3/(a+b)^3/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3-8/d*b^9/(a-b)^3/(a+b)^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^3+14/d*b^6/(a-b)^3/(a+b)^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2/a*tan(1/2*d*x+1/2*c)^2+21/d*b^8/(a-b)^3/(a+b)^3/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2-14/d*b^10/(a-b)^3/(a+b)^3/a^5/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)^2+41/d*b^7/(a-b)^3/(a+b)^3/a^2/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)-20/d*b^9/(a-b)^3/(a+b)^3/a^4/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2*tan(1/2*d*x+1/2*c)+14/d*b^6/(a-b)^3/(a+b)^3/a/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2-7/d*b^8/(a-b)^3/(a+b)^3/a^3/(tan(1/2*d*x+1/2*c)^2*a+2*tan(1/2*d*x+1/2*c)*b+a)^2+42/d*b^5/(a-b)^3/(a+b)^3/a/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))-39/d*b^7/(a-b)^3/(a+b)^3/a^3/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))+12/d*b^9/(a-b)^3/(a+b)^3/a^5/(a^2-b^2)^(1/2)*arctan(1/2*(2*a*tan(1/2*d*x+1/2*c)+2*b)/(a^2-b^2)^(1/2))","B"
1478,1,666,142,0.723000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2),x)","-\frac{\left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) \sqrt{-a^{2}+b^{2}}+\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) \sin \left(f x +e \right) b -\sqrt{2}\, \cos \left(f x +e \right) \sin \left(f x +e \right) b -\sqrt{2}\, \cos \left(f x +e \right) a +\sqrt{2}\, b \sin \left(f x +e \right)+\sqrt{2}\, a \right) \sin \left(f x +e \right) \sqrt{2}}{2 f \left(-1+\cos \left(f x +e \right)\right) \cos \left(f x +e \right) \sqrt{d \sin \left(f x +e \right)}\, \sqrt{a +b \sin \left(f x +e \right)}}"," ",0,"-1/2/f*((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*sin(f*x+e)*(-a^2+b^2)^(1/2)+(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*sin(f*x+e)*b-2^(1/2)*cos(f*x+e)*sin(f*x+e)*b-2^(1/2)*cos(f*x+e)*a+2^(1/2)*b*sin(f*x+e)+2^(1/2)*a)*sin(f*x+e)/(-1+cos(f*x+e))/cos(f*x+e)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2)*2^(1/2)","B"
1479,1,2377,287,0.611000," ","int(sec(f*x+e)^2*(a+b*sin(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2),x)","-\frac{\left(2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, b^{2}-2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) b^{3}-\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \left(\cos^{2}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, a^{2}+2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}\, b^{2}-2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) a^{2} b +2 \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) b^{3}-\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) \cos \left(f x +e \right) \sqrt{-a^{2}+b^{2}}\, a^{2}+\sin \left(f x +e \right) \sqrt{2}\, \cos \left(f x +e \right) a \,b^{2}+\sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b -\sin \left(f x +e \right) \sqrt{2}\, a^{3}-\sin \left(f x +e \right) \sqrt{2}\, a \,b^{2}+\sqrt{2}\, \cos \left(f x +e \right) a^{2} b -2 \sqrt{2}\, a^{2} b \right) \sqrt{2}}{2 f \cos \left(f x +e \right) \sqrt{d \sin \left(f x +e \right)}\, \sqrt{a +b \sin \left(f x +e \right)}\, a}"," ",0,"-1/2/f*(2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*b^2-2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)^2*a^2*b+2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)^2*b^3-(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)^2*(-a^2+b^2)^(1/2)*a^2+2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*(-a^2+b^2)^(1/2)*b^2-2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*a^2*b+2*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*b^3-(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*cos(f*x+e)*(-a^2+b^2)^(1/2)*a^2+sin(f*x+e)*2^(1/2)*cos(f*x+e)*a*b^2+2^(1/2)*cos(f*x+e)^2*a^2*b-sin(f*x+e)*2^(1/2)*a^3-sin(f*x+e)*2^(1/2)*a*b^2+2^(1/2)*cos(f*x+e)*a^2*b-2*2^(1/2)*a^2*b)/cos(f*x+e)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2)*2^(1/2)/a","B"
1480,1,2490,329,0.716000," ","int(sec(f*x+e)^4*(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x)","-\frac{\left(10 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) b^{2}-5 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) a^{2}-10 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) a^{2} b +10 \left(\cos^{4}\left(f x +e \right)\right) \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) b^{3}+10 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) b^{2}-5 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-a^{2}+b^{2}}\, \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticF \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) a^{2}-10 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) a^{2} b +10 \left(\cos^{3}\left(f x +e \right)\right) \sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \sqrt{\frac{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(f x +e \right)\right)}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}\, \EllipticE \left(\sqrt{-\frac{-\sqrt{-a^{2}+b^{2}}\, \sin \left(f x +e \right)-b \sin \left(f x +e \right)+\cos \left(f x +e \right) a -a}{\left(b +\sqrt{-a^{2}+b^{2}}\right) \sin \left(f x +e \right)}}, \frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-a^{2}+b^{2}}}{\sqrt{-a^{2}+b^{2}}}}}{2}\right) b^{3}+5 \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{3}\left(f x +e \right)\right) a \,b^{2}+5 \sqrt{2}\, \left(\cos^{4}\left(f x +e \right)\right) a^{2} b -2 \sqrt{2}\, \left(\cos^{4}\left(f x +e \right)\right) b^{3}-5 \sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a^{3}+\sqrt{2}\, \sin \left(f x +e \right) \left(\cos^{2}\left(f x +e \right)\right) a \,b^{2}+5 \sqrt{2}\, \left(\cos^{3}\left(f x +e \right)\right) a^{2} b -4 \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) a^{2} b +4 \sqrt{2}\, \left(\cos^{2}\left(f x +e \right)\right) b^{3}-2 \sin \left(f x +e \right) \sqrt{2}\, a^{3}-6 \sin \left(f x +e \right) \sqrt{2}\, a \,b^{2}-6 \sqrt{2}\, a^{2} b -2 \sqrt{2}\, b^{3}\right) \sqrt{2}}{12 f \cos \left(f x +e \right)^{3} \sqrt{d \sin \left(f x +e \right)}\, \sqrt{a +b \sin \left(f x +e \right)}}"," ",0,"-1/12/f*(10*cos(f*x+e)^4*(-a^2+b^2)^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2-5*cos(f*x+e)^4*(-a^2+b^2)^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2-10*cos(f*x+e)^4*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b+10*cos(f*x+e)^4*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^3+10*cos(f*x+e)^3*(-a^2+b^2)^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^2-5*cos(f*x+e)^3*(-a^2+b^2)^(1/2)*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticF((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2-10*cos(f*x+e)^3*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*a^2*b+10*cos(f*x+e)^3*(-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*(((-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(-a^2+b^2)^(1/2)/sin(f*x+e))^(1/2)*(a*(-1+cos(f*x+e))/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2)*EllipticE((-(-(-a^2+b^2)^(1/2)*sin(f*x+e)-b*sin(f*x+e)+cos(f*x+e)*a-a)/(b+(-a^2+b^2)^(1/2))/sin(f*x+e))^(1/2),1/2*2^(1/2)*((b+(-a^2+b^2)^(1/2))/(-a^2+b^2)^(1/2))^(1/2))*b^3+5*2^(1/2)*sin(f*x+e)*cos(f*x+e)^3*a*b^2+5*2^(1/2)*cos(f*x+e)^4*a^2*b-2*2^(1/2)*cos(f*x+e)^4*b^3-5*2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*a^3+2^(1/2)*sin(f*x+e)*cos(f*x+e)^2*a*b^2+5*2^(1/2)*cos(f*x+e)^3*a^2*b-4*2^(1/2)*cos(f*x+e)^2*a^2*b+4*2^(1/2)*cos(f*x+e)^2*b^3-2*sin(f*x+e)*2^(1/2)*a^3-6*sin(f*x+e)*2^(1/2)*a*b^2-6*2^(1/2)*a^2*b-2*2^(1/2)*b^3)/cos(f*x+e)^3/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2)*2^(1/2)","B"
1481,1,219,139,0.243000," ","int(sec(d*x+c)^5*sin(d*x+c)^7*(a+b*sin(d*x+c)),x)","\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 a \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 b \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 b \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{7 b \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{35 b \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{35 b \sin \left(d x +c \right)}{8 d}+\frac{35 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*a*sin(d*x+c)^8/cos(d*x+c)^2-1/2*a*sin(d*x+c)^6/d-3/4*a*sin(d*x+c)^4/d-3/2*a*sin(d*x+c)^2/d-3*a*ln(cos(d*x+c))/d+1/4/d*b*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*b*sin(d*x+c)^9/cos(d*x+c)^2-5/8*b*sin(d*x+c)^7/d-7/8*b*sin(d*x+c)^5/d-35/24*b*sin(d*x+c)^3/d-35/8*b*sin(d*x+c)/d+35/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1482,1,205,121,0.238000," ","int(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c)),x)","\frac{a \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a \sin \left(d x +c \right)}{8 d}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{b \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 b \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 b \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a*sin(d*x+c)^5/d-5/8*a*sin(d*x+c)^3/d-15/8*a*sin(d*x+c)/d+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*b*sin(d*x+c)^8/cos(d*x+c)^2-1/2*b*sin(d*x+c)^6/d-3/4*b*sin(d*x+c)^4/d-3/2*b*sin(d*x+c)^2/d-3*b*ln(cos(d*x+c))/d","A"
1483,1,147,106,0.243000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 b \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 b \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 b \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 b \sin \left(d x +c \right)}{8 d}+\frac{15 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4*a*tan(d*x+c)^4/d-1/2*a*tan(d*x+c)^2/d-a*ln(cos(d*x+c))/d+1/4/d*b*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*b*sin(d*x+c)^7/cos(d*x+c)^2-3/8*b*sin(d*x+c)^5/d-5/8*b*sin(d*x+c)^3/d-15/8*b*sin(d*x+c)/d+15/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1484,1,133,93,0.235000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x)","\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a \sin \left(d x +c \right)}{8 d}+\frac{3 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a*sin(d*x+c)^3/d-3/8*a*sin(d*x+c)/d+3/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4*b*tan(d*x+c)^4/d-1/2*b*tan(d*x+c)^2/d-b*ln(cos(d*x+c))/d","A"
1485,1,114,66,0.233000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x)","\frac{a \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b \sin \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*b*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b*sin(d*x+c)^5/cos(d*x+c)^2-1/8*b*sin(d*x+c)^3/d-3/8*b*sin(d*x+c)/d+3/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1486,1,100,66,0.230000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x)","\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a \sin \left(d x +c \right)}{8 d}-\frac{a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a*sin(d*x+c)/d-1/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b*sin(d*x+c)^4/cos(d*x+c)^4","A"
1487,1,92,66,0.196000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\frac{a}{4 d \cos \left(d x +c \right)^{4}}+\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b \sin \left(d x +c \right)}{8 d}-\frac{b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/cos(d*x+c)^4+1/4/d*b*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b*sin(d*x+c)/d-1/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1488,1,100,91,0.431000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a}{4 d \cos \left(d x +c \right)^{4}}+\frac{a}{2 d \cos \left(d x +c \right)^{2}}+\frac{a \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 b \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/cos(d*x+c)^4+1/2/d*a/cos(d*x+c)^2+a*ln(tan(d*x+c))/d+1/4*b*sec(d*x+c)^3*tan(d*x+c)/d+3/8*b*sec(d*x+c)*tan(d*x+c)/d+3/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1489,1,120,105,0.304000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a}{8 d \sin \left(d x +c \right)}+\frac{15 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b}{4 d \cos \left(d x +c \right)^{4}}+\frac{b}{2 d \cos \left(d x +c \right)^{2}}+\frac{b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a/sin(d*x+c)/cos(d*x+c)^2-15/8/d*a/sin(d*x+c)+15/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b/cos(d*x+c)^4+1/2/d*b/cos(d*x+c)^2+b*ln(tan(d*x+c))/d","A"
1490,1,151,121,0.355000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 b}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 b}{8 d \sin \left(d x +c \right)}+\frac{15 b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a/sin(d*x+c)^2+3*a*ln(tan(d*x+c))/d+1/4/d*b/sin(d*x+c)/cos(d*x+c)^4+5/8/d*b/sin(d*x+c)/cos(d*x+c)^2-15/8/d*b/sin(d*x+c)+15/8/d*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1491,1,173,139,0.371000," ","int(csc(d*x+c)^4*sec(d*x+c)^5*(a+b*sin(d*x+c)),x)","\frac{a}{4 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{4}}-\frac{7 a}{12 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{2}}+\frac{35 a}{24 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{35 a}{8 d \sin \left(d x +c \right)}+\frac{35 a \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 b}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 b}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 b \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a/sin(d*x+c)^3/cos(d*x+c)^4-7/12/d*a/sin(d*x+c)^3/cos(d*x+c)^2+35/24/d*a/sin(d*x+c)/cos(d*x+c)^2-35/8/d*a/sin(d*x+c)+35/8/d*a*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*b/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*b/sin(d*x+c)^2+3*b*ln(tan(d*x+c))/d","A"
1492,1,355,179,0.320000," ","int(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 a^{2} \sin \left(d x +c \right)}{8 d}+\frac{15 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{a b \left(\sin^{8}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}-\frac{a b \left(\sin^{6}\left(d x +c \right)\right)}{d}-\frac{3 a b \left(\sin^{4}\left(d x +c \right)\right)}{2 d}-\frac{3 a b \left(\sin^{2}\left(d x +c \right)\right)}{d}-\frac{6 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 b^{2} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{7 b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{35 b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{35 b^{2} \sin \left(d x +c \right)}{8 d}+\frac{35 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*a^2*sin(d*x+c)^7/cos(d*x+c)^2-3/8*a^2*sin(d*x+c)^5/d-5/8*a^2*sin(d*x+c)^3/d-15/8*a^2*sin(d*x+c)/d+15/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b*sin(d*x+c)^8/cos(d*x+c)^4-1/d*a*b*sin(d*x+c)^8/cos(d*x+c)^2-a*b*sin(d*x+c)^6/d-3/2*a*b*sin(d*x+c)^4/d-3*a*b*sin(d*x+c)^2/d-6/d*a*b*ln(cos(d*x+c))+1/4/d*b^2*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*b^2*sin(d*x+c)^9/cos(d*x+c)^2-5/8*b^2*sin(d*x+c)^7/d-7/8*b^2*sin(d*x+c)^5/d-35/24*b^2*sin(d*x+c)^3/d-35/8*b^2*sin(d*x+c)/d+35/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
1493,1,270,151,0.315000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{a b \left(\sin^{7}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{3 a b \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{3 a b \left(\sin^{5}\left(d x +c \right)\right)}{4 d}-\frac{5 a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{15 a b \sin \left(d x +c \right)}{4 d}+\frac{15 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{2} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^2*tan(d*x+c)^4-1/2/d*a^2*tan(d*x+c)^2-1/d*a^2*ln(cos(d*x+c))+1/2/d*a*b*sin(d*x+c)^7/cos(d*x+c)^4-3/4/d*a*b*sin(d*x+c)^7/cos(d*x+c)^2-3/4*a*b*sin(d*x+c)^5/d-5/4*a*b*sin(d*x+c)^3/d-15/4*a*b*sin(d*x+c)/d+15/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^2*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*b^2*sin(d*x+c)^8/cos(d*x+c)^2-1/2*b^2*sin(d*x+c)^6/d-3/4*b^2*sin(d*x+c)^4/d-3/2*b^2*sin(d*x+c)^2/d-3/d*b^2*ln(cos(d*x+c))","A"
1494,1,262,142,0.316000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a^{2} \sin \left(d x +c \right)}{8 d}+\frac{3 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b \left(\tan^{4}\left(d x +c \right)\right)}{2 d}-\frac{a b \left(\tan^{2}\left(d x +c \right)\right)}{d}-\frac{2 a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{5 b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 b^{2} \sin \left(d x +c \right)}{8 d}+\frac{15 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^2*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a^2*sin(d*x+c)^3/d-3/8*a^2*sin(d*x+c)/d+3/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b*tan(d*x+c)^4-1/d*a*b*tan(d*x+c)^2-2/d*a*b*ln(cos(d*x+c))+1/4/d*b^2*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*b^2*sin(d*x+c)^7/cos(d*x+c)^2-3/8*b^2*sin(d*x+c)^5/d-5/8*b^2*sin(d*x+c)^3/d-15/8*b^2*sin(d*x+c)/d+15/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
1495,1,168,108,0.304000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}-\frac{a b \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}-\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d}-\frac{3 a b \sin \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^2*sin(d*x+c)^4/cos(d*x+c)^4+1/2/d*a*b*sin(d*x+c)^5/cos(d*x+c)^4-1/4/d*a*b*sin(d*x+c)^5/cos(d*x+c)^2-1/4*a*b*sin(d*x+c)^3/d-3/4*a*b*sin(d*x+c)/d+3/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^2*tan(d*x+c)^4-1/2/d*b^2*tan(d*x+c)^2-1/d*b^2*ln(cos(d*x+c))","A"
1496,1,209,87,0.297000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x)","\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \sin \left(d x +c \right)}{8 d}-\frac{a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b \left(\sin^{4}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b^{2} \sin \left(d x +c \right)}{8 d}+\frac{3 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a^2*sin(d*x+c)/d-1/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*b^2*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b^2*sin(d*x+c)^5/cos(d*x+c)^2-1/8*b^2*sin(d*x+c)^3/d-3/8*b^2*sin(d*x+c)/d+3/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","B"
1497,1,122,66,0.257000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{a b \sin \left(d x +c \right)}{4 d}-\frac{a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2/cos(d*x+c)^4+1/2/d*a*b*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*a*b*sin(d*x+c)^3/cos(d*x+c)^2+1/4*a*b*sin(d*x+c)/d-1/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^2*sin(d*x+c)^4/cos(d*x+c)^4","A"
1498,1,125,118,0.606000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 a b \tan \left(d x +c \right) \sec \left(d x +c \right)}{4 d}+\frac{3 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2/cos(d*x+c)^4+1/2/d*a^2/cos(d*x+c)^2+1/d*a^2*ln(tan(d*x+c))+1/2/d*a*b*tan(d*x+c)*sec(d*x+c)^3+3/4/d*a*b*tan(d*x+c)*sec(d*x+c)+3/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^2/cos(d*x+c)^4","A"
1499,1,195,160,0.604000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a^{2}}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a^{2}}{8 d \sin \left(d x +c \right)}+\frac{15 a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a b}{2 d \cos \left(d x +c \right)^{4}}+\frac{a b}{d \cos \left(d x +c \right)^{2}}+\frac{2 a b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^2/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a^2/sin(d*x+c)/cos(d*x+c)^2-15/8/d*a^2/sin(d*x+c)+15/8/d*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*b/cos(d*x+c)^4+1/d*a*b/cos(d*x+c)^2+2/d*a*b*ln(tan(d*x+c))+1/4/d*b^2*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^2*tan(d*x+c)*sec(d*x+c)+3/8/d*b^2*ln(sec(d*x+c)+tan(d*x+c))","A"
1500,1,209,174,0.545000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x)","\frac{a^{2}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{2}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a^{2}}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{a b}{2 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a b}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a b}{4 d \sin \left(d x +c \right)}+\frac{15 a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{b^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{b^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^2/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a^2/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a^2/sin(d*x+c)^2+3/d*a^2*ln(tan(d*x+c))+1/2/d*a*b/sin(d*x+c)/cos(d*x+c)^4+5/4/d*a*b/sin(d*x+c)/cos(d*x+c)^2-15/4/d*a*b/sin(d*x+c)+15/4/d*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^2/cos(d*x+c)^4+1/2/d*b^2/cos(d*x+c)^2+1/d*b^2*ln(tan(d*x+c))","A"
1501,1,420,188,0.336000," ","int(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{a^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{a^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{9 a^{2} b \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{9 a^{2} b \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{15 a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{45 a^{2} b \sin \left(d x +c \right)}{8 d}+\frac{45 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a \,b^{2} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \,b^{2} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{9 a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d}-\frac{9 a \,b^{2} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{9 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{9}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{5 b^{3} \left(\sin^{9}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{5 b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d}-\frac{7 \left(\sin^{5}\left(d x +c \right)\right) b^{3}}{8 d}-\frac{35 b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{24 d}-\frac{35 b^{3} \sin \left(d x +c \right)}{8 d}+\frac{35 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3*tan(d*x+c)^4-1/2/d*a^3*tan(d*x+c)^2-1/d*a^3*ln(cos(d*x+c))+3/4/d*a^2*b*sin(d*x+c)^7/cos(d*x+c)^4-9/8/d*a^2*b*sin(d*x+c)^7/cos(d*x+c)^2-9/8/d*a^2*b*sin(d*x+c)^5-15/8/d*a^2*b*sin(d*x+c)^3-45/8*a^2*b*sin(d*x+c)/d+45/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a*b^2*sin(d*x+c)^8/cos(d*x+c)^4-3/2/d*a*b^2*sin(d*x+c)^8/cos(d*x+c)^2-3/2/d*a*b^2*sin(d*x+c)^6-9/4/d*a*b^2*sin(d*x+c)^4-9/2*a*b^2*sin(d*x+c)^2/d-9/d*a*b^2*ln(cos(d*x+c))+1/4/d*b^3*sin(d*x+c)^9/cos(d*x+c)^4-5/8/d*b^3*sin(d*x+c)^9/cos(d*x+c)^2-5/8/d*b^3*sin(d*x+c)^7-7/8/d*sin(d*x+c)^5*b^3-35/24*b^3*sin(d*x+c)^3/d-35/8*b^3*sin(d*x+c)/d+35/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","B"
1502,1,385,165,0.331000," ","int(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{a^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 a^{3} \sin \left(d x +c \right)}{8 d}+\frac{3 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a^{2} b \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a^{2} b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{9 a \,b^{2} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{9 a \,b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d}-\frac{15 a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{45 a \,b^{2} \sin \left(d x +c \right)}{8 d}+\frac{45 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3} \left(\sin^{8}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{3} \left(\sin^{8}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}-\frac{b^{3} \left(\sin^{6}\left(d x +c \right)\right)}{2 d}-\frac{3 \left(\sin^{4}\left(d x +c \right)\right) b^{3}}{4 d}-\frac{3 b^{3} \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^3*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*a^3*sin(d*x+c)^5/cos(d*x+c)^2-1/8*a^3*sin(d*x+c)^3/d-3/8*a^3*sin(d*x+c)/d+3/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^2*b*tan(d*x+c)^4-3/2/d*a^2*b*tan(d*x+c)^2-3/d*a^2*b*ln(cos(d*x+c))+3/4/d*a*b^2*sin(d*x+c)^7/cos(d*x+c)^4-9/8/d*a*b^2*sin(d*x+c)^7/cos(d*x+c)^2-9/8/d*a*b^2*sin(d*x+c)^5-15/8/d*a*b^2*sin(d*x+c)^3-45/8*a*b^2*sin(d*x+c)/d+45/8/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^3*sin(d*x+c)^8/cos(d*x+c)^4-1/2/d*b^3*sin(d*x+c)^8/cos(d*x+c)^2-1/2/d*b^3*sin(d*x+c)^6-3/4/d*sin(d*x+c)^4*b^3-3/2*b^3*sin(d*x+c)^2/d-3/d*b^3*ln(cos(d*x+c))","B"
1503,1,297,132,0.325000," ","int(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a^{2} b \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{9 a^{2} b \sin \left(d x +c \right)}{8 d}+\frac{9 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a \,b^{2} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{3 a \,b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{3 a \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 b^{3} \left(\sin^{7}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 \left(\sin^{5}\left(d x +c \right)\right) b^{3}}{8 d}-\frac{5 b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{15 b^{3} \sin \left(d x +c \right)}{8 d}+\frac{15 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3*sin(d*x+c)^4/cos(d*x+c)^4+3/4/d*a^2*b*sin(d*x+c)^5/cos(d*x+c)^4-3/8/d*a^2*b*sin(d*x+c)^5/cos(d*x+c)^2-3/8/d*a^2*b*sin(d*x+c)^3-9/8*a^2*b*sin(d*x+c)/d+9/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a*b^2*tan(d*x+c)^4-3/2/d*a*b^2*tan(d*x+c)^2-3/d*a*b^2*ln(cos(d*x+c))+1/4/d*b^3*sin(d*x+c)^7/cos(d*x+c)^4-3/8/d*b^3*sin(d*x+c)^7/cos(d*x+c)^2-3/8/d*sin(d*x+c)^5*b^3-5/8*b^3*sin(d*x+c)^3/d-15/8*b^3*sin(d*x+c)/d+15/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","B"
1504,1,263,136,0.317000," ","int(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x)","\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \sin \left(d x +c \right)}{8 d}-\frac{a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a \,b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{3 a \,b^{2} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{3 a \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{9 a \,b^{2} \sin \left(d x +c \right)}{8 d}+\frac{9 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3} \left(\tan^{4}\left(d x +c \right)\right)}{4 d}-\frac{b^{3} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}-\frac{b^{3} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*a^3*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*a^3*sin(d*x+c)^3/cos(d*x+c)^2+1/8*a^3*sin(d*x+c)/d-1/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^2*b*sin(d*x+c)^4/cos(d*x+c)^4+3/4/d*a*b^2*sin(d*x+c)^5/cos(d*x+c)^4-3/8/d*a*b^2*sin(d*x+c)^5/cos(d*x+c)^2-3/8/d*a*b^2*sin(d*x+c)^3-9/8*a*b^2*sin(d*x+c)/d+9/8/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^3*tan(d*x+c)^4-1/2/d*b^3*tan(d*x+c)^2-1/d*b^3*ln(cos(d*x+c))","A"
1505,1,231,84,0.307000," ","int(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b \sin \left(d x +c \right)}{8 d}-\frac{3 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}-\frac{b^{3} \left(\sin^{5}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}-\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d}-\frac{3 b^{3} \sin \left(d x +c \right)}{8 d}+\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3/cos(d*x+c)^4+3/4/d*a^2*b*sin(d*x+c)^3/cos(d*x+c)^4+3/8/d*a^2*b*sin(d*x+c)^3/cos(d*x+c)^2+3/8*a^2*b*sin(d*x+c)/d-3/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a*b^2*sin(d*x+c)^4/cos(d*x+c)^4+1/4/d*b^3*sin(d*x+c)^5/cos(d*x+c)^4-1/8/d*b^3*sin(d*x+c)^5/cos(d*x+c)^2-1/8*b^3*sin(d*x+c)^3/d-3/8*b^3*sin(d*x+c)/d+3/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","B"
1506,1,216,157,0.684000," ","int(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{4 d \cos \left(d x +c \right)^{4}}+\frac{a^{3}}{2 d \cos \left(d x +c \right)^{2}}+\frac{a^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a^{2} b \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{9 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a \,b^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{b^{3} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b^{3} \sin \left(d x +c \right)}{8 d}-\frac{b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3/cos(d*x+c)^4+1/2/d*a^3/cos(d*x+c)^2+1/d*a^3*ln(tan(d*x+c))+3/4/d*a^2*b*tan(d*x+c)*sec(d*x+c)^3+9/8/d*a^2*b*tan(d*x+c)*sec(d*x+c)+9/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a*b^2/cos(d*x+c)^4+1/4/d*b^3*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*b^3*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b^3*sin(d*x+c)/d-1/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
1507,1,221,163,0.641000," ","int(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{5 a^{3}}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{15 a^{3}}{8 d \sin \left(d x +c \right)}+\frac{15 a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a^{2} b}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a^{2} b}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a^{2} b \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 a \,b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 a \,b^{2} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{9 a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{b^{3}}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^3/sin(d*x+c)/cos(d*x+c)^4+5/8/d*a^3/sin(d*x+c)/cos(d*x+c)^2-15/8/d*a^3/sin(d*x+c)+15/8/d*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a^2*b/cos(d*x+c)^4+3/2/d*a^2*b/cos(d*x+c)^2+3/d*a^2*b*ln(tan(d*x+c))+3/4/d*a*b^2*tan(d*x+c)*sec(d*x+c)^3+9/8/d*a*b^2*tan(d*x+c)*sec(d*x+c)+9/8/d*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*b^3/cos(d*x+c)^4","A"
1508,1,285,211,0.739000," ","int(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x)","\frac{a^{3}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{4}}+\frac{3 a^{3}}{4 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{2}}-\frac{3 a^{3}}{2 d \sin \left(d x +c \right)^{2}}+\frac{3 a^{3} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b}{4 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}+\frac{15 a^{2} b}{8 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}-\frac{45 a^{2} b}{8 d \sin \left(d x +c \right)}+\frac{45 a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 a \,b^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{3 a \,b^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{3 a \,b^{2} \ln \left(\tan \left(d x +c \right)\right)}{d}+\frac{b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{3} \tan \left(d x +c \right) \sec \left(d x +c \right)}{8 d}+\frac{3 b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a^3/sin(d*x+c)^2/cos(d*x+c)^4+3/4/d*a^3/sin(d*x+c)^2/cos(d*x+c)^2-3/2/d*a^3/sin(d*x+c)^2+3/d*a^3*ln(tan(d*x+c))+3/4/d*a^2*b/sin(d*x+c)/cos(d*x+c)^4+15/8/d*a^2*b/sin(d*x+c)/cos(d*x+c)^2-45/8/d*a^2*b/sin(d*x+c)+45/8/d*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*a*b^2/cos(d*x+c)^4+3/2/d*a*b^2/cos(d*x+c)^2+3/d*a*b^2*ln(tan(d*x+c))+1/4/d*b^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^3*tan(d*x+c)*sec(d*x+c)+3/8/d*b^3*ln(sec(d*x+c)+tan(d*x+c))","A"
1509,0,0,283,5.405000," ","int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{4}\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x)","F"
1510,0,0,176,5.232000," ","int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{3}\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x)","F"
1511,0,0,150,4.755000," ","int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{2}\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x)","F"
1512,0,0,85,1.700000," ","int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x)","F"
1513,0,0,362,1.908000," ","int(sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x)","\int \frac{\left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right)}{a +b \sin \left(d x +c \right)}\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x)","F"
1514,0,0,475,2.260000," ","int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x)","\int \left(\sec^{5}\left(d x +c \right)\right) \left(\sin^{n}\left(d x +c \right)\right) \left(a +b \sin \left(d x +c \right)\right)^{p}\, dx"," ",0,"int(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x)","F"
1515,1,5578,461,1.104000," ","int(sec(f*x+e)^6*(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
1516,0,0,402,3.051000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x)","F"
1517,0,0,289,1.068000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x)","F"
1518,0,0,113,0.541000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x)","F"
1519,0,0,35,0.993000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x)","F"
1520,0,0,35,5.776000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x)","F"
1521,0,0,35,0.988000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x)","F"
1522,0,0,35,0.751000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right)^{m} \left(c +d \sin \left(f x +e \right)\right)^{\frac{4}{3}}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x)","F"
1523,0,0,524,3.253000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right)^{2} \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x)","F"
1524,0,0,347,1.188000," ","int(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(a +b \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x)","F"
1525,0,0,123,0.565000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x)","\int \left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x)","F"
1526,0,0,35,1.752000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{a +b \sin \left(f x +e \right)}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x)","F"
1527,0,0,35,6.540000," ","int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x)","\int \frac{\left(\cos^{2}\left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{n}}{\left(a +b \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x)","F"
1528,1,128,172,0.462000," ","int(cos(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{B b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)-\frac{A b \left(\cos^{8}\left(d x +c \right)\right)}{8}-\frac{a B \left(\cos^{8}\left(d x +c \right)\right)}{8}+\frac{a A \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}}{d}"," ",0,"1/d*(B*b*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))-1/8*A*b*cos(d*x+c)^8-1/8*a*B*cos(d*x+c)^8+1/7*a*A*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))","A"
1529,1,108,131,0.461000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{B b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)-\frac{A b \left(\cos^{6}\left(d x +c \right)\right)}{6}-\frac{a B \left(\cos^{6}\left(d x +c \right)\right)}{6}+\frac{a A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}}{d}"," ",0,"1/d*(B*b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))-1/6*A*b*cos(d*x+c)^6-1/6*a*B*cos(d*x+c)^6+1/5*a*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))","A"
1530,1,88,89,0.458000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{B b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)-\frac{A b \left(\cos^{4}\left(d x +c \right)\right)}{4}-\frac{a B \left(\cos^{4}\left(d x +c \right)\right)}{4}+\frac{a A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(B*b*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))-1/4*A*b*cos(d*x+c)^4-1/4*a*B*cos(d*x+c)^4+1/3*a*A*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
1531,1,44,48,0.225000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{\frac{B \left(\sin^{3}\left(d x +c \right)\right) b}{3}+\frac{\left(A b +a B \right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+A \sin \left(d x +c \right) a}{d}"," ",0,"1/d*(1/3*B*sin(d*x+c)^3*b+1/2*(A*b+B*a)*sin(d*x+c)^2+A*sin(d*x+c)*a)","A"
1532,1,83,60,0.358000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{A b \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{b B \sin \left(d x +c \right)}{d}+\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{a B \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))-1/d*A*b*ln(cos(d*x+c))-b*B*sin(d*x+c)/d+1/d*B*b*ln(sec(d*x+c)+tan(d*x+c))-1/d*a*B*ln(cos(d*x+c))","A"
1533,1,129,55,0.553000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a B}{2 d \cos \left(d x +c \right)^{2}}+\frac{A b}{2 d \cos \left(d x +c \right)^{2}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{b B \sin \left(d x +c \right)}{2 d}-\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*a*A*sec(d*x+c)*tan(d*x+c)+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*a*B/cos(d*x+c)^2+1/2/d*A*b/cos(d*x+c)^2+1/2/d*B*b*sin(d*x+c)^3/cos(d*x+c)^2+1/2*b*B*sin(d*x+c)/d-1/2/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","B"
1534,1,173,82,0.530000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a B}{4 d \cos \left(d x +c \right)^{4}}+\frac{A b}{4 d \cos \left(d x +c \right)^{4}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{b B \sin \left(d x +c \right)}{8 d}-\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/4/d*a*A*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a*A*sec(d*x+c)*tan(d*x+c)+3/8/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*a*B/cos(d*x+c)^4+1/4/d*A*b/cos(d*x+c)^4+1/4/d*B*b*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*B*b*sin(d*x+c)^3/cos(d*x+c)^2+1/8*b*B*sin(d*x+c)/d-1/8/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","B"
1535,1,217,110,0.556000," ","int(sec(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\frac{a A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a A \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{a B}{6 d \cos \left(d x +c \right)^{6}}+\frac{A b}{6 d \cos \left(d x +c \right)^{6}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{B b \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{b B \sin \left(d x +c \right)}{16 d}-\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}"," ",0,"1/6/d*a*A*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a*A*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a*A*sec(d*x+c)*tan(d*x+c)+5/16/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*a*B/cos(d*x+c)^6+1/6/d*A*b/cos(d*x+c)^6+1/6/d*B*b*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*B*b*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*B*b*sin(d*x+c)^3/cos(d*x+c)^2+1/16*b*B*sin(d*x+c)/d-1/16/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","A"
1536,1,229,333,0.479000," ","int(cos(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{a^{2} A \left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{7}-\frac{B \,a^{2} \left(\cos^{8}\left(d x +c \right)\right)}{8}-\frac{A a b \left(\cos^{8}\left(d x +c \right)\right)}{4}+2 B a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+A \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{8}\left(d x +c \right)\right)}{9}+\frac{\left(\frac{16}{5}+\cos^{6}\left(d x +c \right)+\frac{6 \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{8 \left(\cos^{2}\left(d x +c \right)\right)}{5}\right) \sin \left(d x +c \right)}{63}\right)+B \,b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{8}\left(d x +c \right)\right)}{10}-\frac{\left(\cos^{8}\left(d x +c \right)\right)}{40}\right)}{d}"," ",0,"1/d*(1/7*a^2*A*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c)-1/8*B*a^2*cos(d*x+c)^8-1/4*A*a*b*cos(d*x+c)^8+2*B*a*b*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+A*b^2*(-1/9*sin(d*x+c)*cos(d*x+c)^8+1/63*(16/5+cos(d*x+c)^6+6/5*cos(d*x+c)^4+8/5*cos(d*x+c)^2)*sin(d*x+c))+B*b^2*(-1/10*sin(d*x+c)^2*cos(d*x+c)^8-1/40*cos(d*x+c)^8))","A"
1537,1,199,219,0.540000," ","int(cos(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{a^{2} A \left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{5}-\frac{B \,a^{2} \left(\cos^{6}\left(d x +c \right)\right)}{6}-\frac{A a b \left(\cos^{6}\left(d x +c \right)\right)}{3}+2 B a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+A \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{6}\left(d x +c \right)\right)}{7}+\frac{\left(\frac{8}{3}+\cos^{4}\left(d x +c \right)+\frac{4 \left(\cos^{2}\left(d x +c \right)\right)}{3}\right) \sin \left(d x +c \right)}{35}\right)+B \,b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{6}\left(d x +c \right)\right)}{8}-\frac{\left(\cos^{6}\left(d x +c \right)\right)}{24}\right)}{d}"," ",0,"1/d*(1/5*a^2*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)-1/6*B*a^2*cos(d*x+c)^6-1/3*A*a*b*cos(d*x+c)^6+2*B*a*b*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+A*b^2*(-1/7*sin(d*x+c)*cos(d*x+c)^6+1/35*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c))+B*b^2*(-1/8*sin(d*x+c)^2*cos(d*x+c)^6-1/24*cos(d*x+c)^6))","A"
1538,1,169,124,0.480000," ","int(cos(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}-\frac{B \,a^{2} \left(\cos^{4}\left(d x +c \right)\right)}{4}-\frac{A a b \left(\cos^{4}\left(d x +c \right)\right)}{2}+2 B a b \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+A \,b^{2} \left(-\frac{\sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right)}{5}+\frac{\left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{15}\right)+B \,b^{2} \left(-\frac{\left(\sin^{2}\left(d x +c \right)\right) \left(\cos^{4}\left(d x +c \right)\right)}{6}-\frac{\left(\cos^{4}\left(d x +c \right)\right)}{12}\right)}{d}"," ",0,"1/d*(1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)-1/4*B*a^2*cos(d*x+c)^4-1/2*A*a*b*cos(d*x+c)^4+2*B*a*b*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+A*b^2*(-1/5*sin(d*x+c)*cos(d*x+c)^4+1/15*(2+cos(d*x+c)^2)*sin(d*x+c))+B*b^2*(-1/6*sin(d*x+c)^2*cos(d*x+c)^4-1/12*cos(d*x+c)^4))","A"
1539,1,73,50,0.240000," ","int(cos(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{\frac{B \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4}+\frac{\left(A \,b^{2}+2 B a b \right) \left(\sin^{3}\left(d x +c \right)\right)}{3}+\frac{\left(2 A a b +B \,a^{2}\right) \left(\sin^{2}\left(d x +c \right)\right)}{2}+a^{2} A \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/4*B*b^2*sin(d*x+c)^4+1/3*(A*b^2+2*B*a*b)*sin(d*x+c)^3+1/2*(2*A*a*b+B*a^2)*sin(d*x+c)^2+a^2*A*sin(d*x+c))","A"
1540,1,161,88,0.375000," ","int(sec(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{B \,a^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}-\frac{2 A a b \ln \left(\cos \left(d x +c \right)\right)}{d}+\frac{2 B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{2 B a b \sin \left(d x +c \right)}{d}+\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}-\frac{A \,b^{2} \sin \left(d x +c \right)}{d}-\frac{b^{2} B \left(\sin^{2}\left(d x +c \right)\right)}{2 d}-\frac{B \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))-1/d*B*a^2*ln(cos(d*x+c))-2/d*A*a*b*ln(cos(d*x+c))+2/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))-2/d*B*a*b*sin(d*x+c)+1/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))-1/d*A*b^2*sin(d*x+c)-1/2*b^2*B*sin(d*x+c)^2/d-1/d*B*b^2*ln(cos(d*x+c))","A"
1541,1,231,106,0.584000," ","int(sec(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{B \,a^{2}}{2 d \cos \left(d x +c \right)^{2}}+\frac{A a b}{d \cos \left(d x +c \right)^{2}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{d \cos \left(d x +c \right)^{2}}+\frac{B a b \sin \left(d x +c \right)}{d}-\frac{B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{2}}+\frac{A \,b^{2} \sin \left(d x +c \right)}{2 d}-\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{B \,b^{2} \left(\tan^{2}\left(d x +c \right)\right)}{2 d}+\frac{B \,b^{2} \ln \left(\cos \left(d x +c \right)\right)}{d}"," ",0,"1/2/d*a^2*A*sec(d*x+c)*tan(d*x+c)+1/2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*B*a^2/cos(d*x+c)^2+1/d*A*a*b/cos(d*x+c)^2+1/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^2+1/d*B*a*b*sin(d*x+c)-1/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/2/d*A*b^2*sin(d*x+c)-1/2/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*B*b^2*tan(d*x+c)^2+1/d*B*b^2*ln(cos(d*x+c))","B"
1542,1,299,116,0.556000," ","int(sec(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{B \,a^{2}}{4 d \cos \left(d x +c \right)^{4}}+\frac{A a b}{2 d \cos \left(d x +c \right)^{4}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{2 d \cos \left(d x +c \right)^{4}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{2}}+\frac{B a b \sin \left(d x +c \right)}{4 d}-\frac{B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{A \,b^{2} \sin \left(d x +c \right)}{8 d}-\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{B \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}"," ",0,"1/4/d*a^2*A*tan(d*x+c)*sec(d*x+c)^3+3/8/d*a^2*A*sec(d*x+c)*tan(d*x+c)+3/8/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*B*a^2/cos(d*x+c)^4+1/2/d*A*a*b/cos(d*x+c)^4+1/2/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^4+1/4/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^2+1/4/d*B*a*b*sin(d*x+c)-1/4/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/8/d*A*b^2*sin(d*x+c)-1/8/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*B*b^2*sin(d*x+c)^4/cos(d*x+c)^4","B"
1543,1,396,152,0.583000," ","int(sec(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x)","\frac{a^{2} A \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{5 a^{2} A \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{5 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{5 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{B \,a^{2}}{6 d \cos \left(d x +c \right)^{6}}+\frac{A a b}{3 d \cos \left(d x +c \right)^{6}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{3 d \cos \left(d x +c \right)^{6}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{4 d \cos \left(d x +c \right)^{4}}+\frac{B a b \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{2}}+\frac{B a b \sin \left(d x +c \right)}{8 d}-\frac{B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{8 d \cos \left(d x +c \right)^{4}}+\frac{A \,b^{2} \left(\sin^{3}\left(d x +c \right)\right)}{16 d \cos \left(d x +c \right)^{2}}+\frac{A \,b^{2} \sin \left(d x +c \right)}{16 d}-\frac{A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{B \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{6 d \cos \left(d x +c \right)^{6}}+\frac{B \,b^{2} \left(\sin^{4}\left(d x +c \right)\right)}{12 d \cos \left(d x +c \right)^{4}}"," ",0,"1/6/d*a^2*A*tan(d*x+c)*sec(d*x+c)^5+5/24/d*a^2*A*tan(d*x+c)*sec(d*x+c)^3+5/16/d*a^2*A*sec(d*x+c)*tan(d*x+c)+5/16/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*B*a^2/cos(d*x+c)^6+1/3/d*A*a*b/cos(d*x+c)^6+1/3/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^6+1/4/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^4+1/8/d*B*a*b*sin(d*x+c)^3/cos(d*x+c)^2+1/8/d*B*a*b*sin(d*x+c)-1/8/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^6+1/8/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^4+1/16/d*A*b^2*sin(d*x+c)^3/cos(d*x+c)^2+1/16/d*A*b^2*sin(d*x+c)-1/16/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*B*b^2*sin(d*x+c)^4/cos(d*x+c)^6+1/12/d*B*b^2*sin(d*x+c)^4/cos(d*x+c)^4","B"
1544,1,689,303,0.399000," ","int(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","-\frac{3 A \left(\sin^{2}\left(d x +c \right)\right)}{2 d b}-\frac{A \left(\sin^{6}\left(d x +c \right)\right)}{6 d b}+\frac{3 A \sin \left(d x +c \right) a}{d \,b^{2}}+\frac{3 B \sin \left(d x +c \right) a^{4}}{d \,b^{5}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A}{d b}-\frac{3 B \sin \left(d x +c \right) a^{2}}{d \,b^{3}}+\frac{A \left(\sin^{3}\left(d x +c \right)\right) a^{3}}{3 d \,b^{4}}-\frac{B \left(\sin^{3}\left(d x +c \right)\right) a^{4}}{3 d \,b^{5}}-\frac{B \left(\sin^{3}\left(d x +c \right)\right)}{b d}-\frac{B \left(\sin^{7}\left(d x +c \right)\right)}{7 b d}+\frac{3 B \left(\sin^{5}\left(d x +c \right)\right)}{5 b d}+\frac{B \left(\sin^{6}\left(d x +c \right)\right) a}{6 d \,b^{2}}+\frac{B \left(\sin^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{3}}+\frac{B \left(\sin^{4}\left(d x +c \right)\right) a^{3}}{4 d \,b^{4}}+\frac{3 B \left(\sin^{2}\left(d x +c \right)\right) a}{2 d \,b^{2}}-\frac{B \left(\sin^{5}\left(d x +c \right)\right) a^{2}}{5 d \,b^{3}}-\frac{A \left(\sin^{4}\left(d x +c \right)\right) a^{2}}{4 d \,b^{3}}-\frac{3 B \left(\sin^{4}\left(d x +c \right)\right) a}{4 d \,b^{2}}-\frac{A \left(\sin^{2}\left(d x +c \right)\right) a^{4}}{2 d \,b^{5}}+\frac{3 A \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{3}}+\frac{B \left(\sin^{2}\left(d x +c \right)\right) a^{5}}{2 d \,b^{6}}-\frac{3 B \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{2 d \,b^{4}}+\frac{3 A \left(\sin^{4}\left(d x +c \right)\right)}{4 d b}-\frac{3 A \sin \left(d x +c \right) a^{3}}{d \,b^{4}}-\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{5}}{d \,b^{6}}+\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{3}}{d \,b^{4}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B a}{d \,b^{2}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{6}}{d \,b^{7}}-\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{2}}{d \,b^{3}}+\frac{B \sin \left(d x +c \right)}{b d}+\frac{A \left(\sin^{5}\left(d x +c \right)\right) a}{5 d \,b^{2}}+\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{4}}{d \,b^{5}}-\frac{B \sin \left(d x +c \right) a^{6}}{d \,b^{7}}+\frac{A \sin \left(d x +c \right) a^{5}}{d \,b^{6}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{7}}{d \,b^{8}}-\frac{A \left(\sin^{3}\left(d x +c \right)\right) a}{d \,b^{2}}"," ",0,"3/d/b^2*A*sin(d*x+c)*a+3/d/b^5*B*sin(d*x+c)*a^4-3/2/d/b*A*sin(d*x+c)^2+1/d/b*ln(a+b*sin(d*x+c))*A-1/6/d/b*A*sin(d*x+c)^6+3/4/d/b*A*sin(d*x+c)^4-3/d/b^3*B*sin(d*x+c)*a^2+1/6/d/b^2*B*sin(d*x+c)^6*a+1/5/d/b^2*A*sin(d*x+c)^5*a-1/5/d/b^3*B*sin(d*x+c)^5*a^2-1/4/d/b^3*A*sin(d*x+c)^4*a^2-3/d/b^4*A*sin(d*x+c)*a^3-3/d/b^6*ln(a+b*sin(d*x+c))*B*a^5+3/d/b^4*ln(a+b*sin(d*x+c))*B*a^3-1/d/b^2*ln(a+b*sin(d*x+c))*B*a-3/4/d/b^2*B*sin(d*x+c)^4*a+1/3/d/b^4*A*sin(d*x+c)^3*a^3-1/3/d/b^5*B*sin(d*x+c)^3*a^4-1/d/b^7*ln(a+b*sin(d*x+c))*A*a^6-3/d/b^3*ln(a+b*sin(d*x+c))*A*a^2-1/2/d/b^5*A*sin(d*x+c)^2*a^4+3/2/d/b^3*A*sin(d*x+c)^2*a^2+1/2/d/b^6*B*sin(d*x+c)^2*a^5-3/2/d/b^4*B*sin(d*x+c)^2*a^3-1/7*B*sin(d*x+c)^7/b/d+3/5*B*sin(d*x+c)^5/b/d-B*sin(d*x+c)^3/b/d+B*sin(d*x+c)/b/d-1/d/b^2*A*sin(d*x+c)^3*a+3/d/b^5*ln(a+b*sin(d*x+c))*A*a^4-1/d/b^7*B*sin(d*x+c)*a^6+1/d/b^6*A*sin(d*x+c)*a^5+1/d/b^8*ln(a+b*sin(d*x+c))*B*a^7+1/d/b^3*B*sin(d*x+c)^3*a^2+1/4/d/b^4*B*sin(d*x+c)^4*a^3+3/2/d/b^2*B*sin(d*x+c)^2*a","B"
1545,1,397,194,0.404000," ","int(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\frac{B \left(\sin^{5}\left(d x +c \right)\right)}{5 b d}+\frac{A \left(\sin^{4}\left(d x +c \right)\right)}{4 d b}-\frac{B \left(\sin^{4}\left(d x +c \right)\right) a}{4 d \,b^{2}}-\frac{A \left(\sin^{3}\left(d x +c \right)\right) a}{3 d \,b^{2}}+\frac{B \left(\sin^{3}\left(d x +c \right)\right) a^{2}}{3 d \,b^{3}}-\frac{2 B \left(\sin^{3}\left(d x +c \right)\right)}{3 b d}+\frac{A \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{3}}-\frac{A \left(\sin^{2}\left(d x +c \right)\right)}{d b}-\frac{B \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{2 d \,b^{4}}+\frac{B \left(\sin^{2}\left(d x +c \right)\right) a}{d \,b^{2}}-\frac{A \sin \left(d x +c \right) a^{3}}{d \,b^{4}}+\frac{2 A \sin \left(d x +c \right) a}{d \,b^{2}}+\frac{B \sin \left(d x +c \right) a^{4}}{d \,b^{5}}-\frac{2 B \sin \left(d x +c \right) a^{2}}{d \,b^{3}}+\frac{B \sin \left(d x +c \right)}{b d}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{4}}{d \,b^{5}}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A}{d b}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{5}}{d \,b^{6}}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{3}}{d \,b^{4}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B a}{d \,b^{2}}"," ",0,"1/5*B*sin(d*x+c)^5/b/d+1/4/d/b*A*sin(d*x+c)^4-1/4/d/b^2*B*sin(d*x+c)^4*a-1/3/d/b^2*A*sin(d*x+c)^3*a+1/3/d/b^3*B*sin(d*x+c)^3*a^2-2/3*B*sin(d*x+c)^3/b/d+1/2/d/b^3*A*sin(d*x+c)^2*a^2-1/d/b*A*sin(d*x+c)^2-1/2/d/b^4*B*sin(d*x+c)^2*a^3+1/d/b^2*B*sin(d*x+c)^2*a-1/d/b^4*A*sin(d*x+c)*a^3+2/d/b^2*A*sin(d*x+c)*a+1/d/b^5*B*sin(d*x+c)*a^4-2/d/b^3*B*sin(d*x+c)*a^2+B*sin(d*x+c)/b/d+1/d/b^5*ln(a+b*sin(d*x+c))*A*a^4-2/d/b^3*ln(a+b*sin(d*x+c))*A*a^2+1/d/b*ln(a+b*sin(d*x+c))*A-1/d/b^6*ln(a+b*sin(d*x+c))*B*a^5+2/d/b^4*ln(a+b*sin(d*x+c))*B*a^3-1/d/b^2*ln(a+b*sin(d*x+c))*B*a","B"
1546,1,186,107,0.395000," ","int(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","-\frac{B \left(\sin^{3}\left(d x +c \right)\right)}{3 b d}-\frac{A \left(\sin^{2}\left(d x +c \right)\right)}{2 d b}+\frac{B \left(\sin^{2}\left(d x +c \right)\right) a}{2 d \,b^{2}}+\frac{A \sin \left(d x +c \right) a}{d \,b^{2}}-\frac{B \sin \left(d x +c \right) a^{2}}{d \,b^{3}}+\frac{B \sin \left(d x +c \right)}{b d}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{2}}{d \,b^{3}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A}{d b}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{3}}{d \,b^{4}}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B a}{d \,b^{2}}"," ",0,"-1/3*B*sin(d*x+c)^3/b/d-1/2/d/b*A*sin(d*x+c)^2+1/2/d/b^2*B*sin(d*x+c)^2*a+1/d/b^2*A*sin(d*x+c)*a-1/d/b^3*B*sin(d*x+c)*a^2+B*sin(d*x+c)/b/d-1/d/b^3*ln(a+b*sin(d*x+c))*A*a^2+1/d/b*ln(a+b*sin(d*x+c))*A+1/d/b^4*ln(a+b*sin(d*x+c))*B*a^3-1/d/b^2*ln(a+b*sin(d*x+c))*B*a","A"
1547,1,56,41,0.253000," ","int(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\frac{B \sin \left(d x +c \right)}{b d}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A}{d b}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B a}{d \,b^{2}}"," ",0,"B*sin(d*x+c)/b/d+1/d/b*ln(a+b*sin(d*x+c))*A-1/d/b^2*ln(a+b*sin(d*x+c))*B*a","A"
1548,1,156,86,0.445000," ","int(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A}{d \left(2 a +2 b \right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{d \left(2 a +2 b \right)}-\frac{\ln \left(a +b \sin \left(d x +c \right)\right) A b}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) a B}{d \left(a +b \right) \left(a -b \right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{d \left(2 a -2 b \right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{d \left(2 a -2 b \right)}"," ",0,"-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)*A-1/d/(2*a+2*b)*ln(sin(d*x+c)-1)*B-1/d/(a+b)/(a-b)*ln(a+b*sin(d*x+c))*A*b+1/d/(a+b)/(a-b)*ln(a+b*sin(d*x+c))*a*B+1/d/(2*a-2*b)*ln(1+sin(d*x+c))*A-1/d/(2*a-2*b)*ln(1+sin(d*x+c))*B","A"
1549,1,297,153,0.496000," ","int(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","-\frac{A}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{B}{d \left(4 a +4 b \right) \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a A}{4 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A b}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B b}{4 d \left(a +b \right)^{2}}+\frac{b^{3} \ln \left(a +b \sin \left(d x +c \right)\right) A}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{b^{2} \ln \left(a +b \sin \left(d x +c \right)\right) a B}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}-\frac{A}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{B}{d \left(4 a -4 b \right) \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a A}{4 d \left(a -b \right)^{2}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) A b}{2 d \left(a -b \right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B b}{4 d \left(a -b \right)^{2}}"," ",0,"-1/d/(4*a+4*b)/(sin(d*x+c)-1)*A-1/d/(4*a+4*b)/(sin(d*x+c)-1)*B-1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*a*A-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*A*b-1/4/d/(a+b)^2*ln(sin(d*x+c)-1)*B*b+1/d*b^3/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*A-1/d*b^2/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*a*B-1/d/(4*a-4*b)/(1+sin(d*x+c))*A+1/d/(4*a-4*b)/(1+sin(d*x+c))*B+1/4/d/(a-b)^2*ln(1+sin(d*x+c))*a*A-1/2/d/(a-b)^2*ln(1+sin(d*x+c))*A*b+1/4/d/(a-b)^2*ln(1+sin(d*x+c))*B*b","A"
1550,1,586,255,0.506000," ","int(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\frac{A}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{B}{2 d \left(8 a +8 b \right) \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{3 a A}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{5 A b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{a B}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 B b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2} A}{16 d \left(a +b \right)^{3}}-\frac{9 \ln \left(\sin \left(d x +c \right)-1\right) A a b}{16 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A \,b^{2}}{2 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B a b}{16 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) B \,b^{2}}{16 d \left(a +b \right)^{3}}-\frac{b^{5} \ln \left(a +b \sin \left(d x +c \right)\right) A}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}+\frac{b^{4} \ln \left(a +b \sin \left(d x +c \right)\right) a B}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{A}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{2 d \left(8 a -8 b \right) \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 a A}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{5 A b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{a B}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}-\frac{3 B b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2} A}{16 d \left(a -b \right)^{3}}-\frac{9 \ln \left(1+\sin \left(d x +c \right)\right) A a b}{16 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A \,b^{2}}{2 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B a b}{16 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) B \,b^{2}}{16 d \left(a -b \right)^{3}}"," ",0,"1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2*A+1/2/d/(8*a+8*b)/(sin(d*x+c)-1)^2*B-3/16/d/(a+b)^2/(sin(d*x+c)-1)*a*A-5/16/d/(a+b)^2/(sin(d*x+c)-1)*A*b-1/16/d/(a+b)^2/(sin(d*x+c)-1)*a*B-3/16/d/(a+b)^2/(sin(d*x+c)-1)*B*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*a^2*A-9/16/d/(a+b)^3*ln(sin(d*x+c)-1)*A*a*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*A*b^2-1/16/d/(a+b)^3*ln(sin(d*x+c)-1)*B*a*b-3/16/d/(a+b)^3*ln(sin(d*x+c)-1)*B*b^2-1/d*b^5/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*A+1/d*b^4/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*a*B-1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2*A+1/2/d/(8*a-8*b)/(1+sin(d*x+c))^2*B-3/16/d/(a-b)^2/(1+sin(d*x+c))*a*A+5/16/d/(a-b)^2/(1+sin(d*x+c))*A*b+1/16/d/(a-b)^2/(1+sin(d*x+c))*a*B-3/16/d/(a-b)^2/(1+sin(d*x+c))*B*b+3/16/d/(a-b)^3*ln(1+sin(d*x+c))*a^2*A-9/16/d/(a-b)^3*ln(1+sin(d*x+c))*A*a*b+1/2/d/(a-b)^3*ln(1+sin(d*x+c))*A*b^2+1/16/d/(a-b)^3*ln(1+sin(d*x+c))*B*a*b-3/16/d/(a-b)^3*ln(1+sin(d*x+c))*B*b^2","B"
1551,1,990,373,0.505000," ","int(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","-\frac{\ln \left(1+\sin \left(d x +c \right)\right) A \,b^{3}}{2 d \left(a -b \right)^{4}}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) B \,b^{3}}{32 d \left(a -b \right)^{4}}-\frac{5 a^{2} A}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}+\frac{a B}{32 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B \,a^{2} b}{32 d \left(a +b \right)^{4}}-\frac{29 \ln \left(\sin \left(d x +c \right)-1\right) A a \,b^{2}}{32 d \left(a +b \right)^{4}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) B \,b^{3}}{32 d \left(a +b \right)^{4}}-\frac{5 a^{2} A}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{11 A \,b^{2}}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{B \,a^{2}}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{B a b}{8 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{A}{3 d \left(16 a +16 b \right) \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{B}{3 d \left(16 a +16 b \right) \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{A}{3 d \left(16 a -16 b \right) \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{3 d \left(16 a -16 b \right) \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{3 A b}{32 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5 B \,b^{2}}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{7 A a b}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) a^{3} A}{32 d \left(a -b \right)^{4}}-\frac{b^{6} \ln \left(a +b \sin \left(d x +c \right)\right) a B}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B a \,b^{2}}{8 d \left(a +b \right)^{4}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B \,a^{2} b}{32 d \left(a -b \right)^{4}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) A \,a^{2} b}{8 d \left(a +b \right)^{4}}+\frac{b^{7} \ln \left(a +b \sin \left(d x +c \right)\right) A}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) A \,a^{2} b}{8 d \left(a -b \right)^{4}}-\frac{a A}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{3 A b}{32 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{7 A a b}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{29 \ln \left(1+\sin \left(d x +c \right)\right) A a \,b^{2}}{32 d \left(a -b \right)^{4}}-\frac{B a b}{8 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) B a \,b^{2}}{8 d \left(a -b \right)^{4}}+\frac{5 B \,b^{2}}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{B \,a^{2}}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}+\frac{B b}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{a A}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) a^{3} A}{32 d \left(a +b \right)^{4}}+\frac{a B}{32 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{11 A \,b^{2}}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{B b}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A \,b^{3}}{2 d \left(a +b \right)^{4}}"," ",0,"-1/2/d/(a-b)^4*ln(1+sin(d*x+c))*A*b^3+5/32/d/(a-b)^4*ln(1+sin(d*x+c))*B*b^3-5/32/d/(a+b)^3/(sin(d*x+c)-1)*a^2*A+1/32/d/(a-b)^2/(1+sin(d*x+c))^2*a*B-1/32/d/(a+b)^4*ln(sin(d*x+c)-1)*B*a^2*b-29/32/d/(a+b)^4*ln(sin(d*x+c)-1)*A*a*b^2-5/32/d/(a+b)^4*ln(sin(d*x+c)-1)*B*b^3-5/32/d/(a-b)^3/(1+sin(d*x+c))*a^2*A-11/32/d/(a-b)^3/(1+sin(d*x+c))*A*b^2+1/32/d/(a-b)^3/(1+sin(d*x+c))*B*a^2-1/8/d/(a+b)^3/(sin(d*x+c)-1)*B*a*b-1/3/d/(16*a+16*b)/(sin(d*x+c)-1)^3*A-1/3/d/(16*a+16*b)/(sin(d*x+c)-1)^3*B-1/3/d/(16*a-16*b)/(1+sin(d*x+c))^3*A+1/3/d/(16*a-16*b)/(1+sin(d*x+c))^3*B+3/32/d/(a+b)^2/(sin(d*x+c)-1)^2*A*b-5/32/d/(a+b)^3/(sin(d*x+c)-1)*B*b^2-7/16/d/(a+b)^3/(sin(d*x+c)-1)*A*a*b+5/32/d/(a-b)^4*ln(1+sin(d*x+c))*a^3*A-1/d*b^6/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*a*B-1/8/d/(a+b)^4*ln(sin(d*x+c)-1)*B*a*b^2+1/32/d/(a-b)^4*ln(1+sin(d*x+c))*B*a^2*b-5/8/d/(a+b)^4*ln(sin(d*x+c)-1)*A*a^2*b+1/d*b^7/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*A-5/8/d/(a-b)^4*ln(1+sin(d*x+c))*A*a^2*b-1/16/d/(a-b)^2/(1+sin(d*x+c))^2*a*A+3/32/d/(a-b)^2/(1+sin(d*x+c))^2*A*b+7/16/d/(a-b)^3/(1+sin(d*x+c))*A*a*b+29/32/d/(a-b)^4*ln(1+sin(d*x+c))*A*a*b^2-1/8/d/(a-b)^3/(1+sin(d*x+c))*B*a*b-1/8/d/(a-b)^4*ln(1+sin(d*x+c))*B*a*b^2+5/32/d/(a-b)^3/(1+sin(d*x+c))*B*b^2-1/32/d/(a+b)^3/(sin(d*x+c)-1)*B*a^2+1/16/d/(a+b)^2/(sin(d*x+c)-1)^2*B*b+1/16/d/(a+b)^2/(sin(d*x+c)-1)^2*a*A-5/32/d/(a+b)^4*ln(sin(d*x+c)-1)*a^3*A+1/32/d/(a+b)^2/(sin(d*x+c)-1)^2*a*B-11/32/d/(a+b)^3/(sin(d*x+c)-1)*A*b^2-1/16/d/(a-b)^2/(1+sin(d*x+c))^2*B*b-1/2/d/(a+b)^4*ln(sin(d*x+c)-1)*A*b^3","B"
1552,1,721,314,0.695000," ","int(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","\frac{4 B \left(\sin^{3}\left(d x +c \right)\right) a^{3}}{3 d \,b^{5}}-\frac{3 B \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}-\frac{A \left(\sin^{5}\left(d x +c \right)\right)}{5 d \,b^{2}}+\frac{A \left(\sin^{3}\left(d x +c \right)\right)}{d \,b^{2}}-\frac{B \left(\sin^{6}\left(d x +c \right)\right)}{6 b^{2} d}+\frac{3 B \left(\sin^{4}\left(d x +c \right)\right)}{4 b^{2} d}-\frac{3 A \sin \left(d x +c \right)}{d \,b^{2}}-\frac{A}{d b \left(a +b \sin \left(d x +c \right)\right)}+\frac{6 B \,a^{5} \sin \left(d x +c \right)}{d \,b^{7}}-\frac{12 B \,a^{3} \sin \left(d x +c \right)}{d \,b^{5}}+\frac{9 A \,a^{2} \sin \left(d x +c \right)}{d \,b^{4}}+\frac{3 B \,a^{5}}{d \,b^{6} \left(a +b \sin \left(d x +c \right)\right)}-\frac{3 B \,a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a B}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}-\frac{B \,a^{7}}{d \,b^{8} \left(a +b \sin \left(d x +c \right)\right)}-\frac{7 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{6}}{d \,b^{8}}+\frac{15 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{4}}{d \,b^{6}}-\frac{9 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \,b^{4}}+\frac{A \,a^{6}}{d \,b^{7} \left(a +b \sin \left(d x +c \right)\right)}-\frac{3 A \,a^{4}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 B \left(\sin^{3}\left(d x +c \right)\right) a}{d \,b^{3}}+\frac{2 A \left(\sin^{2}\left(d x +c \right)\right) a^{3}}{d \,b^{5}}-\frac{3 A \left(\sin^{2}\left(d x +c \right)\right) a}{d \,b^{3}}-\frac{5 B \left(\sin^{2}\left(d x +c \right)\right) a^{4}}{2 d \,b^{6}}+\frac{9 B \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{4}}+\frac{2 B \left(\sin^{5}\left(d x +c \right)\right) a}{5 d \,b^{3}}+\frac{A \left(\sin^{4}\left(d x +c \right)\right) a}{2 d \,b^{3}}-\frac{3 B \left(\sin^{4}\left(d x +c \right)\right) a^{2}}{4 d \,b^{4}}-\frac{A \left(\sin^{3}\left(d x +c \right)\right) a^{2}}{d \,b^{4}}+\frac{3 A \,a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{5 A \,a^{4} \sin \left(d x +c \right)}{d \,b^{6}}+\frac{6 B a \sin \left(d x +c \right)}{d \,b^{3}}+\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{5}}{d \,b^{7}}-\frac{12 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{3}}{d \,b^{5}}+\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \,b^{3}}+\frac{B \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{2} d}"," ",0,"2/5/d/b^3*B*sin(d*x+c)^5*a-1/5/d/b^2*A*sin(d*x+c)^5+1/d/b^2*A*sin(d*x+c)^3-3/d/b^2*A*sin(d*x+c)-1/d/b/(a+b*sin(d*x+c))*A+1/2/d/b^3*A*sin(d*x+c)^4*a-3/4/d/b^4*B*sin(d*x+c)^4*a^2-1/d/b^4*A*sin(d*x+c)^3*a^2+6/d/b^7*B*a^5*sin(d*x+c)-12/d/b^5*B*a^3*sin(d*x+c)+9/d/b^4*A*a^2*sin(d*x+c)+3/d/b^6/(a+b*sin(d*x+c))*B*a^5-3/d/b^4/(a+b*sin(d*x+c))*B*a^3+1/d/b^2/(a+b*sin(d*x+c))*a*B-1/d/b^8/(a+b*sin(d*x+c))*B*a^7-7/d/b^8*ln(a+b*sin(d*x+c))*B*a^6+15/d/b^6*ln(a+b*sin(d*x+c))*B*a^4-9/d/b^4*ln(a+b*sin(d*x+c))*B*a^2+1/d/b^7/(a+b*sin(d*x+c))*A*a^6-3/d/b^5/(a+b*sin(d*x+c))*A*a^4-1/6*B*sin(d*x+c)^6/b^2/d+3/4*B*sin(d*x+c)^4/b^2/d-3/2*B*sin(d*x+c)^2/b^2/d+3/d/b^3/(a+b*sin(d*x+c))*A*a^2+4/3/d/b^5*B*sin(d*x+c)^3*a^3-2/d/b^3*B*sin(d*x+c)^3*a+2/d/b^5*A*sin(d*x+c)^2*a^3-3/d/b^3*A*sin(d*x+c)^2*a-5/2/d/b^6*B*sin(d*x+c)^2*a^4+9/2/d/b^4*B*sin(d*x+c)^2*a^2-5/d/b^6*A*a^4*sin(d*x+c)+6/d/b^3*B*a*sin(d*x+c)+6/d/b^7*ln(a+b*sin(d*x+c))*A*a^5-12/d/b^5*ln(a+b*sin(d*x+c))*A*a^3+6/d/b^3*ln(a+b*sin(d*x+c))*A*a+B*ln(a+b*sin(d*x+c))/b^2/d","B"
1553,1,422,200,0.661000," ","int(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","\frac{B \left(\sin^{4}\left(d x +c \right)\right)}{4 b^{2} d}+\frac{A \left(\sin^{3}\left(d x +c \right)\right)}{3 d \,b^{2}}-\frac{2 B \left(\sin^{3}\left(d x +c \right)\right) a}{3 d \,b^{3}}-\frac{A \left(\sin^{2}\left(d x +c \right)\right) a}{d \,b^{3}}+\frac{3 B \left(\sin^{2}\left(d x +c \right)\right) a^{2}}{2 d \,b^{4}}-\frac{B \left(\sin^{2}\left(d x +c \right)\right)}{b^{2} d}+\frac{3 A \,a^{2} \sin \left(d x +c \right)}{d \,b^{4}}-\frac{2 A \sin \left(d x +c \right)}{d \,b^{2}}-\frac{4 B \,a^{3} \sin \left(d x +c \right)}{d \,b^{5}}+\frac{4 B a \sin \left(d x +c \right)}{d \,b^{3}}-\frac{4 \ln \left(a +b \sin \left(d x +c \right)\right) A \,a^{3}}{d \,b^{5}}+\frac{4 \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \,b^{3}}+\frac{5 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{4}}{d \,b^{6}}-\frac{6 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \,b^{4}}+\frac{B \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{2} d}-\frac{A \,a^{4}}{d \,b^{5} \left(a +b \sin \left(d x +c \right)\right)}+\frac{2 A \,a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{A}{d b \left(a +b \sin \left(d x +c \right)\right)}+\frac{B \,a^{5}}{d \,b^{6} \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 B \,a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a B}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"1/4*B*sin(d*x+c)^4/b^2/d+1/3/d/b^2*A*sin(d*x+c)^3-2/3/d/b^3*B*sin(d*x+c)^3*a-1/d/b^3*A*sin(d*x+c)^2*a+3/2/d/b^4*B*sin(d*x+c)^2*a^2-B*sin(d*x+c)^2/b^2/d+3/d/b^4*A*a^2*sin(d*x+c)-2/d/b^2*A*sin(d*x+c)-4/d/b^5*B*a^3*sin(d*x+c)+4/d/b^3*B*a*sin(d*x+c)-4/d/b^5*ln(a+b*sin(d*x+c))*A*a^3+4/d/b^3*ln(a+b*sin(d*x+c))*A*a+5/d/b^6*ln(a+b*sin(d*x+c))*B*a^4-6/d/b^4*ln(a+b*sin(d*x+c))*B*a^2+B*ln(a+b*sin(d*x+c))/b^2/d-1/d/b^5/(a+b*sin(d*x+c))*A*a^4+2/d/b^3/(a+b*sin(d*x+c))*A*a^2-1/d/b/(a+b*sin(d*x+c))*A+1/d/b^6/(a+b*sin(d*x+c))*B*a^5-2/d/b^4/(a+b*sin(d*x+c))*B*a^3+1/d/b^2/(a+b*sin(d*x+c))*a*B","B"
1554,1,202,111,0.662000," ","int(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","-\frac{B \left(\sin^{2}\left(d x +c \right)\right)}{2 b^{2} d}-\frac{A \sin \left(d x +c \right)}{d \,b^{2}}+\frac{2 B a \sin \left(d x +c \right)}{d \,b^{3}}+\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \,b^{3}}-\frac{3 \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \,b^{4}}+\frac{B \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{2} d}+\frac{A \,a^{2}}{d \,b^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{A}{d b \left(a +b \sin \left(d x +c \right)\right)}-\frac{B \,a^{3}}{d \,b^{4} \left(a +b \sin \left(d x +c \right)\right)}+\frac{a B}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-1/2*B*sin(d*x+c)^2/b^2/d-1/d/b^2*A*sin(d*x+c)+2/d/b^3*B*a*sin(d*x+c)+2/d/b^3*ln(a+b*sin(d*x+c))*A*a-3/d/b^4*ln(a+b*sin(d*x+c))*B*a^2+B*ln(a+b*sin(d*x+c))/b^2/d+1/d/b^3/(a+b*sin(d*x+c))*A*a^2-1/d/b/(a+b*sin(d*x+c))*A-1/d/b^4/(a+b*sin(d*x+c))*B*a^3+1/d/b^2/(a+b*sin(d*x+c))*a*B","A"
1555,1,63,47,0.412000," ","int(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","\frac{B \ln \left(a +b \sin \left(d x +c \right)\right)}{b^{2} d}-\frac{A}{d b \left(a +b \sin \left(d x +c \right)\right)}+\frac{a B}{d \,b^{2} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"B*ln(a+b*sin(d*x+c))/b^2/d-1/d/b/(a+b*sin(d*x+c))*A+1/d/b^2/(a+b*sin(d*x+c))*a*B","A"
1556,1,240,131,0.686000," ","int(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) A}{2 d \left(a +b \right)^{2}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B}{2 d \left(a +b \right)^{2}}+\frac{A b}{d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)}-\frac{a B}{d \left(a +b \right) \left(a -b \right) \left(a +b \sin \left(d x +c \right)\right)}-\frac{2 \ln \left(a +b \sin \left(d x +c \right)\right) A a b}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(a +b \sin \left(d x +c \right)\right) B \,b^{2}}{d \left(a +b \right)^{2} \left(a -b \right)^{2}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) A}{2 d \left(a -b \right)^{2}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) B}{2 d \left(a -b \right)^{2}}"," ",0,"-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*A-1/2/d/(a+b)^2*ln(sin(d*x+c)-1)*B+1/d/(a+b)/(a-b)/(a+b*sin(d*x+c))*A*b-1/d/(a+b)/(a-b)/(a+b*sin(d*x+c))*a*B-2/d/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*A*a*b+1/d/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*B*a^2+1/d/(a+b)^2/(a-b)^2*ln(a+b*sin(d*x+c))*B*b^2+1/2/d/(a-b)^2*ln(1+sin(d*x+c))*A-1/2/d/(a-b)^2*ln(1+sin(d*x+c))*B","A"
1557,1,388,220,0.805000," ","int(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","-\frac{A}{4 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{B}{4 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) a A}{4 d \left(a +b \right)^{3}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) A b}{4 d \left(a +b \right)^{3}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B b}{2 d \left(a +b \right)^{3}}-\frac{b^{3} A}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{b^{2} a B}{d \left(a +b \right)^{2} \left(a -b \right)^{2} \left(a +b \sin \left(d x +c \right)\right)}+\frac{4 b^{3} \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{3 b^{2} \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{b^{4} \ln \left(a +b \sin \left(d x +c \right)\right) B}{d \left(a +b \right)^{3} \left(a -b \right)^{3}}-\frac{A}{4 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{B}{4 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) a A}{4 d \left(a -b \right)^{3}}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) A b}{4 d \left(a -b \right)^{3}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B b}{2 d \left(a -b \right)^{3}}"," ",0,"-1/4/d/(a+b)^2/(sin(d*x+c)-1)*A-1/4/d/(a+b)^2/(sin(d*x+c)-1)*B-1/4/d/(a+b)^3*ln(sin(d*x+c)-1)*a*A-3/4/d/(a+b)^3*ln(sin(d*x+c)-1)*A*b-1/2/d/(a+b)^3*ln(sin(d*x+c)-1)*B*b-1/d*b^3/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))*A+1/d*b^2/(a+b)^2/(a-b)^2/(a+b*sin(d*x+c))*a*B+4/d*b^3/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*A*a-3/d*b^2/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*B*a^2-1/d*b^4/(a+b)^3/(a-b)^3*ln(a+b*sin(d*x+c))*B-1/4/d/(a-b)^2/(1+sin(d*x+c))*A+1/4/d/(a-b)^2/(1+sin(d*x+c))*B+1/4/d/(a-b)^3*ln(1+sin(d*x+c))*a*A-3/4/d/(a-b)^3*ln(1+sin(d*x+c))*A*b+1/2/d/(a-b)^3*ln(1+sin(d*x+c))*B*b","A"
1558,1,675,362,0.816000," ","int(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B a b}{8 d \left(a +b \right)^{4}}+\frac{b^{6} \ln \left(a +b \sin \left(d x +c \right)\right) B}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{b^{5} A}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}-\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) A a b}{4 d \left(a -b \right)^{4}}+\frac{a B}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}-\frac{5 B b}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{3 \ln \left(1+\sin \left(d x +c \right)\right) a^{2} A}{16 d \left(a -b \right)^{4}}+\frac{A}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{B}{16 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{A}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{B}{16 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{6 b^{5} \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}+\frac{5 b^{4} \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \left(a +b \right)^{4} \left(a -b \right)^{4}}-\frac{b^{4} a B}{d \left(a +b \right)^{3} \left(a -b \right)^{3} \left(a +b \sin \left(d x +c \right)\right)}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B a b}{8 d \left(a -b \right)^{4}}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) A a b}{4 d \left(a +b \right)^{4}}+\frac{7 A b}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}+\frac{15 \ln \left(1+\sin \left(d x +c \right)\right) A \,b^{2}}{16 d \left(a -b \right)^{4}}-\frac{\ln \left(1+\sin \left(d x +c \right)\right) B \,b^{2}}{2 d \left(a -b \right)^{4}}-\frac{3 a A}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{7 A b}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{a B}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{5 B b}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)}-\frac{3 \ln \left(\sin \left(d x +c \right)-1\right) a^{2} A}{16 d \left(a +b \right)^{4}}-\frac{15 \ln \left(\sin \left(d x +c \right)-1\right) A \,b^{2}}{16 d \left(a +b \right)^{4}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B \,b^{2}}{2 d \left(a +b \right)^{4}}-\frac{3 a A}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)}"," ",0,"-1/8/d/(a+b)^4*ln(sin(d*x+c)-1)*B*a*b+1/d*b^6/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*B+1/d*b^5/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))*A-3/4/d/(a-b)^4*ln(1+sin(d*x+c))*A*a*b+1/16/d/(a-b)^3/(1+sin(d*x+c))*a*B-5/16/d/(a-b)^3/(1+sin(d*x+c))*B*b+3/16/d/(a-b)^4*ln(1+sin(d*x+c))*a^2*A+1/16/d/(a+b)^2/(sin(d*x+c)-1)^2*A+1/16/d/(a+b)^2/(sin(d*x+c)-1)^2*B-1/16/d/(a-b)^2/(1+sin(d*x+c))^2*A+1/16/d/(a-b)^2/(1+sin(d*x+c))^2*B-6/d*b^5/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*A*a+5/d*b^4/(a+b)^4/(a-b)^4*ln(a+b*sin(d*x+c))*B*a^2-1/d*b^4/(a+b)^3/(a-b)^3/(a+b*sin(d*x+c))*a*B+1/8/d/(a-b)^4*ln(1+sin(d*x+c))*B*a*b-3/4/d/(a+b)^4*ln(sin(d*x+c)-1)*A*a*b+7/16/d/(a-b)^3/(1+sin(d*x+c))*A*b+15/16/d/(a-b)^4*ln(1+sin(d*x+c))*A*b^2-1/2/d/(a-b)^4*ln(1+sin(d*x+c))*B*b^2-3/16/d/(a+b)^3/(sin(d*x+c)-1)*a*A-7/16/d/(a+b)^3/(sin(d*x+c)-1)*A*b-1/16/d/(a+b)^3/(sin(d*x+c)-1)*a*B-5/16/d/(a+b)^3/(sin(d*x+c)-1)*B*b-3/16/d/(a+b)^4*ln(sin(d*x+c)-1)*a^2*A-15/16/d/(a+b)^4*ln(sin(d*x+c)-1)*A*b^2-1/2/d/(a+b)^4*ln(sin(d*x+c)-1)*B*b^2-3/16/d/(a-b)^3/(1+sin(d*x+c))*a*A","A"
1559,1,1080,538,0.859000," ","int(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x)","-\frac{19 A \,b^{2}}{32 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{a A}{16 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{A b}{8 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{a B}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}+\frac{3 B b}{32 d \left(a +b \right)^{3} \left(\sin \left(d x +c \right)-1\right)^{2}}-\frac{5 a^{2} A}{32 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{19 A \,b^{2}}{32 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{B \,a^{2}}{32 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{11 B \,b^{2}}{32 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}+\frac{B \,a^{2}}{32 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{11 B \,b^{2}}{32 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) a^{3} A}{32 d \left(a -b \right)^{5}}-\frac{35 \ln \left(1+\sin \left(d x +c \right)\right) b^{3} A}{32 d \left(a -b \right)^{5}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B \,b^{3}}{2 d \left(a -b \right)^{5}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) a^{3} A}{32 d \left(a +b \right)^{5}}-\frac{35 \ln \left(\sin \left(d x +c \right)-1\right) b^{3} A}{32 d \left(a +b \right)^{5}}+\frac{9 A a b}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}+\frac{8 b^{7} \ln \left(a +b \sin \left(d x +c \right)\right) A a}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}-\frac{7 b^{6} \ln \left(a +b \sin \left(d x +c \right)\right) B \,a^{2}}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}+\frac{b^{6} a B}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)}-\frac{A}{48 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{B}{48 d \left(a +b \right)^{2} \left(\sin \left(d x +c \right)-1\right)^{3}}-\frac{A}{48 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{B}{48 d \left(a -b \right)^{2} \left(1+\sin \left(d x +c \right)\right)^{3}}+\frac{A b}{8 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}+\frac{a B}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 B b}{32 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{5 a^{2} A}{32 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B \,b^{3}}{2 d \left(a +b \right)^{5}}-\frac{a A}{16 d \left(a -b \right)^{3} \left(1+\sin \left(d x +c \right)\right)^{2}}-\frac{3 B a b}{16 d \left(a -b \right)^{4} \left(1+\sin \left(d x +c \right)\right)}-\frac{25 \ln \left(1+\sin \left(d x +c \right)\right) A \,a^{2} b}{32 d \left(a -b \right)^{5}}-\frac{3 B a b}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}-\frac{25 \ln \left(\sin \left(d x +c \right)-1\right) A \,a^{2} b}{32 d \left(a +b \right)^{5}}-\frac{47 \ln \left(\sin \left(d x +c \right)-1\right) A a \,b^{2}}{32 d \left(a +b \right)^{5}}-\frac{\ln \left(\sin \left(d x +c \right)-1\right) B \,a^{2} b}{16 d \left(a +b \right)^{5}}-\frac{9 A a b}{16 d \left(a +b \right)^{4} \left(\sin \left(d x +c \right)-1\right)}+\frac{47 \ln \left(1+\sin \left(d x +c \right)\right) A a \,b^{2}}{32 d \left(a -b \right)^{5}}+\frac{\ln \left(1+\sin \left(d x +c \right)\right) B \,a^{2} b}{16 d \left(a -b \right)^{5}}-\frac{5 \ln \left(1+\sin \left(d x +c \right)\right) B a \,b^{2}}{16 d \left(a -b \right)^{5}}-\frac{5 \ln \left(\sin \left(d x +c \right)-1\right) B a \,b^{2}}{16 d \left(a +b \right)^{5}}-\frac{b^{8} \ln \left(a +b \sin \left(d x +c \right)\right) B}{d \left(a +b \right)^{5} \left(a -b \right)^{5}}-\frac{b^{7} A}{d \left(a +b \right)^{4} \left(a -b \right)^{4} \left(a +b \sin \left(d x +c \right)\right)}"," ",0,"-19/32/d/(a-b)^4/(1+sin(d*x+c))*A*b^2+1/16/d/(a+b)^3/(sin(d*x+c)-1)^2*a*A+1/8/d/(a+b)^3/(sin(d*x+c)-1)^2*A*b+1/32/d/(a+b)^3/(sin(d*x+c)-1)^2*a*B+3/32/d/(a+b)^3/(sin(d*x+c)-1)^2*B*b-5/32/d/(a+b)^4/(sin(d*x+c)-1)*a^2*A-19/32/d/(a+b)^4/(sin(d*x+c)-1)*A*b^2-1/32/d/(a+b)^4/(sin(d*x+c)-1)*B*a^2-11/32/d/(a+b)^4/(sin(d*x+c)-1)*B*b^2+1/32/d/(a-b)^4/(1+sin(d*x+c))*B*a^2+11/32/d/(a-b)^4/(1+sin(d*x+c))*B*b^2+5/32/d/(a-b)^5*ln(1+sin(d*x+c))*a^3*A-35/32/d/(a-b)^5*ln(1+sin(d*x+c))*b^3*A+1/2/d/(a-b)^5*ln(1+sin(d*x+c))*B*b^3-5/32/d/(a+b)^5*ln(sin(d*x+c)-1)*a^3*A-35/32/d/(a+b)^5*ln(sin(d*x+c)-1)*b^3*A+9/16/d/(a-b)^4/(1+sin(d*x+c))*A*a*b+8/d*b^7/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*A*a-7/d*b^6/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*B*a^2+1/d*b^6/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))*a*B-1/48/d/(a+b)^2/(sin(d*x+c)-1)^3*A-1/48/d/(a+b)^2/(sin(d*x+c)-1)^3*B-1/48/d/(a-b)^2/(1+sin(d*x+c))^3*A+1/48/d/(a-b)^2/(1+sin(d*x+c))^3*B+1/8/d/(a-b)^3/(1+sin(d*x+c))^2*A*b+1/32/d/(a-b)^3/(1+sin(d*x+c))^2*a*B-3/32/d/(a-b)^3/(1+sin(d*x+c))^2*B*b-5/32/d/(a-b)^4/(1+sin(d*x+c))*a^2*A-1/2/d/(a+b)^5*ln(sin(d*x+c)-1)*B*b^3-1/16/d/(a-b)^3/(1+sin(d*x+c))^2*a*A-3/16/d/(a-b)^4/(1+sin(d*x+c))*B*a*b-25/32/d/(a-b)^5*ln(1+sin(d*x+c))*A*a^2*b-3/16/d/(a+b)^4/(sin(d*x+c)-1)*B*a*b-25/32/d/(a+b)^5*ln(sin(d*x+c)-1)*A*a^2*b-47/32/d/(a+b)^5*ln(sin(d*x+c)-1)*A*a*b^2-1/16/d/(a+b)^5*ln(sin(d*x+c)-1)*B*a^2*b-9/16/d/(a+b)^4/(sin(d*x+c)-1)*A*a*b+47/32/d/(a-b)^5*ln(1+sin(d*x+c))*A*a*b^2+1/16/d/(a-b)^5*ln(1+sin(d*x+c))*B*a^2*b-5/16/d/(a-b)^5*ln(1+sin(d*x+c))*B*a*b^2-5/16/d/(a+b)^5*ln(sin(d*x+c)-1)*B*a*b^2-1/d*b^8/(a+b)^5/(a-b)^5*ln(a+b*sin(d*x+c))*B-1/d*b^7/(a+b)^4/(a-b)^4/(a+b*sin(d*x+c))*A","B"
1560,0,0,39,2.558000," ","int((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","\int \left(g \cos \left(f x +e \right)\right)^{-1-m} \left(a +b \sin \left(f x +e \right)\right)^{m} \left(A +B \sin \left(f x +e \right)\right)\, dx"," ",0,"int((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x)","F"
1561,0,0,298,3.784000," ","int((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p}}{\left(a +b \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)}\, dx"," ",0,"int((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","F"
1562,0,0,460,3.411000," ","int((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","\int \frac{\left(g \cos \left(f x +e \right)\right)^{p}}{\left(a +b \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)^{2}}\, dx"," ",0,"int((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x)","F"
1563,0,0,292,4.095000," ","int((g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\int \frac{\left(g \sec \left(f x +e \right)\right)^{p}}{\left(a +b \sin \left(f x +e \right)\right) \left(c +d \sin \left(f x +e \right)\right)}\, dx"," ",0,"int((g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","F"