1,1,518,199,2.027000," ","int((b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 i A \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-9 i B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+9 i B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+5 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-9 i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+9 i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-5 A \left(\cos^{3}\left(d x +c \right)\right)-9 B \left(\cos^{3}\left(d x +c \right)\right)+6 B \left(\cos^{2}\left(d x +c \right)\right)+5 A \cos \left(d x +c \right)+3 B \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right)^{5}}"," ",0,"2/15/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(5*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*cos(d*x+c)^3-9*I*B*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+9*I*B*cos(d*x+c)^3*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+5*I*A*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-9*I*B*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+9*I*B*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-5*A*cos(d*x+c)^3-9*B*cos(d*x+c)^3+6*B*cos(d*x+c)^2+5*A*cos(d*x+c)+3*B)*(b/cos(d*x+c))^(5/2)/sin(d*x+c)^5","C"
2,1,499,172,1.414000," ","int((b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{2 \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(3 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+3 i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-3 A \left(\cos^{2}\left(d x +c \right)\right)-B \left(\cos^{2}\left(d x +c \right)\right)+3 A \cos \left(d x +c \right)+B \right) \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right)^{5}}"," ",0,"2/3/d*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(3*I*A*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*A*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*B*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+3*I*A*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*I*A*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)-3*A*cos(d*x+c)^2-B*cos(d*x+c)^2+3*A*cos(d*x+c)+B)*(b/cos(d*x+c))^(3/2)/sin(d*x+c)^5","C"
3,1,453,146,1.521000," ","int((b*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","\frac{2 \sqrt{\frac{b}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+i A \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)+i B \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-B \cos \left(d x +c \right)+B \right)}{d \sin \left(d x +c \right)^{5}}"," ",0,"2/d*(b/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)+I*B*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)+B)/sin(d*x+c)^5","C"
4,1,445,126,1.520000," ","int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/2),x)","\frac{2 \left(i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)-i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+i A \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-i A \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-A \left(\cos^{2}\left(d x +c \right)\right)+A \cos \left(d x +c \right)\right) \sqrt{\frac{b}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) b}"," ",0,"2/d*(I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-I*A*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)^2+A*cos(d*x+c))*(b/cos(d*x+c))^(1/2)/sin(d*x+c)/b","C"
5,1,470,154,1.324000," ","int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(3/2),x)","\frac{\frac{2 i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{3}-2 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \cos \left(d x +c \right)+2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)+\frac{2 i A \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{3}-2 i B \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)-\frac{2 A \left(\cos^{3}\left(d x +c \right)\right)}{3}-2 B \left(\cos^{2}\left(d x +c \right)\right)+\frac{2 A \cos \left(d x +c \right)}{3}+2 B \cos \left(d x +c \right)}{d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"2/3/d*(I*A*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)-3*I*B*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)+3*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-3*I*B*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)^3-3*B*cos(d*x+c)^2+A*cos(d*x+c)+3*B*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)^2/(b/cos(d*x+c))^(3/2)","C"
6,1,482,179,1.327000," ","int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(5/2),x)","\frac{\frac{6 i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{5}-\frac{6 i A \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{5}+\frac{2 i B \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right)}{3}+\frac{6 i A \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5}-\frac{6 i A \sin \left(d x +c \right) \EllipticE \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}{5}+\frac{2 i B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{i \left(-1+\cos \left(d x +c \right)\right)}{\sin \left(d x +c \right)}, i\right)}{3}-\frac{2 A \left(\cos^{4}\left(d x +c \right)\right)}{5}-\frac{2 B \left(\cos^{3}\left(d x +c \right)\right)}{3}-\frac{4 A \left(\cos^{2}\left(d x +c \right)\right)}{5}+\frac{6 A \cos \left(d x +c \right)}{5}+\frac{2 B \cos \left(d x +c \right)}{3}}{d \cos \left(d x +c \right)^{3} \left(\frac{b}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)}"," ",0,"2/15/d*(9*I*A*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*cos(d*x+c)-9*I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+5*I*B*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)+9*I*A*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-9*I*A*EllipticE(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+5*I*B*sin(d*x+c)*EllipticF(I*(-1+cos(d*x+c))/sin(d*x+c),I)*(1/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-3*A*cos(d*x+c)^4-5*B*cos(d*x+c)^3-6*A*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c))/cos(d*x+c)^3/(b/cos(d*x+c))^(5/2)/sin(d*x+c)","C"
7,0,0,99,0.765000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
8,0,0,96,0.712000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
9,0,0,94,0.971000," ","int((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
10,0,0,97,1.938000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
11,0,0,99,2.657000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
12,0,0,99,0.766000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
13,0,0,96,0.752000," ","int(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
14,0,0,94,0.985000," ","int((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
15,0,0,97,2.164000," ","int(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
16,0,0,99,3.102000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
17,0,0,99,0.740000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{\left(\sec^{2}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
18,0,0,96,0.716000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{\sec \left(d x +c \right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
19,0,0,94,0.951000," ","int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
20,0,0,96,0.046000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{\sec \left(d x +c \right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
21,0,0,99,0.038000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{\left(\sec^{2}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
22,0,0,99,0.698000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{\left(\sec^{2}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
23,0,0,96,0.753000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{\sec \left(d x +c \right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
24,0,0,94,0.800000," ","int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
25,0,0,96,0.040000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{\sec \left(d x +c \right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
26,0,0,99,0.034000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{\left(\sec^{2}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
27,0,0,143,1.736000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
28,0,0,141,1.869000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
29,0,0,141,1.530000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","F"
30,0,0,141,1.244000," ","int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/3),x)","\int \frac{\left(\sec^{m}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(1/3),x)","F"
31,0,0,141,1.236000," ","int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","\int \frac{\left(\sec^{m}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(2/3),x)","F"
32,0,0,149,1.219000," ","int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","\int \frac{\left(\sec^{m}\left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)}{\left(b \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int(sec(d*x+c)^m*(A+B*sec(d*x+c))/(b*sec(d*x+c))^(4/3),x)","F"
33,0,0,152,4.106000," ","int(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
34,0,0,125,3.651000," ","int(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(\sec^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
35,0,0,118,2.947000," ","int(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \sec \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
36,0,0,119,3.007000," ","int((b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
37,0,0,131,4.005000," ","int(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \cos \left(d x +c \right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
38,0,0,133,4.487000," ","int(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(\cos^{2}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(cos(d*x+c)^2*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
39,0,0,139,1.769000," ","int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(\sec^{\frac{3}{2}}\left(d x +c \right)\right) \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^(3/2)*(b*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
40,0,0,139,1.570000," ","int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","\int \left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right) \left(\sqrt{\sec}\left(d x +c \right)\right)\, dx"," ",0,"int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","F"
41,0,0,139,1.639000," ","int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\int \frac{\left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)}{\sqrt{\sec \left(d x +c \right)}}\, dx"," ",0,"int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","F"
42,0,0,139,1.702000," ","int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","\int \frac{\left(b \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)}{\sec \left(d x +c \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b*sec(d*x+c))^n*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","F"
43,1,213,122,1.204000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{2 a A \tan \left(d x +c \right)}{3 d}+\frac{a A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{a B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a A \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \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{8 a B \tan \left(d x +c \right)}{15 d}+\frac{a B \left(\sec^{4}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{4 a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"2/3*a*A*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*B*sec(d*x+c)^3*tan(d*x+c)/d+3/8/d*a*B*sec(d*x+c)*tan(d*x+c)+3/8/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d+3/8*a*A*sec(d*x+c)*tan(d*x+c)/d+3/8/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*a*B*tan(d*x+c)+1/5*a*B*sec(d*x+c)^4*tan(d*x+c)/d+4/15/d*a*B*tan(d*x+c)*sec(d*x+c)^2","A"
44,1,171,98,1.125000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(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{2 a B \tan \left(d x +c \right)}{3 d}+\frac{a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 a A \tan \left(d x +c \right)}{3 d}+\frac{a A \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{a B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 a B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*B*tan(d*x+c)+1/3/d*a*B*tan(d*x+c)*sec(d*x+c)^2+2/3*a*A*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*B*sec(d*x+c)^3*tan(d*x+c)/d+3/8/d*a*B*sec(d*x+c)*tan(d*x+c)+3/8/d*a*B*ln(sec(d*x+c)+tan(d*x+c))","A"
45,1,128,78,1.146000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{a A \tan \left(d x +c \right)}{d}+\frac{a B \sec \left(d x +c \right) \tan \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{2 a B \tan \left(d x +c \right)}{3 d}+\frac{a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a*A*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*B*tan(d*x+c)+1/3/d*a*B*tan(d*x+c)*sec(d*x+c)^2","A"
46,1,86,52,0.941000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(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 \tan \left(d x +c \right)}{d}+\frac{a A \tan \left(d x +c \right)}{d}+\frac{a B \sec \left(d x +c \right) \tan \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}"," ",0,"1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)+a*A*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))","A"
47,1,65,32,0.707000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","a A x +\frac{a A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A a c}{d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a B \tan \left(d x +c \right)}{d}"," ",0,"a*A*x+1/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a*c+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)","A"
48,1,56,32,0.622000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","a A x +B x a +\frac{a A \sin \left(d x +c \right)}{d}+\frac{A a c}{d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B a c}{d}"," ",0,"a*A*x+B*x*a+a*A*sin(d*x+c)/d+1/d*A*a*c+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a*c","A"
49,1,57,43,0.755000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{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)+a A \sin \left(d x +c \right)+a B \sin \left(d x +c \right)+B \left(d x +c \right) a}{d}"," ",0,"1/d*(a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*A*sin(d*x+c)+a*B*sin(d*x+c)+B*(d*x+c)*a)","A"
50,1,85,69,1.134000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{\frac{a A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \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)+a B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a B \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a*A*(2+cos(d*x+c)^2)*sin(d*x+c)+a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*sin(d*x+c))","A"
51,1,107,89,1.287000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{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)+\frac{a A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a B \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*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)+1/3*a*A*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c)+a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
52,1,128,113,1.601000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{\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}+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)+a B \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{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}}{d}"," ",0,"1/d*(1/5*a*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+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*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c))","A"
53,1,235,157,1.400000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{7 a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{7 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{6 a^{2} B \tan \left(d x +c \right)}{5 d}+\frac{3 a^{2} B \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{5 d}+\frac{4 a^{2} A \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} A \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{3 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{a^{2} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"7/8/d*a^2*A*sec(d*x+c)*tan(d*x+c)+7/8/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+6/5*a^2*B*tan(d*x+c)/d+3/5*a^2*B*sec(d*x+c)^2*tan(d*x+c)/d+4/3*a^2*A*tan(d*x+c)/d+2/3/d*a^2*A*tan(d*x+c)*sec(d*x+c)^2+1/2*a^2*B*sec(d*x+c)^3*tan(d*x+c)/d+3/4*a^2*B*sec(d*x+c)*tan(d*x+c)/d+3/4/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+1/5/d*a^2*B*tan(d*x+c)*sec(d*x+c)^4","A"
54,1,187,128,1.347000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{5 a^{2} A \tan \left(d x +c \right)}{3 d}+\frac{7 a^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{7 B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{a^{2} A \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{2} B \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} B \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{a^{2} A \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{2} B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}"," ",0,"5/3*a^2*A*tan(d*x+c)/d+7/8*a^2*B*sec(d*x+c)*tan(d*x+c)/d+7/8/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^2*A*sec(d*x+c)*tan(d*x+c)+1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+4/3*a^2*B*tan(d*x+c)/d+2/3*a^2*B*sec(d*x+c)^2*tan(d*x+c)/d+1/3/d*a^2*A*tan(d*x+c)*sec(d*x+c)^2+1/4*a^2*B*sec(d*x+c)^3*tan(d*x+c)/d","A"
55,1,141,95,1.149000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{3 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{5 a^{2} B \tan \left(d x +c \right)}{3 d}+\frac{2 a^{2} A \tan \left(d x +c \right)}{d}+\frac{a^{2} B \sec \left(d x +c \right) \tan \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{a^{2} B \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}"," ",0,"3/2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+5/3*a^2*B*tan(d*x+c)/d+2*a^2*A*tan(d*x+c)/d+a^2*B*sec(d*x+c)*tan(d*x+c)/d+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)+1/3*a^2*B*sec(d*x+c)^2*tan(d*x+c)/d","A"
56,1,113,76,0.897000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","a^{2} A x +\frac{A \,a^{2} c}{d}+\frac{3 B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a^{2} B \tan \left(d x +c \right)}{d}+\frac{a^{2} A \tan \left(d x +c \right)}{d}+\frac{a^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"a^2*A*x+1/d*A*a^2*c+3/2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+2*a^2*B*tan(d*x+c)/d+a^2*A*tan(d*x+c)/d+1/2*a^2*B*sec(d*x+c)*tan(d*x+c)/d","A"
57,1,107,73,0.928000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","2 a^{2} A x +a^{2} B x +\frac{a^{2} A \sin \left(d x +c \right)}{d}+\frac{a^{2} A \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 A \,a^{2} c}{d}+\frac{a^{2} B \tan \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}+\frac{B \,a^{2} c}{d}"," ",0,"2*a^2*A*x+a^2*B*x+1/d*a^2*A*sin(d*x+c)+1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a^2*c+a^2*B*tan(d*x+c)/d+2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a^2*c","A"
58,1,108,82,0.820000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{a^{2} A \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 a^{2} A x}{2}+\frac{3 A \,a^{2} c}{2 d}+\frac{B \,a^{2} \sin \left(d x +c \right)}{d}+\frac{2 a^{2} A \sin \left(d x +c \right)}{d}+2 a^{2} B x +\frac{2 B \,a^{2} c}{d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^2*A*cos(d*x+c)*sin(d*x+c)/d+3/2*a^2*A*x+3/2/d*A*a^2*c+1/d*B*a^2*sin(d*x+c)+2/d*a^2*A*sin(d*x+c)+2*a^2*B*x+2/d*B*a^2*c+1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))","A"
59,1,116,94,1.051000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^2*(A+B*sec(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}+2 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)+B \,a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a^{2} A \sin \left(d x +c \right)+2 B \,a^{2} \sin \left(d x +c \right)+B \,a^{2} \left(d x +c \right)}{d}"," ",0,"1/d*(1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+2*a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^2*A*sin(d*x+c)+2*B*a^2*sin(d*x+c)+B*a^2*(d*x+c))","A"
60,1,154,125,1.285000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{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(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{2 a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 B \,a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\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)+B \,a^{2} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(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)+1/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+2/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+2*B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^2*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*a^2*sin(d*x+c))","A"
61,1,186,148,1.624000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^2*(A+B*sec(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}+B \,a^{2} \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)+2 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{2 B \,a^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{a^{2} A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B \,a^{2} \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*(1/5*a^2*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+B*a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*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)+2/3*B*a^2*(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)+B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
62,1,281,196,1.632000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{13 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{13 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{34 a^{3} B \tan \left(d x +c \right)}{15 d}+\frac{17 a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{38 A \,a^{3} \tan \left(d x +c \right)}{15 d}+\frac{19 A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{23 a^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{23 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{23 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{3 A \,a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 a^{3} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}"," ",0,"13/8/d*A*a^3*sec(d*x+c)*tan(d*x+c)+13/8/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+34/15/d*a^3*B*tan(d*x+c)+17/15/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2+38/15/d*A*a^3*tan(d*x+c)+19/15/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+23/24/d*a^3*B*tan(d*x+c)*sec(d*x+c)^3+23/16/d*a^3*B*sec(d*x+c)*tan(d*x+c)+23/16/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/4/d*A*a^3*tan(d*x+c)*sec(d*x+c)^3+3/5/d*a^3*B*tan(d*x+c)*sec(d*x+c)^4+1/5/d*A*a^3*tan(d*x+c)*sec(d*x+c)^4+1/6/d*a^3*B*tan(d*x+c)*sec(d*x+c)^5","A"
63,1,234,151,1.702000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{3 A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{13 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{13 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{15 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{15 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{38 a^{3} B \tan \left(d x +c \right)}{15 d}+\frac{19 a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 a^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"3/d*A*a^3*tan(d*x+c)+13/8/d*a^3*B*sec(d*x+c)*tan(d*x+c)+13/8/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+15/8/d*A*a^3*sec(d*x+c)*tan(d*x+c)+15/8/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+38/15/d*a^3*B*tan(d*x+c)+19/15/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2+1/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+3/4/d*a^3*B*tan(d*x+c)*sec(d*x+c)^3+1/4/d*A*a^3*tan(d*x+c)*sec(d*x+c)^3+1/5/d*a^3*B*tan(d*x+c)*sec(d*x+c)^4","A"
64,1,188,117,1.385000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{5 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 a^{3} B \tan \left(d x +c \right)}{d}+\frac{11 A \,a^{3} \tan \left(d x +c \right)}{3 d}+\frac{15 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{15 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{3 A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}"," ",0,"5/2/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*B*tan(d*x+c)+11/3/d*A*a^3*tan(d*x+c)+15/8/d*a^3*B*sec(d*x+c)*tan(d*x+c)+15/8/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a^3*sec(d*x+c)*tan(d*x+c)+1/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2+1/3/d*A*a^3*tan(d*x+c)*sec(d*x+c)^2+1/4/d*a^3*B*tan(d*x+c)*sec(d*x+c)^3","A"
65,1,158,103,1.164000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","a^{3} A x +\frac{A \,a^{3} c}{d}+\frac{5 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{7 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{11 a^{3} B \tan \left(d x +c \right)}{3 d}+\frac{3 A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{3 a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,a^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a^3*A*x+1/d*A*a^3*c+5/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+7/2/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+11/3/d*a^3*B*tan(d*x+c)+3/d*A*a^3*tan(d*x+c)+3/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)+1/2/d*A*a^3*sec(d*x+c)*tan(d*x+c)+1/3/d*a^3*B*tan(d*x+c)*sec(d*x+c)^2","A"
66,1,144,102,1.114000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{a^{3} A \sin \left(d x +c \right)}{d}+a^{3} B x +\frac{a^{3} B c}{d}+3 a^{3} A x +\frac{3 A \,a^{3} c}{d}+\frac{7 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{3} B \tan \left(d x +c \right)}{d}+\frac{A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"a^3*A*sin(d*x+c)/d+a^3*B*x+1/d*a^3*B*c+3*a^3*A*x+3/d*A*a^3*c+7/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^3*B*tan(d*x+c)+1/d*A*a^3*tan(d*x+c)+1/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)","A"
67,1,145,109,0.885000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{7 a^{3} A x}{2}+\frac{7 A \,a^{3} c}{2 d}+\frac{a^{3} B \sin \left(d x +c \right)}{d}+\frac{3 a^{3} A \sin \left(d x +c \right)}{d}+3 a^{3} B x +\frac{3 a^{3} B c}{d}+\frac{3 a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{3} B \tan \left(d x +c \right)}{d}"," ",0,"1/2/d*A*a^3*cos(d*x+c)*sin(d*x+c)+7/2*a^3*A*x+7/2/d*A*a^3*c+a^3*B*sin(d*x+c)/d+3*a^3*A*sin(d*x+c)/d+3*a^3*B*x+3/d*a^3*B*c+3/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3*B*tan(d*x+c)","A"
68,1,153,117,1.073000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{3}}{3 d}+\frac{11 a^{3} A \sin \left(d x +c \right)}{3 d}+\frac{a^{3} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{7 a^{3} B x}{2}+\frac{7 a^{3} B c}{2 d}+\frac{3 A \,a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{5 a^{3} A x}{2}+\frac{5 A \,a^{3} c}{2 d}+\frac{3 a^{3} B \sin \left(d x +c \right)}{d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^3+11/3*a^3*A*sin(d*x+c)/d+1/2/d*a^3*B*cos(d*x+c)*sin(d*x+c)+7/2*a^3*B*x+7/2/d*a^3*B*c+3/2/d*A*a^3*cos(d*x+c)*sin(d*x+c)+5/2*a^3*A*x+5/2/d*A*a^3*c+3*a^3*B*sin(d*x+c)/d+1/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
69,1,176,116,1.324000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \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)+A \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+3 A \,a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 a^{3} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,a^{3} \sin \left(d x +c \right)+3 a^{3} B \sin \left(d x +c \right)+B \left(d x +c \right) a^{3}}{d}"," ",0,"1/d*(A*a^3*(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*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+3*A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*a^3*sin(d*x+c)+3*a^3*B*sin(d*x+c)+B*(d*x+c)*a^3)","A"
70,1,223,164,1.798000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{\frac{A \,a^{3} \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}+a^{3} B \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)+3 A \,a^{3} \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)+a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+A \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 a^{3} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,a^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a^{3} B \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*A*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+a^3*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+3*A*a^3*(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^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+3*a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*a^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^3*B*sin(d*x+c))","A"
71,1,266,187,1.981000," ","int(cos(d*x+c)^6*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \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{a^{3} B \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{3 A \,a^{3} \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}+3 a^{3} B \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)+3 A \,a^{3} \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)+a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{A \,a^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{3} B \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*a^3*(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)+1/5*a^3*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3/5*A*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+3*a^3*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+3*A*a^3*(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^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*A*a^3*(2+cos(d*x+c)^2)*sin(d*x+c)+a^3*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
72,1,280,180,1.798000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{83 A \,a^{4} \tan \left(d x +c \right)}{15 d}+\frac{49 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{49 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{7 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{7 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{24 a^{4} B \tan \left(d x +c \right)}{5 d}+\frac{12 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{5 d}+\frac{34 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{41 a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{4 a^{4} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}"," ",0,"83/15/d*A*a^4*tan(d*x+c)+49/16/d*a^4*B*sec(d*x+c)*tan(d*x+c)+49/16/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+7/2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+7/2/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+24/5/d*a^4*B*tan(d*x+c)+12/5/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+34/15/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+41/24/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3+1/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+4/5/d*a^4*B*tan(d*x+c)*sec(d*x+c)^4+1/5/d*A*a^4*tan(d*x+c)*sec(d*x+c)^4+1/6/d*a^4*B*tan(d*x+c)*sec(d*x+c)^5","A"
73,1,234,147,1.704000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{35 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{83 a^{4} B \tan \left(d x +c \right)}{15 d}+\frac{20 A \,a^{4} \tan \left(d x +c \right)}{3 d}+\frac{7 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{7 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{27 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{34 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}"," ",0,"35/8/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+83/15/d*a^4*B*tan(d*x+c)+20/3/d*A*a^4*tan(d*x+c)+7/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+7/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+27/8/d*A*a^4*sec(d*x+c)*tan(d*x+c)+34/15/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+4/3/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+1/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3+1/4/d*A*a^4*tan(d*x+c)*sec(d*x+c)^3+1/5/d*a^4*B*tan(d*x+c)*sec(d*x+c)^4","A"
74,1,204,141,1.422000," ","int((a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","A \,a^{4} x +\frac{A \,a^{4} c}{d}+\frac{35 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{6 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{20 a^{4} B \tan \left(d x +c \right)}{3 d}+\frac{20 A \,a^{4} \tan \left(d x +c \right)}{3 d}+\frac{27 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{2 A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{4 a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{A \,a^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}"," ",0,"A*a^4*x+1/d*A*a^4*c+35/8/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+6/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+20/3/d*a^4*B*tan(d*x+c)+20/3/d*A*a^4*tan(d*x+c)+27/8/d*a^4*B*sec(d*x+c)*tan(d*x+c)+2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+4/3/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2+1/3/d*A*a^4*tan(d*x+c)*sec(d*x+c)^2+1/4/d*a^4*B*tan(d*x+c)*sec(d*x+c)^3","A"
75,1,189,141,1.327000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \sin \left(d x +c \right)}{d}+a^{4} B x +\frac{a^{4} B c}{d}+4 A \,a^{4} x +\frac{4 A \,a^{4} c}{d}+\frac{6 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{13 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{20 a^{4} B \tan \left(d x +c \right)}{3 d}+\frac{4 A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{2 a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{A \,a^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{4} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/d*A*a^4*sin(d*x+c)+a^4*B*x+1/d*a^4*B*c+4*A*a^4*x+4/d*A*a^4*c+6/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+13/2/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+20/3/d*a^4*B*tan(d*x+c)+4/d*A*a^4*tan(d*x+c)+2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+1/2/d*A*a^4*sec(d*x+c)*tan(d*x+c)+1/3/d*a^4*B*tan(d*x+c)*sec(d*x+c)^2","A"
76,1,182,148,1.055000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 A \,a^{4} x}{2}+\frac{13 A \,a^{4} c}{2 d}+\frac{a^{4} B \sin \left(d x +c \right)}{d}+\frac{4 A \,a^{4} \sin \left(d x +c \right)}{d}+4 a^{4} B x +\frac{4 a^{4} B c}{d}+\frac{13 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{4 A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{4} B \tan \left(d x +c \right)}{d}+\frac{A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}"," ",0,"1/2/d*A*a^4*cos(d*x+c)*sin(d*x+c)+13/2*A*a^4*x+13/2/d*A*a^4*c+1/d*a^4*B*sin(d*x+c)+4/d*A*a^4*sin(d*x+c)+4*a^4*B*x+4/d*a^4*B*c+13/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+4/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+4/d*a^4*B*tan(d*x+c)+1/d*A*a^4*tan(d*x+c)+1/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)","A"
77,1,190,155,1.145000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 A \,a^{4} \sin \left(d x +c \right)}{3 d}+\frac{a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{13 a^{4} B x}{2}+\frac{13 a^{4} B c}{2 d}+\frac{2 A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+6 A \,a^{4} x +\frac{6 A \,a^{4} c}{d}+\frac{4 a^{4} B \sin \left(d x +c \right)}{d}+\frac{4 a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{4} B \tan \left(d x +c \right)}{d}"," ",0,"1/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*A*a^4*sin(d*x+c)+1/2/d*a^4*B*cos(d*x+c)*sin(d*x+c)+13/2*a^4*B*x+13/2/d*a^4*B*c+2/d*A*a^4*cos(d*x+c)*sin(d*x+c)+6*A*a^4*x+6/d*A*a^4*c+4/d*a^4*B*sin(d*x+c)+4/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^4*B*tan(d*x+c)","A"
78,1,199,163,1.213000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{27 A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{35 A \,a^{4} x}{8}+\frac{35 A \,a^{4} c}{8 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 a^{4} B \sin \left(d x +c \right)}{3 d}+\frac{4 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{20 A \,a^{4} \sin \left(d x +c \right)}{3 d}+\frac{2 a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{d}+6 a^{4} B x +\frac{6 a^{4} B c}{d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*A*a^4*sin(d*x+c)*cos(d*x+c)^3+27/8/d*A*a^4*cos(d*x+c)*sin(d*x+c)+35/8*A*a^4*x+35/8/d*A*a^4*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*a^4*B*sin(d*x+c)+4/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^4+20/3/d*A*a^4*sin(d*x+c)+2/d*a^4*B*cos(d*x+c)*sin(d*x+c)+6*a^4*B*x+6/d*a^4*B*c+1/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))","A"
79,1,248,146,1.497000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{\frac{A \,a^{4} \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}+4 A \,a^{4} \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)+a^{4} B \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)+2 A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{4 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 A \,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)+6 a^{4} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,a^{4} \sin \left(d x +c \right)+4 a^{4} B \sin \left(d x +c \right)+a^{4} B \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*A*a^4*(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^4*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+4/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+4*A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+6*a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*a^4*sin(d*x+c)+4*a^4*B*sin(d*x+c)+a^4*B*(d*x+c))","A"
80,1,306,206,1.995000," ","int(cos(d*x+c)^6*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \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{a^{4} B \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{4 A \,a^{4} \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}+4 a^{4} B \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)+6 A \,a^{4} \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)+2 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{4 A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 a^{4} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,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)+a^{4} B \sin \left(d x +c \right)}{d}"," ",0,"1/d*(A*a^4*(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)+1/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*a^4*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+6*A*a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+4/3*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+4*a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*a^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a^4*B*sin(d*x+c))","A"
81,1,358,225,2.154000," ","int(cos(d*x+c)^7*(a+a*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{\frac{A \,a^{4} \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}+a^{4} B \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)+4 A \,a^{4} \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{4 a^{4} B \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{6 A \,a^{4} \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}+6 a^{4} B \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)+4 A \,a^{4} \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{4 a^{4} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{A \,a^{4} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+a^{4} B \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*(1/7*A*a^4*(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^4*B*(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)+4*A*a^4*(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)+4/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+6/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+6*a^4*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4*A*a^4*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+4/3*a^4*B*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*A*a^4*(2+cos(d*x+c)^2)*sin(d*x+c)+a^4*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
82,1,340,125,0.572000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 a d}-\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 a d}-\frac{5 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{3 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{3 A}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 a d}+\frac{3 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)-1/3/a/d*B/(tan(1/2*d*x+1/2*c)-1)^3-1/a/d/(tan(1/2*d*x+1/2*c)-1)^2*B+1/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)^2+3/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)-5/2/a/d/(tan(1/2*d*x+1/2*c)-1)*B+3/2/a/d*A/(tan(1/2*d*x+1/2*c)-1)-1/3/a/d*B/(tan(1/2*d*x+1/2*c)+1)^3-1/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)^2+1/a/d/(tan(1/2*d*x+1/2*c)+1)^2*B-5/2/a/d/(tan(1/2*d*x+1/2*c)+1)*B+3/2/a/d*A/(tan(1/2*d*x+1/2*c)+1)-3/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B+3/2/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)","B"
83,1,252,104,0.580000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{3 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 a d}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}-\frac{B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 a d}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}+\frac{3 B}{2 a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*tan(1/2*d*x+1/2*c)+1/2/a/d/(tan(1/2*d*x+1/2*c)-1)^2*B+3/2/a/d/(tan(1/2*d*x+1/2*c)-1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)-1)-3/2/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B+1/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)-1/2/a/d/(tan(1/2*d*x+1/2*c)+1)^2*B+3/2/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B-1/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)+3/2/a/d/(tan(1/2*d*x+1/2*c)+1)*B-1/a/d*A/(tan(1/2*d*x+1/2*c)+1)","B"
84,1,163,62,0.563000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{a d}-\frac{B}{a d \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)-1/a/d/(tan(1/2*d*x+1/2*c)-1)*B-1/a/d*A*ln(tan(1/2*d*x+1/2*c)-1)+1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B-1/a/d/(tan(1/2*d*x+1/2*c)+1)*B+1/a/d*A*ln(tan(1/2*d*x+1/2*c)+1)-1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
85,1,78,43,0.679000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*ln(tan(1/2*d*x+1/2*c)+1)*B-1/a/d*B*tan(1/2*d*x+1/2*c)-1/a/d*ln(tan(1/2*d*x+1/2*c)-1)*B","A"
86,1,56,35,0.734000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+2/a/d*A*arctan(tan(1/2*d*x+1/2*c))+1/a/d*B*tan(1/2*d*x+1/2*c)","A"
87,1,108,60,1.089000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{2 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \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)}{a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*tan(1/2*d*x+1/2*c)+2/d/a*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/a/d*A*arctan(tan(1/2*d*x+1/2*c))+2/a/d*arctan(tan(1/2*d*x+1/2*c))*B","A"
88,1,211,94,1.066000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{3 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{A \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 B \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{3 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"-1/a/d*A*tan(1/2*d*x+1/2*c)+1/a/d*B*tan(1/2*d*x+1/2*c)-3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)+2/a/d/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+3/a/d*A*arctan(tan(1/2*d*x+1/2*c))-2/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
89,1,281,116,1.415000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{a d}-\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{16 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 a d \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{B \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{3 A \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{3 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{a d}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"1/a/d*A*tan(1/2*d*x+1/2*c)-1/a/d*B*tan(1/2*d*x+1/2*c)-3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B+5/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A-4/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*B+16/3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A-1/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)+3/a/d/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)-3/a/d*A*arctan(tan(1/2*d*x+1/2*c))+3/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
90,1,382,169,1.050000," ","int(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{9 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{3 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{7 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{2 d \,a^{2}}+\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{2}}-\frac{5 B}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{7 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{2 d \,a^{2}}-\frac{5 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}+\frac{3 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{5 B}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 A}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B}{3 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*A*tan(1/2*d*x+1/2*c)+9/2/d/a^2*B*tan(1/2*d*x+1/2*c)+1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)^2-3/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2*B-7/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)+5/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B-5/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B+5/2/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)-1/3/d/a^2*B/(tan(1/2*d*x+1/2*c)-1)^3+7/2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)-5/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B+3/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2*B-1/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)^2-5/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B+5/2/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)-1/3/d/a^2*B/(tan(1/2*d*x+1/2*c)+1)^3","B"
91,1,294,146,0.680000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{5 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{5 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}-\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d \,a^{2}}+\frac{B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{5 B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}+\frac{7 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d \,a^{2}}-\frac{B}{2 d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*A*tan(1/2*d*x+1/2*c)-7/2/d/a^2*B*tan(1/2*d*x+1/2*c)-1/d/a^2*A/(tan(1/2*d*x+1/2*c)-1)+5/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B+2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)-7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B+1/2/d/a^2/(tan(1/2*d*x+1/2*c)-1)^2*B-1/d/a^2*A/(tan(1/2*d*x+1/2*c)+1)+5/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B-2/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)+7/2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^2/(tan(1/2*d*x+1/2*c)+1)^2*B","B"
92,1,205,104,0.696000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{3 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{5 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,a^{2}}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{2}}-\frac{B}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{A \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,a^{2}}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}-\frac{B}{d \,a^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*A*tan(1/2*d*x+1/2*c)+5/2/d/a^2*B*tan(1/2*d*x+1/2*c)-1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)-1)+2/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^2/(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^2*A*ln(tan(1/2*d*x+1/2*c)+1)-2/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^2/(tan(1/2*d*x+1/2*c)+1)*B","A"
93,1,119,75,0.849000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{3 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+1/2/d/a^2*A*tan(1/2*d*x+1/2*c)-3/2/d/a^2*B*tan(1/2*d*x+1/2*c)-1/d/a^2*ln(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^2*ln(tan(1/2*d*x+1/2*c)+1)*B","A"
94,1,60,61,0.845000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}"," ",0,"1/2/d/a^2*(-1/3*tan(1/2*d*x+1/2*c)^3*A+1/3*B*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
95,1,97,66,0.920000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{3 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{B \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) A}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-3/2/d/a^2*A*tan(1/2*d*x+1/2*c)+1/2/d/a^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A","A"
96,1,149,94,1.212000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{5 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{3 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{2 A \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)}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+5/2/d/a^2*A*tan(1/2*d*x+1/2*c)-3/2/d/a^2*B*tan(1/2*d*x+1/2*c)+2/d/a^2*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","A"
97,1,252,133,1.112000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{5 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \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)^{2}}-\frac{3 A \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{2 B \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{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3-7/2/d/a^2*A*tan(1/2*d*x+1/2*c)+5/2/d/a^2*B*tan(1/2*d*x+1/2*c)-5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+7/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A-4/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","A"
98,1,322,160,1.169000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{2}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{2}}+\frac{9 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 d \,a^{2}}+\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{5 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{40 A \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)^{3}}-\frac{8 B \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)^{3}}+\frac{6 A \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{3 B \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 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}+\frac{7 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"-1/6/d/a^2*tan(1/2*d*x+1/2*c)^3*A+1/6/d/a^2*B*tan(1/2*d*x+1/2*c)^3+9/2/d/a^2*A*tan(1/2*d*x+1/2*c)-7/2/d/a^2*B*tan(1/2*d*x+1/2*c)+10/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A-5/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B+40/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)^3-8/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^3+6/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)-3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)-10/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A+7/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","B"
99,1,334,190,0.697000," ","int(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{2 d \,a^{3}}-\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{17 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{31 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A}{d \,a^{3}}-\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d \,a^{3}}+\frac{7 B}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{7 B}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A}{d \,a^{3}}+\frac{13 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d \,a^{3}}-\frac{B}{2 d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+1/2/d/a^3*tan(1/2*d*x+1/2*c)^3*A-2/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*A*tan(1/2*d*x+1/2*c)-31/4/d/a^3*B*tan(1/2*d*x+1/2*c)+3/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*A-13/2/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B+7/2/d/a^3/(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*A+1/2/d/a^3*B/(tan(1/2*d*x+1/2*c)-1)^2+7/2/d/a^3/(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*A-3/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*A+13/2/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^3*B/(tan(1/2*d*x+1/2*c)+1)^2","A"
100,1,245,150,0.602000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{17 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A}{d \,a^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{3}}-\frac{B}{d \,a^{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)+1\right) A}{d \,a^{3}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{3}}-\frac{B}{d \,a^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-1/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A+1/2/d/a^3*B*tan(1/2*d*x+1/2*c)^3-7/4/d/a^3*A*tan(1/2*d*x+1/2*c)+17/4/d/a^3*B*tan(1/2*d*x+1/2*c)-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*A+3/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^3/(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*A-3/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^3/(tan(1/2*d*x+1/2*c)+1)*B","A"
101,1,159,119,0.749000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{3}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{3}}+\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{3}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}"," ",0,"1/4/d/a^3*A*tan(1/2*d*x+1/2*c)-1/d/a^3*ln(tan(1/2*d*x+1/2*c)-1)*B-7/4/d/a^3*B*tan(1/2*d*x+1/2*c)+1/d/a^3*ln(tan(1/2*d*x+1/2*c)+1)*B+1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+1/6/d/a^3*tan(1/2*d*x+1/2*c)^3*A-1/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3","A"
102,1,64,96,0.730000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{\frac{\left(-A +B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*(-A+B)*tan(1/2*d*x+1/2*c)^5+2/3*B*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
103,1,64,96,0.752000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{\frac{\left(A -B \right) \left(\tan^{5}\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}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}"," ",0,"1/4/d/a^3*(1/5*(A-B)*tan(1/2*d*x+1/2*c)^5-2/3*tan(1/2*d*x+1/2*c)^3*A+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
104,1,137,102,0.796000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 d \,a^{3}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+1/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A-1/6/d/a^3*B*tan(1/2*d*x+1/2*c)^3-7/4/d/a^3*A*tan(1/2*d*x+1/2*c)+1/4/d/a^3*B*tan(1/2*d*x+1/2*c)+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A","A"
105,1,189,130,1.043000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{2 d \,a^{3}}+\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{17 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{2 A \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)}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-1/2/d/a^3*tan(1/2*d*x+1/2*c)^3*A+1/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+17/4/d/a^3*A*tan(1/2*d*x+1/2*c)-7/4/d/a^3*B*tan(1/2*d*x+1/2*c)+2/d/a^3*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-6/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
106,1,292,175,1.221000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{3}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 d \,a^{3}}-\frac{31 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{17 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{7 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \left(\tan^{3}\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{5 A \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{2 B \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{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"-1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5+1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5+2/3/d/a^3*tan(1/2*d*x+1/2*c)^3*A-1/2/d/a^3*B*tan(1/2*d*x+1/2*c)^3-31/4/d/a^3*A*tan(1/2*d*x+1/2*c)+17/4/d/a^3*B*tan(1/2*d*x+1/2*c)-7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3-5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+13/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A-6/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
107,1,362,204,1.284000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{20 d \,a^{3}}-\frac{5 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{6 d \,a^{3}}+\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{3}}+\frac{49 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}-\frac{31 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{4 d \,a^{3}}+\frac{17 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{7 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{76 A \left(\tan^{3}\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)^{3}}-\frac{12 B \left(\tan^{3}\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{11 A \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{5 B \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{23 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}+\frac{13 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"1/20/d/a^3*A*tan(1/2*d*x+1/2*c)^5-1/20/d/a^3*B*tan(1/2*d*x+1/2*c)^5-5/6/d/a^3*tan(1/2*d*x+1/2*c)^3*A+2/3/d/a^3*B*tan(1/2*d*x+1/2*c)^3+49/4/d/a^3*A*tan(1/2*d*x+1/2*c)-31/4/d/a^3*B*tan(1/2*d*x+1/2*c)+17/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A-7/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B+76/3/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)^3-12/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^3+11/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)-5/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)-23/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A+13/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","A"
108,1,374,224,0.628000," ","int(sec(d*x+c)^6*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{7 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{9 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}-\frac{13 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{49 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{111 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A}{d \,a^{4}}-\frac{21 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d \,a^{4}}+\frac{9 B}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{A}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{9 B}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{A}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A}{d \,a^{4}}+\frac{21 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d \,a^{4}}-\frac{B}{2 d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-9/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5+23/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A-13/8/d/a^4*B*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*A*tan(1/2*d*x+1/2*c)-111/8/d/a^4*B*tan(1/2*d*x+1/2*c)+4/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*A-21/2/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B+9/2/d/a^4/(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)*A+1/2/d/a^4*B/(tan(1/2*d*x+1/2*c)-1)^2+9/2/d/a^4/(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^4/(tan(1/2*d*x+1/2*c)+1)*A-4/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*A+21/2/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B-1/2/d/a^4*B/(tan(1/2*d*x+1/2*c)+1)^2","A"
109,1,285,186,0.686000," ","int(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{7 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}+\frac{23 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{15 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{49 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A}{d \,a^{4}}+\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{4}}-\frac{B}{d \,a^{4} \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)+1\right) A}{d \,a^{4}}-\frac{4 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{4}}-\frac{B}{d \,a^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-1/8/d/a^4*A*tan(1/2*d*x+1/2*c)^5+7/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5-11/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A+23/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3-15/8/d/a^4*A*tan(1/2*d*x+1/2*c)+49/8/d/a^4*B*tan(1/2*d*x+1/2*c)-1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*A+4/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B-1/d/a^4/(tan(1/2*d*x+1/2*c)-1)*B+1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*A-4/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B-1/d/a^4/(tan(1/2*d*x+1/2*c)+1)*B","A"
110,1,199,155,0.714000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,a^{4}}-\frac{15 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,a^{4}}+\frac{3 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{8 d \,a^{4}}-\frac{11 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}"," ",0,"1/8/d/a^4*A*tan(1/2*d*x+1/2*c)+1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-1/d/a^4*ln(tan(1/2*d*x+1/2*c)-1)*B-15/8/d/a^4*B*tan(1/2*d*x+1/2*c)+1/d/a^4*ln(tan(1/2*d*x+1/2*c)+1)*B+3/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^5+1/8/d/a^4*tan(1/2*d*x+1/2*c)^3*A-11/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3","A"
111,1,88,138,0.740000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\frac{\left(-A +B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(-A +3 B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(A +3 B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(-A+B)*tan(1/2*d*x+1/2*c)^7+1/5*(-A+3*B)*tan(1/2*d*x+1/2*c)^5+1/3*(A+3*B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
112,1,88,130,0.716000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\frac{\left(A -B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(-A -B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(-A +B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(A-B)*tan(1/2*d*x+1/2*c)^7+1/5*(-A-B)*tan(1/2*d*x+1/2*c)^5+1/3*(-A+B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
113,1,90,130,0.739000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\frac{\left(-A +B \right) \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{7}+\frac{\left(3 A -B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{5}+\frac{\left(-3 A -B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)+B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}"," ",0,"1/8/d/a^4*(1/7*(-A+B)*tan(1/2*d*x+1/2*c)^7+1/5*(3*A-B)*tan(1/2*d*x+1/2*c)^5+1/3*(-3*A-B)*tan(1/2*d*x+1/2*c)^3+A*tan(1/2*d*x+1/2*c)+B*tan(1/2*d*x+1/2*c))","A"
114,1,177,130,0.799000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{3 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{11 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}-\frac{B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{15 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-1/8/d/a^4*A*tan(1/2*d*x+1/2*c)^5+3/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5+11/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A-1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^3-15/8/d/a^4*A*tan(1/2*d*x+1/2*c)+1/8/d/a^4*B*tan(1/2*d*x+1/2*c)+2/d/a^4*A*arctan(tan(1/2*d*x+1/2*c))","A"
115,1,229,158,1.228000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{7 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}-\frac{23 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}+\frac{11 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}+\frac{49 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{15 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{2 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}-\frac{8 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+7/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-1/8/d/a^4*B*tan(1/2*d*x+1/2*c)^5-23/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A+11/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3+49/8/d/a^4*A*tan(1/2*d*x+1/2*c)-15/8/d/a^4*B*tan(1/2*d*x+1/2*c)+2/d/a^4*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-8/d/a^4*A*arctan(tan(1/2*d*x+1/2*c))+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
116,1,332,209,1.165000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}-\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}-\frac{9 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{7 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}+\frac{13 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{8 d \,a^{4}}-\frac{23 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{24 d \,a^{4}}-\frac{111 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{49 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{9 A \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{7 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{21 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4}}"," ",0,"1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A-1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7-9/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5+7/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5+13/8/d/a^4*tan(1/2*d*x+1/2*c)^3*A-23/24/d/a^4*B*tan(1/2*d*x+1/2*c)^3-111/8/d/a^4*A*tan(1/2*d*x+1/2*c)+49/8/d/a^4*B*tan(1/2*d*x+1/2*c)-9/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)^3+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3-7/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+21/d/a^4*A*arctan(tan(1/2*d*x+1/2*c))-8/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
117,1,402,240,1.257000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^4,x)","-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{56 d \,a^{4}}+\frac{B \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{56 d \,a^{4}}+\frac{11 A \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{9 B \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{40 d \,a^{4}}-\frac{59 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{24 d \,a^{4}}+\frac{13 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{8 d \,a^{4}}+\frac{209 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}-\frac{111 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{8 d \,a^{4}}+\frac{26 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{9 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{124 A \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{16 B \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{18 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{7 B \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{44 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{21 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{4}}"," ",0,"-1/56/d/a^4*tan(1/2*d*x+1/2*c)^7*A+1/56/d/a^4*B*tan(1/2*d*x+1/2*c)^7+11/40/d/a^4*A*tan(1/2*d*x+1/2*c)^5-9/40/d/a^4*B*tan(1/2*d*x+1/2*c)^5-59/24/d/a^4*tan(1/2*d*x+1/2*c)^3*A+13/8/d/a^4*B*tan(1/2*d*x+1/2*c)^3+209/8/d/a^4*A*tan(1/2*d*x+1/2*c)-111/8/d/a^4*B*tan(1/2*d*x+1/2*c)+26/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A-9/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B+124/3/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)^3-16/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)^3+18/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*A*tan(1/2*d*x+1/2*c)-7/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*B*tan(1/2*d*x+1/2*c)-44/d/a^4*A*arctan(tan(1/2*d*x+1/2*c))+21/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B","A"
118,1,138,167,1.637000," ","int(sec(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(144 A \left(\cos^{4}\left(d x +c \right)\right)+128 B \left(\cos^{4}\left(d x +c \right)\right)+72 A \left(\cos^{3}\left(d x +c \right)\right)+64 B \left(\cos^{3}\left(d x +c \right)\right)+54 A \left(\cos^{2}\left(d x +c \right)\right)+48 B \left(\cos^{2}\left(d x +c \right)\right)+45 A \cos \left(d x +c \right)+40 B \cos \left(d x +c \right)+35 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(144*A*cos(d*x+c)^4+128*B*cos(d*x+c)^4+72*A*cos(d*x+c)^3+64*B*cos(d*x+c)^3+54*A*cos(d*x+c)^2+48*B*cos(d*x+c)^2+45*A*cos(d*x+c)+40*B*cos(d*x+c)+35*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/sin(d*x+c)","A"
119,1,116,128,1.513000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(56 A \left(\cos^{3}\left(d x +c \right)\right)+48 B \left(\cos^{3}\left(d x +c \right)\right)+28 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)+21 A \cos \left(d x +c \right)+18 B \cos \left(d x +c \right)+15 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{105 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(56*A*cos(d*x+c)^3+48*B*cos(d*x+c)^3+28*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2+21*A*cos(d*x+c)+18*B*cos(d*x+c)+15*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)","A"
120,1,94,89,1.454000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(10 A \left(\cos^{2}\left(d x +c \right)\right)+8 B \left(\cos^{2}\left(d x +c \right)\right)+5 A \cos \left(d x +c \right)+4 B \cos \left(d x +c \right)+3 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(10*A*cos(d*x+c)^2+8*B*cos(d*x+c)^2+5*A*cos(d*x+c)+4*B*cos(d*x+c)+3*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)","A"
121,1,70,54,1.762000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(3 A \cos \left(d x +c \right)+2 B \cos \left(d x +c \right)+B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(3*A*cos(d*x+c)+2*B*cos(d*x+c)+B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)","A"
122,1,118,58,1.581000," ","int((a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 B \cos \left(d x +c \right)-2 B \right)}{d \sin \left(d x +c \right)}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*B*cos(d*x+c)-2*B)/sin(d*x+c)","B"
123,1,198,60,1.517000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*(A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)^2-2*A*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","B"
124,1,398,101,1.701000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(-3 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-4 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-4 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 A \left(\cos^{4}\left(d x +c \right)\right)+4 A \left(\cos^{3}\left(d x +c \right)\right)+16 B \left(\cos^{3}\left(d x +c \right)\right)-12 A \left(\cos^{2}\left(d x +c \right)\right)-16 B \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"-1/16/d*(-3*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-4*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-3*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-4*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*A*cos(d*x+c)^4+4*A*cos(d*x+c)^3+16*B*cos(d*x+c)^3-12*A*cos(d*x+c)^2-16*B*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)","B"
125,1,580,140,1.887000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(15 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+18 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+30 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+36 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+15 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+18 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+64 A \left(\cos^{6}\left(d x +c \right)\right)+16 A \left(\cos^{5}\left(d x +c \right)\right)+96 B \left(\cos^{5}\left(d x +c \right)\right)+40 A \left(\cos^{4}\left(d x +c \right)\right)+48 B \left(\cos^{4}\left(d x +c \right)\right)-120 A \left(\cos^{3}\left(d x +c \right)\right)-144 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/192/d*(15*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+18*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+30*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+36*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+15*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+18*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+64*A*cos(d*x+c)^6+16*A*cos(d*x+c)^5+96*B*cos(d*x+c)^5+40*A*cos(d*x+c)^4+48*B*cos(d*x+c)^4-120*A*cos(d*x+c)^3-144*B*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^2","B"
126,1,762,179,1.677000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^(1/2)*(A+B*sec(d*x+c)),x)","\frac{\left(105 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+120 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+315 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+360 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+315 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+360 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+105 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+120 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-768 A \left(\cos^{8}\left(d x +c \right)\right)-128 A \left(\cos^{7}\left(d x +c \right)\right)-1024 B \left(\cos^{7}\left(d x +c \right)\right)-224 A \left(\cos^{6}\left(d x +c \right)\right)-256 B \left(\cos^{6}\left(d x +c \right)\right)-560 A \left(\cos^{5}\left(d x +c \right)\right)-640 B \left(\cos^{5}\left(d x +c \right)\right)+1680 A \left(\cos^{4}\left(d x +c \right)\right)+1920 B \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3072 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"1/3072/d*(105*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3+120*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3+315*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+360*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+315*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)+360*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)+105*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+120*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-768*A*cos(d*x+c)^8-128*A*cos(d*x+c)^7-1024*B*cos(d*x+c)^7-224*A*cos(d*x+c)^6-256*B*cos(d*x+c)^6-560*A*cos(d*x+c)^5-640*B*cos(d*x+c)^5+1680*A*cos(d*x+c)^4+1920*B*cos(d*x+c)^4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^3","B"
127,1,139,169,1.603000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(312 A \left(\cos^{4}\left(d x +c \right)\right)+272 B \left(\cos^{4}\left(d x +c \right)\right)+156 A \left(\cos^{3}\left(d x +c \right)\right)+136 B \left(\cos^{3}\left(d x +c \right)\right)+117 A \left(\cos^{2}\left(d x +c \right)\right)+102 B \left(\cos^{2}\left(d x +c \right)\right)+45 A \cos \left(d x +c \right)+85 B \cos \left(d x +c \right)+35 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{315 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(312*A*cos(d*x+c)^4+272*B*cos(d*x+c)^4+156*A*cos(d*x+c)^3+136*B*cos(d*x+c)^3+117*A*cos(d*x+c)^2+102*B*cos(d*x+c)^2+45*A*cos(d*x+c)+85*B*cos(d*x+c)+35*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/sin(d*x+c)*a","A"
128,1,117,122,1.431000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(126 A \left(\cos^{3}\left(d x +c \right)\right)+104 B \left(\cos^{3}\left(d x +c \right)\right)+63 A \left(\cos^{2}\left(d x +c \right)\right)+52 B \left(\cos^{2}\left(d x +c \right)\right)+21 A \cos \left(d x +c \right)+39 B \cos \left(d x +c \right)+15 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{105 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(126*A*cos(d*x+c)^3+104*B*cos(d*x+c)^3+63*A*cos(d*x+c)^2+52*B*cos(d*x+c)^2+21*A*cos(d*x+c)+39*B*cos(d*x+c)+15*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)*a","A"
129,1,95,89,1.412000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(25 A \left(\cos^{2}\left(d x +c \right)\right)+18 B \left(\cos^{2}\left(d x +c \right)\right)+5 A \cos \left(d x +c \right)+9 B \cos \left(d x +c \right)+3 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{15 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(25*A*cos(d*x+c)^2+18*B*cos(d*x+c)^2+5*A*cos(d*x+c)+9*B*cos(d*x+c)+3*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)*a","A"
130,1,237,91,1.484000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-12 A \left(\cos^{2}\left(d x +c \right)\right)-20 B \left(\cos^{2}\left(d x +c \right)\right)+12 A \cos \left(d x +c \right)+16 B \cos \left(d x +c \right)+4 B \right) a}{6 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+3*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-12*A*cos(d*x+c)^2-20*B*cos(d*x+c)^2+12*A*cos(d*x+c)+16*B*cos(d*x+c)+4*B)/cos(d*x+c)/sin(d*x+c)*a","B"
131,1,212,93,1.472000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(3 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)+4 B \cos \left(d x +c \right)-4 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{2 d \sin \left(d x +c \right)}"," ",0,"-1/2/d*(3*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)^2-2*A*cos(d*x+c)+4*B*cos(d*x+c)-4*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)*a","B"
132,1,399,103,1.576000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(-7 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-12 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-7 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-12 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 A \left(\cos^{4}\left(d x +c \right)\right)+20 A \left(\cos^{3}\left(d x +c \right)\right)+16 B \left(\cos^{3}\left(d x +c \right)\right)-28 A \left(\cos^{2}\left(d x +c \right)\right)-16 B \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"-1/16/d*(-7*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-12*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-7*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-12*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*A*cos(d*x+c)^4+20*A*cos(d*x+c)^3+16*B*cos(d*x+c)^3-28*A*cos(d*x+c)^2-16*B*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)*a","B"
133,1,581,144,1.807000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(33 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+42 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+66 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+84 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+33 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+42 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+64 A \left(\cos^{6}\left(d x +c \right)\right)+112 A \left(\cos^{5}\left(d x +c \right)\right)+96 B \left(\cos^{5}\left(d x +c \right)\right)+88 A \left(\cos^{4}\left(d x +c \right)\right)+240 B \left(\cos^{4}\left(d x +c \right)\right)-264 A \left(\cos^{3}\left(d x +c \right)\right)-336 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{192 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-1/192/d*(33*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+42*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+66*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+84*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+33*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+42*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+64*A*cos(d*x+c)^6+112*A*cos(d*x+c)^5+96*B*cos(d*x+c)^5+88*A*cos(d*x+c)^4+240*B*cos(d*x+c)^4-264*A*cos(d*x+c)^3-336*B*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)*a","B"
134,1,763,185,1.624000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{\left(225 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+264 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)+675 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+792 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+675 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+792 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+225 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+264 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-768 A \left(\cos^{8}\left(d x +c \right)\right)-1152 A \left(\cos^{7}\left(d x +c \right)\right)-1024 B \left(\cos^{7}\left(d x +c \right)\right)-480 A \left(\cos^{6}\left(d x +c \right)\right)-1792 B \left(\cos^{6}\left(d x +c \right)\right)-1200 A \left(\cos^{5}\left(d x +c \right)\right)-1408 B \left(\cos^{5}\left(d x +c \right)\right)+3600 A \left(\cos^{4}\left(d x +c \right)\right)+4224 B \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a}{3072 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{3}}"," ",0,"1/3072/d*(225*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3+264*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3+675*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+792*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+675*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)+792*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)+225*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+264*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-768*A*cos(d*x+c)^8-1152*A*cos(d*x+c)^7-1024*B*cos(d*x+c)^7-480*A*cos(d*x+c)^6-1792*B*cos(d*x+c)^6-1200*A*cos(d*x+c)^5-1408*B*cos(d*x+c)^5+3600*A*cos(d*x+c)^4+4224*B*cos(d*x+c)^4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^3*a","B"
135,1,163,213,1.640000," ","int(sec(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(6424 A \left(\cos^{5}\left(d x +c \right)\right)+5680 B \left(\cos^{5}\left(d x +c \right)\right)+3212 A \left(\cos^{4}\left(d x +c \right)\right)+2840 B \left(\cos^{4}\left(d x +c \right)\right)+2409 A \left(\cos^{3}\left(d x +c \right)\right)+2130 B \left(\cos^{3}\left(d x +c \right)\right)+1430 A \left(\cos^{2}\left(d x +c \right)\right)+1775 B \left(\cos^{2}\left(d x +c \right)\right)+385 A \cos \left(d x +c \right)+1120 B \cos \left(d x +c \right)+315 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{3465 d \cos \left(d x +c \right)^{5} \sin \left(d x +c \right)}"," ",0,"-2/3465/d*(-1+cos(d*x+c))*(6424*A*cos(d*x+c)^5+5680*B*cos(d*x+c)^5+3212*A*cos(d*x+c)^4+2840*B*cos(d*x+c)^4+2409*A*cos(d*x+c)^3+2130*B*cos(d*x+c)^3+1430*A*cos(d*x+c)^2+1775*B*cos(d*x+c)^2+385*A*cos(d*x+c)+1120*B*cos(d*x+c)+315*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^5/sin(d*x+c)*a^2","A"
136,1,141,155,1.515000," ","int(sec(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(690 A \left(\cos^{4}\left(d x +c \right)\right)+584 B \left(\cos^{4}\left(d x +c \right)\right)+345 A \left(\cos^{3}\left(d x +c \right)\right)+292 B \left(\cos^{3}\left(d x +c \right)\right)+180 A \left(\cos^{2}\left(d x +c \right)\right)+219 B \left(\cos^{2}\left(d x +c \right)\right)+45 A \cos \left(d x +c \right)+130 B \cos \left(d x +c \right)+35 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{315 d \cos \left(d x +c \right)^{4} \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(690*A*cos(d*x+c)^4+584*B*cos(d*x+c)^4+345*A*cos(d*x+c)^3+292*B*cos(d*x+c)^3+180*A*cos(d*x+c)^2+219*B*cos(d*x+c)^2+45*A*cos(d*x+c)+130*B*cos(d*x+c)+35*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^4/sin(d*x+c)*a^2","A"
137,1,119,122,1.327000," ","int(sec(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(301 A \left(\cos^{3}\left(d x +c \right)\right)+230 B \left(\cos^{3}\left(d x +c \right)\right)+98 A \left(\cos^{2}\left(d x +c \right)\right)+115 B \left(\cos^{2}\left(d x +c \right)\right)+21 A \cos \left(d x +c \right)+60 B \cos \left(d x +c \right)+15 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{105 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(301*A*cos(d*x+c)^3+230*B*cos(d*x+c)^3+98*A*cos(d*x+c)^2+115*B*cos(d*x+c)^2+21*A*cos(d*x+c)+60*B*cos(d*x+c)+15*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)*a^2","A"
138,1,341,124,1.441000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+30 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+15 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+320 A \left(\cos^{3}\left(d x +c \right)\right)+344 B \left(\cos^{3}\left(d x +c \right)\right)-280 A \left(\cos^{2}\left(d x +c \right)\right)-232 B \left(\cos^{2}\left(d x +c \right)\right)-40 A \cos \left(d x +c \right)-88 B \cos \left(d x +c \right)-24 B \right) a^{2}}{60 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{2}}"," ",0,"-1/60/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+30*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+15*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+320*A*cos(d*x+c)^3+344*B*cos(d*x+c)^3-280*A*cos(d*x+c)^2-232*B*cos(d*x+c)^2-40*A*cos(d*x+c)-88*B*cos(d*x+c)-24*B)/sin(d*x+c)/cos(d*x+c)^2*a^2","B"
139,1,256,127,1.447000," ","int(cos(d*x+c)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(15 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+6 A \left(\cos^{3}\left(d x +c \right)\right)+6 A \left(\cos^{2}\left(d x +c \right)\right)+32 B \left(\cos^{2}\left(d x +c \right)\right)-12 A \cos \left(d x +c \right)-28 B \cos \left(d x +c \right)-4 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{6 d \cos \left(d x +c \right) \sin \left(d x +c \right)}"," ",0,"-1/6/d*(15*A*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+6*B*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+6*A*cos(d*x+c)^3+6*A*cos(d*x+c)^2+32*B*cos(d*x+c)^2-12*A*cos(d*x+c)-28*B*cos(d*x+c)-4*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)*a^2","B"
140,1,410,134,1.685000," ","int(cos(d*x+c)^2*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(19 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+20 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+19 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+20 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 A \left(\cos^{4}\left(d x +c \right)\right)-36 A \left(\cos^{3}\left(d x +c \right)\right)-16 B \left(\cos^{3}\left(d x +c \right)\right)+44 A \left(\cos^{2}\left(d x +c \right)\right)-16 B \left(\cos^{2}\left(d x +c \right)\right)+32 B \cos \left(d x +c \right)\right) a^{2}}{16 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"1/16/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(19*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+20*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+19*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+20*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*A*cos(d*x+c)^4-36*A*cos(d*x+c)^3-16*B*cos(d*x+c)^3+44*A*cos(d*x+c)^2-16*B*cos(d*x+c)^2+32*B*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)*a^2","B"
141,1,583,144,1.708000," ","int(cos(d*x+c)^3*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(75 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+114 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+150 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+228 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+75 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+114 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+64 A \left(\cos^{6}\left(d x +c \right)\right)+208 A \left(\cos^{5}\left(d x +c \right)\right)+96 B \left(\cos^{5}\left(d x +c \right)\right)+328 A \left(\cos^{4}\left(d x +c \right)\right)+432 B \left(\cos^{4}\left(d x +c \right)\right)-600 A \left(\cos^{3}\left(d x +c \right)\right)-528 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{192 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)}"," ",0,"-1/192/d*(75*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+114*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+150*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+228*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+75*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+114*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+64*A*cos(d*x+c)^6+208*A*cos(d*x+c)^5+96*B*cos(d*x+c)^5+328*A*cos(d*x+c)^4+432*B*cos(d*x+c)^4-600*A*cos(d*x+c)^3-528*B*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)*a^2","B"
142,1,765,185,1.495000," ","int(cos(d*x+c)^4*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(-489 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-600 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)-1467 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-1800 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-1467 A \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-1800 B \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-489 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-600 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+768 A \left(\cos^{8}\left(d x +c \right)\right)+2176 A \left(\cos^{7}\left(d x +c \right)\right)+1024 B \left(\cos^{7}\left(d x +c \right)\right)+2272 A \left(\cos^{6}\left(d x +c \right)\right)+3328 B \left(\cos^{6}\left(d x +c \right)\right)+2608 A \left(\cos^{5}\left(d x +c \right)\right)+5248 B \left(\cos^{5}\left(d x +c \right)\right)-7824 A \left(\cos^{4}\left(d x +c \right)\right)-9600 B \left(\cos^{4}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{3072 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right)}"," ",0,"-1/3072/d*(-489*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3-600*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^3-1467*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-1800*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-1467*A*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)-1800*B*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)*cos(d*x+c)-489*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-600*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+768*A*cos(d*x+c)^8+2176*A*cos(d*x+c)^7+1024*B*cos(d*x+c)^7+2272*A*cos(d*x+c)^6+3328*B*cos(d*x+c)^6+2608*A*cos(d*x+c)^5+5248*B*cos(d*x+c)^5-7824*A*cos(d*x+c)^4-9600*B*cos(d*x+c)^4)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)*a^2","B"
143,1,947,226,1.611000," ","int(cos(d*x+c)^5*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(4245 A \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+4890 B \sin \left(d x +c \right) \left(\cos^{4}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+16980 A \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+19560 B \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+25470 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+29340 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+16980 A \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+19560 B \sin \left(d x +c \right) \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sqrt{2}+4245 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)+4890 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \sin \left(d x +c \right)+12288 A \left(\cos^{10}\left(d x +c \right)\right)+32256 A \left(\cos^{9}\left(d x +c \right)\right)+15360 B \left(\cos^{9}\left(d x +c \right)\right)+27904 A \left(\cos^{8}\left(d x +c \right)\right)+43520 B \left(\cos^{8}\left(d x +c \right)\right)+18112 A \left(\cos^{7}\left(d x +c \right)\right)+45440 B \left(\cos^{7}\left(d x +c \right)\right)+45280 A \left(\cos^{6}\left(d x +c \right)\right)+52160 B \left(\cos^{6}\left(d x +c \right)\right)-135840 A \left(\cos^{5}\left(d x +c \right)\right)-156480 B \left(\cos^{5}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, a^{2}}{61440 d \sin \left(d x +c \right) \cos \left(d x +c \right)^{4}}"," ",0,"-1/61440/d*(4245*A*sin(d*x+c)*cos(d*x+c)^4*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+4890*B*sin(d*x+c)*cos(d*x+c)^4*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+16980*A*sin(d*x+c)*cos(d*x+c)^3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+19560*B*sin(d*x+c)*cos(d*x+c)^3*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+25470*A*sin(d*x+c)*cos(d*x+c)^2*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+29340*B*sin(d*x+c)*cos(d*x+c)^2*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+16980*A*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+19560*B*sin(d*x+c)*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*2^(1/2)+4245*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*sin(d*x+c)+4890*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*sin(d*x+c)+12288*A*cos(d*x+c)^10+32256*A*cos(d*x+c)^9+15360*B*cos(d*x+c)^9+27904*A*cos(d*x+c)^8+43520*B*cos(d*x+c)^8+18112*A*cos(d*x+c)^7+45440*B*cos(d*x+c)^7+45280*A*cos(d*x+c)^6+52160*B*cos(d*x+c)^6-135840*A*cos(d*x+c)^5-156480*B*cos(d*x+c)^5)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^4*a^2","B"
144,1,785,177,1.876000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(105 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-105 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+315 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-315 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+315 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-315 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \cos \left(d x +c \right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+105 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-105 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \sin \left(d x +c \right)-1456 A \left(\cos^{4}\left(d x +c \right)\right)+688 B \left(\cos^{4}\left(d x +c \right)\right)+1568 A \left(\cos^{3}\left(d x +c \right)\right)-1184 B \left(\cos^{3}\left(d x +c \right)\right)-448 A \left(\cos^{2}\left(d x +c \right)\right)+544 B \left(\cos^{2}\left(d x +c \right)\right)+336 A \cos \left(d x +c \right)-288 B \cos \left(d x +c \right)+240 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{840 d \cos \left(d x +c \right)^{3} \sin \left(d x +c \right) a}"," ",0,"1/840/d*(105*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-105*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+315*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-315*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)^2*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+315*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)-315*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*cos(d*x+c)*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+105*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)-105*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*sin(d*x+c)-1456*A*cos(d*x+c)^4+688*B*cos(d*x+c)^4+1568*A*cos(d*x+c)^3-1184*B*cos(d*x+c)^3-448*A*cos(d*x+c)^2+544*B*cos(d*x+c)^2+336*A*cos(d*x+c)-288*B*cos(d*x+c)+240*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^3/sin(d*x+c)/a","B"
145,1,595,138,1.696000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(15 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-15 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+30 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-30 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+15 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-15 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+40 A \left(\cos^{3}\left(d x +c \right)\right)-104 B \left(\cos^{3}\left(d x +c \right)\right)-80 A \left(\cos^{2}\left(d x +c \right)\right)+112 B \left(\cos^{2}\left(d x +c \right)\right)+40 A \cos \left(d x +c \right)-32 B \cos \left(d x +c \right)+24 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{60 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right) a}"," ",0,"1/60/d*(15*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2-15*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2+30*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-30*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+15*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)-15*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+40*A*cos(d*x+c)^3-104*B*cos(d*x+c)^3-80*A*cos(d*x+c)^2+112*B*cos(d*x+c)^2+40*A*cos(d*x+c)-32*B*cos(d*x+c)+24*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)/a","B"
146,1,405,101,1.664000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-3 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+3 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+12 A \left(\cos^{2}\left(d x +c \right)\right)-4 B \left(\cos^{2}\left(d x +c \right)\right)-12 A \cos \left(d x +c \right)+8 B \cos \left(d x +c \right)-4 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{6 d \sin \left(d x +c \right) \cos \left(d x +c \right) a}"," ",0,"-1/6/d*(-3*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+3*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-3*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+3*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+12*A*cos(d*x+c)^2-4*B*cos(d*x+c)^2-12*A*cos(d*x+c)+8*B*cos(d*x+c)-4*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)/a","B"
147,1,200,67,1.587000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 B \cos \left(d x +c \right)+2 B \right)}{d \sin \left(d x +c \right) a}"," ",0,"1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*B*cos(d*x+c)+2*B)/sin(d*x+c)/a","B"
148,1,194,76,1.593000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right)+A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)\right)}{d a}"," ",0,"-1/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))+A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c)))/a","B"
149,1,353,102,1.686000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+2 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \left(\cos^{2}\left(d x +c \right)\right)+2 A \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right) a}"," ",0,"1/2/d*(A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+2*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*cos(d*x+c)^2+2*A*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/a","B"
150,1,717,140,1.864000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(7 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-4 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+7 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+8 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-4 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+8 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-8 A \left(\cos^{4}\left(d x +c \right)\right)+12 A \left(\cos^{3}\left(d x +c \right)\right)-16 B \left(\cos^{3}\left(d x +c \right)\right)-4 A \left(\cos^{2}\left(d x +c \right)\right)+16 B \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right) a}"," ",0,"1/16/d*(7*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-4*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+7*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+8*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-4*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+8*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-8*A*cos(d*x+c)^4+12*A*cos(d*x+c)^3-16*B*cos(d*x+c)^3-4*A*cos(d*x+c)^2+16*B*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)/a","B"
151,1,1067,177,1.776000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-27 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)+42 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-48 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-54 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+48 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+84 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)-96 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-27 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+96 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+42 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-48 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+48 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+64 A \left(\cos^{6}\left(d x +c \right)\right)-80 A \left(\cos^{5}\left(d x +c \right)\right)+96 B \left(\cos^{5}\left(d x +c \right)\right)+184 A \left(\cos^{4}\left(d x +c \right)\right)-144 B \left(\cos^{4}\left(d x +c \right)\right)-168 A \left(\cos^{3}\left(d x +c \right)\right)+48 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right) a}"," ",0,"-1/192/d*(-27*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+42*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2-48*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2-54*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+48*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2+84*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)-96*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-27*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)+96*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+42*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-48*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+48*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+64*A*cos(d*x+c)^6-80*A*cos(d*x+c)^5+96*B*cos(d*x+c)^5+184*A*cos(d*x+c)^4-144*B*cos(d*x+c)^4-168*A*cos(d*x+c)^3+48*B*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)/a","B"
152,1,793,189,2.013000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(165 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-225 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)+495 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-675 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+495 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-675 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+165 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-225 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+760 A \left(\cos^{4}\left(d x +c \right)\right)-1176 B \left(\cos^{4}\left(d x +c \right)\right)-280 A \left(\cos^{3}\left(d x +c \right)\right)+312 B \left(\cos^{3}\left(d x +c \right)\right)-640 A \left(\cos^{2}\left(d x +c \right)\right)+960 B \left(\cos^{2}\left(d x +c \right)\right)+160 A \cos \left(d x +c \right)-192 B \cos \left(d x +c \right)+96 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{240 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/240/d*(-1+cos(d*x+c))*(165*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-225*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))+495*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2-675*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2+495*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-675*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+165*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)-225*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)+760*A*cos(d*x+c)^4-1176*B*cos(d*x+c)^4-280*A*cos(d*x+c)^3+312*B*cos(d*x+c)^3-640*A*cos(d*x+c)^2+960*B*cos(d*x+c)^2+160*A*cos(d*x+c)-192*B*cos(d*x+c)+96*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^3/a^2","B"
153,1,603,148,2.135000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(21 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-33 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+42 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-66 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+21 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-33 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-60 A \left(\cos^{3}\left(d x +c \right)\right)+76 B \left(\cos^{3}\left(d x +c \right)\right)+12 A \left(\cos^{2}\left(d x +c \right)\right)-28 B \left(\cos^{2}\left(d x +c \right)\right)+48 A \cos \left(d x +c \right)-64 B \cos \left(d x +c \right)+16 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{24 d \sin \left(d x +c \right)^{3} \cos \left(d x +c \right) a^{2}}"," ",0,"-1/24/d*(-1+cos(d*x+c))*(21*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2-33*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2+42*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-66*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+21*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-33*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-60*A*cos(d*x+c)^3+76*B*cos(d*x+c)^3+12*A*cos(d*x+c)^2-28*B*cos(d*x+c)^2+48*A*cos(d*x+c)-64*B*cos(d*x+c)+16*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/cos(d*x+c)/a^2","B"
154,1,405,101,1.773000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-7 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-7 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-10 B \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)+2 B \cos \left(d x +c \right)+8 B \right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(3*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-7*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-7*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)^2-10*B*cos(d*x+c)^2-2*A*cos(d*x+c)+2*B*cos(d*x+c)+8*B)/sin(d*x+c)^3/a^2","B"
155,1,404,72,1.416000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-2 B \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)+2 B \cos \left(d x +c \right)\right)}{4 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-3*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)^2-2*B*cos(d*x+c)^2-2*A*cos(d*x+c)+2*B*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^2","B"
156,1,554,106,1.395000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+5 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+4 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+5 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \left(\cos^{2}\left(d x +c \right)\right)+2 B \left(\cos^{2}\left(d x +c \right)\right)+2 A \cos \left(d x +c \right)-2 B \cos \left(d x +c \right)\right)}{4 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right) a^{2}}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*A*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+5*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+4*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+5*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*cos(d*x+c)^2+2*B*cos(d*x+c)^2+2*A*cos(d*x+c)-2*B*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)/a^2","B"
157,1,713,145,1.616000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(6 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-4 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+9 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+6 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-5 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-4 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+9 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 A \left(\cos^{3}\left(d x +c \right)\right)-5 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \left(\cos^{2}\left(d x +c \right)\right)+2 B \left(\cos^{2}\left(d x +c \right)\right)+6 A \cos \left(d x +c \right)-2 B \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*(6*A*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-4*B*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+9*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+6*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-4*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+9*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*A*cos(d*x+c)^3-5*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*cos(d*x+c)^2+2*B*cos(d*x+c)^2+6*A*cos(d*x+c)-2*B*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/a^2","B"
158,1,1075,190,1.796000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(19 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-12 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+38 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+26 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-24 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}-18 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+19 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+52 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-12 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-36 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-8 A \left(\cos^{5}\left(d x +c \right)\right)+26 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-18 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+20 A \left(\cos^{4}\left(d x +c \right)\right)-16 B \left(\cos^{4}\left(d x +c \right)\right)+16 A \left(\cos^{3}\left(d x +c \right)\right)-8 B \left(\cos^{3}\left(d x +c \right)\right)-28 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/16/d*(-1+cos(d*x+c))*(19*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)-12*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)+38*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+26*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2-24*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)-18*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2+19*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+52*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-12*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-36*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-8*A*cos(d*x+c)^5+26*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-18*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+20*A*cos(d*x+c)^4-16*B*cos(d*x+c)^4+16*A*cos(d*x+c)^3-8*B*cos(d*x+c)^3-28*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^3/a^2","B"
159,1,1425,233,1.682000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(423 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)-342 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \cos \left(d x +c \right)+612 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)-468 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \cos \left(d x +c \right)+204 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)-156 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right)+504 A \left(\cos^{3}\left(d x +c \right)\right)+612 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-468 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+112 A \left(\cos^{6}\left(d x +c \right)\right)-208 A \left(\cos^{4}\left(d x +c \right)\right)+141 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)-114 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sin \left(d x +c \right)+141 A \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)-114 B \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right)+423 A \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-342 B \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \left(\cos^{2}\left(d x +c \right)\right)-64 A \left(\cos^{7}\left(d x +c \right)\right)+240 B \left(\cos^{5}\left(d x +c \right)\right)+204 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-156 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right)-344 A \left(\cos^{5}\left(d x +c \right)\right)+192 B \left(\cos^{4}\left(d x +c \right)\right)-96 B \left(\cos^{6}\left(d x +c \right)\right)-336 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/192/d*(-1+cos(d*x+c))*(423*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)-342*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)+204*A*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-156*B*cos(d*x+c)^3*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))-208*A*cos(d*x+c)^4+192*B*cos(d*x+c)^4+141*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)-342*B*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+423*A*sin(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^2+612*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2-468*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)^2+612*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)-468*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)*cos(d*x+c)+504*A*cos(d*x+c)^3-336*B*cos(d*x+c)^3-344*A*cos(d*x+c)^5+240*B*cos(d*x+c)^5+204*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)-156*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*sin(d*x+c)-114*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*cos(d*x+c)^3*sin(d*x+c)+112*A*cos(d*x+c)^6-64*A*cos(d*x+c)^7+141*A*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-114*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*sin(d*x+c)-96*B*cos(d*x+c)^6)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^3/a^2","B"
160,1,795,189,1.750000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-225 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+489 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-675 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+1467 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-675 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+1467 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-225 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+489 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+588 A \left(\cos^{4}\left(d x +c \right)\right)-1196 B \left(\cos^{4}\left(d x +c \right)\right)+432 A \left(\cos^{3}\left(d x +c \right)\right)-816 B \left(\cos^{3}\left(d x +c \right)\right)-636 A \left(\cos^{2}\left(d x +c \right)\right)+1372 B \left(\cos^{2}\left(d x +c \right)\right)-384 A \cos \left(d x +c \right)+768 B \cos \left(d x +c \right)-128 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{192 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) a^{3}}"," ",0,"-1/192/d*(-1+cos(d*x+c))^2*(-225*A*cos(d*x+c)^3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+489*B*cos(d*x+c)^3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-675*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2+1467*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2-675*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+1467*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-225*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+489*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+588*A*cos(d*x+c)^4-1196*B*cos(d*x+c)^4+432*A*cos(d*x+c)^3-816*B*cos(d*x+c)^3-636*A*cos(d*x+c)^2+1372*B*cos(d*x+c)^2-384*A*cos(d*x+c)+768*B*cos(d*x+c)-128*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/cos(d*x+c)/a^3","B"
161,1,597,146,1.632000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(19 A \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-75 B \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+38 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-150 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+19 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+18 A \left(\cos^{3}\left(d x +c \right)\right)-75 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-98 B \left(\cos^{3}\left(d x +c \right)\right)+8 A \left(\cos^{2}\left(d x +c \right)\right)-72 B \left(\cos^{2}\left(d x +c \right)\right)-26 A \cos \left(d x +c \right)+106 B \cos \left(d x +c \right)+64 B \right)}{32 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(19*A*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-75*B*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+38*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-150*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+19*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+18*A*cos(d*x+c)^3-75*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-98*B*cos(d*x+c)^3+8*A*cos(d*x+c)^2-72*B*cos(d*x+c)^2-26*A*cos(d*x+c)+106*B*cos(d*x+c)+64*B)/sin(d*x+c)^5/a^3","B"
162,1,602,107,1.674000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(-5 A \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-19 B \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-10 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-38 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+2 A \left(\cos^{3}\left(d x +c \right)\right)-5 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-18 B \left(\cos^{3}\left(d x +c \right)\right)-19 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8 A \left(\cos^{2}\left(d x +c \right)\right)-8 B \left(\cos^{2}\left(d x +c \right)\right)-10 A \cos \left(d x +c \right)+26 B \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-5*A*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-19*B*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-10*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-38*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)^3-5*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-18*B*cos(d*x+c)^3-19*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*A*cos(d*x+c)^2-8*B*cos(d*x+c)^2-10*A*cos(d*x+c)+26*B*cos(d*x+c))/(1+cos(d*x+c))/sin(d*x+c)^3/a^3","B"
163,1,594,107,1.487000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 A \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+5 B \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+10 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+3 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-14 A \left(\cos^{3}\left(d x +c \right)\right)+5 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 B \left(\cos^{3}\left(d x +c \right)\right)+8 A \left(\cos^{2}\left(d x +c \right)\right)-8 B \left(\cos^{2}\left(d x +c \right)\right)+6 A \cos \left(d x +c \right)+10 B \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) a^{3}}"," ",0,"1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*A*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+5*B*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+6*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+10*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-14*A*cos(d*x+c)^3+5*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*B*cos(d*x+c)^3+8*A*cos(d*x+c)^2-8*B*cos(d*x+c)^2+6*A*cos(d*x+c)+10*B*cos(d*x+c))/(1+cos(d*x+c))^2/sin(d*x+c)/a^3","B"
164,1,824,139,1.433000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(32 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+43 A \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+64 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-3 B \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+86 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+32 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-6 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+43 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-30 A \left(\cos^{3}\left(d x +c \right)\right)-3 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+14 B \left(\cos^{3}\left(d x +c \right)\right)+8 A \left(\cos^{2}\left(d x +c \right)\right)-8 B \left(\cos^{2}\left(d x +c \right)\right)+22 A \cos \left(d x +c \right)-6 B \cos \left(d x +c \right)\right)}{32 d \left(1+\cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right) a^{3}}"," ",0,"-1/32/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(32*A*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+43*A*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+64*A*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-3*B*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+86*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+32*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+43*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-30*A*cos(d*x+c)^3-3*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+14*B*cos(d*x+c)^3+8*A*cos(d*x+c)^2-8*B*cos(d*x+c)^2+22*A*cos(d*x+c)-6*B*cos(d*x+c))/(1+cos(d*x+c))^2/sin(d*x+c)/a^3","B"
165,1,1065,178,1.627000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(80 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-32 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+115 A \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+160 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}-43 B \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-64 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}+230 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+80 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-32 A \left(\cos^{4}\left(d x +c \right)\right)-86 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}-32 B \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \sqrt{2}\, \sin \left(d x +c \right)+115 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-78 A \left(\cos^{3}\left(d x +c \right)\right)-43 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+30 B \left(\cos^{3}\left(d x +c \right)\right)+40 A \left(\cos^{2}\left(d x +c \right)\right)-8 B \left(\cos^{2}\left(d x +c \right)\right)+70 A \cos \left(d x +c \right)-22 B \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{32 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/32/d*(-1+cos(d*x+c))^2*(80*A*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-32*B*sin(d*x+c)*cos(d*x+c)^2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+115*A*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+160*A*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)-43*B*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-64*B*sin(d*x+c)*cos(d*x+c)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)+230*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+80*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-32*A*cos(d*x+c)^4-86*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)-32*B*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*2^(1/2)*sin(d*x+c)+115*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-78*A*cos(d*x+c)^3-43*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+30*B*cos(d*x+c)^3+40*A*cos(d*x+c)^2-8*B*cos(d*x+c)^2+70*A*cos(d*x+c)-22*B*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/a^3","B"
166,1,1427,229,1.901000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(219 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-115 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)+156 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-252 A \left(\cos^{2}\left(d x +c \right)\right)-128 A \left(\cos^{3}\left(d x +c \right)\right)-32 A \left(\cos^{6}\left(d x +c \right)\right)-240 B \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+468 A \cos \left(d x +c \right) \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}+300 A \left(\cos^{4}\left(d x +c \right)\right)+219 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}-115 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+657 A \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-345 B \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+156 A \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-80 B \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-345 B \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+468 A \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-240 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)-80 B \sqrt{2}\, \arctanh \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \sqrt{2}}{2 \cos \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)-64 B \left(\cos^{5}\left(d x +c \right)\right)+657 A \cos \left(d x +c \right) \sin \left(d x +c \right) \ln \left(-\frac{-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+\cos \left(d x +c \right)-1}{\sin \left(d x +c \right)}\right) \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}+140 B \left(\cos^{2}\left(d x +c \right)\right)+112 A \left(\cos^{5}\left(d x +c \right)\right)-156 B \left(\cos^{4}\left(d x +c \right)\right)+80 B \left(\cos^{3}\left(d x +c \right)\right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{64 d \sin \left(d x +c \right)^{5} \cos \left(d x +c \right) a^{3}}"," ",0,"1/64/d*(-1+cos(d*x+c))^2*(140*B*cos(d*x+c)^2-252*A*cos(d*x+c)^2+300*A*cos(d*x+c)^4-156*B*cos(d*x+c)^4+468*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)+219*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-115*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)-240*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*sin(d*x+c)-128*A*cos(d*x+c)^3+80*B*cos(d*x+c)^3-240*B*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+468*A*cos(d*x+c)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)+112*A*cos(d*x+c)^5-64*B*cos(d*x+c)^5-80*B*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+219*A*cos(d*x+c)^3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-115*B*cos(d*x+c)^3*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)-32*A*cos(d*x+c)^6+657*A*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2-345*B*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*cos(d*x+c)^2-345*B*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+156*A*2^(1/2)*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)+657*A*cos(d*x+c)*sin(d*x+c)*ln(-(-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+cos(d*x+c)-1)/sin(d*x+c))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+156*A*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)*cos(d*x+c)^3-80*B*arctanh(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)/cos(d*x+c)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*sin(d*x+c)*2^(1/2)*cos(d*x+c)^3)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/cos(d*x+c)/a^3","B"
167,1,120,74,1.541000," ","int((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x)","\frac{A \left(\arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+\arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \sqrt{2}}{d \sin \left(d x +c \right) a}"," ",0,"A/d*(arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))*(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*(1+cos(d*x+c))/sin(d*x+c)/a*2^(1/2)","A"
168,1,154,98,1.715000," ","int(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x)","-\frac{A \left(1+\cos \left(d x +c \right)\right) \left(-2 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}+\cos \left(d x +c \right) \sqrt{2}-3 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{2}}{2 d \sin \left(d x +c \right) a}"," ",0,"-1/2*A/d*(1+cos(d*x+c))*(-2*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+cos(d*x+c)*2^(1/2)-3*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/a*2^(1/2)","A"
169,1,367,130,1.945000," ","int(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x)","\frac{A \left(-1+\cos \left(d x +c \right)\right)^{2} \left(-16 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+6 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-16 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+27 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+48 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}+4 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+48 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+15 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+66 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+66 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{24 d \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"1/24*A/d*(-1+cos(d*x+c))^2*(-16*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)+6*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)-16*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+27*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)+48*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)+4*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)+48*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+15*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+66*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)+66*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3*2^(1/2)","B"
170,1,625,163,2.118000," ","int(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(1/2),x)","-\frac{A \left(-1+\cos \left(d x +c \right)\right)^{3} \left(96 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+192 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}+40 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+96 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}-160 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+190 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-320 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+465 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+480 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-160 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}-49 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+960 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}+155 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+690 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)+480 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+135 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+1380 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+690 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{240 d \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5}}"," ",0,"-1/240*A/d*(-1+cos(d*x+c))^3*(96*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)+192*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+40*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)+96*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)-160*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)+190*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)-320*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)+465*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+480*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-160*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)-49*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)+960*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)+155*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)+690*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+480*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+135*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+1380*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)+690*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5*2^(1/2)","B"
171,1,298,99,1.543000," ","int((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x)","-\frac{A \left(-1+\cos \left(d x +c \right)\right)^{2} \left(\left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+\left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}-\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-3 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+4 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)-4 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{d \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{3} \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}"," ",0,"-A/d*(-1+cos(d*x+c))^2*((-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)+(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)+3*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)-(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-3*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+4*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-4*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(a*(-1+cos(d*x+c))/cos(d*x+c))^(3/2)/sin(d*x+c)^3/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)","B"
172,1,462,127,1.643000," ","int(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x)","\frac{A \left(-1+\cos \left(d x +c \right)\right)^{3} \left(-3 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-6 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}-7 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+3 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+21 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-2 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+7 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+30 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)+5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}-21 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}-6 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-30 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{3 d \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{5}}"," ",0,"1/3*A/d*(-1+cos(d*x+c))^3*(-3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)-6*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)-7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)-3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+21*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)+7*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+30*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)-21*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)-6*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-30*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(3/2)/sin(d*x+c)^5*2^(1/2)","B"
173,1,883,167,1.926000," ","int(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x)","-\frac{A \left(-1+\cos \left(d x +c \right)\right)^{4} \left(220 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+132 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+660 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-930 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+660 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{3}\left(d x +c \right)\right)+132 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)+180 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)-220 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-278 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+180 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)-195 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-660 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}-660 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}-40 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+288 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+60 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)+195 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-220 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+30 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-132 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}-930 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+930 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right)-132 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+220 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+60 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+930 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{2}}{60 d \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{7}}"," ",0,"-1/60*A/d*(-1+cos(d*x+c))^4*(220*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)-930*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+60*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^3+180*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^2+180*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)+132*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3-220*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+660*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-195*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+132*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)-660*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)-278*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+288*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)-660*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)-40*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)-132*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+30*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)-220*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)+195*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)+660*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-930*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-132*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+930*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+220*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+930*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+60*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(3/2)/sin(d*x+c)^7*2^(1/2)","B"
174,1,1104,205,1.856000," ","int(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(3/2),x)","\frac{A \left(-1+\cos \left(d x +c \right)\right)^{5} \left(1680 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+2520 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)+504 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{4}\left(d x +c \right)\right)-360 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right)-840 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)-672 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right)-3570 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+5040 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{3}\left(d x +c \right)\right)+1008 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)-1680 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+1130 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+720 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)-735 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+350 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{6}\left(d x +c \right)\right)-2520 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}-5040 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}-875 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+56 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{7}\left(d x +c \right)\right)-1008 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{2}\left(d x +c \right)\right)-168 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{4}\left(d x +c \right)\right)-672 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{3}\left(d x +c \right)\right)+952 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+3570 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right)-720 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)-2103 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+1225 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-1008 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}-168 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}}-7140 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+7140 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right)-504 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+840 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+360 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}\right) \sqrt{2}}{168 d \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sin \left(d x +c \right)^{9}}"," ",0,"1/168*A/d*(-1+cos(d*x+c))^5*(1680*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)-360*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^4-672*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)+504*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^4-840*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4+2520*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4+56*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^7+350*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^6-3570*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-720*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^3+720*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)+1008*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3-1680*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+5040*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-735*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-2520*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+1130*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+952*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)-5040*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)-875*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)-168*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^4-672*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^3-1008*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^2-1008*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+1225*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)-2103*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)-168*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)+3570*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4-7140*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-504*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+840*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+7140*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+360*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(3/2)/sin(d*x+c)^9*2^(1/2)","B"
175,1,695,127,1.554000," ","int((A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x)","\frac{A \left(-1+\cos \left(d x +c \right)\right)^{4} \left(-21 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)-33 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-23 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)-3 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}+23 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+9 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+5 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+69 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{3}\left(d x +c \right)\right)+23 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+96 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right)+11 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-69 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-23 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}-96 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-37 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}-69 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}-96 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+21 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+69 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+96 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{12 d \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{7} \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}"," ",0,"1/12*A/d*(-1+cos(d*x+c))^4*(-21*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3-33*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)-23*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3-3*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+23*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)+9*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+5*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+69*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3+23*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)+96*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+11*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)-69*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-23*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)-96*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-37*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)-69*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)-96*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)+21*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+69*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+96*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(a*(-1+cos(d*x+c))/cos(d*x+c))^(5/2)/sin(d*x+c)^7/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)","B"
176,1,788,155,1.772000," ","int(cos(d*x+c)*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x)","-\frac{A \left(-1+\cos \left(d x +c \right)\right)^{5} \left(195 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right)+450 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)+237 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{4}\left(d x +c \right)\right)+180 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)-210 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)-395 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)-474 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-135 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}+120 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-343 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}+1185 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)+790 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+237 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+1680 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right)+736 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}-578 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-2370 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-395 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}-3360 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-280 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}+345 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+1185 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}+1680 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)\right) \sqrt{2}}{60 d \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{9}}"," ",0,"-1/60*A/d*(-1+cos(d*x+c))^5*(195*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^4+450*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^3+237*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^4+180*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^2-210*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)-395*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4-474*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)-135*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)+120*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)-343*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)+1185*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4+790*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)+237*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+1680*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4+736*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)-578*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)-2370*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-395*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)-3360*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-280*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)+345*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+1185*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+1680*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(5/2)/sin(d*x+c)^9*2^(1/2)","B"
177,1,1475,201,1.886000," ","int(cos(d*x+c)^2*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x)","-\frac{A \left(-1+\cos \left(d x +c \right)\right)^{6} \left(5845 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \cos \left(d x +c \right) \sqrt{2}+7014 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+35070 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-17535 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{4}\left(d x +c \right)\right)-3507 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{4}\left(d x +c \right)\right)+2505 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right)+5845 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{4}\left(d x +c \right)\right)-4305 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \cos \left(d x +c \right)-24780 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right)+35070 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{3}\left(d x +c \right)\right)+7014 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{3}\left(d x +c \right)\right)-5010 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{2}\left(d x +c \right)\right)-11690 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{3}\left(d x +c \right)\right)+1322 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}+2505 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \cos \left(d x +c \right)-3507 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{5}\left(d x +c \right)\right)+1995 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{5}\left(d x +c \right)\right)-17535 \sqrt{2}\, \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \left(\cos^{5}\left(d x +c \right)\right)+2505 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{5}\left(d x +c \right)\right)-5145 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}-3570 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{6}\left(d x +c \right)\right)-17535 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \sqrt{2}-17535 \arctan \left(\frac{1}{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}}\right) \cos \left(d x +c \right) \sqrt{2}-1015 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sqrt{2}-420 \sqrt{2}\, \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{7}\left(d x +c \right)\right)-1470 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{2}\left(d x +c \right)\right)+6405 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{4}\left(d x +c \right)\right)+5670 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}} \left(\cos^{3}\left(d x +c \right)\right)+12768 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+5845 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{5}\left(d x +c \right)\right)-24780 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{4}\left(d x +c \right)\right)-5010 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right)-15573 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}-11690 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+11633 \sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-3507 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \cos \left(d x +c \right) \sqrt{2}-1575 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{9}{2}}-24780 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \cos \left(d x +c \right)+49560 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{3}\left(d x +c \right)\right)-3507 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{2}+5845 \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{2}+2505 \sqrt{2}\, \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{7}{2}}-24780 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{5}\left(d x +c \right)\right)+49560 \arctan \left(\frac{\sqrt{-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{2}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)\right) \sqrt{2}}{420 d \left(-\frac{2 \cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\frac{a \left(-1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sin \left(d x +c \right)^{11}}"," ",0,"-1/420*A/d*(-1+cos(d*x+c))^6*(5845*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)-17535*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^5+1995*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^5+2505*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^5-3507*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^5+2505*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^4-4305*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)-3507*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^4+5845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4-17535*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4-420*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^7-3570*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^6-24780*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))-5010*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^3-5010*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^2+2505*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)+7014*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3-11690*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3+35070*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-5145*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)+7014*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)-17535*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)+5845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^5+1322*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)+12768*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)-17535*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)-1015*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)-24780*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^5+6405*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^4+5670*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^3-1470*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^2-3507*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+11633*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)-11690*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)-15573*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)+35070*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)-1575*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)-24780*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4-24780*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)-3507*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)+49560*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2+5845*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)+49560*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3+2505*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(5/2)/sin(d*x+c)^11*2^(1/2)","B"
178,1,1964,241,2.066000," ","int(cos(d*x+c)^3*(A+A*sec(d*x+c))/(a-a*sec(d*x+c))^(5/2),x)","\text{Expression too large to display}"," ",0,"-1/180*A/d*(-1+cos(d*x+c))^7*(-8610*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)*2^(1/2)+2583*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^6+25830*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^5+2870*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^5-3690*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^5+5166*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^5+1845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^4+2870*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)-2583*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^4+4305*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^4-12915*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^4+4215*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^7-15112*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^6+18270*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))+7380*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^3+1845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^2-3690*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)-10332*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^3+17220*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^3-51660*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^3-4305*2^(1/2)*cos(d*x+c)^6*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)+12915*2^(1/2)*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^6+1125*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)^6+4680*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)^5+1435*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^6+6525*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)^4+1800*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)^3-1845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2)*cos(d*x+c)^6-3825*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)^2-3600*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)*cos(d*x+c)+120*2^(1/2)*cos(d*x+c)^9*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+930*2^(1/2)*cos(d*x+c)^8*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)+3780*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2)-2583*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)^2*2^(1/2)+12915*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*2^(1/2)-8610*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^5-10335*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*2^(1/2)-8652*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*2^(1/2)+25830*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)*2^(1/2)+4515*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*2^(1/2)+36540*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^5-1435*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^4-5740*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^3-1435*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)*cos(d*x+c)^2-945*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(11/2)+18270*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^6+5166*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*cos(d*x+c)*2^(1/2)+14285*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^5*2^(1/2)+4305*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*cos(d*x+c)^2*2^(1/2)+6254*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*2^(1/2)-12915*arctan(1/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2*2^(1/2)+1435*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(9/2)-18270*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^4+36540*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)+2583*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)*2^(1/2)-18270*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^2-4305*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(3/2)*2^(1/2)-73080*arctan(1/2*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*2^(1/2))*cos(d*x+c)^3-1845*2^(1/2)*(-2*cos(d*x+c)/(1+cos(d*x+c)))^(7/2))/(-2*cos(d*x+c)/(1+cos(d*x+c)))^(5/2)/(a*(-1+cos(d*x+c))/cos(d*x+c))^(5/2)/sin(d*x+c)^13*2^(1/2)","B"
179,1,691,223,12.410000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{4 \left(\frac{A}{2}+\frac{B}{2}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+2 A \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-4/5*(1/2*A+1/2*B)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*A*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
180,1,662,200,12.301000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 \left(\frac{A}{2}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*(1/2*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
181,1,427,171,10.069000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","-\frac{a \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{4 \left(\frac{A}{2}+\frac{B}{2}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+4*(1/2*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
182,1,240,148,4.863000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{2 a \left(A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*a*(A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
183,1,321,148,4.983000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(4 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(4*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
184,1,355,173,4.372000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(44 A +20 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-16 A -10 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-24*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(44*A+20*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-16*A-10*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
185,1,383,200,4.197000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(240 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-528 A -168 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(448 A +308 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-122 A -112 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(240*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-528*A-168*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(448*A+308*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-122*A-112*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+35*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
186,1,852,258,15.561000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{a^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(8 \left(\frac{A}{2}+\frac{B}{4}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{8 \left(\frac{A}{4}+\frac{B}{2}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(8*(1/2*A+1/4*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-8/5*(1/4*A+1/2*B)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
187,1,743,227,13.120000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","-\frac{a^{2} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+8 \left(\frac{A}{4}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{8 \left(\frac{A}{2}+\frac{B}{4}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+8*(1/4*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+8*(1/2*A+1/4*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
188,1,513,194,5.141000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{4 a^{2} \left(6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A +2 B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A +7 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(3 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+3 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*a^2*(6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A+2*B)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A+7*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2+3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
189,1,388,192,4.635000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{4 a^{2} \left(2 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A +3 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-3 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*a^2*(2*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A+3*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
190,1,357,198,4.533000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-12 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(32 A +10 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-13 A -5 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+10 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-12*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(32*A+10*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-13*A-5*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+10*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
191,1,385,229,4.427000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(120 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-348 A -84 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(378 A +224 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-117 A -91 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-84 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(120*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-348*A-84*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(378*A+224*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-117*A-91*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+30*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+35*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-84*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
192,1,413,258,4.720000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-560 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(1840 A +360 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2368 A -1044 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(1568 A +1134 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-387 A -351 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+75 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-168 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+90 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-560*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(1840*A+360*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2368*A-1044*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1568*A+1134*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-387*A-351*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+75*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-168*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+90*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
193,1,1180,297,18.522000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","-\frac{a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 \left(\frac{3 A}{8}+\frac{B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{16 \left(\frac{3 A}{8}+\frac{3 B}{8}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+16 \left(\frac{A}{8}+\frac{3 B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{144 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{180 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*(3/8*A+1/8*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-16/5*(3/8*A+3/8*B)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+16*(1/8*A+3/8*B)*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*B*(-1/144*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
194,1,931,268,15.402000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","-\frac{a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+16 \left(\frac{3 A}{8}+\frac{3 B}{8}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{16 \left(\frac{3 A}{8}+\frac{B}{8}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{16 \left(\frac{A}{8}+\frac{3 B}{8}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+16*(3/8*A+3/8*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+16*(3/8*A+1/8*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-16/5*(1/8*A+3/8*B)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
195,1,916,239,12.877000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\frac{4 a^{3} \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(100 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-180 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+60 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+108 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-216 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-100 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+190 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-60 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-108 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+246 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+25 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-50 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+27 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-72 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{15 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"4/15*a^3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^3*(100*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^4+60*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-180*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+60*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^4+108*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^4-216*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-100*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2-60*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+190*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-60*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2-108*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*sin(1/2*d*x+1/2*c)^2+246*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+25*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-50*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+27*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-72*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
196,1,654,229,5.722000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{4 a^{3} \left(-4 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(5 A +9 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 A +5 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-3 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+3 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*a^3*(-4*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A+9*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A+5*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
197,1,519,239,4.783000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{4 a^{3} \left(-12 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(21 A +5 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(9 A +10 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-27 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+25 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-15 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/15*a^3*(-12*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(21*A+5*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(9*A+10*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-27*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+25*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-15*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
198,1,385,239,5.016000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(120 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-432 A -84 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(602 A +294 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-208 A -126 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+65 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(120*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-432*A-84*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(602*A+294*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-208*A-126*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+65*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+105*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
199,1,413,268,4.459000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(-560 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2200 A +360 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-3412 A -1296 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(2702 A +1806 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-738 A -624 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+165 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+195 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-441 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(-560*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2200*A+360*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-3412*A-1296*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(2702*A+1806*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-738*A-624*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+165*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+195*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-441*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
200,1,441,297,4.476000," ","int((a+a*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{3} \left(10080 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-43680 A -6160 B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(77280 A +24200 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-72240 A -37532 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(39270 A +29722 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-8820 A -8118 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+1575 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3465 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+1815 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3927 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*(10080*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-43680*A-6160*B)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(77280*A+24200*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-72240*A-37532*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(39270*A+29722*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-8820*A-8118*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+1575*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3465*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+1815*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3927*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
201,1,806,255,14.321000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(2 A -2 B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(-2 A +2 B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\left(A -B \right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*((2*A-2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+(-2*A+2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+(A-B)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
202,1,493,226,11.618000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(2 A -2 B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\left(-A +B \right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+(-A+B)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
203,1,318,193,8.625000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -3 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -5 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-3*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-5*B)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^3/(2*sin(1/2*d*x+1/2*c)^2-1)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
204,1,243,165,4.813000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
205,1,244,170,4.412000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
206,1,262,200,4.997000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-8 A \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(18 A -6 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-7 A +3 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-8*A*sin(1/2*d*x+1/2*c)^6+(18*A-6*B)*sin(1/2*d*x+1/2*c)^4+(-7*A+3*B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
207,1,282,227,4.901000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(25 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+63 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-25 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-45 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 A \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-56 A -40 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-30 A +90 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(23 A -35 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{15 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(25*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+63*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-25*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-45*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*A*sin(1/2*d*x+1/2*c)^8+(-56*A-40*B)*sin(1/2*d*x+1/2*c)^6+(-30*A+90*B)*sin(1/2*d*x+1/2*c)^4+(23*A-35*B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
208,1,300,256,5.003000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(225 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+441 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-175 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-441 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-480 A \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(864 A +336 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-888 A -392 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(930 A -210 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-321 A +161 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{105 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(225*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+441*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-175*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-441*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-480*A*sin(1/2*d*x+1/2*c)^10+(864*A+336*B)*sin(1/2*d*x+1/2*c)^8+(-888*A-392*B)*sin(1/2*d*x+1/2*c)^6+(930*A-210*B)*sin(1/2*d*x+1/2*c)^4+(-321*A+161*B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
209,1,750,265,15.795000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(-A +B \right) \left(2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(-1+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{\left(4 A -8 B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\left(-2 A +4 B \right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{2 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^2*(4*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+1/3*(-A+B)*(2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^6+20*sin(1/2*d*x+1/2*c)^4-7*sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/(-1+sin(1/2*d*x+1/2*c)^2)+(4*A-8*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+(-2*A+4*B)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
210,1,492,236,5.877000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -4 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 A -43 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(7 A -37 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-4*B)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*A-43*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A-37*B)*sin(1/2*d*x+1/2*c)^2)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
211,1,350,197,5.030000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^6+4*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*A*cos(1/2*d*x+1/2*c)^4+16*B*cos(1/2*d*x+1/2*c)^4-3*A*cos(1/2*d*x+1/2*c)^2-3*B*cos(1/2*d*x+1/2*c)^2+A-B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
212,1,350,202,5.660000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-20 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^6+4*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-20*A*cos(1/2*d*x+1/2*c)^4+2*B*cos(1/2*d*x+1/2*c)^4+9*A*cos(1/2*d*x+1/2*c)^2-3*B*cos(1/2*d*x+1/2*c)^2-A+B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
213,1,421,211,5.823000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/sec(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+24 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*A*cos(1/2*d*x+1/2*c)^6+10*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+24*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^6-4*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*A*cos(1/2*d*x+1/2*c)^4+20*B*cos(1/2*d*x+1/2*c)^4+15*A*cos(1/2*d*x+1/2*c)^2-9*B*cos(1/2*d*x+1/2*c)^2-A+B)/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
214,1,435,241,6.279000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+42 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-48 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*A*cos(1/2*d*x+1/2*c)^8+12*A*cos(1/2*d*x+1/2*c)^6+20*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+42*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*B*cos(1/2*d*x+1/2*c)^6-10*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-24*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-48*A*cos(1/2*d*x+1/2*c)^4+38*B*cos(1/2*d*x+1/2*c)^4+21*A*cos(1/2*d*x+1/2*c)^2-15*B*cos(1/2*d*x+1/2*c)^2-A+B)/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
215,1,465,270,5.617000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(96 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-352 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-150 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-336 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+60 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+210 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+266 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-240 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-135 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 A -5 B \right)}{30 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/30/a^2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(96*A*cos(1/2*d*x+1/2*c)^10-352*A*cos(1/2*d*x+1/2*c)^8+80*B*cos(1/2*d*x+1/2*c)^8+120*A*cos(1/2*d*x+1/2*c)^6-150*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-336*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+60*B*cos(1/2*d*x+1/2*c)^6+100*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+210*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+266*A*cos(1/2*d*x+1/2*c)^4-240*B*cos(1/2*d*x+1/2*c)^4-135*A*cos(1/2*d*x+1/2*c)^2+105*B*cos(1/2*d*x+1/2*c)^2+5*A-5*B)/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
216,1,876,312,6.971000," ","int(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{-4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+165 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+165 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+165 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(147 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-357 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+165 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-168 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(7 A -17 B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+8 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(482 A -1167 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(461 A -1111 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+14 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(169 A -404 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(439 A -1029 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-1/60*(-4*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+165*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+10*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+165*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+165*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-357*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+165*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-168*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A-17*B)*sin(1/2*d*x+1/2*c)^10+8*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(482*A-1167*B)*sin(1/2*d*x+1/2*c)^8-10*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(461*A-1111*B)*sin(1/2*d*x+1/2*c)^6+14*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(169*A-404*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(439*A-1029*B)*sin(1/2*d*x+1/2*c)^2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/d","B"
217,1,685,285,6.015000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(9 A -49 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(147 A -817 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(43 A -248 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(69 A -439 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*(-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(9*A-49*B)*sin(1/2*d*x+1/2*c)^8-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A-817*B)*sin(1/2*d*x+1/2*c)^6+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(43*A-248*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(69*A-439*B)*sin(1/2*d*x+1/2*c)^2)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
218,1,451,248,5.149000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+54 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-138 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^8-10*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+108*B*cos(1/2*d*x+1/2*c)^8-30*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+54*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*A*cos(1/2*d*x+1/2*c)^6-138*B*cos(1/2*d*x+1/2*c)^6+6*A*cos(1/2*d*x+1/2*c)^4+24*B*cos(1/2*d*x+1/2*c)^4+7*A*cos(1/2*d*x+1/2*c)^2+3*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
219,1,451,244,4.830000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+22 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^8+10*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^8+10*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)^6+22*B*cos(1/2*d*x+1/2*c)^6-24*A*cos(1/2*d*x+1/2*c)^4-6*B*cos(1/2*d*x+1/2*c)^4+17*A*cos(1/2*d*x+1/2*c)^2-7*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
220,1,451,250,6.000000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+54 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+6 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-198 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(108*A*cos(1/2*d*x+1/2*c)^8+30*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+54*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*cos(1/2*d*x+1/2*c)^8+10*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-198*A*cos(1/2*d*x+1/2*c)^6-2*B*cos(1/2*d*x+1/2*c)^6+114*A*cos(1/2*d*x+1/2*c)^4-24*B*cos(1/2*d*x+1/2*c)^4-27*A*cos(1/2*d*x+1/2*c)^2+17*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
221,1,451,256,5.188000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/sec(d*x+c)^(1/2),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(348 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+294 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-54 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+198 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-114 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+27 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(348*A*cos(1/2*d*x+1/2*c)^8+130*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+294*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-108*B*cos(1/2*d*x+1/2*c)^8-30*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-54*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*A*cos(1/2*d*x+1/2*c)^6+198*B*cos(1/2*d*x+1/2*c)^6+264*A*cos(1/2*d*x+1/2*c)^4-114*B*cos(1/2*d*x+1/2*c)^4-37*A*cos(1/2*d*x+1/2*c)^2+27*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
222,1,465,285,5.295000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+468 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+714 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-348 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-130 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-294 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1058 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+578 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-264 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+37 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(160*A*cos(1/2*d*x+1/2*c)^10+468*A*cos(1/2*d*x+1/2*c)^8+330*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+714*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-348*B*cos(1/2*d*x+1/2*c)^8-130*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-294*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1058*A*cos(1/2*d*x+1/2*c)^6+578*B*cos(1/2*d*x+1/2*c)^6+474*A*cos(1/2*d*x+1/2*c)^4-264*B*cos(1/2*d*x+1/2*c)^4-47*A*cos(1/2*d*x+1/2*c)^2+37*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
223,1,493,314,5.900000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(192 A \left(\cos^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-864 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+160 B \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-228 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-630 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1386 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+468 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+714 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+1590 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1058 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-744 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+57 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60/a^3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(192*A*cos(1/2*d*x+1/2*c)^12-864*A*cos(1/2*d*x+1/2*c)^10+160*B*cos(1/2*d*x+1/2*c)^10-228*A*cos(1/2*d*x+1/2*c)^8-630*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1386*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+468*B*cos(1/2*d*x+1/2*c)^8+330*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+714*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+1590*A*cos(1/2*d*x+1/2*c)^6-1058*B*cos(1/2*d*x+1/2*c)^6-744*A*cos(1/2*d*x+1/2*c)^4+474*B*cos(1/2*d*x+1/2*c)^4+57*A*cos(1/2*d*x+1/2*c)^2-47*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
224,1,408,150,2.428000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(18 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-18 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+15 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-15 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+36 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+30 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+20 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{96 d \sin \left(d x +c \right)^{2}}"," ",0,"1/96/d*(18*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-18*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+15*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-15*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+36*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+30*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+20*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)","B"
225,1,344,111,2.481000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-4 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+3 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-3 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(4*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-4*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+3*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-3*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+6*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","B"
226,1,277,68,2.190000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{2 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/2/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-2*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)","B"
227,1,178,66,2.516000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 A \cos \left(d x +c \right)-4 A \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*A*cos(d*x+c)-4*A)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(1/cos(d*x+c))^(1/2)","B"
228,1,75,70,2.598000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(A \cos \left(d x +c \right)+2 A +3 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(A*cos(d*x+c)+2*A+3*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)","A"
229,1,96,112,2.484000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(3 A \left(\cos^{2}\left(d x +c \right)\right)+4 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+8 A +10 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(3*A*cos(d*x+c)^2+4*A*cos(d*x+c)+5*B*cos(d*x+c)+8*A+10*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)","A"
230,1,118,151,2.954000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+18 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+24 A \cos \left(d x +c \right)+28 B \cos \left(d x +c \right)+48 A +56 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right)}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+18*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+24*A*cos(d*x+c)+28*B*cos(d*x+c)+48*A+56*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^4/sin(d*x+c)","A"
231,1,479,195,2.421000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{\left(264 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-264 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+225 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-225 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+528 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+450 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+352 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+300 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+128 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+240 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+96 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a}{768 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"1/768/d*(264*A*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-264*A*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+225*B*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-225*B*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+528*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+450*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+352*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+300*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+128*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+240*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+96*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)*(cos(d*x+c)^2-1)*a","B"
232,1,415,154,2.417000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(42 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-42 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+33 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-33 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+84 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+66 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+44 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a}{48 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)}"," ",0,"-1/48/d*(-1+cos(d*x+c))*(42*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-42*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+33*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-33*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+84*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+66*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+44*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)*a","B"
233,1,353,113,2.112000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(12 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-12 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+7 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-7 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-14 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a}{8 d \cos \left(d x +c \right) \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(12*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)-12*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)+7*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)-7*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-14*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/cos(d*x+c)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)*a","B"
234,1,346,110,2.543000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+8 A \left(\cos^{2}\left(d x +c \right)\right)-8 A \cos \left(d x +c \right)+4 B \cos \left(d x +c \right)-4 B \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a}{4 d \sin \left(d x +c \right)}"," ",0,"-1/4/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(2*A*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-2*A*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+3*B*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-3*B*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+8*A*cos(d*x+c)^2-8*A*cos(d*x+c)+4*B*cos(d*x+c)-4*B)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)*a","B"
235,1,211,107,2.606000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+4 A \left(\cos^{2}\left(d x +c \right)\right)+16 A \cos \left(d x +c \right)+12 B \cos \left(d x +c \right)-20 A -12 B \right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a}{6 d \sin \left(d x +c \right)}"," ",0,"-1/6/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*A*cos(d*x+c)^2+16*A*cos(d*x+c)+12*B*cos(d*x+c)-20*A-12*B)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)*a","A"
236,1,97,113,2.617000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(3 A \left(\cos^{2}\left(d x +c \right)\right)+9 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+18 A +25 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(3*A*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c)+18*A+25*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)*a","A"
237,1,119,157,2.595000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+39 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+52 A \cos \left(d x +c \right)+63 B \cos \left(d x +c \right)+104 A +126 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{4}\left(d x +c \right)\right) a}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+39*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+52*A*cos(d*x+c)+63*B*cos(d*x+c)+104*A+126*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^4/sin(d*x+c)*a","A"
238,1,141,198,3.123000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(35 A \left(\cos^{4}\left(d x +c \right)\right)+85 A \left(\cos^{3}\left(d x +c \right)\right)+45 B \left(\cos^{3}\left(d x +c \right)\right)+102 A \left(\cos^{2}\left(d x +c \right)\right)+117 B \left(\cos^{2}\left(d x +c \right)\right)+136 A \cos \left(d x +c \right)+156 B \cos \left(d x +c \right)+272 A +312 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(35*A*cos(d*x+c)^4+85*A*cos(d*x+c)^3+45*B*cos(d*x+c)^3+102*A*cos(d*x+c)^2+117*B*cos(d*x+c)^2+136*A*cos(d*x+c)+156*B*cos(d*x+c)+272*A+312*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)*a","A"
239,1,543,236,2.463000," ","int(sec(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\frac{\left(-4890 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+4890 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-4245 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+4245 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+9780 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+8490 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+6520 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+5660 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+3680 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4528 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+960 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+2784 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+768 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}{7680 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{2}}"," ",0,"1/7680/d*(-4890*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+4890*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)-4245*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+4245*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+9780*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)+8490*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)+6520*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+5660*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+3680*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+4528*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+960*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+2784*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+768*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(5/2)*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a^2","B"
240,1,479,195,2.457000," ","int(sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-600 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+600 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-489 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+489 B \left(\cos^{4}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+1200 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+978 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+544 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+652 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+128 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+368 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+96 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a^{2}}{384 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{2}}"," ",0,"-1/384/d*(-1+cos(d*x+c))*(-600*A*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+600*A*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-489*B*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+489*B*cos(d*x+c)^4*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+1200*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+978*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+544*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+652*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+128*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+368*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+96*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^2*a^2","B"
241,1,419,154,2.162000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","\frac{\left(114 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-114 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+75 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-75 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+132 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+150 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+68 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right) a^{2}}{96 d \cos \left(d x +c \right)^{2} \sin \left(d x +c \right)^{2}}"," ",0,"1/96/d*(114*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-114*A*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+75*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-75*B*cos(d*x+c)^3*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+132*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+150*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+68*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^2/sin(d*x+c)^2*(cos(d*x+c)^2-1)*a^2","B"
242,1,386,154,2.988000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(20 A \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-20 A \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+19 B \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-19 B \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+32 A \left(\cos^{3}\left(d x +c \right)\right)-16 A \left(\cos^{2}\left(d x +c \right)\right)+44 B \left(\cos^{2}\left(d x +c \right)\right)-16 A \cos \left(d x +c \right)-36 B \cos \left(d x +c \right)-8 B \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{2}}{16 d \sin \left(d x +c \right) \cos \left(d x +c \right)}"," ",0,"-1/16/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(20*A*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-20*A*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+19*B*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-19*B*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+32*A*cos(d*x+c)^3-16*A*cos(d*x+c)^2+44*B*cos(d*x+c)^2-16*A*cos(d*x+c)-36*B*cos(d*x+c)-8*B)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)*a^2","B"
243,1,376,153,3.287000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+15 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-15 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+8 A \left(\cos^{3}\left(d x +c \right)\right)+56 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)-64 A \cos \left(d x +c \right)-12 B \cos \left(d x +c \right)-12 B \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} a^{2}}{12 d \sin \left(d x +c \right)}"," ",0,"-1/12/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(6*A*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-6*A*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+15*B*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-15*B*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+8*A*cos(d*x+c)^3+56*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2-64*A*cos(d*x+c)-12*B*cos(d*x+c)-12*B)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)*a^2","B"
244,1,235,148,2.718000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+12 A \left(\cos^{3}\left(d x +c \right)\right)+44 A \left(\cos^{2}\left(d x +c \right)\right)+20 B \left(\cos^{2}\left(d x +c \right)\right)+116 A \cos \left(d x +c \right)+140 B \cos \left(d x +c \right)-172 A -160 B \right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} a^{2}}{30 d \sin \left(d x +c \right)}"," ",0,"-1/30/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+12*A*cos(d*x+c)^3+44*A*cos(d*x+c)^2+20*B*cos(d*x+c)^2+116*A*cos(d*x+c)+140*B*cos(d*x+c)-172*A-160*B)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)*a^2","A"
245,1,121,154,2.612000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+60 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+115 A \cos \left(d x +c \right)+98 B \cos \left(d x +c \right)+230 A +301 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} a^{2}}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+60*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+115*A*cos(d*x+c)+98*B*cos(d*x+c)+230*A+301*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)*a^2","A"
246,1,143,198,2.684000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(35 A \left(\cos^{4}\left(d x +c \right)\right)+130 A \left(\cos^{3}\left(d x +c \right)\right)+45 B \left(\cos^{3}\left(d x +c \right)\right)+219 A \left(\cos^{2}\left(d x +c \right)\right)+180 B \left(\cos^{2}\left(d x +c \right)\right)+292 A \cos \left(d x +c \right)+345 B \cos \left(d x +c \right)+584 A +690 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{5}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{9}{2}} a^{2}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(35*A*cos(d*x+c)^4+130*A*cos(d*x+c)^3+45*B*cos(d*x+c)^3+219*A*cos(d*x+c)^2+180*B*cos(d*x+c)^2+292*A*cos(d*x+c)+345*B*cos(d*x+c)+584*A+690*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)*a^2","A"
247,1,165,239,2.788000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(315 A \left(\cos^{5}\left(d x +c \right)\right)+1120 A \left(\cos^{4}\left(d x +c \right)\right)+385 B \left(\cos^{4}\left(d x +c \right)\right)+1775 A \left(\cos^{3}\left(d x +c \right)\right)+1430 B \left(\cos^{3}\left(d x +c \right)\right)+2130 A \left(\cos^{2}\left(d x +c \right)\right)+2409 B \left(\cos^{2}\left(d x +c \right)\right)+2840 A \cos \left(d x +c \right)+3212 B \cos \left(d x +c \right)+5680 A +6424 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{6}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{11}{2}} a^{2}}{3465 d \sin \left(d x +c \right)}"," ",0,"-2/3465/d*(-1+cos(d*x+c))*(315*A*cos(d*x+c)^5+1120*A*cos(d*x+c)^4+385*B*cos(d*x+c)^4+1775*A*cos(d*x+c)^3+1430*B*cos(d*x+c)^3+2130*A*cos(d*x+c)^2+2409*B*cos(d*x+c)^2+2840*A*cos(d*x+c)+3212*B*cos(d*x+c)+5680*A+6424*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^6*(1/cos(d*x+c))^(11/2)/sin(d*x+c)*a^2","A"
248,1,423,159,2.641000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(-4 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+4 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+7 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-7 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)-2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-16 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \left(\cos^{2}\left(d x +c \right)\right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{16 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/16/d*(-4*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)+4*A*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+7*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-7*B*cos(d*x+c)^2*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2-2*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-16*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^2+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
249,1,352,120,2.587000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)+B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \cos \left(d x +c \right)-4 A \cos \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+4 B \cos \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/4/d*(2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)+B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)-4*A*cos(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+4*B*cos(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+2*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
250,1,211,83,2.347000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+2 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-2 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{2 d \sin \left(d x +c \right)^{2} a}"," ",0,"1/2/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+2*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-2*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2*(cos(d*x+c)^2-1)/a","B"
251,1,150,84,2.372000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-\arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-2 A \cos \left(d x +c \right)+2 A \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) a}"," ",0,"1/d*(arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-2*A*cos(d*x+c)+2*A)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/a","A"
252,1,183,119,2.524000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-4 A \cos \left(d x +c \right)+6 B \cos \left(d x +c \right)+2 A -6 B \right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) a}"," ",0,"-1/3/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+2*A*cos(d*x+c)^2-4*A*cos(d*x+c)+6*B*cos(d*x+c)+2*A-6*B)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/a","A"
253,1,205,158,2.671000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(6 A \left(\cos^{3}\left(d x +c \right)\right)-15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)+15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-8 A \left(\cos^{2}\left(d x +c \right)\right)+10 B \left(\cos^{2}\left(d x +c \right)\right)+28 A \cos \left(d x +c \right)-20 B \cos \left(d x +c \right)-26 A +10 B \right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{15 d \sin \left(d x +c \right) a}"," ",0,"-1/15/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(6*A*cos(d*x+c)^3-15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)+15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-8*A*cos(d*x+c)^2+10*B*cos(d*x+c)^2+28*A*cos(d*x+c)-20*B*cos(d*x+c)-26*A+10*B)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/a","A"
254,1,227,195,2.839000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(30 A \left(\cos^{4}\left(d x +c \right)\right)+105 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-36 A \left(\cos^{3}\left(d x +c \right)\right)-105 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+42 B \left(\cos^{3}\left(d x +c \right)\right)+68 A \left(\cos^{2}\left(d x +c \right)\right)-56 B \left(\cos^{2}\left(d x +c \right)\right)-148 A \cos \left(d x +c \right)+196 B \cos \left(d x +c \right)+86 A -182 B \right) \left(\cos^{4}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{105 d \sin \left(d x +c \right) a}"," ",0,"-1/105/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(30*A*cos(d*x+c)^4+105*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-36*A*cos(d*x+c)^3-105*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+42*B*cos(d*x+c)^3+68*A*cos(d*x+c)^2-56*B*cos(d*x+c)^2-148*A*cos(d*x+c)+196*B*cos(d*x+c)+86*A-182*B)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/a","A"
255,1,541,208,2.365000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(12 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-12 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-19 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+19 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+36 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-12 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-52 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+14 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-8 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+8 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-10 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(12*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-12*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-19*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+19*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+36*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-12*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-52*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2+14*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-8*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+8*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-10*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(7/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/a^2","B"
256,1,479,166,2.378000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}} \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-5 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-3 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+9 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(1/cos(d*x+c))^(5/2)*cos(d*x+c)^2*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+2*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+3*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-3*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-5*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-3*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+9*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+2*B*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","B"
257,1,313,120,2.560000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(2 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-2 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{2 d \sin \left(d x +c \right)^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"-1/2/d*(2*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-2*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+A*(-2/(1+cos(d*x+c)))^(1/2)-B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^3/(-2/(1+cos(d*x+c)))^(1/2)/a^2","B"
258,1,219,88,2.180000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+3 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)-1\right)}{4 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/4/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+3*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)+B*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3*(cos(d*x+c)^2-1)/a^2","B"
259,1,287,131,2.457000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(7 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-3 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+7 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-8 A \left(\cos^{2}\left(d x +c \right)\right)-2 A \cos \left(d x +c \right)+2 B \cos \left(d x +c \right)+10 A -2 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{4 d \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*(7*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-3*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+7*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-8*A*cos(d*x+c)^2-2*A*cos(d*x+c)+2*B*cos(d*x+c)+10*A-2*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^3/(1/cos(d*x+c))^(1/2)/a^2","B"
260,1,317,172,2.501000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(33 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-21 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+8 A \left(\cos^{3}\left(d x +c \right)\right)+33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-21 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-32 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)-14 A \cos \left(d x +c \right)+6 B \cos \left(d x +c \right)+38 A -30 B \right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{12 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"1/12/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(33*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-21*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+8*A*cos(d*x+c)^3+33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-21*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-32*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2-14*A*cos(d*x+c)+6*B*cos(d*x+c)+38*A-30*B)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^3/a^2","A"
261,1,339,213,2.803000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(225 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-24 A \left(\cos^{4}\left(d x +c \right)\right)-165 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+225 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)+48 A \left(\cos^{3}\left(d x +c \right)\right)-165 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-40 B \left(\cos^{3}\left(d x +c \right)\right)-240 A \left(\cos^{2}\left(d x +c \right)\right)+160 B \left(\cos^{2}\left(d x +c \right)\right)-78 A \cos \left(d x +c \right)+70 B \cos \left(d x +c \right)+294 A -190 B \right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{60 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/60/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(225*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-24*A*cos(d*x+c)^4-165*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+225*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)+48*A*cos(d*x+c)^3-165*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-40*B*cos(d*x+c)^3-240*A*cos(d*x+c)^2+160*B*cos(d*x+c)^2-78*A*cos(d*x+c)+70*B*cos(d*x+c)+294*A-190*B)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)^3/a^2","A"
262,1,831,209,2.640000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{7}{2}} \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(16 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-16 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-40 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+40 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+16 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-16 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+43 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-11 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-40 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+40 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-115 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+35 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+43 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-115 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+20 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+15 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-39 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/16/d*(1/cos(d*x+c))^(7/2)*cos(d*x+c)^3*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(16*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-16*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-40*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+40*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+16*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-16*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+43*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-11*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-40*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+40*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-115*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2+35*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+43*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-115*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+20*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+15*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-39*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-16*B*(-2/(1+cos(d*x+c)))^(1/2))/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","B"
263,1,550,163,2.824000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(16 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-16 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-3 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+16 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-16 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-43 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+11 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-43 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+7 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-15 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(16*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-16*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+3*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-3*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+16*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-16*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)-43*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+11*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+3*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-43*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+7*A*(-2/(1+cos(d*x+c)))^(1/2)-15*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
264,1,350,131,2.633000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-5 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+3 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-3 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-7 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/16/d*(-1+cos(d*x+c))^2*(5*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-5*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+3*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-3*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)-7*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","B"
265,1,347,131,2.380000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(13 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+19 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-5 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+5 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+19 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+5 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-9 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(1/cos(d*x+c))^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(-1+cos(d*x+c))^2*(13*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+19*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-5*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+5*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+19*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+5*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-9*A*(-2/(1+cos(d*x+c)))^(1/2)+B*(-2/(1+cos(d*x+c)))^(1/2))/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
266,1,419,172,2.742000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-75 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+19 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-150 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+38 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+64 A \left(\cos^{3}\left(d x +c \right)\right)-75 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)+19 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+106 A \left(\cos^{2}\left(d x +c \right)\right)-26 B \left(\cos^{2}\left(d x +c \right)\right)-72 A \cos \left(d x +c \right)+8 B \cos \left(d x +c \right)-98 A +18 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{32 d \sin \left(d x +c \right)^{5} \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/32/d*(-1+cos(d*x+c))^2*(-75*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+19*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-150*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+38*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+64*A*cos(d*x+c)^3-75*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)+19*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+106*A*cos(d*x+c)^2-26*B*cos(d*x+c)^2-72*A*cos(d*x+c)+8*B*cos(d*x+c)-98*A+18*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/(1/cos(d*x+c))^(1/2)/a^3","B"
267,1,449,213,2.876000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(489 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-225 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+978 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+64 A \left(\cos^{4}\left(d x +c \right)\right)-450 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-384 A \left(\cos^{3}\left(d x +c \right)\right)-225 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+192 B \left(\cos^{3}\left(d x +c \right)\right)-686 A \left(\cos^{2}\left(d x +c \right)\right)+318 B \left(\cos^{2}\left(d x +c \right)\right)+408 A \cos \left(d x +c \right)-216 B \cos \left(d x +c \right)+598 A -294 B \right) \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{96 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"-1/96/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(489*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-225*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+978*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+64*A*cos(d*x+c)^4-450*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-384*A*cos(d*x+c)^3-225*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+192*B*cos(d*x+c)^3-686*A*cos(d*x+c)^2+318*B*cos(d*x+c)^2+408*A*cos(d*x+c)-216*B*cos(d*x+c)+598*A-294*B)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)^5/a^3","B"
268,1,471,254,3.024000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(4245 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-192 A \left(\cos^{5}\left(d x +c \right)\right)-2445 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8490 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+512 A \left(\cos^{4}\left(d x +c \right)\right)-4890 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-320 B \left(\cos^{4}\left(d x +c \right)\right)+4245 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-3456 A \left(\cos^{3}\left(d x +c \right)\right)-2445 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+1920 B \left(\cos^{3}\left(d x +c \right)\right)-5974 A \left(\cos^{2}\left(d x +c \right)\right)+3430 B \left(\cos^{2}\left(d x +c \right)\right)+3768 A \cos \left(d x +c \right)-2040 B \cos \left(d x +c \right)+5342 A -2990 B \right) \left(\cos^{3}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{5}{2}}}{480 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/480/d*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(4245*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-192*A*cos(d*x+c)^5-2445*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8490*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+512*A*cos(d*x+c)^4-4890*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-320*B*cos(d*x+c)^4+4245*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-3456*A*cos(d*x+c)^3-2445*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+1920*B*cos(d*x+c)^3-5974*A*cos(d*x+c)^2+3430*B*cos(d*x+c)^2+3768*A*cos(d*x+c)-2040*B*cos(d*x+c)+5342*A-2990*B)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)^5/a^3","A"
269,0,0,435,1.253000," ","int((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
270,0,0,391,1.324000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/3),x)","F"
271,0,0,444,1.520000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(4/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{4}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(4/3),x)","F"
272,0,0,845,1.731000," ","int((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{4}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^(4/3)*(A+B*sec(d*x+c)),x)","F"
273,0,0,808,1.461000," ","int((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","\int \left(a +a \sec \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((a+a*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","F"
274,0,0,832,1.322000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(2/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(a +a \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(2/3),x)","F"
275,0,0,181,5.063000," ","int((c*sec(f*x+e))^n*(a+a*sec(f*x+e))^m*(A+B*sec(f*x+e)),x)","\int \left(c \sec \left(f x +e \right)\right)^{n} \left(a +a \sec \left(f x +e \right)\right)^{m} \left(A +B \sec \left(f x +e \right)\right)\, dx"," ",0,"int((c*sec(f*x+e))^n*(a+a*sec(f*x+e))^m*(A+B*sec(f*x+e)),x)","F"
276,0,0,162,4.560000," ","int(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","\int \left(\sec^{-1-n}\left(d x +c \right)\right) \left(a +a \sec \left(d x +c \right)\right)^{n} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^(-1-n)*(a+a*sec(d*x+c))^n*(A+B*sec(d*x+c)),x)","F"
277,1,171,106,1.247000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(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{2 a B \tan \left(d x +c \right)}{3 d}+\frac{a B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 A b \tan \left(d x +c \right)}{3 d}+\frac{A b \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{b B \left(\sec^{3}\left(d x +c \right)\right) \tan \left(d x +c \right)}{4 d}+\frac{3 b B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/2/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*a*B*tan(d*x+c)+1/3/d*a*B*tan(d*x+c)*sec(d*x+c)^2+2/3*A*b*tan(d*x+c)/d+1/3*A*b*sec(d*x+c)^2*tan(d*x+c)/d+1/4*b*B*sec(d*x+c)^3*tan(d*x+c)/d+3/8*b*B*sec(d*x+c)*tan(d*x+c)/d+3/8/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","A"
278,1,128,85,1.221000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{a A \tan \left(d x +c \right)}{d}+\frac{a B \sec \left(d x +c \right) \tan \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 b \sec \left(d x +c \right) \tan \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{2 b B \tan \left(d x +c \right)}{3 d}+\frac{b B \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}"," ",0,"a*A*tan(d*x+c)/d+1/2/d*a*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+1/2*A*b*sec(d*x+c)*tan(d*x+c)/d+1/2/d*A*b*ln(sec(d*x+c)+tan(d*x+c))+2/3*b*B*tan(d*x+c)/d+1/3*b*B*sec(d*x+c)^2*tan(d*x+c)/d","A"
279,1,86,57,0.965000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(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 \tan \left(d x +c \right)}{d}+\frac{A b \tan \left(d x +c \right)}{d}+\frac{b B \sec \left(d x +c \right) \tan \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/d*a*A*ln(sec(d*x+c)+tan(d*x+c))+1/d*a*B*tan(d*x+c)+A*b*tan(d*x+c)/d+1/2*b*B*sec(d*x+c)*tan(d*x+c)/d+1/2/d*B*b*ln(sec(d*x+c)+tan(d*x+c))","A"
280,1,65,35,0.729000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","a A x +\frac{A b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A a c}{d}+\frac{a B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b B \tan \left(d x +c \right)}{d}"," ",0,"a*A*x+1/d*A*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*a*c+1/d*a*B*ln(sec(d*x+c)+tan(d*x+c))+b*B*tan(d*x+c)/d","A"
281,1,56,35,0.805000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","A b x +B x a +\frac{a A \sin \left(d x +c \right)}{d}+\frac{A b c}{d}+\frac{B b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B a c}{d}"," ",0,"A*b*x+B*x*a+a*A*sin(d*x+c)/d+1/d*A*b*c+1/d*B*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a*c","A"
282,1,57,48,0.783000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{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)+A b \sin \left(d x +c \right)+a B \sin \left(d x +c \right)+B \left(d x +c \right) b}{d}"," ",0,"1/d*(a*A*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b*sin(d*x+c)+a*B*sin(d*x+c)+B*(d*x+c)*b)","A"
283,1,85,76,1.313000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{\frac{a A \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+A b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+a B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+B \sin \left(d x +c \right) b}{d}"," ",0,"1/d*(1/3*a*A*(2+cos(d*x+c)^2)*sin(d*x+c)+A*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+a*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*sin(d*x+c)*b)","A"
284,1,107,97,1.517000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\frac{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)+\frac{A b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{a B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+B b \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*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)+1/3*A*b*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a*B*(2+cos(d*x+c)^2)*sin(d*x+c)+B*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
285,1,312,186,1.523000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(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{2 a^{2} B \tan \left(d x +c \right)}{3 d}+\frac{a^{2} B \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{4 a A b \tan \left(d x +c \right)}{3 d}+\frac{2 a A b \left(\sec^{2}\left(d x +c \right)\right) \tan \left(d x +c \right)}{3 d}+\frac{B a b \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{3 B a b \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{3 B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{A \,b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 b^{2} B \tan \left(d x +c \right)}{15 d}+\frac{b^{2} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 b^{2} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 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))+2/3*a^2*B*tan(d*x+c)/d+1/3*a^2*B*sec(d*x+c)^2*tan(d*x+c)/d+4/3*a*A*b*tan(d*x+c)/d+2/3*a*A*b*sec(d*x+c)^2*tan(d*x+c)/d+1/2/d*B*a*b*tan(d*x+c)*sec(d*x+c)^3+3/4/d*B*a*b*sec(d*x+c)*tan(d*x+c)+3/4/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*A*b^2*tan(d*x+c)*sec(d*x+c)^3+3/8/d*A*b^2*sec(d*x+c)*tan(d*x+c)+3/8/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+8/15*b^2*B*tan(d*x+c)/d+1/5/d*b^2*B*tan(d*x+c)*sec(d*x+c)^4+4/15/d*b^2*B*tan(d*x+c)*sec(d*x+c)^2","A"
286,1,241,169,1.428000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{a^{2} A \tan \left(d x +c \right)}{d}+\frac{a^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{a A b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{A a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 B a b \tan \left(d x +c \right)}{3 d}+\frac{2 B a b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 A \,b^{2} \tan \left(d x +c \right)}{3 d}+\frac{A \,b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{2} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"a^2*A*tan(d*x+c)/d+1/2*a^2*B*sec(d*x+c)*tan(d*x+c)/d+1/2/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+a*A*b*sec(d*x+c)*tan(d*x+c)/d+1/d*A*a*b*ln(sec(d*x+c)+tan(d*x+c))+4/3/d*B*a*b*tan(d*x+c)+2/3/d*B*a*b*tan(d*x+c)*sec(d*x+c)^2+2/3/d*A*b^2*tan(d*x+c)+1/3/d*A*b^2*tan(d*x+c)*sec(d*x+c)^2+1/4/d*b^2*B*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^2*B*sec(d*x+c)*tan(d*x+c)+3/8/d*b^2*B*ln(sec(d*x+c)+tan(d*x+c))","A"
287,1,174,108,1.182000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(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{a^{2} B \tan \left(d x +c \right)}{d}+\frac{2 a A b \tan \left(d x +c \right)}{d}+\frac{B a b \sec \left(d x +c \right) \tan \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} \sec \left(d x +c \right) \tan \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{2 b^{2} B \tan \left(d x +c \right)}{3 d}+\frac{b^{2} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/d*a^2*A*ln(sec(d*x+c)+tan(d*x+c))+a^2*B*tan(d*x+c)/d+2*a*A*b*tan(d*x+c)/d+1/d*B*a*b*sec(d*x+c)*tan(d*x+c)+1/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^2*sec(d*x+c)*tan(d*x+c)+1/2/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/3*b^2*B*tan(d*x+c)/d+1/3/d*b^2*B*tan(d*x+c)*sec(d*x+c)^2","A"
288,1,133,80,0.945000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","a^{2} A x +\frac{A \,a^{2} c}{d}+\frac{B \,a^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 A a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 B a b \tan \left(d x +c \right)}{d}+\frac{A \,b^{2} \tan \left(d x +c \right)}{d}+\frac{b^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a^2*A*x+1/d*A*a^2*c+1/d*B*a^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a*b*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a*b*tan(d*x+c)+1/d*A*b^2*tan(d*x+c)+1/2/d*b^2*B*sec(d*x+c)*tan(d*x+c)+1/2/d*b^2*B*ln(sec(d*x+c)+tan(d*x+c))","A"
289,1,104,60,0.867000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","2 A x a b +a^{2} B x +\frac{a^{2} A \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{2 A a b c}{d}+\frac{b^{2} B \tan \left(d x +c \right)}{d}+\frac{2 B a b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B \,a^{2} c}{d}"," ",0,"2*A*x*a*b+a^2*B*x+1/d*a^2*A*sin(d*x+c)+1/d*A*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*A*a*b*c+b^2*B*tan(d*x+c)/d+2/d*B*a*b*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*a^2*c","A"
290,1,120,76,0.713000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{a^{2} A \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{2} A x}{2}+\frac{A \,a^{2} c}{2 d}+\frac{B \,a^{2} \sin \left(d x +c \right)}{d}+\frac{2 A a b \sin \left(d x +c \right)}{d}+2 B x a b +\frac{2 B a b c}{d}+A x \,b^{2}+\frac{A \,b^{2} c}{d}+\frac{b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/2*a^2*A*cos(d*x+c)*sin(d*x+c)/d+1/2*a^2*A*x+1/2/d*A*a^2*c+1/d*B*a^2*sin(d*x+c)+2/d*A*a*b*sin(d*x+c)+2*B*x*a*b+2/d*B*a*b*c+A*x*b^2+1/d*A*b^2*c+1/d*b^2*B*ln(sec(d*x+c)+tan(d*x+c))","A"
291,1,114,99,1.064000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^2*(A+B*sec(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}+2 A a b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+B \,a^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{2} \sin \left(d x +c \right)+2 B a b \sin \left(d x +c \right)+B \left(d x +c \right) b^{2}}{d}"," ",0,"1/d*(1/3*a^2*A*(2+cos(d*x+c)^2)*sin(d*x+c)+2*A*a*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*a^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^2*sin(d*x+c)+2*B*a*b*sin(d*x+c)+B*(d*x+c)*b^2)","A"
292,1,152,128,1.409000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\frac{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(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{2 A a b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+2 B a b \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{2} B \sin \left(d x +c \right)}{d}"," ",0,"1/d*(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)+1/3*B*a^2*(2+cos(d*x+c)^2)*sin(d*x+c)+2/3*A*a*b*(2+cos(d*x+c)^2)*sin(d*x+c)+2*B*a*b*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^2*B*sin(d*x+c))","A"
293,1,184,168,1.576000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^2*(A+B*sec(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}+B \,a^{2} \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)+2 A a b \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{2 B a b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+\frac{A \,b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+b^{2} B \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*(1/5*a^2*A*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+B*a^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*A*a*b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2/3*B*a*b*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*A*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+b^2*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c))","A"
294,1,382,240,1.708000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \tan \left(d x +c \right)}{d}+\frac{a^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A \,a^{2} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 A \,a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 a^{2} b B \tan \left(d x +c \right)}{d}+\frac{a^{2} b B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{2 A a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{A a \,b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{3 B a \,b^{2} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{9 B a \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{9 B a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{A \,b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 b^{3} B \tan \left(d x +c \right)}{15 d}+\frac{b^{3} B \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 b^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/d*A*a^3*tan(d*x+c)+1/2/d*a^3*B*sec(d*x+c)*tan(d*x+c)+1/2/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a^2*b*sec(d*x+c)*tan(d*x+c)+3/2/d*A*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+2/d*a^2*b*B*tan(d*x+c)+1/d*a^2*b*B*tan(d*x+c)*sec(d*x+c)^2+2/d*A*a*b^2*tan(d*x+c)+1/d*A*a*b^2*tan(d*x+c)*sec(d*x+c)^2+3/4/d*B*a*b^2*tan(d*x+c)*sec(d*x+c)^3+9/8/d*B*a*b^2*sec(d*x+c)*tan(d*x+c)+9/8/d*B*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*A*b^3*tan(d*x+c)*sec(d*x+c)^3+3/8/d*A*b^3*sec(d*x+c)*tan(d*x+c)+3/8/d*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*b^3*B*tan(d*x+c)+1/5/d*b^3*B*tan(d*x+c)*sec(d*x+c)^4+4/15/d*b^3*B*tan(d*x+c)*sec(d*x+c)^2","A"
295,1,290,170,1.379000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{3} B \tan \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 a^{2} b B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{3 A a \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 A a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 B a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{B a \,b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{2 A \,b^{3} \tan \left(d x +c \right)}{3 d}+\frac{A \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{b^{3} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 b^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 b^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"1/d*A*a^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^3*B*tan(d*x+c)+3/d*A*a^2*b*tan(d*x+c)+3/2/d*a^2*b*B*sec(d*x+c)*tan(d*x+c)+3/2/d*a^2*b*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*A*a*b^2*sec(d*x+c)*tan(d*x+c)+3/2/d*A*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+2/d*B*a*b^2*tan(d*x+c)+1/d*B*a*b^2*tan(d*x+c)*sec(d*x+c)^2+2/3/d*A*b^3*tan(d*x+c)+1/3/d*A*b^3*tan(d*x+c)*sec(d*x+c)^2+1/4/d*b^3*B*tan(d*x+c)*sec(d*x+c)^3+3/8/d*b^3*B*sec(d*x+c)*tan(d*x+c)+3/8/d*b^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
296,1,223,129,1.181000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","a^{3} A x +\frac{A \,a^{3} c}{d}+\frac{a^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{2} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 a^{2} b B \tan \left(d x +c \right)}{d}+\frac{3 A a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{3 B a \,b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 B a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{A \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 b^{3} B \tan \left(d x +c \right)}{3 d}+\frac{b^{3} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"a^3*A*x+1/d*A*a^3*c+1/d*a^3*B*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a^2*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*a^2*b*B*tan(d*x+c)+3/d*A*a*b^2*tan(d*x+c)+3/2/d*B*a*b^2*sec(d*x+c)*tan(d*x+c)+3/2/d*B*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^3*sec(d*x+c)*tan(d*x+c)+1/2/d*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*b^3*B*tan(d*x+c)+1/3/d*b^3*B*tan(d*x+c)*sec(d*x+c)^2","A"
297,1,172,113,1.171000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{a^{3} A \sin \left(d x +c \right)}{d}+a^{3} B x +\frac{a^{3} B c}{d}+3 A x \,a^{2} b +\frac{3 A \,a^{2} b c}{d}+\frac{3 a^{2} b B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 B a \,b^{2} \tan \left(d x +c \right)}{d}+\frac{A \,b^{3} \tan \left(d x +c \right)}{d}+\frac{b^{3} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{b^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"a^3*A*sin(d*x+c)/d+a^3*B*x+1/d*a^3*B*c+3*A*x*a^2*b+3/d*A*a^2*b*c+3/d*a^2*b*B*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+3/d*B*a*b^2*tan(d*x+c)+1/d*A*b^3*tan(d*x+c)+1/2/d*b^3*B*sec(d*x+c)*tan(d*x+c)+1/2/d*b^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
298,1,168,118,0.951000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} A x}{2}+\frac{A \,a^{3} c}{2 d}+\frac{a^{3} B \sin \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b \sin \left(d x +c \right)}{d}+3 B x \,a^{2} b +\frac{3 B \,a^{2} b c}{d}+3 A x a \,b^{2}+\frac{3 A a \,b^{2} c}{d}+\frac{3 B a \,b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{b^{3} B \tan \left(d x +c \right)}{d}"," ",0,"1/2/d*A*a^3*cos(d*x+c)*sin(d*x+c)+1/2*a^3*A*x+1/2/d*A*a^3*c+a^3*B*sin(d*x+c)/d+3/d*A*a^2*b*sin(d*x+c)+3*B*x*a^2*b+3/d*B*a^2*b*c+3*A*x*a*b^2+3/d*A*a*b^2*c+3/d*B*a*b^2*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*b^3*B*tan(d*x+c)","A"
299,1,207,137,2.004000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) a^{3}}{3 d}+\frac{2 a^{3} A \sin \left(d x +c \right)}{3 d}+\frac{a^{3} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{3} B x}{2}+\frac{a^{3} B c}{2 d}+\frac{3 A \,a^{2} b \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{3 A x \,a^{2} b}{2}+\frac{3 A \,a^{2} b c}{2 d}+\frac{3 a^{2} b B \sin \left(d x +c \right)}{d}+\frac{3 A a \,b^{2} \sin \left(d x +c \right)}{d}+3 B x a \,b^{2}+\frac{3 B a \,b^{2} c}{d}+A x \,b^{3}+\frac{A \,b^{3} c}{d}+\frac{b^{3} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/3/d*A*cos(d*x+c)^2*sin(d*x+c)*a^3+2/3*a^3*A*sin(d*x+c)/d+1/2/d*a^3*B*cos(d*x+c)*sin(d*x+c)+1/2*a^3*B*x+1/2/d*a^3*B*c+3/2/d*A*a^2*b*cos(d*x+c)*sin(d*x+c)+3/2*A*x*a^2*b+3/2/d*A*a^2*b*c+3/d*a^2*b*B*sin(d*x+c)+3/d*A*a*b^2*sin(d*x+c)+3*B*x*a*b^2+3/d*B*a*b^2*c+A*x*b^3+1/d*A*b^3*c+1/d*b^3*B*ln(sec(d*x+c)+tan(d*x+c))","A"
300,1,180,169,1.622000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{A \,a^{3} \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)+A \,a^{2} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{a^{3} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+3 A a \,b^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+3 a^{2} b B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{3} \sin \left(d x +c \right)+3 B a \,b^{2} \sin \left(d x +c \right)+B \left(d x +c \right) b^{3}}{d}"," ",0,"1/d*(A*a^3*(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*a^2*b*(2+cos(d*x+c)^2)*sin(d*x+c)+1/3*a^3*B*(2+cos(d*x+c)^2)*sin(d*x+c)+3*A*a*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+3*a^2*b*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^3*sin(d*x+c)+3*B*a*b^2*sin(d*x+c)+B*(d*x+c)*b^3)","A"
301,1,227,209,2.108000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\frac{\frac{A \,a^{3} \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}+a^{3} B \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)+3 A \,a^{2} b \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)+a^{2} b B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+A a \,b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+3 B a \,b^{2} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+b^{3} B \sin \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*A*a^3*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+a^3*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+3*A*a^2*b*(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^2*b*B*(2+cos(d*x+c)^2)*sin(d*x+c)+A*a*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+3*B*a*b^2*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+b^3*B*sin(d*x+c))","A"
302,1,550,320,1.850000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,b^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 A \,b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{A \,a^{4} \tan \left(d x +c \right)}{d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{9 a^{2} b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{4 d}+\frac{3 a A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{5 B \,b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{16 d}+\frac{32 B a \,b^{3} \tan \left(d x +c \right)}{15 d}+\frac{8 B \,a^{3} b \tan \left(d x +c \right)}{3 d}+\frac{4 A \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{5 B \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{16 d}+\frac{8 A \,b^{4} \tan \left(d x +c \right)}{15 d}+\frac{5 B \,b^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{24 d}+\frac{B \,b^{4} \tan \left(d x +c \right) \left(\sec^{5}\left(d x +c \right)\right)}{6 d}+\frac{4 B a \,b^{3} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{3 a A \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{2 A \,a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{9 a^{2} b^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{4 d}+\frac{16 B a \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}+\frac{4 B \,a^{3} b \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{3 a^{2} b^{2} B \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{2 d}+\frac{a A \,b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{2 A \,a^{2} b^{2} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{a^{4} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{2 A \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/d*A*a^4*tan(d*x+c)+1/2/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+9/4/d*a^2*b^2*B*ln(sec(d*x+c)+tan(d*x+c))+3/2/d*a*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/6/d*B*b^4*tan(d*x+c)*sec(d*x+c)^5+5/24/d*B*b^4*tan(d*x+c)*sec(d*x+c)^3+5/16/d*B*b^4*sec(d*x+c)*tan(d*x+c)+32/15/d*B*a*b^3*tan(d*x+c)+8/3/d*B*a^3*b*tan(d*x+c)+4/d*A*a^2*b^2*tan(d*x+c)+5/16/d*B*b^4*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*A*b^4*tan(d*x+c)+3/2/d*a*A*b^3*sec(d*x+c)*tan(d*x+c)+4/5/d*B*a*b^3*tan(d*x+c)*sec(d*x+c)^4+16/15/d*B*a*b^3*tan(d*x+c)*sec(d*x+c)^2+4/3/d*B*a^3*b*tan(d*x+c)*sec(d*x+c)^2+2/d*A*a^3*b*sec(d*x+c)*tan(d*x+c)+3/2/d*a^2*b^2*B*tan(d*x+c)*sec(d*x+c)^3+9/4/d*a^2*b^2*B*sec(d*x+c)*tan(d*x+c)+1/d*a*A*b^3*tan(d*x+c)*sec(d*x+c)^3+2/d*A*a^2*b^2*tan(d*x+c)*sec(d*x+c)^2+1/2/d*a^4*B*sec(d*x+c)*tan(d*x+c)+2/d*A*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+1/5/d*A*b^4*tan(d*x+c)*sec(d*x+c)^4+4/15/d*A*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
303,1,431,238,1.671000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{a^{4} B \tan \left(d x +c \right)}{d}+\frac{4 A \,a^{3} b \tan \left(d x +c \right)}{d}+\frac{2 B \,a^{3} b \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 B \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{3 A \,a^{2} b^{2} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{3 A \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a^{2} b^{2} B \tan \left(d x +c \right)}{d}+\frac{2 a^{2} b^{2} B \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{d}+\frac{8 a A \,b^{3} \tan \left(d x +c \right)}{3 d}+\frac{4 a A \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{B a \,b^{3} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{d}+\frac{3 B a \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{3 B a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{A \,b^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 A \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}+\frac{8 B \,b^{4} \tan \left(d x +c \right)}{15 d}+\frac{B \,b^{4} \tan \left(d x +c \right) \left(\sec^{4}\left(d x +c \right)\right)}{5 d}+\frac{4 B \,b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{15 d}"," ",0,"1/d*A*a^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*a^4*B*tan(d*x+c)+4/d*A*a^3*b*tan(d*x+c)+2/d*B*a^3*b*sec(d*x+c)*tan(d*x+c)+2/d*B*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+3/d*A*a^2*b^2*sec(d*x+c)*tan(d*x+c)+3/d*A*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+4/d*a^2*b^2*B*tan(d*x+c)+2/d*a^2*b^2*B*tan(d*x+c)*sec(d*x+c)^2+8/3/d*a*A*b^3*tan(d*x+c)+4/3/d*a*A*b^3*tan(d*x+c)*sec(d*x+c)^2+1/d*B*a*b^3*tan(d*x+c)*sec(d*x+c)^3+3/2/d*B*a*b^3*sec(d*x+c)*tan(d*x+c)+3/2/d*B*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/4/d*A*b^4*tan(d*x+c)*sec(d*x+c)^3+3/8/d*A*b^4*sec(d*x+c)*tan(d*x+c)+3/8/d*A*b^4*ln(sec(d*x+c)+tan(d*x+c))+8/15/d*B*b^4*tan(d*x+c)+1/5/d*B*b^4*tan(d*x+c)*sec(d*x+c)^4+4/15/d*B*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
304,1,338,190,1.378000," ","int((a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","A \,a^{4} x +\frac{A \,a^{4} c}{d}+\frac{a^{4} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 A \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 B \,a^{3} b \tan \left(d x +c \right)}{d}+\frac{6 A \,a^{2} b^{2} \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b^{2} B \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{3 a^{2} b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{2 a A \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 a A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{8 B a \,b^{3} \tan \left(d x +c \right)}{3 d}+\frac{4 B a \,b^{3} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{2 A \,b^{4} \tan \left(d x +c \right)}{3 d}+\frac{A \,b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}+\frac{B \,b^{4} \tan \left(d x +c \right) \left(\sec^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 B \,b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{8 d}+\frac{3 B \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{8 d}"," ",0,"A*a^4*x+1/d*A*a^4*c+1/d*a^4*B*ln(sec(d*x+c)+tan(d*x+c))+4/d*A*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+4/d*B*a^3*b*tan(d*x+c)+6/d*A*a^2*b^2*tan(d*x+c)+3/d*a^2*b^2*B*sec(d*x+c)*tan(d*x+c)+3/d*a^2*b^2*B*ln(sec(d*x+c)+tan(d*x+c))+2/d*a*A*b^3*sec(d*x+c)*tan(d*x+c)+2/d*a*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+8/3/d*B*a*b^3*tan(d*x+c)+4/3/d*B*a*b^3*tan(d*x+c)*sec(d*x+c)^2+2/3/d*A*b^4*tan(d*x+c)+1/3/d*A*b^4*tan(d*x+c)*sec(d*x+c)^2+1/4/d*B*b^4*tan(d*x+c)*sec(d*x+c)^3+3/8/d*B*b^4*sec(d*x+c)*tan(d*x+c)+3/8/d*B*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
305,1,262,187,1.480000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \sin \left(d x +c \right)}{d}+a^{4} B x +\frac{a^{4} B c}{d}+4 A \,a^{3} b x +\frac{4 A \,a^{3} b c}{d}+\frac{4 B \,a^{3} b \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 A \,a^{2} b^{2} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{6 a^{2} b^{2} B \tan \left(d x +c \right)}{d}+\frac{4 a A \,b^{3} \tan \left(d x +c \right)}{d}+\frac{2 B a \,b^{3} \sec \left(d x +c \right) \tan \left(d x +c \right)}{d}+\frac{2 B a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{A \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}+\frac{2 B \,b^{4} \tan \left(d x +c \right)}{3 d}+\frac{B \,b^{4} \tan \left(d x +c \right) \left(\sec^{2}\left(d x +c \right)\right)}{3 d}"," ",0,"1/d*A*a^4*sin(d*x+c)+a^4*B*x+1/d*a^4*B*c+4*A*a^3*b*x+4/d*A*a^3*b*c+4/d*B*a^3*b*ln(sec(d*x+c)+tan(d*x+c))+6/d*A*a^2*b^2*ln(sec(d*x+c)+tan(d*x+c))+6/d*a^2*b^2*B*tan(d*x+c)+4/d*a*A*b^3*tan(d*x+c)+2/d*B*a*b^3*sec(d*x+c)*tan(d*x+c)+2/d*B*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/2/d*A*b^4*sec(d*x+c)*tan(d*x+c)+1/2/d*A*b^4*ln(sec(d*x+c)+tan(d*x+c))+2/3/d*B*b^4*tan(d*x+c)+1/3/d*B*b^4*tan(d*x+c)*sec(d*x+c)^2","A"
306,1,236,197,1.072000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{A \,a^{4} x}{2}+\frac{A \,a^{4} c}{2 d}+\frac{a^{4} B \sin \left(d x +c \right)}{d}+\frac{4 A \,a^{3} b \sin \left(d x +c \right)}{d}+4 B x \,a^{3} b +\frac{4 B \,a^{3} b c}{d}+6 A x \,a^{2} b^{2}+\frac{6 A \,a^{2} b^{2} c}{d}+\frac{6 a^{2} b^{2} B \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 a A \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{4 B a \,b^{3} \tan \left(d x +c \right)}{d}+\frac{A \,b^{4} \tan \left(d x +c \right)}{d}+\frac{B \,b^{4} \sec \left(d x +c \right) \tan \left(d x +c \right)}{2 d}+\frac{B \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{2 d}"," ",0,"1/2/d*A*a^4*cos(d*x+c)*sin(d*x+c)+1/2*A*a^4*x+1/2/d*A*a^4*c+1/d*a^4*B*sin(d*x+c)+4/d*A*a^3*b*sin(d*x+c)+4*B*x*a^3*b+4/d*B*a^3*b*c+6*A*x*a^2*b^2+6/d*A*a^2*b^2*c+6/d*a^2*b^2*B*ln(sec(d*x+c)+tan(d*x+c))+4/d*a*A*b^3*ln(sec(d*x+c)+tan(d*x+c))+4/d*B*a*b^3*tan(d*x+c)+1/d*A*b^4*tan(d*x+c)+1/2/d*B*b^4*sec(d*x+c)*tan(d*x+c)+1/2/d*B*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
307,1,255,188,1.158000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{2 A \,a^{4} \sin \left(d x +c \right)}{3 d}+\frac{a^{4} B \cos \left(d x +c \right) \sin \left(d x +c \right)}{2 d}+\frac{a^{4} B x}{2}+\frac{a^{4} B c}{2 d}+\frac{2 A \,a^{3} b \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}+2 A \,a^{3} b x +\frac{2 A \,a^{3} b c}{d}+\frac{4 B \,a^{3} b \sin \left(d x +c \right)}{d}+\frac{6 A \,a^{2} b^{2} \sin \left(d x +c \right)}{d}+6 B \,a^{2} b^{2} x +\frac{6 B \,a^{2} b^{2} c}{d}+4 A a \,b^{3} x +\frac{4 A a \,b^{3} c}{d}+\frac{4 B a \,b^{3} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{A \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}+\frac{B \,b^{4} \tan \left(d x +c \right)}{d}"," ",0,"1/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^4+2/3/d*A*a^4*sin(d*x+c)+1/2/d*a^4*B*cos(d*x+c)*sin(d*x+c)+1/2*a^4*B*x+1/2/d*a^4*B*c+2/d*A*a^3*b*sin(d*x+c)*cos(d*x+c)+2*A*a^3*b*x+2/d*A*a^3*b*c+4/d*B*a^3*b*sin(d*x+c)+6/d*A*a^2*b^2*sin(d*x+c)+6*B*a^2*b^2*x+6/d*B*a^2*b^2*c+4*A*a*b^3*x+4/d*A*a*b^3*c+4/d*B*a*b^3*ln(sec(d*x+c)+tan(d*x+c))+1/d*A*b^4*ln(sec(d*x+c)+tan(d*x+c))+1/d*B*b^4*tan(d*x+c)","A"
308,1,319,206,1.184000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \sin \left(d x +c \right) \left(\cos^{3}\left(d x +c \right)\right)}{4 d}+\frac{3 A \,a^{4} \cos \left(d x +c \right) \sin \left(d x +c \right)}{8 d}+\frac{3 A \,a^{4} x}{8}+\frac{3 A \,a^{4} c}{8 d}+\frac{B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{4}}{3 d}+\frac{2 a^{4} B \sin \left(d x +c \right)}{3 d}+\frac{4 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{3} b}{3 d}+\frac{8 A \,a^{3} b \sin \left(d x +c \right)}{3 d}+\frac{2 B \,a^{3} b \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}+2 B x \,a^{3} b +\frac{2 B \,a^{3} b c}{d}+\frac{3 A \,a^{2} b^{2} \sin \left(d x +c \right) \cos \left(d x +c \right)}{d}+3 A x \,a^{2} b^{2}+\frac{3 A \,a^{2} b^{2} c}{d}+\frac{6 a^{2} b^{2} B \sin \left(d x +c \right)}{d}+\frac{4 a A \,b^{3} \sin \left(d x +c \right)}{d}+4 B x a \,b^{3}+\frac{4 B a \,b^{3} c}{d}+A x \,b^{4}+\frac{A \,b^{4} c}{d}+\frac{B \,b^{4} \ln \left(\sec \left(d x +c \right)+\tan \left(d x +c \right)\right)}{d}"," ",0,"1/4/d*A*a^4*sin(d*x+c)*cos(d*x+c)^3+3/8/d*A*a^4*cos(d*x+c)*sin(d*x+c)+3/8*A*a^4*x+3/8/d*A*a^4*c+1/3/d*B*sin(d*x+c)*cos(d*x+c)^2*a^4+2/3/d*a^4*B*sin(d*x+c)+4/3/d*A*sin(d*x+c)*cos(d*x+c)^2*a^3*b+8/3/d*A*a^3*b*sin(d*x+c)+2/d*B*a^3*b*sin(d*x+c)*cos(d*x+c)+2*B*x*a^3*b+2/d*B*a^3*b*c+3/d*A*a^2*b^2*sin(d*x+c)*cos(d*x+c)+3*A*x*a^2*b^2+3/d*A*a^2*b^2*c+6/d*a^2*b^2*B*sin(d*x+c)+4/d*a*A*b^3*sin(d*x+c)+4*B*x*a*b^3+4/d*B*a*b^3*c+A*x*b^4+1/d*A*b^4*c+1/d*B*b^4*ln(sec(d*x+c)+tan(d*x+c))","A"
309,1,258,246,1.563000," ","int(cos(d*x+c)^5*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{\frac{A \,a^{4} \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}+4 A \,a^{3} b \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)+a^{4} B \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)+2 A \,a^{2} b^{2} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{4 B \,a^{3} b \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 a A \,b^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+6 a^{2} b^{2} B \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{4} \sin \left(d x +c \right)+4 B a \,b^{3} \sin \left(d x +c \right)+B \,b^{4} \left(d x +c \right)}{d}"," ",0,"1/d*(1/5*A*a^4*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*A*a^3*b*(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^4*B*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*A*a^2*b^2*(2+cos(d*x+c)^2)*sin(d*x+c)+4/3*B*a^3*b*(2+cos(d*x+c)^2)*sin(d*x+c)+4*a*A*b^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+6*a^2*b^2*B*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^4*sin(d*x+c)+4*B*a*b^3*sin(d*x+c)+B*b^4*(d*x+c))","A"
310,1,316,295,1.850000," ","int(cos(d*x+c)^6*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\frac{A \,a^{4} \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{a^{4} B \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{4 A \,a^{3} b \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}+4 B \,a^{3} b \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)+6 A \,a^{2} b^{2} \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)+2 a^{2} b^{2} B \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)+\frac{4 a A \,b^{3} \left(2+\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right)}{3}+4 B a \,b^{3} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+A \,b^{4} \left(\frac{\cos \left(d x +c \right) \sin \left(d x +c \right)}{2}+\frac{d x}{2}+\frac{c}{2}\right)+B \,b^{4} \sin \left(d x +c \right)}{d}"," ",0,"1/d*(A*a^4*(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)+1/5*a^4*B*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4/5*A*a^3*b*(8/3+cos(d*x+c)^4+4/3*cos(d*x+c)^2)*sin(d*x+c)+4*B*a^3*b*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+6*A*a^2*b^2*(1/4*(cos(d*x+c)^3+3/2*cos(d*x+c))*sin(d*x+c)+3/8*d*x+3/8*c)+2*a^2*b^2*B*(2+cos(d*x+c)^2)*sin(d*x+c)+4/3*a*A*b^3*(2+cos(d*x+c)^2)*sin(d*x+c)+4*B*a*b^3*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+A*b^4*(1/2*cos(d*x+c)*sin(d*x+c)+1/2*d*x+1/2*c)+B*b^4*sin(d*x+c))","A"
311,1,688,170,0.583000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{3} B}{d \,b^{4}}-\frac{a B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}+\frac{B}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A}{2 d b}+\frac{A}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{A}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A}{2 d b}+\frac{A a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}-\frac{B}{3 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{3}}+\frac{A}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{B}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A \,a^{2}}{d \,b^{3}}+\frac{a B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{a^{2} B}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B a}{2 d \,b^{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)-1\right) A \,a^{2}}{d \,b^{3}}-\frac{a^{2} B}{d \,b^{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)-1\right) B a}{2 d \,b^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B a}{2 d \,b^{2}}+\frac{A a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{B a}{2 d \,b^{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)-1\right) a^{3} B}{d \,b^{4}}"," ",0,"2/d*a^4/b^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-2/d*a^3/b^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-1/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^3*B-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)^2*a*B+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2*B+1/2/d/b*ln(tan(1/2*d*x+1/2*c)+1)*A+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)*A-1/d/b/(tan(1/2*d*x+1/2*c)+1)*B+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)*A-1/d/b/(tan(1/2*d*x+1/2*c)-1)*B-1/3/d*B/b/(tan(1/2*d*x+1/2*c)+1)^3-1/2/d/b*ln(tan(1/2*d*x+1/2*c)-1)*A+1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*A*a-1/3/d*B/b/(tan(1/2*d*x+1/2*c)-1)^3+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2*A-1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2*B-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2*A+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*A*a^2+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)^2*a*B-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a^2*B-1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*B*a-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*A*a^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a^2*B+1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*B*a-1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*B*a+1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*A*a-1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*B*a+1/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^3*B","B"
312,1,410,130,0.653000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B}{2 d b \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)-1\right) A a}{d \,b^{2}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2} B}{d \,b^{3}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d b}-\frac{B}{2 d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{A}{d b \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B a}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B}{2 d b \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)+1\right) A a}{d \,b^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2} B}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d b}"," ",0,"2/d*a^2/b^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*a^3/b^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)^2*B-1/d/b/(tan(1/2*d*x+1/2*c)-1)*A+1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*B*a+1/2/d/b/(tan(1/2*d*x+1/2*c)-1)*B+1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*A*a-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*a^2*B-1/2/d/b*ln(tan(1/2*d*x+1/2*c)-1)*B-1/2/d/b/(tan(1/2*d*x+1/2*c)+1)^2*B-1/d/b/(tan(1/2*d*x+1/2*c)+1)*A+1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*B*a+1/2/d/b/(tan(1/2*d*x+1/2*c)+1)*B-1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*A*a+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*a^2*B+1/2/d/b*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
313,1,228,89,0.533000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{B}{d b \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)-1\right) A}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B a}{d \,b^{2}}-\frac{B}{d b \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)+1\right) A}{d b}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B a}{d \,b^{2}}"," ",0,"-2/d*a/b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+2/d*a^2/b^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/d/b/(tan(1/2*d*x+1/2*c)-1)*B-1/d/b*ln(tan(1/2*d*x+1/2*c)-1)*A+1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*B*a-1/d/b/(tan(1/2*d*x+1/2*c)+1)*B+1/d/b*ln(tan(1/2*d*x+1/2*c)+1)*A-1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*B*a","B"
314,1,135,67,0.752000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{d b \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d b}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d b}"," ",0,"2/d/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d/b/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B-1/d/b*ln(tan(1/2*d*x+1/2*c)-1)*B+1/d/b*ln(tan(1/2*d*x+1/2*c)+1)*B","A"
315,1,113,58,0.800000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A b}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}"," ",0,"-2/d/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b+2/d/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d*A/a*arctan(tan(1/2*d*x+1/2*c))","A"
316,1,172,81,1.247000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d a \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 A \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d a \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) b}{d \,a^{2}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}"," ",0,"2/d*b^2/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*b/a/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-2/d/a^2*A*arctan(tan(1/2*d*x+1/2*c))*b+2/a/d*arctan(tan(1/2*d*x+1/2*c))*B","B"
317,1,367,121,1.139000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d a \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 a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d a}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{3}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{2}}"," ",0,"-2/d*b^3/a^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+2/d*b^2/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A*b+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B+1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A*b+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B+1/d*A/a*arctan(tan(1/2*d*x+1/2*c))+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A*b^2-2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B*b","B"
318,1,641,161,1.218000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{3} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b B}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b B}{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) A}{d a \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) A \,b^{2}}{d \,a^{3} \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) b B}{d \,a^{2} \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 b}{d \,a^{2} \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) B}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{2}}-\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{3}}{d \,a^{4}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{a d}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B \,b^{2}}{d \,a^{3}}"," ",0,"2/d*b^4/a^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*b^3/a^3/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A*b+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A*b^2-1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b*B+4/3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A+4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A*b^2-4/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*b*B+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A*b^2-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b*B-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A*b+1/d/a/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*B-1/d/a^2*A*arctan(tan(1/2*d*x+1/2*c))*b-2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*A*b^3+1/a/d*arctan(tan(1/2*d*x+1/2*c))*B+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B*b^2","B"
319,1,1212,221,1.177000," ","int(cos(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{3 d \,a^{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) B \,b^{3}}{d \,a^{4}}+\frac{3 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{4 d a}+\frac{3 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{4 d a \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 \,b^{2}}{d \,a^{3} \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 \,b^{3}}{d \,a^{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) b^{2} B}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{5} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{4}}{d \,a^{5}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{4} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b^{2} B}{d \,a^{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) B b}{d \,a^{2} \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) A}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b^{2} B}{d \,a^{3} \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) b^{2} B}{d \,a^{3} \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) B b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{\left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{2} \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) A \,b^{2}}{d \,a^{3}}-\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{2}}-\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A \,b^{3}}{d \,a^{4} \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 \,b^{2}}{d \,a^{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) A \,b^{2}}{d \,a^{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) A}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \left(\tan^{7}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d a \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 \,b^{3}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{10 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{3 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{2 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}+\frac{10 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{3 d a \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}{4 d a \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}"," ",0,"2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*b^2*B+10/3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*B+5/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*A-2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B*b^3+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*B+3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*A+2/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*B+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*B*b+2/d*b^4/a^4/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+3/4/d*A/a*arctan(tan(1/2*d*x+1/2*c))-2/d*b^5/a^5/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+10/3/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*B-3/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*A+2/d/a^5*arctan(tan(1/2*d*x+1/2*c))*A*b^4+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*A*b^2-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*A*b-10/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*A*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*A*b^3+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*b^2*B-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*A*b^2-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*A*b^3+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*A*b^2-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*B*b-2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)*A*b^3+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*b^2*B-10/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*A*b-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*A*b^2-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*A*b^3+1/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A*b^2-1/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B*b+6/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^5*b^2*B-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^3*B*b+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*B*b-2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*A*b-5/4/d/a/(1+tan(1/2*d*x+1/2*c)^2)^4*tan(1/2*d*x+1/2*c)^7*A","B"
320,1,698,259,0.572000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{4 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 a B}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A a}{d \,b^{3}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2} B}{d \,b^{4}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{2 d \,b^{2}}-\frac{B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{A}{d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{2 a B}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B}{2 d \,b^{2} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A a}{d \,b^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2} B}{d \,b^{4}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{2 d \,b^{2}}"," ",0,"-2/d*a^3/b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A+2/d*a^4/b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B+4/d*a^4/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-6/d*a^2/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-6/d*a^5/b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+8/d*a^3/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+1/2/d*B/b^2/(tan(1/2*d*x+1/2*c)-1)^2-1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*A+2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*a*B+1/2/d/b^2/(tan(1/2*d*x+1/2*c)-1)*B+2/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*A*a-3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a^2*B-1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*B-1/2/d*B/b^2/(tan(1/2*d*x+1/2*c)+1)^2-1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*A+2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*a*B+1/2/d/b^2/(tan(1/2*d*x+1/2*c)+1)*B-2/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*A*a+3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a^2*B+1/2/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
321,1,510,155,0.661000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 a \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d b \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{B}{d \,b^{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)-1\right) A}{d \,b^{2}}+\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a B}{d \,b^{3}}-\frac{B}{d \,b^{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)+1\right) A}{d \,b^{2}}-\frac{2 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a B}{d \,b^{3}}"," ",0,"2/d*a^2/b/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A-2/d*a^3/b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B-2/d*a^3/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+4/d*a/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+4/d*a^4/b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-6/d*a^2/b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/d/b^2/(tan(1/2*d*x+1/2*c)-1)*B-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*A+2/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*a*B-1/d/b^2/(tan(1/2*d*x+1/2*c)+1)*B+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*A-2/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*a*B","B"
322,1,350,122,0.749000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d b \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{4 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B a}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,b^{2}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,b^{2}}"," ",0,"-2/d*a/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A+2/d/b*a^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B-2/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*a^3/b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+4/d/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B*a-1/d/b^2*ln(tan(1/2*d*x+1/2*c)-1)*B+1/d/b^2*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
323,1,132,91,0.718000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","\frac{\frac{2 \left(A b -a B \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 \left(a A -B b \right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(A*b-B*a)/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)+2*(A*a-B*b)/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
324,1,328,115,0.789000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d a \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 b \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{4 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{3}}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B a}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}"," ",0,"-2/d/a*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A+2/d*b/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B-4/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+2/d/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^3+2/d/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B*a+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A","B"
325,1,453,171,1.149000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d a \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{6 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d a \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 A \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)}-\frac{4 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}"," ",0,"2/d/a^2*b^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A-2/d/a*b^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B+6/d/a*b^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-4/d/a^3*b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-4/d*b/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^2*b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^2*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-4/d/a^3*A*arctan(tan(1/2*d*x+1/2*c))*b+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B","B"
326,1,651,248,1.099000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,a^{2} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{8 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{3}}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d a \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{4 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \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)^{2}}+\frac{A \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 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \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{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{4}}-\frac{4 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{3}}"," ",0,"-2/d*b^4/a^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A+2/d*b^3/a^2/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B-8/d/a^2/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^3+6/d*b^5/a^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+6/d*b^2/a/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-4/d*b^4/a^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A*b+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A*b+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)+1/d/a^2*arctan(tan(1/2*d*x+1/2*c))*A+6/d/a^4*arctan(tan(1/2*d*x+1/2*c))*A*b^2-4/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B*b","B"
327,1,926,329,1.403000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","\frac{2 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{4} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,a^{3} \left(a^{2}-b^{2}\right) \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)}+\frac{10 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{3} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{5} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{2} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{4} \left(a -b \right) \left(a +b \right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{2 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{\left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b B}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{4 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{12 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{8 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b B}{d \,a^{3} \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) A}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}+\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A \,b^{2}}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{4 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) b B}{d \,a^{3} \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) A b}{d \,a^{3} \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) B}{d \,a^{2} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{3}}-\frac{8 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{3}}{d \,a^{5}}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2}}+\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B \,b^{2}}{d \,a^{4}}"," ",0,"2/d*b^5/a^4/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*A-2/d*b^4/a^3/(a^2-b^2)*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)*B+10/d/a^3*b^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-8/d*b^6/a^5/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-8/d/a^2*b^3/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+6/d*b^5/a^4/(a-b)/(a+b)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A*b+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*A*b^2-1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*B-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^5*b*B+4/3/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A+12/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*A*b^2-8/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)^3*b*B+2/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A+6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A*b^2-4/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*b*B-2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*A*b+1/d/a^2/(1+tan(1/2*d*x+1/2*c)^2)^3*tan(1/2*d*x+1/2*c)*B-2/d/a^3*A*arctan(tan(1/2*d*x+1/2*c))*b-8/d/a^5*arctan(tan(1/2*d*x+1/2*c))*A*b^3+1/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B+6/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B*b^2","B"
328,1,1599,388,0.883000," ","int(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) A a}{d \,b^{4}}+\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a^{2} B}{d \,b^{5}}-\frac{20 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{10 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{8 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{6 a^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{10 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{8 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{4 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{29 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 a^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{B}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)^{2}}-\frac{A}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{B}{2 d \,b^{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)-1\right) B}{2 d \,b^{3}}-\frac{B}{2 d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)^{2}}-\frac{A}{d \,b^{3} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{B}{2 d \,b^{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)+1\right) B}{2 d \,b^{3}}-\frac{12 a^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{5} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) A a}{d \,b^{4}}+\frac{3 a B}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}+\frac{3 a B}{d \,b^{4} \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}+\frac{12 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a^{2} B}{d \,b^{5}}"," ",0,"-3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*A*a+6/d/b^5*ln(tan(1/2*d*x+1/2*c)+1)*a^2*B-10/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+6/d*a^6/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-1/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-6/d*a^6/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-1/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+10/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-20/d*a^3/b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-15/d*a^4/b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+1/2/d*B/b^3/(tan(1/2*d*x+1/2*c)-1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*A+1/2/d/b^3/(tan(1/2*d*x+1/2*c)-1)*B-1/2/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*B-1/2/d*B/b^3/(tan(1/2*d*x+1/2*c)+1)^2-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*A+1/2/d/b^3/(tan(1/2*d*x+1/2*c)+1)*B+1/2/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*B-12/d*a^7/b^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+29/d*a^5/b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+6/d*a^6/b^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*A*a+3/d/b^4/(tan(1/2*d*x+1/2*c)-1)*a*B+3/d/b^4/(tan(1/2*d*x+1/2*c)+1)*a*B+12/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-6/d/b^5*ln(tan(1/2*d*x+1/2*c)-1)*a^2*B","B"
329,1,1406,274,0.687000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\frac{2 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 a^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{8 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{6 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{4 a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{8 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{2 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 a b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 a^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 a^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{B}{d \,b^{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)-1\right) A}{d \,b^{3}}+\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) a B}{d \,b^{4}}-\frac{B}{d \,b^{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)+1\right) A}{d \,b^{3}}-\frac{3 \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) a B}{d \,b^{4}}"," ",0,"2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-6/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+6/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+4/d*a^5/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+1/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-8/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-2/d*a^5/b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+5/d*a^3/b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-6/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+6/d*a^6/b^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-15/d*a^4/b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+12/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-1/d/b^3/(tan(1/2*d*x+1/2*c)-1)*B-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*A+3/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*a*B-1/d/b^3/(tan(1/2*d*x+1/2*c)+1)*B+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*A-3/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*a*B","B"
330,1,1085,207,0.803000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\frac{a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 b a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{4 b a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{2 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{6 a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,b^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 a^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d b \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right) B}{d \,b^{3}}+\frac{\ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right) B}{d \,b^{3}}"," ",0,"1/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+4/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*a/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*a^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-4/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*a/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-2/d*a^4/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-1/d*a^3/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*a^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+1/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+2/d*b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*a^5/b^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+5/d*a^3/b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-6/d*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B-1/d/b^3*ln(tan(1/2*d*x+1/2*c)-1)*B+1/d/b^3*ln(tan(1/2*d*x+1/2*c)+1)*B","B"
331,1,238,167,0.717000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\frac{\frac{-\frac{\left(2 a^{2} A +A a b +2 A \,b^{2}-a^{2} B -4 B a b \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(2 a^{2} A -A a b +2 A \,b^{2}+a^{2} B -4 B a b \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2}}-\frac{\left(3 A a b -a^{2} B -2 b^{2} B \right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(-1/2*(2*A*a^2+A*a*b+2*A*b^2-B*a^2-4*B*a*b)/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(2*A*a^2-A*a*b+2*A*b^2+B*a^2-4*B*a*b)/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2-(3*A*a*b-B*a^2-2*B*b^2)/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
332,1,236,151,0.718000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\frac{-\frac{2 \left(-\frac{\left(4 A a b +A \,b^{2}-2 a^{2} B -B a b -2 b^{2} B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\left(4 A a b -A \,b^{2}-2 a^{2} B +B a b -2 b^{2} B \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{2}-2 a b +b^{2}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2}}+\frac{\left(2 a^{2} A +A \,b^{2}-3 B a b \right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(4*A*a*b+A*b^2-2*B*a^2-B*a*b-2*B*b^2)/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(4*A*a*b-A*b^2-2*B*a^2+B*a*b-2*B*b^2)/(a+b)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2+(2*A*a^2+A*b^2-3*B*a*b)/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
333,1,1063,192,0.864000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","-\frac{6 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 a b \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{4 a b \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{6 a b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{3}}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{5}}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 a^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{\arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{2} B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}"," ",0,"-6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-1/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^3/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+2/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+4/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-1/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^3/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-2/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-4/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+1/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-6/d*a*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+5/d/a/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^3-2/d/a^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^5+2/d*a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+1/d/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*b^2*B+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A","B"
334,1,1349,275,1.179000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\frac{8 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 b^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{6 b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{2 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{12 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{5 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{5} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 A \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)}-\frac{6 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) b}{d \,a^{4}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3}}"," ",0,"8/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^3/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+1/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-1/d*b^3/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+2/d*b^4/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-8/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^3/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+1/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+6/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-1/d*b^3/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-2/d*b^4/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+12/d*b^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-15/d*b^4/a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+6/d*b^6/a^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-6/d*b/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B+5/d*b^3/a/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-2/d*b^5/a^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^3*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)-6/d/a^4*A*arctan(tan(1/2*d*x+1/2*c))*b+2/d/a^3*arctan(tan(1/2*d*x+1/2*c))*B","B"
335,1,1552,374,1.319000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","-\frac{6 \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{8 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{8 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{4 b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{4 b^{5} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{\arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3}}-\frac{6 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}+\frac{6 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{4} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{10 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a +b \right) \left(a -b \right)^{2}}-\frac{10 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{2} \left(a -b \right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{12 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) A \,b^{2}}{d \,a^{5}}-\frac{6 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{4}}-\frac{12 b^{7} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \,a^{5} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{15 b^{4} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{2} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{6 b^{6} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{4} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{20 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{3}}{d a \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{29 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{5}}{d \,a^{3} \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{12 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) b^{2} B}{d \left(a^{4}-2 a^{2} b^{2}+b^{4}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{6 \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A b}{d \,a^{4} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}-\frac{\left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(1+\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{2 B \left(\tan^{3}\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{A \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{2 B \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}}"," ",0,"10/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-10/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2*b^4/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+6/d*b^6/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-6/d*b^6/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A+4/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B-1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A+1/d/a^3*arctan(tan(1/2*d*x+1/2*c))*A-1/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+8/d*b^3/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*b^4/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a-b)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-1/d*b^5/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*A-8/d*b^3/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+1/d*b^4/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^2/(a+b)/(a-b)^2*tan(1/2*d*x+1/2*c)*B+12/d/a^5*arctan(tan(1/2*d*x+1/2*c))*A*b^2-6/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B*b+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)^3+1/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*A*tan(1/2*d*x+1/2*c)+2/d/a^3/(1+tan(1/2*d*x+1/2*c)^2)^2*B*tan(1/2*d*x+1/2*c)-12/d*b^7/a^5/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-15/d*b^4/a^2/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+6/d*b^6/a^4/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-20/d/a/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^3+29/d/a^3/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^5+12/d/(a^4-2*a^2*b^2+b^4)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*b^2*B-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A*b-6/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A*b","B"
336,1,2948,401,0.651000," ","int(sec(d*x+c)^5*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\text{output too large to display}"," ",0,"35/d*a^4/b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-20/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+8/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+8/d*a^8/b^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-20/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+40/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-20/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+7/d*a^5/b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-2/d*a^7/b^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-28/d*a^6/b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+44/3/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+12/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+18/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+18/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+5/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+12/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-116/3/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+12/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-4/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-6/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-6/d*a^7/b^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-24/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-5/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-8/d*a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-1/d*B/b^4/(tan(1/2*d*x+1/2*c)-1)-1/d/b^4*ln(tan(1/2*d*x+1/2*c)-1)*A-1/d*B/b^4/(tan(1/2*d*x+1/2*c)+1)+1/d/b^4*ln(tan(1/2*d*x+1/2*c)+1)*A+4/d/b^5*ln(tan(1/2*d*x+1/2*c)-1)*a*B-4/d/b^5*ln(tan(1/2*d*x+1/2*c)+1)*a*B","B"
337,1,2264,295,0.738000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\frac{44 a^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{3 d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 a^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{6 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{12 b \,a^{2} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{12 b \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{12 b^{2} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 a^{2} b \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 a^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{24 b \,a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{a^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{6 a^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{3 a^{2} b \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{a^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{2 a^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 a^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \,b^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{B \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)+1\right)}{d \,b^{4}}-\frac{B \ln \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)-1\right)}{d \,b^{4}}-\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{7} B}{d \,b^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{3 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} A}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{7 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{5} B}{d \,b^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{4 a^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{4 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{4 a^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 a^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{8 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} B}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+12/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+12/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-6/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-2/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+4/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-2/d*a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+44/3/d/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^4/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-4/d/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^6/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-24/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-1/d*a^5/b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+4/3/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-2/d/b^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^7*B-3/d*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^2*A+7/d/b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^5*B-3/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+3/d*a^2*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+2/d*a^6/b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-6/d*a^4/b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+1/d*B/b^4*ln(tan(1/2*d*x+1/2*c)+1)-1/d*B/b^4*ln(tan(1/2*d*x+1/2*c)-1)+8/d*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B-8/d/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^3*B-2/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A","B"
338,1,375,259,0.807000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{\left(A \,a^{3}+6 A \,a^{2} b +2 A a \,b^{2}+2 A \,b^{3}-2 a^{3} B -3 a^{2} b B -6 B a \,b^{2}\right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 \left(7 A \,a^{2} b +3 A \,b^{3}-a^{3} B -9 B a \,b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}+\frac{\left(A \,a^{3}-6 A \,a^{2} b +2 A a \,b^{2}-2 A \,b^{3}+2 a^{3} B -3 a^{2} b B +6 B a \,b^{2}\right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}+\frac{\left(A \,a^{3}+4 A a \,b^{2}-3 a^{2} b B -2 b^{3} B \right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(A*a^3+6*A*a^2*b+2*A*a*b^2+2*A*b^3-2*B*a^3-3*B*a^2*b-6*B*a*b^2)/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(7*A*a^2*b+3*A*b^3-B*a^3-9*B*a*b^2)/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3+1/2*(A*a^3-6*A*a^2*b+2*A*a*b^2-2*A*b^3+2*B*a^3-3*B*a^2*b+6*B*a*b^2)/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3+(A*a^3+4*A*a*b^2-3*B*a^2*b-2*B*b^3)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
339,1,388,248,0.792000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\frac{\frac{-\frac{\left(2 A \,a^{3}+2 A \,a^{2} b +6 A a \,b^{2}+A \,b^{3}-a^{3} B -6 a^{2} b B -2 B a \,b^{2}-2 b^{3} B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{4 \left(3 A \,a^{3}+7 A a \,b^{2}-7 a^{2} b B -3 b^{3} B \right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(2 A \,a^{3}-2 A \,a^{2} b +6 A a \,b^{2}-A \,b^{3}+a^{3} B -6 a^{2} b B +2 B a \,b^{2}-2 b^{3} B \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{\left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}-\frac{\left(4 A \,a^{2} b +A \,b^{3}-a^{3} B -4 B a \,b^{2}\right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(2*(-1/2*(2*A*a^3+2*A*a^2*b+6*A*a*b^2+A*b^3-B*a^3-6*B*a^2*b-2*B*a*b^2-2*B*b^3)/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(3*A*a^3+7*A*a*b^2-7*B*a^2*b-3*B*b^3)/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(2*A*a^3-2*A*a^2*b+6*A*a*b^2-A*b^3+B*a^3-6*B*a^2*b+2*B*a*b^2-2*B*b^3)/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3-(4*A*a^2*b+A*b^3-B*a^3-4*B*a*b^2)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
340,1,376,222,0.728000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\frac{-\frac{2 \left(-\frac{\left(6 A \,a^{2} b +3 A a \,b^{2}+2 A \,b^{3}-2 a^{3} B -2 a^{2} b B -6 B a \,b^{2}-b^{3} B \right) \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{2 \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 \left(9 A \,a^{2} b +A \,b^{3}-3 a^{3} B -7 B a \,b^{2}\right) \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3 \left(a^{2}+2 a b +b^{2}\right) \left(a^{2}-2 a b +b^{2}\right)}-\frac{\left(6 A \,a^{2} b -3 A a \,b^{2}+2 A \,b^{3}-2 a^{3} B +2 a^{2} b B -6 B a \,b^{2}+b^{3} B \right) \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{2 \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}\right)}{\left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3}}+\frac{\left(2 A \,a^{3}+3 A a \,b^{2}-4 a^{2} b B -b^{3} B \right) \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{\left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}}{d}"," ",0,"1/d*(-2*(-1/2*(6*A*a^2*b+3*A*a*b^2+2*A*b^3-2*B*a^3-2*B*a^2*b-6*B*a*b^2-B*b^3)/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5+2/3*(9*A*a^2*b+A*b^3-3*B*a^3-7*B*a*b^2)/(a^2+2*a*b+b^2)/(a^2-2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3-1/2*(6*A*a^2*b-3*A*a*b^2+2*A*b^3-2*B*a^3+2*B*a^2*b-6*B*a*b^2+B*b^3)/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c))/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3+(2*A*a^3+3*A*a*b^2-4*B*a^2*b-B*b^3)/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2)))","A"
341,1,2242,277,0.890000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","-\frac{12 b^{2} a \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 b^{4} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 b \,a^{2} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{12 b^{2} a \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{6 b \,a^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{24 b^{2} a \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{12 b \,a^{2} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{44 b^{4} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{3 d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{b^{5} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{2 b^{6} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{b^{5} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{2} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{2 b^{6} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{3 a \,b^{2} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{6 b^{4} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d a \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{4 b^{6} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \,a^{3} \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}-\frac{3 a \,b^{2} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{2 A \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,a^{4}}+\frac{2 b^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}-\frac{4 b^{3} \left(\tan^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a -b \right) \left(a^{3}+3 a^{2} b +3 b^{2} a +b^{3}\right)}+\frac{2 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) B}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}+\frac{4 b^{3} \tan \left(\frac{d x}{2}+\frac{c}{2}\right) A}{d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a +b \right) \left(a^{3}-3 a^{2} b +3 b^{2} a -b^{3}\right)}-\frac{4 b^{3} \left(\tan^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) B}{3 d \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b -a -b \right)^{3} \left(a^{2}-2 a b +b^{2}\right) \left(a^{2}+2 a b +b^{2}\right)}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{7}}{d \,a^{4} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{8 b \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2} A}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{7 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A \,b^{5}}{d \,a^{2} \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{3 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a B}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{3} B}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{8 b^{3} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) A}{d \left(a^{6}-3 a^{4} b^{2}+3 b^{4} a^{2}-b^{6}\right) \sqrt{\left(a -b \right) \left(a +b \right)}}"," ",0,"6/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+24/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+6/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+4/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-3/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^2/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+6/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-12/d*b^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+2/d/a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^7+2/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+6/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-44/3/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-1/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-2/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-12/d*b/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*a^2/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+1/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-8/d*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^2*A-2/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+3/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^2/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-4/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-7/d/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^5+2/d*A/a^4*arctan(tan(1/2*d*x+1/2*c))+3/d*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B+2/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+4/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-4/3/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+2/d/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^3*B+8/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A","B"
342,1,2891,394,1.413000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\text{output too large to display}"," ",0,"5/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-12/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^2/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+2/d*b^7/a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-40/d*b^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-35/d*b^4/a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+28/d*b^6/a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-8/d*b^8/a^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-7/d*b^5/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-8/d*a^2*b/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+20/d*a*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A-4/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-5/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-18/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+2/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-18/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+2/d/a^4*arctan(tan(1/2*d*x+1/2*c))*B-2/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-12/d*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^2/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+20/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-44/3/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+4/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+6/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+116/3/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-12/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+24/d*b^2*a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+6/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-1/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+1/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+4/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+20/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-8/d/a^5*A*arctan(tan(1/2*d*x+1/2*c))*b+8/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^4*A*tan(1/2*d*x+1/2*c)/(1+tan(1/2*d*x+1/2*c)^2)","B"
343,1,3099,517,1.152000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^4,x)","\text{output too large to display}"," ",0,"-30/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-212/3/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A-35/d*b^4/a/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+28/d*b^6/a^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B-69/d/a^4/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^7+20/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-30/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+60/d/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^4/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+6/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+34/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-6/d/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^5/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A-8/d*b^8/a^5/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+20/d*b^9/a^6/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+34/d/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^6/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+84/d/a^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A*b^5-12/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+116/3/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B-12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A-12/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-5/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+5/d*b^4/a/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-18/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-18/d*b^5/a^2/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*A+3/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*A+2/d*b^6/a^3/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B+1/d*A/a^4*arctan(tan(1/2*d*x+1/2*c))+20/d*b^2/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a*B+20/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a+b)/(a^3-3*a^2*b+3*a*b^2-b^3)*tan(1/2*d*x+1/2*c)*B-40/d/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3*b^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*B+6/d*b^7/a^4/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a-b)/(a^3+3*a^2*b+3*a*b^2+b^3)*tan(1/2*d*x+1/2*c)^5*B-1/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A-40/d*b^3/(a^6-3*a^4*b^2+3*a^2*b^4-b^6)/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*A+24/d*b^8/a^5/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b-a-b)^3/(a^2-2*a*b+b^2)/(a^2+2*a*b+b^2)*tan(1/2*d*x+1/2*c)^3*A+1/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*B+20/d/a^6*arctan(tan(1/2*d*x+1/2*c))*A*b^2-8/d/a^5*arctan(tan(1/2*d*x+1/2*c))*B*b-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)*A*b-8/d/a^5/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*A*b+2/d/a^4/(1+tan(1/2*d*x+1/2*c)^2)^2*tan(1/2*d*x+1/2*c)^3*B","B"
344,1,116,52,1.029000," ","int((b*B/a+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 B \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \sqrt{\left(a -b \right) \left(a +b \right)}}-\frac{2 b^{2} \arctanh \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) B}{d \,a^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right) B b}{d \,a^{2}}"," ",0,"2/d*B/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))-2/d*b^2/a^2/((a-b)*(a+b))^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*B+2/d/a^2*arctan(tan(1/2*d*x+1/2*c))*B*b","B"
345,1,7,6,0.043000," ","int((a*B/b+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{B x}{b}"," ",0,"B*x/b","A"
346,1,163,77,0.800000," ","int((a+b*sec(d*x+c))/(b+a*sec(d*x+c))^2,x)","-\frac{2 a \tan \left(\frac{d x}{2}+\frac{c}{2}\right)}{d b \left(a \left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\left(\tan^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) b +a +b \right)}-\frac{2 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right) a^{2}}{d \,b^{2} \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 \arctan \left(\frac{\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \left(a -b \right)}{\sqrt{\left(a -b \right) \left(a +b \right)}}\right)}{d \sqrt{\left(a -b \right) \left(a +b \right)}}+\frac{2 a \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d \,b^{2}}"," ",0,"-2/d/b*a*tan(1/2*d*x+1/2*c)/(a*tan(1/2*d*x+1/2*c)^2-tan(1/2*d*x+1/2*c)^2*b+a+b)-2/d/b^2/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))*a^2+2/d/((a-b)*(a+b))^(1/2)*arctan(tan(1/2*d*x+1/2*c)*(a-b)/((a-b)*(a+b))^(1/2))+2/d*a/b^2*arctan(tan(1/2*d*x+1/2*c))","B"
347,1,39,69,0.836000," ","int((3+sec(d*x+c))/(2-sec(d*x+c)),x)","\frac{5 \sqrt{3}\, \arctanh \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{3}\right)}{3 d}+\frac{3 \arctan \left(\tan \left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{d}"," ",0,"5/3/d*3^(1/2)*arctanh(tan(1/2*d*x+1/2*c)*3^(1/2))+3/d*arctan(tan(1/2*d*x+1/2*c))","A"
348,1,4394,447,3.220000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-2/315/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-54*A*cos(d*x+c)^2*a*b^4+B*cos(d*x+c)^2*a^2*b^3-40*B*cos(d*x+c)*a*b^4-22*B*cos(d*x+c)^3*a*b^4-30*A*cos(d*x+c)^3*b^5-24*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+8*B*cos(d*x+c)^6*a^4*b-24*B*cos(d*x+c)^6*a^3*b^2+13*B*cos(d*x+c)^6*a^2*b^3+147*B*cos(d*x+c)^6*a*b^4-16*B*cos(d*x+c)^5*a^4*b+26*B*cos(d*x+c)^5*a^3*b^2-24*B*cos(d*x+c)^5*a^2*b^3-85*B*cos(d*x+c)^5*a*b^4+8*B*cos(d*x+c)^4*a^4*b-35*B*b^5+24*A*cos(d*x+c)^6*a^4*b-12*A*cos(d*x+c)^6*a^3*b^2+57*A*cos(d*x+c)^6*a^2*b^3+75*A*cos(d*x+c)^6*a*b^4-24*A*cos(d*x+c)^5*a^4*b+24*A*cos(d*x+c)^5*a^3*b^2-60*A*cos(d*x+c)^5*a^2*b^3+57*A*cos(d*x+c)^5*a*b^4-12*A*cos(d*x+c)^4*a^3*b^2-78*A*cos(d*x+c)^4*a*b^4+3*A*cos(d*x+c)^3*a^2*b^3+10*B*cos(d*x+c)^4*a^2*b^3-2*B*cos(d*x+c)^3*a^3*b^2+75*A*cos(d*x+c)^5*b^5+16*B*cos(d*x+c)^5*a^5-16*B*cos(d*x+c)^6*a^5-98*B*cos(d*x+c)^4*b^5-45*A*cos(d*x+c)*b^5+147*B*cos(d*x+c)^5*b^5-14*B*cos(d*x+c)^2*b^5+24*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+24*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-16*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-4*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-24*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+111*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+75*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+16*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+75*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+16*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-24*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-57*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-57*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+24*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+6*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+57*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+16*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+24*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+24*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-16*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-4*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-24*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+111*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-24*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-24*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-57*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-57*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+24*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+6*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+57*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+16*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b)/(b+a*cos(d*x+c))/cos(d*x+c)^4/sin(d*x+c)^5/b^4","B"
349,1,3438,363,2.740000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-14*A*cos(d*x+c)^5*a^3*b+7*A*cos(d*x+c)^5*a^2*b^2+63*A*cos(d*x+c)^5*a*b^3-4*B*cos(d*x+c)^5*a^3*b+19*B*cos(d*x+c)^5*a^2*b^2+14*A*cos(d*x+c)^4*a^3*b-14*A*cos(d*x+c)^4*a^2*b^2+8*B*cos(d*x+c)^4*a^3*b+7*A*cos(d*x+c)^3*a^2*b^2-4*B*cos(d*x+c)^3*a^3*b-26*B*cos(d*x+c)^3*a*b^3+B*cos(d*x+c)^2*a^2*b^2-18*B*cos(d*x+c)*a*b^3-28*A*cos(d*x+c)^2*a*b^3-42*A*cos(d*x+c)^3*b^4+25*B*cos(d*x+c)^4*b^4-10*B*cos(d*x+c)^2*b^4+19*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-35*A*cos(d*x+c)^4*a*b^3+25*B*cos(d*x+c)^5*a*b^3-20*B*cos(d*x+c)^4*a^2*b^2-15*B*b^4-8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-19*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-19*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+2*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+19*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+14*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+14*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-14*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+49*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-8*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-19*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-19*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+8*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+2*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+8*B*cos(d*x+c)^5*a^4+14*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+14*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-14*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+49*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+63*A*cos(d*x+c)^4*b^4-8*B*cos(d*x+c)^4*a^4-21*A*cos(d*x+c)*b^4-63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-8*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+25*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+25*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+19*B*cos(d*x+c)^4*a*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b^3","B"
350,1,2498,284,2.293000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+5*A*cos(d*x+c)^3*b^3+2*B*cos(d*x+c)^3*a^3-3*b^3*B+9*B*cos(d*x+c)^3*b^3-6*B*cos(d*x+c)^2*b^3+5*A*cos(d*x+c)^3*a*b^2-10*A*cos(d*x+c)^2*a*b^2+9*B*cos(d*x+c)^4*a*b^2-2*B*cos(d*x+c)^3*a^2*b+B*cos(d*x+c)^2*a^2*b-4*B*cos(d*x+c)*a*b^2-5*A*cos(d*x+c)*b^3-5*B*cos(d*x+c)^3*a*b^2+5*A*cos(d*x+c)^4*a^2*b+5*A*cos(d*x+c)^4*a*b^2-5*A*cos(d*x+c)^3*a^2*b+B*cos(d*x+c)^4*a^2*b-2*B*cos(d*x+c)^4*a^3-2*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+7*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+2*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+7*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+2*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b^2","B"
351,1,1752,230,2.007000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(B \left(\cos^{2}\left(d x +c \right)\right) b^{2}-B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+3 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -b^{2} B -3 A \cos \left(d x +c \right) b^{2}-2 B \cos \left(d x +c \right) a b -3 A \left(\cos^{2}\left(d x +c \right)\right) a b +B \left(\cos^{3}\left(d x +c \right)\right) a b +B \left(\cos^{2}\left(d x +c \right)\right) a b +3 A \left(\cos^{3}\left(d x +c \right)\right) a b +B \left(\cos^{3}\left(d x +c \right)\right) a^{2}-3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} b}"," ",0,"-2/3/d*(-1+cos(d*x+c))^2*(-B*cos(d*x+c)^2*a^2+B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)^2*b^2-b^2*B+3*A*cos(d*x+c)^2*b^2-3*A*cos(d*x+c)*b^2-3*A*cos(d*x+c)^2*a*b+B*cos(d*x+c)^3*a*b+B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+3*A*cos(d*x+c)^3*a*b+B*cos(d*x+c)^3*a^2-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5/b","B"
352,1,1372,293,2.048000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a -B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a -B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -B \left(\cos^{2}\left(d x +c \right)\right) a +B \cos \left(d x +c \right) a -b B \cos \left(d x +c \right)+B b \right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right)}"," ",0,"2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a-B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-B*cos(d*x+c)^2*a+B*cos(d*x+c)*a-b*B*cos(d*x+c)+B*b)/sin(d*x+c)^5/(b+a*cos(d*x+c))","B"
353,1,1389,315,1.983000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +2 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -2 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -4 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a +2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+2 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -2 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -4 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-A \left(\cos^{3}\left(d x +c \right)\right) a +A \left(\cos^{2}\left(d x +c \right)\right) a -A \left(\cos^{2}\left(d x +c \right)\right) b +A \cos \left(d x +c \right) b \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5}}"," ",0,"1/d*(-1+cos(d*x+c))^2*(2*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+2*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-2*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-A*cos(d*x+c)^3*a+A*cos(d*x+c)^2*a-A*cos(d*x+c)^2*b+A*cos(d*x+c)*b)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
354,1,2065,388,1.962000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-4*B*cos(d*x+c)^2*a^2+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-8*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+A*cos(d*x+c)^2*b^2-A*cos(d*x+c)*b^2+8*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+4*B*cos(d*x+c)^2*a*b-4*B*cos(d*x+c)*a*b-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+3*A*cos(d*x+c)^3*a*b+4*B*cos(d*x+c)^3*a^2+8*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-2*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-4*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-2*A*cos(d*x+c)^2*a^2+2*A*cos(d*x+c)^4*a^2+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
355,1,2954,464,2.493000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"-1/24/d*(-1+cos(d*x+c))^2*(16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+8*A*cos(d*x+c)^3*a^3-16*A*cos(d*x+c)^2*a^3-3*A*cos(d*x+c)^2*b^3-12*B*cos(d*x+c)^2*a^3-A*cos(d*x+c)^3*a*b^2+6*A*cos(d*x+c)^2*a^2*b+3*A*cos(d*x+c)^2*a*b^2-16*A*cos(d*x+c)*a^2*b-2*A*cos(d*x+c)*a*b^2+18*B*cos(d*x+c)^3*a^2*b-6*B*cos(d*x+c)^2*a^2*b+6*B*cos(d*x+c)^2*a*b^2-12*B*cos(d*x+c)*a^2*b-6*B*cos(d*x+c)*a*b^2+3*A*cos(d*x+c)*b^3+10*A*cos(d*x+c)^4*a^2*b-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+12*B*cos(d*x+c)^4*a^3-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+24*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-28*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+12*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+6*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+6*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+8*A*cos(d*x+c)^5*a^3+6*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+24*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-28*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+2*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+16*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b+6*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a^2","B"
356,1,4395,437,4.003000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"2/315/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(117*A*cos(d*x+c)^2*a*b^4+53*B*cos(d*x+c)^2*a^2*b^3+85*B*cos(d*x+c)*a*b^4+52*B*cos(d*x+c)^3*a*b^4+30*A*cos(d*x+c)^3*b^5-18*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+4*B*cos(d*x+c)^6*a^4*b-33*B*cos(d*x+c)^6*a^3*b^2-88*B*cos(d*x+c)^6*a^2*b^3-147*B*cos(d*x+c)^6*a*b^4-8*B*cos(d*x+c)^5*a^4*b+34*B*cos(d*x+c)^5*a^3*b^2-33*B*cos(d*x+c)^5*a^2*b^3+10*B*cos(d*x+c)^5*a*b^4+4*B*cos(d*x+c)^4*a^4*b+35*B*b^5+18*A*cos(d*x+c)^6*a^4*b-9*A*cos(d*x+c)^6*a^3*b^2-246*A*cos(d*x+c)^6*a^2*b^3-75*A*cos(d*x+c)^6*a*b^4-18*A*cos(d*x+c)^5*a^4*b+18*A*cos(d*x+c)^5*a^3*b^2+165*A*cos(d*x+c)^5*a^2*b^3-246*A*cos(d*x+c)^5*a*b^4-9*A*cos(d*x+c)^4*a^3*b^2+204*A*cos(d*x+c)^4*a*b^4+81*A*cos(d*x+c)^3*a^2*b^3+68*B*cos(d*x+c)^4*a^2*b^3-B*cos(d*x+c)^3*a^3*b^2-75*A*cos(d*x+c)^5*b^5+8*B*cos(d*x+c)^5*a^5-8*B*cos(d*x+c)^6*a^5+98*B*cos(d*x+c)^4*b^5+45*A*cos(d*x+c)*b^5-147*B*cos(d*x+c)^5*b^5+14*B*cos(d*x+c)^2*b^5+33*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+33*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-8*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-2*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-33*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-186*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-75*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+8*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5+147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-75*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+8*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5+147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-18*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+246*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+246*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+18*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-153*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-246*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+8*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+33*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+33*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-8*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-2*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-33*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-186*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-18*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-18*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+246*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+246*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+18*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-153*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-246*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+8*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b)/(b+a*cos(d*x+c))/cos(d*x+c)^4/sin(d*x+c)^5/b^3","B"
357,1,3424,354,2.918000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-2/105/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(21*A*cos(d*x+c)^5*a^3*b+42*A*cos(d*x+c)^5*a^2*b^2+63*A*cos(d*x+c)^5*a*b^3+3*B*cos(d*x+c)^5*a^3*b+82*B*cos(d*x+c)^5*a^2*b^2-21*A*cos(d*x+c)^4*a^3*b+21*A*cos(d*x+c)^4*a^2*b^2-6*B*cos(d*x+c)^4*a^3*b-63*A*cos(d*x+c)^3*a^2*b^2+3*B*cos(d*x+c)^3*a^3*b-68*B*cos(d*x+c)^3*a*b^3-27*B*cos(d*x+c)^2*a^2*b^2-39*B*cos(d*x+c)*a*b^3-63*A*cos(d*x+c)^2*a*b^3-42*A*cos(d*x+c)^3*b^4+25*B*cos(d*x+c)^4*b^4-10*B*cos(d*x+c)^2*b^4+82*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+25*B*cos(d*x+c)^5*a*b^3-55*B*cos(d*x+c)^4*a^2*b^2-15*B*b^4+6*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-82*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-82*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-6*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+51*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+82*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-21*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-21*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+21*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+84*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+6*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-82*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-82*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-6*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+51*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-6*B*cos(d*x+c)^5*a^4-21*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-21*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+21*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+84*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+63*A*cos(d*x+c)^4*b^4+6*B*cos(d*x+c)^4*a^4-21*A*cos(d*x+c)*b^4-63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+6*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+25*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+6*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+25*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+82*B*cos(d*x+c)^4*a*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b^2","B"
358,1,2683,282,2.184000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+5*A*cos(d*x+c)^3*b^3-3*B*cos(d*x+c)^3*a^3-3*b^3*B+9*B*cos(d*x+c)^3*b^3-6*B*cos(d*x+c)^2*b^3+20*A*cos(d*x+c)^3*a*b^2-25*A*cos(d*x+c)^2*a*b^2+9*B*cos(d*x+c)^4*a*b^2+3*B*cos(d*x+c)^3*a^2*b-9*B*cos(d*x+c)^2*a^2*b-9*B*cos(d*x+c)*a*b^2-5*A*cos(d*x+c)*b^3+20*A*cos(d*x+c)^4*a^2*b+5*A*cos(d*x+c)^4*a*b^2-20*A*cos(d*x+c)^3*a^2*b+6*B*cos(d*x+c)^4*a^2*b+3*B*cos(d*x+c)^4*a^3+3*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+12*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-3*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+20*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-20*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-20*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+3*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+12*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-3*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+20*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-20*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-20*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+15*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+15*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-3*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-3*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b","B"
359,1,2337,346,2.053000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(-1+cos(d*x+c))^2*(-4*B*cos(d*x+c)^2*a^2+4*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+6*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-4*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+6*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)^2*b^2-b^2*B+3*A*cos(d*x+c)^2*b^2-3*A*cos(d*x+c)*b^2-3*A*cos(d*x+c)^2*a*b+B*cos(d*x+c)^3*a*b+4*B*cos(d*x+c)^2*a*b-5*B*cos(d*x+c)*a*b+3*A*cos(d*x+c)^3*a*b+4*B*cos(d*x+c)^3*a^2+6*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-3*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-4*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-3*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+6*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+3*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+3*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5","B"
360,1,2196,332,2.042000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-4*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-2*b^2*B+6*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b-2*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+A*cos(d*x+c)^2*a*b-A*cos(d*x+c)*a*b+2*B*cos(d*x+c)^2*a*b-2*B*cos(d*x+c)*a*b+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*b^2*B*cos(d*x+c)-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-A*cos(d*x+c)^2*a^2+A*cos(d*x+c)^3*a^2+2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2+6*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-2*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
361,1,2439,387,1.910000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+8*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-4*B*cos(d*x+c)^2*a^2+5*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-16*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+5*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+5*A*cos(d*x+c)^2*b^2-5*A*cos(d*x+c)*b^2+24*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b-5*A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+4*B*cos(d*x+c)^2*a*b-4*B*cos(d*x+c)*a*b-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-8*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+7*A*cos(d*x+c)^3*a*b+4*B*cos(d*x+c)^3*a^2+8*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+6*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-4*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+5*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-16*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-2*A*cos(d*x+c)^2*a^2+2*A*cos(d*x+c)^4*a^2+5*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-8*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+8*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
362,1,3142,475,2.146000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/24/d*(-1+cos(d*x+c))^2*(16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+8*A*cos(d*x+c)^3*a^3-16*A*cos(d*x+c)^2*a^3+3*A*cos(d*x+c)^2*b^3-12*B*cos(d*x+c)^2*a^3+17*A*cos(d*x+c)^3*a*b^2-6*A*cos(d*x+c)^2*a^2*b-3*A*cos(d*x+c)^2*a*b^2-16*A*cos(d*x+c)*a^2*b-14*A*cos(d*x+c)*a*b^2+42*B*cos(d*x+c)^3*a^2*b-30*B*cos(d*x+c)^2*a^2*b+30*B*cos(d*x+c)^2*a*b^2-12*B*cos(d*x+c)*a^2*b-30*B*cos(d*x+c)*a*b^2-3*A*cos(d*x+c)*b^3+22*A*cos(d*x+c)^4*a^2*b+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+12*B*cos(d*x+c)^4*a^3-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+72*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-52*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+14*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+36*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+12*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+30*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+30*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+8*A*cos(d*x+c)^5*a^3-48*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+30*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+72*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-52*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+14*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+16*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+36*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b+30*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c))*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
363,1,5368,524,4.067000," ","int(sec(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","B"
364,1,4395,431,3.132000," ","int(sec(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-2/315/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-180*A*cos(d*x+c)^2*a*b^4-170*B*cos(d*x+c)^2*a^2*b^3-130*B*cos(d*x+c)*a*b^4-82*B*cos(d*x+c)^3*a*b^4-30*A*cos(d*x+c)^3*b^5-45*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+5*B*cos(d*x+c)^6*a^4*b+279*B*cos(d*x+c)^6*a^3*b^2+163*B*cos(d*x+c)^6*a^2*b^3+147*B*cos(d*x+c)^6*a*b^4-10*B*cos(d*x+c)^5*a^4*b-199*B*cos(d*x+c)^5*a^3*b^2+279*B*cos(d*x+c)^5*a^2*b^3+65*B*cos(d*x+c)^5*a*b^4+5*B*cos(d*x+c)^4*a^4*b-35*B*b^5+45*A*cos(d*x+c)^6*a^4*b+135*A*cos(d*x+c)^6*a^3*b^2+435*A*cos(d*x+c)^6*a^2*b^3+75*A*cos(d*x+c)^6*a*b^4-45*A*cos(d*x+c)^5*a^4*b+45*A*cos(d*x+c)^5*a^3*b^2-165*A*cos(d*x+c)^5*a^2*b^3+435*A*cos(d*x+c)^5*a*b^4-180*A*cos(d*x+c)^4*a^3*b^2-330*A*cos(d*x+c)^4*a*b^4-270*A*cos(d*x+c)^3*a^2*b^3-272*B*cos(d*x+c)^4*a^2*b^3-80*B*cos(d*x+c)^3*a^3*b^2+75*A*cos(d*x+c)^5*b^5+10*B*cos(d*x+c)^5*a^5-10*B*cos(d*x+c)^6*a^5-98*B*cos(d*x+c)^4*b^5-45*A*cos(d*x+c)*b^5+147*B*cos(d*x+c)^5*b^5-14*B*cos(d*x+c)^2*b^5-279*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-279*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-10*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+155*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+279*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+261*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+75*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+10*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+75*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+10*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^5-147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5+147*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^5-45*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-435*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-435*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+45*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+405*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+435*A*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+10*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-279*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-279*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-147*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-10*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b+155*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+279*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+261*B*cos(d*x+c)^5*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4-45*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b-45*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2-435*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3-435*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+45*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b^2+405*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^3+435*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^4+10*B*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4*b)/(b+a*cos(d*x+c))/cos(d*x+c)^4/sin(d*x+c)^5/b^2","B"
365,1,3637,350,2.689000," ","int(sec(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"2/105/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-161*A*cos(d*x+c)^5*a^3*b-77*A*cos(d*x+c)^5*a^2*b^2-63*A*cos(d*x+c)^5*a*b^3-45*B*cos(d*x+c)^5*a^3*b-145*B*cos(d*x+c)^5*a^2*b^2+161*A*cos(d*x+c)^4*a^3*b-161*A*cos(d*x+c)^4*a^2*b^2-15*B*cos(d*x+c)^4*a^3*b+238*A*cos(d*x+c)^3*a^2*b^2+60*B*cos(d*x+c)^3*a^3*b+110*B*cos(d*x+c)^3*a*b^3+90*B*cos(d*x+c)^2*a^2*b^2+60*B*cos(d*x+c)*a*b^3+98*A*cos(d*x+c)^2*a*b^3+42*A*cos(d*x+c)^3*b^4-25*B*cos(d*x+c)^4*b^4+10*B*cos(d*x+c)^2*b^4-145*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-35*A*cos(d*x+c)^4*a*b^3-25*B*cos(d*x+c)^5*a*b^3+55*B*cos(d*x+c)^4*a^2*b^2+15*B*b^4+15*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+145*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+145*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-15*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-135*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-145*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+161*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+161*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-161*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-119*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+15*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+145*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+145*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-15*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-135*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-15*B*cos(d*x+c)^5*a^4-105*A*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-105*A*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+161*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+161*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-161*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-119*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-63*A*cos(d*x+c)^4*b^4+15*B*cos(d*x+c)^4*a^4+21*A*cos(d*x+c)*b^4+63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-63*A*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+15*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-25*B*sin(d*x+c)*cos(d*x+c)^4*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-63*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4+15*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-25*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-145*B*cos(d*x+c)^4*a*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^3/sin(d*x+c)^5/b","B"
366,1,3285,403,2.421000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+5*A*cos(d*x+c)^3*b^3-23*B*cos(d*x+c)^3*a^3-3*b^3*B+9*B*cos(d*x+c)^3*b^3-6*B*cos(d*x+c)^2*b^3+35*A*cos(d*x+c)^3*a*b^2-40*A*cos(d*x+c)^2*a*b^2+9*B*cos(d*x+c)^4*a*b^2+23*B*cos(d*x+c)^3*a^2*b-34*B*cos(d*x+c)^2*a^2*b-14*B*cos(d*x+c)*a*b^2-5*A*cos(d*x+c)*b^3+5*B*cos(d*x+c)^3*a*b^2+35*A*cos(d*x+c)^4*a^2*b+5*A*cos(d*x+c)^4*a*b^2-35*A*cos(d*x+c)^3*a^2*b+11*B*cos(d*x+c)^4*a^2*b+23*B*cos(d*x+c)^4*a^3+23*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+17*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-23*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+35*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-35*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-35*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+23*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+17*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-23*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+35*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-35*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-35*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+45*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+45*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-15*A*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+30*A*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+15*B*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-15*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+30*A*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+15*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-23*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-23*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5","B"
367,1,3215,396,2.285000," ","int(cos(d*x+c)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/3/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-14*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-3*A*cos(d*x+c)^3*a^3+3*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-6*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+12*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3-2*b^3*B+6*A*cos(d*x+c)^2*b^3+2*B*cos(d*x+c)^2*b^3+6*A*cos(d*x+c)^3*a*b^2-3*A*cos(d*x+c)^2*a^2*b-6*A*cos(d*x+c)^2*a*b^2+14*B*cos(d*x+c)^3*a^2*b-14*B*cos(d*x+c)^2*a^2*b+14*B*cos(d*x+c)^2*a*b^2-16*B*cos(d*x+c)*a*b^2+3*A*cos(d*x+c)^4*a^3+30*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b-6*A*cos(d*x+c)*b^3+2*B*cos(d*x+c)^3*a*b^2+3*A*cos(d*x+c)^3*a^2*b-6*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+18*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+3*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-6*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+18*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+14*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-14*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+14*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-14*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-18*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+30*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-18*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+18*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+3*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+18*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b-14*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-6*B*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+6*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/sin(d*x+c)^5/(b+a*cos(d*x+c))/cos(d*x+c)","B"
368,1,3271,409,2.420000," ","int(cos(d*x+c)^2*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"1/4/d*(-1+cos(d*x+c))^2*(-8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+2*A*cos(d*x+c)^2*a^3-4*B*cos(d*x+c)^3*a^3+8*b^3*B+4*B*cos(d*x+c)^2*a^3+9*A*cos(d*x+c)^2*a^2*b-9*A*cos(d*x+c)^2*a*b^2+2*A*cos(d*x+c)*a^2*b+9*A*cos(d*x+c)*a*b^2-4*B*cos(d*x+c)^2*a^2*b-8*B*cos(d*x+c)^2*a*b^2+4*B*cos(d*x+c)*a^2*b+8*B*cos(d*x+c)*a*b^2-2*A*cos(d*x+c)^4*a^3-11*A*cos(d*x+c)^3*a^2*b-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+24*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-9*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-9*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+24*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-24*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+8*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-2*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+24*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-9*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-9*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b-4*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-30*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-40*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b-8*B*cos(d*x+c)*b^3-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-8*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-4*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-40*B*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
369,1,3511,473,2.237000," ","int(cos(d*x+c)^3*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"1/24/d*(-1+cos(d*x+c))^2*(-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-8*A*cos(d*x+c)^3*a^3+16*A*cos(d*x+c)^2*a^3-33*A*cos(d*x+c)^2*b^3+12*B*cos(d*x+c)^2*a^3-59*A*cos(d*x+c)^3*a*b^2+18*A*cos(d*x+c)^2*a^2*b+33*A*cos(d*x+c)^2*a*b^2+16*A*cos(d*x+c)*a^2*b+26*A*cos(d*x+c)*a*b^2-66*B*cos(d*x+c)^3*a^2*b+54*B*cos(d*x+c)^2*a^2*b-54*B*cos(d*x+c)^2*a*b^2+12*B*cos(d*x+c)*a^2*b+54*B*cos(d*x+c)*a*b^2+33*A*cos(d*x+c)*b^3-34*A*cos(d*x+c)^4*a^2*b-33*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-12*B*cos(d*x+c)^4*a^3+48*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-120*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+76*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-26*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-33*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-180*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-12*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-54*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-54*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-33*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-8*A*cos(d*x+c)^5*a^3+144*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-54*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-120*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+76*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-26*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-16*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-33*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-180*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b-54*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+144*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+48*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-48*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5","B"
370,1,4231,568,2.285000," ","int(cos(d*x+c)^4*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/192/d*(-1+cos(d*x+c))^2*(15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)+184*A*cos(d*x+c)^5*a^3*b+254*A*cos(d*x+c)^4*a^2*b^2+272*B*cos(d*x+c)^4*a^3*b-264*B*cos(d*x+c)^2*a^2*b^2+264*B*cos(d*x+c)^2*a*b^3-128*B*cos(d*x+c)*a^3*b-208*B*cos(d*x+c)*a^2*b^2-264*B*cos(d*x+c)*a*b^3-284*A*cos(d*x+c)^2*a^3*b-15*A*cos(d*x+c)^2*a*b^3-284*A*cos(d*x+c)*a^2*b^2-118*A*cos(d*x+c)*a*b^3+15*A*cos(d*x+c)^2*b^4-128*B*cos(d*x+c)^2*a^4+64*B*cos(d*x+c)^3*a^4-72*A*cos(d*x+c)^2*a^4-144*B*cos(d*x+c)^2*a^3*b+172*A*cos(d*x+c)^3*a^3*b+133*A*cos(d*x+c)^3*a*b^3+30*A*cos(d*x+c)^2*a^2*b^2-72*A*cos(d*x+c)*a^3*b+472*B*cos(d*x+c)^3*a^2*b^2-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)+48*A*cos(d*x+c)^6*a^4-30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4+128*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+284*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+284*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+72*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-644*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+118*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+720*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+128*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+264*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+264*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-608*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+208*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-384*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+960*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+240*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+64*B*cos(d*x+c)^5*a^4+128*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)-144*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+288*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+24*A*cos(d*x+c)^4*a^4-15*A*cos(d*x+c)*b^4+720*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))+128*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+264*B*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+264*B*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-608*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+208*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-384*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+960*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*b+240*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^3+284*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+284*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+15*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+72*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-644*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+118*A*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+15*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-144*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+288*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
371,1,2499,299,2.569000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/15/d*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+5*A*cos(d*x+c)^3*b^3-8*B*cos(d*x+c)^3*a^3-3*b^3*B+9*B*cos(d*x+c)^3*b^3-6*B*cos(d*x+c)^2*b^3-10*A*cos(d*x+c)^3*a*b^2+5*A*cos(d*x+c)^2*a*b^2+9*B*cos(d*x+c)^4*a*b^2+8*B*cos(d*x+c)^3*a^2*b-4*B*cos(d*x+c)^2*a^2*b+B*cos(d*x+c)*a*b^2-5*A*cos(d*x+c)*b^3-10*B*cos(d*x+c)^3*a*b^2-10*A*cos(d*x+c)^4*a^2*b+5*A*cos(d*x+c)^4*a*b^2+10*A*cos(d*x+c)^3*a^2*b-4*B*cos(d*x+c)^4*a^2*b+8*B*cos(d*x+c)^4*a^3+8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+2*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-10*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+10*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+10*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+8*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+2*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b-10*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2+10*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b+10*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-8*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3-8*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3-9*B*sin(d*x+c)*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+5*A*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+9*B*sin(d*x+c)*cos(d*x+c)^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)^5/b^3","B"
372,1,1563,235,2.301000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right)^{2} \left(2 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+3 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}-3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +2 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +2 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -2 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -b^{2} B -2 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 A \cos \left(d x +c \right) b^{2}+B \left(\cos^{3}\left(d x +c \right)\right) a b -2 B \left(\cos^{2}\left(d x +c \right)\right) a b +B \cos \left(d x +c \right) a b -3 A \left(\cos^{2}\left(d x +c \right)\right) a b +3 A \left(\cos^{3}\left(d x +c \right)\right) a b -2 B \left(\cos^{3}\left(d x +c \right)\right) a^{2}+B \left(\cos^{2}\left(d x +c \right)\right) b^{2}-3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+3 A \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+2 B \left(\cos^{2}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+2 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}+B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2}}{3 d \left(b +a \cos \left(d x +c \right)\right) \cos \left(d x +c \right) \sin \left(d x +c \right)^{5} b^{2}}"," ",0,"-2/3/d*(-1+cos(d*x+c))^2*(2*B*cos(d*x+c)^2*a^2-2*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)^2*b^2-b^2*B+3*A*cos(d*x+c)^2*b^2-3*A*cos(d*x+c)*b^2-3*A*cos(d*x+c)^2*a*b+B*cos(d*x+c)^3*a*b-2*B*cos(d*x+c)^2*a*b+B*cos(d*x+c)*a*b+3*A*cos(d*x+c)^3*a*b-2*B*cos(d*x+c)^3*a^2-3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+2*B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)^2*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+2*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)^5/b^2","B"
373,1,829,192,2.137000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right)^{2} \left(A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a -B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b +B \left(\cos^{2}\left(d x +c \right)\right) a -B \cos \left(d x +c \right) a +b B \cos \left(d x +c \right)-B b \right)}{d \sin \left(d x +c \right)^{5} \left(b +a \cos \left(d x +c \right)\right) b}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))^2*(A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)^2*a-B*cos(d*x+c)*a+b*B*cos(d*x+c)-B*b)/sin(d*x+c)^5/(b+a*cos(d*x+c))/b","B"
374,1,215,190,2.010000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-1+\cos \left(d x +c \right)\right) \left(A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)-2 A \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right)-B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right)\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{2}}"," ",0,"-2/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1+cos(d*x+c))^2*(-1+cos(d*x+c))*(A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-2*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))-B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2)))/(b+a*cos(d*x+c))/sin(d*x+c)^2","A"
375,1,1025,319,2.170000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b -2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b +4 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a -2 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)-2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(d x +c \right)+4 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a \sin \left(d x +c \right)-2 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a +A \left(\cos^{3}\left(d x +c \right)\right) a -A \left(\cos^{2}\left(d x +c \right)\right) a +A \left(\cos^{2}\left(d x +c \right)\right) b -A \cos \left(d x +c \right) b \right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} a}"," ",0,"-1/d*(-1+cos(d*x+c))^2*(A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a-2*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b*sin(d*x+c)-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+A*cos(d*x+c)^3*a-A*cos(d*x+c)^2*a+A*cos(d*x+c)^2*b-A*cos(d*x+c)*b)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a","B"
376,1,1886,394,2.164000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-4 B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-3 A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+8 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+6 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-3 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+4 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-4 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)+2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -2 A \left(\cos^{2}\left(d x +c \right)\right) a^{2}+2 A \left(\cos^{4}\left(d x +c \right)\right) a^{2}+4 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +3 A \cos \left(d x +c \right) b^{2}-8 B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a b +4 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+4 B \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \cos \left(d x +c \right) a b -4 B \cos \left(d x +c \right) a b +3 A \left(\cos^{2}\left(d x +c \right)\right) a b +6 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-4 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}-8 B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-A \left(\cos^{3}\left(d x +c \right)\right) a b +4 B \left(\cos^{3}\left(d x +c \right)\right) a^{2}+8 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-3 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+4 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}\right) \left(1+\cos \left(d x +c \right)\right)^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{5} a^{2}}"," ",0,"-1/4/d*(-1+cos(d*x+c))^2*(6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-4*B*cos(d*x+c)^2*a^2-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+2*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-3*A*cos(d*x+c)^2*b^2+3*A*cos(d*x+c)*b^2-8*B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b+3*A*cos(d*x+c)^2*a*b-2*A*cos(d*x+c)*a*b+4*B*cos(d*x+c)^2*a*b-4*B*cos(d*x+c)*a*b-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-A*cos(d*x+c)^3*a*b+4*B*cos(d*x+c)^3*a^2+8*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+6*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-4*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-2*A*cos(d*x+c)^2*a^2+2*A*cos(d*x+c)^4*a^2-3*A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+4*B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a^2","B"
377,1,2954,480,2.311000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","\text{output too large to display}"," ",0,"1/24/d*(-1+cos(d*x+c))^2*(-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-8*A*cos(d*x+c)^3*a^3+16*A*cos(d*x+c)^2*a^3-15*A*cos(d*x+c)^2*b^3+12*B*cos(d*x+c)^2*a^3-5*A*cos(d*x+c)^3*a*b^2-18*A*cos(d*x+c)^2*a^2*b+15*A*cos(d*x+c)^2*a*b^2+16*A*cos(d*x+c)*a^2*b-10*A*cos(d*x+c)*a*b^2+6*B*cos(d*x+c)^3*a^2*b-18*B*cos(d*x+c)^2*a^2*b+18*B*cos(d*x+c)^2*a*b^2+12*B*cos(d*x+c)*a^2*b-18*B*cos(d*x+c)*a*b^2+15*A*cos(d*x+c)*b^3+2*A*cos(d*x+c)^4*a^2*b-15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-12*B*cos(d*x+c)^4*a^3+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+24*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+10*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-36*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-12*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+18*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+18*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3-16*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-48*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)-8*A*cos(d*x+c)^5*a^3+18*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+24*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+4*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+10*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-16*A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-36*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b+18*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b)*(1+cos(d*x+c))^2*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^5/a^3","B"
378,1,3333,301,2.549000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/3/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-3*A*cos(d*x+c)^3*a^2*b^2+4*B*cos(d*x+c)^3*a^3*b-B*cos(d*x+c)^3*a*b^3-4*B*cos(d*x+c)^2*a^2*b^2+5*B*cos(d*x+c)^2*a*b^3+4*B*cos(d*x+c)*a^3*b-4*B*cos(d*x+c)*a*b^3-6*A*cos(d*x+c)^2*a^3*b+3*A*cos(d*x+c)^2*a*b^3-3*A*cos(d*x+c)*a^2*b^2+6*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-3*A*cos(d*x+c)^2*b^4-B*cos(d*x+c)^2*b^4+8*B*cos(d*x+c)^2*a^4-8*B*cos(d*x+c)^3*a^4-8*B*cos(d*x+c)^2*a^3*b+6*A*cos(d*x+c)^3*a^3*b-3*A*cos(d*x+c)^3*a*b^3+6*A*cos(d*x+c)^2*a^2*b^2+5*B*cos(d*x+c)^3*a^2*b^2+B*b^4+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-a^2*b^2*B-3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4-6*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-6*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b+3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-8*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-2*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+8*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-5*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-5*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+3*A*cos(d*x+c)*b^4+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-5*B*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-5*B*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+5*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-6*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-6*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+3*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+6*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+3*A*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+8*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4-3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4-B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4+3*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4)/(b+a*cos(d*x+c))/sin(d*x+c)/cos(d*x+c)/(a-b)/(a+b)/b^3","B"
379,1,2276,255,2.309000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-b^3*B+a^2*b*B-2*B*cos(d*x+c)^2*a^3+2*B*cos(d*x+c)*a^3+A*cos(d*x+c)^2*a^2*b-A*cos(d*x+c)^2*a*b^2-A*cos(d*x+c)*a^2*b+A*cos(d*x+c)*a*b^2+B*cos(d*x+c)^2*a^2*b+B*cos(d*x+c)^2*a*b^2-2*B*cos(d*x+c)*a^2*b-B*cos(d*x+c)*a*b^2+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^3+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^3-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*b^3+B*cos(d*x+c)*b^3-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2-B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b+2*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3)/(b+a*cos(d*x+c))/sin(d*x+c)/b^2/(a+b)/(a-b)","B"
380,1,1633,234,2.108000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}-B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-A \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)-A \left(\cos^{2}\left(d x +c \right)\right) a b +A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+B \left(\cos^{2}\left(d x +c \right)\right) a^{2}-B \left(\cos^{2}\left(d x +c \right)\right) a b +A \cos \left(d x +c \right) a b -A \cos \left(d x +c \right) b^{2}-B \cos \left(d x +c \right) a^{2}+B \cos \left(d x +c \right) a b \right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b \left(a +b \right) \left(a -b \right)}"," ",0,"1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-A*cos(d*x+c)^2*a*b+A*cos(d*x+c)^2*b^2+B*cos(d*x+c)^2*a^2-B*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b-A*cos(d*x+c)*b^2-B*cos(d*x+c)*a^2+B*cos(d*x+c)*a*b)/(b+a*cos(d*x+c))/sin(d*x+c)/b/(a+b)/(a-b)","B"
381,1,2010,347,2.098000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\sqrt{4}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(B \left(\cos^{2}\left(d x +c \right)\right) a^{2}+A \left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-2 A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2} \sin \left(d x +c \right)-B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sin \left(d x +c \right)-A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b +A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b -B \cos \left(d x +c \right) a^{2}-A \cos \left(d x +c \right) b^{2}-B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-B \left(\cos^{2}\left(d x +c \right)\right) a b +A \cos \left(d x +c \right) a b +B \cos \left(d x +c \right) a b -A \left(\cos^{2}\left(d x +c \right)\right) a b -2 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) b^{2}-A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+B \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+2 A \cos \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, -1, \sqrt{\frac{a -b}{a +b}}\right) \sin \left(d x +c \right) a^{2}+B \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2} \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right)+B \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)-A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+A \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a b \sin \left(d x +c \right)+A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) b^{2}-B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{\cos \left(d x +c \right)}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{-1+\cos \left(d x +c \right)}{\sin \left(d x +c \right)}, \sqrt{\frac{a -b}{a +b}}\right) a^{2}\right)}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \left(a +b \right) \left(a -b \right)}"," ",0,"-1/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+B*cos(d*x+c)^2*a^2+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b-B*cos(d*x+c)*a^2+A*cos(d*x+c)^2*b^2-A*cos(d*x+c)*b^2-A*cos(d*x+c)^2*a*b+A*cos(d*x+c)*a*b-B*cos(d*x+c)^2*a*b+B*cos(d*x+c)*a*b-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-2*A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2-A*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2-A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b*sin(d*x+c)+A*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^2-B*cos(d*x+c)*sin(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2+B*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a+b)/(a-b)","B"
382,1,2871,396,2.116000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/2/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+A*cos(d*x+c)^3*a^3-A*cos(d*x+c)^2*a^3-3*A*cos(d*x+c)^2*b^3-A*cos(d*x+c)^3*a*b^2+A*cos(d*x+c)^2*a^2*b+3*A*cos(d*x+c)^2*a*b^2-A*cos(d*x+c)*a^2*b-2*A*cos(d*x+c)*a*b^2-2*B*cos(d*x+c)^2*a^2*b+2*B*cos(d*x+c)^2*a*b^2+2*B*cos(d*x+c)*a^2*b-2*B*cos(d*x+c)*a*b^2+3*A*cos(d*x+c)*b^3-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)-2*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b*sin(d*x+c)+2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^2*sin(d*x+c)+6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^3+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+6*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^3*sin(d*x+c)-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*sin(d*x+c)+2*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a-6*A*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+2*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b+2*A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a+A*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b-3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^2-2*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b+2*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*a^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b)/(b+a*cos(d*x+c))/sin(d*x+c)/a^2/(a+b)/(a-b)","B"
383,1,3980,486,2.872000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"-1/8/d*4^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)-2*A*cos(d*x+c)^4*a^2*b^2+12*B*cos(d*x+c)^2*a^2*b^2-12*B*cos(d*x+c)^2*a*b^3-4*B*cos(d*x+c)*a^3*b-8*B*cos(d*x+c)*a^2*b^2+12*B*cos(d*x+c)*a*b^3+7*A*cos(d*x+c)^2*a^3*b-15*A*cos(d*x+c)^2*a*b^3+7*A*cos(d*x+c)*a^2*b^2+10*A*cos(d*x+c)*a*b^3+15*A*cos(d*x+c)^2*b^4-4*B*cos(d*x+c)^2*a^4+4*B*cos(d*x+c)^3*a^4-2*A*cos(d*x+c)^2*a^4+4*B*cos(d*x+c)^2*a^3*b-5*A*cos(d*x+c)^3*a^3*b+5*A*cos(d*x+c)^3*a*b^3-5*A*cos(d*x+c)^2*a^2*b^2-2*A*cos(d*x+c)*a^3*b-4*B*cos(d*x+c)^3*a^2*b^2-30*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4*sin(d*x+c)-30*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*b^4+4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-7*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-7*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+15*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+2*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-10*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+22*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-12*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+8*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+24*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+8*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4*sin(d*x+c)+2*A*cos(d*x+c)^4*a^4-15*A*cos(d*x+c)*b^4+22*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))+4*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-12*B*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-12*B*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+8*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^3*b+24*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a*b^3-7*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-7*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2+15*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+2*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-4*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))-10*A*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+15*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b^4-4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4+8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))/sin(d*x+c),-1,((a-b)/(a+b))^(1/2))*a^4)/(b+a*cos(d*x+c))/sin(d*x+c)/a^3/(a+b)/(a-b)","B"
384,1,5086,581,2.925000," ","int(cos(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
385,1,8044,476,3.432000," ","int(sec(d*x+c)^4*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
386,1,6455,387,2.676000," ","int(sec(d*x+c)^3*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
387,1,5170,357,2.139000," ","int(sec(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
388,1,4213,323,1.977000," ","int(sec(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-1/3/d*4^(1/2)*(A*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4+3*A*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-5*A*cos(d*x+c)^3*a^2*b^2+2*B*cos(d*x+c)^3*a^3*b+2*B*cos(d*x+c)^3*a*b^3+4*B*cos(d*x+c)^2*a^2*b^2-6*B*cos(d*x+c)^2*a*b^3-B*cos(d*x+c)*a^2*b^2+4*B*cos(d*x+c)*a*b^3-4*A*cos(d*x+c)^2*a^3*b-4*A*cos(d*x+c)^2*a*b^3-3*A*cos(d*x+c)*a^2*b^2+4*A*cos(d*x+c)*a*b^3+4*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+A*cos(d*x+c)^3*b^4+3*B*cos(d*x+c)^2*b^4+B*cos(d*x+c)^2*a^4-B*cos(d*x+c)^3*a^4-2*B*cos(d*x+c)^2*a^3*b+4*A*cos(d*x+c)^3*a^3*b+8*A*cos(d*x+c)^2*a^2*b^2-3*B*cos(d*x+c)^3*a^2*b^2-3*B*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4+3*B*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4+B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^4-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+3*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+4*A*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b*sin(d*x+c)+B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)+3*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2*sin(d*x+c)-4*B*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3*sin(d*x+c)-3*B*cos(d*x+c)*b^4+3*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4-4*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-4*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b-4*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2-3*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b+3*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^2+3*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3-A*cos(d*x+c)*b^4+2*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b+4*B*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+6*B*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a-B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^3*b-5*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-7*B*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3-4*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b-8*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a^2*b^2-4*A*sin(d*x+c)*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a*b^3+3*A*a^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*b+7*A*a^2*b^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))+5*A*b^3*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*a+B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4+A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4-3*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))/sin(d*x+c),((a-b)/(a+b))^(1/2))*cos(d*x+c)*(cos(d*x+c)/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^4)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)^2/(a+b)^2/b","B"
389,1,5712,456,2.034000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
390,1,8545,541,2.010000," ","int(cos(d*x+c)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
391,1,10322,637,2.398000," ","int(cos(d*x+c)^2*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
392,1,642,96,2.011000," ","int(sec(f*x+e)*(A+A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 A \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(2 \cos \left(f x +e \right) \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b -\cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) a -\cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b +2 \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) b \sin \left(f x +e \right)-\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) a -\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b +a \left(\cos^{2}\left(f x +e \right)\right)-a \cos \left(f x +e \right)+b \cos \left(f x +e \right)-b \right)}{f \sin \left(f x +e \right)^{5} \left(b +a \cos \left(f x +e \right)\right) b}"," ",0,"-2*A/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(2*cos(f*x+e)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b-cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*a-cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b+2*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*EllipticF((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*b*sin(f*x+e)-EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*a-EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b+a*cos(f*x+e)^2-a*cos(f*x+e)+b*cos(f*x+e)-b)/sin(f*x+e)^5/(b+a*cos(f*x+e))/b","B"
393,1,457,98,1.923000," ","int(sec(f*x+e)*(A-A*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x)","-\frac{2 A \sqrt{\frac{b +a \cos \left(f x +e \right)}{\cos \left(f x +e \right)}}\, \left(1+\cos \left(f x +e \right)\right)^{2} \left(-1+\cos \left(f x +e \right)\right)^{2} \left(\cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) a +\cos \left(f x +e \right) \EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b +\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) a +\EllipticE \left(\frac{-1+\cos \left(f x +e \right)}{\sin \left(f x +e \right)}, \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{\cos \left(f x +e \right)}{1+\cos \left(f x +e \right)}}\, \sqrt{\frac{b +a \cos \left(f x +e \right)}{\left(1+\cos \left(f x +e \right)\right) \left(a +b \right)}}\, \sin \left(f x +e \right) b -a \left(\cos^{2}\left(f x +e \right)\right)+a \cos \left(f x +e \right)-b \cos \left(f x +e \right)+b \right)}{f \sin \left(f x +e \right)^{5} \left(b +a \cos \left(f x +e \right)\right) b}"," ",0,"-2*A/f*((b+a*cos(f*x+e))/cos(f*x+e))^(1/2)*(1+cos(f*x+e))^2*(-1+cos(f*x+e))^2*(cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*a+cos(f*x+e)*EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b+EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*a+EllipticE((-1+cos(f*x+e))/sin(f*x+e),((a-b)/(a+b))^(1/2))*(cos(f*x+e)/(1+cos(f*x+e)))^(1/2)*((b+a*cos(f*x+e))/(1+cos(f*x+e))/(a+b))^(1/2)*sin(f*x+e)*b-a*cos(f*x+e)^2+a*cos(f*x+e)-b*cos(f*x+e)+b)/sin(f*x+e)^5/(b+a*cos(f*x+e))/b","B"
394,1,663,208,12.436000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 \left(A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 B b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*B*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
395,1,428,179,9.666000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 B b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
396,1,244,153,4.593000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{2 \left(A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 B b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-2*B*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
397,1,326,153,4.167000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -2 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b-2*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+3*B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
398,1,371,180,4.342000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a A +20 A b +20 a B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a A -10 A b -10 a B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a+20*A*b+20*B*a)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a-10*A*b-10*B*a)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
399,1,413,208,4.535000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a A -168 A b -168 a B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a A +168 A b +168 a B +140 B b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a A -42 A b -42 a B -70 B b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +35 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*A*a-168*A*b-168*B*a)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a+168*A*b+168*B*a+140*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*A*a-42*A*b-42*B*a-70*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b+35*B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
400,1,859,287,16.161000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{2} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 a^{2} A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 a \left(2 A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b \left(A b +2 a B \right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^2*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*a^2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a*(2*A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b*(A*b+2*B*a)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
401,1,750,249,13.532000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 a \left(2 A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 b^{2} B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+2 b \left(A b +2 a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a*(2*A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*b^2*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b*(A*b+2*B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
402,1,677,211,10.251000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{4 A a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b \left(A b +2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 b^{2} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4*A*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*b*(A*b+2*B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*b^2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
403,1,404,197,4.633000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","-\frac{2 \left(4 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -2 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}-6 B \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2-6*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
404,1,487,203,4.781000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a^{2} A +40 A a b +20 a^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a^{2} A -20 A a b -10 a^{2} B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 A a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+5 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+15 b^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-30 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a^2+40*A*a*b+20*B*a^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a^2-20*A*a*b-10*B*a^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*A*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+5*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+15*b^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-30*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
405,1,548,241,4.632000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{2} A -336 A a b -168 a^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{2} A +336 A a b +140 A \,b^{2}+168 a^{2} B +280 B a b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{2} A -84 A a b -70 A \,b^{2}-42 a^{2} B -140 B a b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-126 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +70 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-105 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*A*a^2-336*A*a*b-168*B*a^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a^2+336*A*a*b+140*A*b^2+168*B*a^2+280*B*a*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*A*a^2-84*A*a*b-70*A*b^2-42*B*a^2-140*B*a*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+35*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-126*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+70*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-105*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
406,1,610,278,4.659000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 a^{2} A +1440 A a b +720 a^{2} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 a^{2} A -2160 A a b -504 A \,b^{2}-1080 a^{2} B -1008 B a b \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 a^{2} A +1680 A a b +504 A \,b^{2}+840 a^{2} B +1008 B a b +420 b^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 a^{2} A -480 A a b -126 A \,b^{2}-240 a^{2} B -252 B a b -210 b^{2} B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-147 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-189 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+150 A a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-378 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +75 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 b^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*A*a^2+1440*A*a*b+720*B*a^2)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*A*a^2-2160*A*a*b-504*A*b^2-1080*B*a^2-1008*B*a*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*A*a^2+1680*A*a*b+504*A*b^2+840*B*a^2+1008*B*a*b+420*B*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*A*a^2-480*A*a*b-126*A*b^2-240*B*a^2-252*B*a*b-210*B*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-147*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-189*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+150*A*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-378*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+75*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
407,1,1193,365,20.417000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 b^{2} \left(A b +3 a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 b^{3} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{144 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{5}}-\frac{7 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{180 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{3}}-\frac{14 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)}{15 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+2 a^{2} \left(3 A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 A \,a^{3} \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{6 a b \left(A b +a B \right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*b^2*(A*b+3*B*a)*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*b^3*B*(-1/144*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^5-7/180*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^3-14/15*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)/(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)+7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-7/15*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))))+2*a^2*(3*A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*A*a^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-6/5*a*b*(A*b+B*a)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
408,1,944,319,16.359000," ","int(sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+2 b^{3} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+6 a b \left(A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 a^{2} \left(3 A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 b^{2} \left(A b +3 a B \right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*b^3*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+6*a*b*(A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*a^2*(3*A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*b^2*(A*b+3*B*a)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
409,1,997,272,13.163000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{6 A \,a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{6 a b \left(A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 b^{2} \left(A b +3 a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 b^{3} B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*a*b*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*b^2*(A*b+3*B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*b^3*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
410,1,1212,269,13.405000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","\frac{2 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(8 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-18 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-8 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 A \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{2} b \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a^{3} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+18 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a \,b^{2} \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-36 B a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+2 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 a^{2} b B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-9 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+18 B a \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \,b^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{3 \left(4 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2/3*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/(4*sin(1/2*d*x+1/2*c)^4-4*sin(1/2*d*x+1/2*c)^2+1)/sin(1/2*d*x+1/2*c)^3*(8*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2+18*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-18*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2+6*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2-8*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-12*A*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+18*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^2*b*sin(1/2*d*x+1/2*c)^2+2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^3*sin(1/2*d*x+1/2*c)^2-6*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a^3*sin(1/2*d*x+1/2*c)^2+18*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*a*b^2*sin(1/2*d*x+1/2*c)^2-36*B*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3+2*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*A*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-9*a^2*b*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-9*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+18*B*a*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+2*B*b^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
411,1,867,264,5.214000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","-\frac{2 \left(-24 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, a^{2} \left(6 a A +15 A b +5 a B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A \,a^{3}+15 A \,a^{2} b +5 a^{3} B +15 b^{3} B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+15 A \,a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+15 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-9 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-45 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+5 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+45 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}-45 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b +15 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*(-24*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+4*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(6*A*a+15*A*b+5*B*a)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A*a^3+15*A*a^2*b+5*B*a^3+15*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+15*A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+15*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-9*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-45*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+5*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+45*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-45*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b+15*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
412,1,664,273,4.501000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 A \,a^{3}-504 A \,a^{2} b -168 a^{3} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 A \,a^{3}+504 A \,a^{2} b +420 A a \,b^{2}+168 a^{3} B +420 a^{2} b B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 A \,a^{3}-126 A \,a^{2} b -210 A a \,b^{2}-42 a^{3} B -210 a^{2} b B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-189 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -105 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+25 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-315 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+105 a^{2} b B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*A*a^3-504*A*a^2*b-168*B*a^3)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a^3+504*A*a^2*b+420*A*a*b^2+168*B*a^3+420*B*a^2*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*A*a^3-126*A*a^2*b-210*A*a*b^2-42*B*a^3-210*B*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-189*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-105*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3+25*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-315*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+105*a^2*b*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
413,1,745,319,4.755000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-1120 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(2240 A \,a^{3}+2160 A \,a^{2} b +720 a^{3} B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2072 A \,a^{3}-3240 A \,a^{2} b -1512 A a \,b^{2}-1080 a^{3} B -1512 a^{2} b B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(952 A \,a^{3}+2520 A \,a^{2} b +1512 A a \,b^{2}+420 A \,b^{3}+840 a^{3} B +1512 a^{2} b B +1260 B a \,b^{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-168 A \,a^{3}-720 A \,a^{2} b -378 A a \,b^{2}-210 A \,b^{3}-240 a^{3} B -378 a^{2} b B -630 B a \,b^{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+225 A \,a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+105 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-147 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-567 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+75 a^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+315 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-567 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -315 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-1120*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(2240*A*a^3+2160*A*a^2*b+720*B*a^3)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2072*A*a^3-3240*A*a^2*b-1512*A*a*b^2-1080*B*a^3-1512*B*a^2*b)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(952*A*a^3+2520*A*a^2*b+1512*A*a*b^2+420*A*b^3+840*B*a^3+1512*B*a^2*b+1260*B*a*b^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-168*A*a^3-720*A*a^2*b-378*A*a*b^2-210*A*b^3-240*B*a^3-378*B*a^2*b-630*B*a*b^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+225*A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+105*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-147*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-567*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+75*a^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+315*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-567*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-315*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
414,1,825,365,4.811000," ","int((a+b*sec(d*x+c))^3*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(20160 A \,a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{12}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-50400 A \,a^{3}-36960 A \,a^{2} b -12320 a^{3} B \right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(56880 A \,a^{3}+73920 A \,a^{2} b +23760 A a \,b^{2}+24640 a^{3} B +23760 a^{2} b B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-34920 A \,a^{3}-68376 A \,a^{2} b -35640 A a \,b^{2}-5544 A \,b^{3}-22792 a^{3} B -35640 a^{2} b B -16632 B a \,b^{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(13860 A \,a^{3}+31416 A \,a^{2} b +27720 A a \,b^{2}+5544 A \,b^{3}+10472 a^{3} B +27720 a^{2} b B +16632 B a \,b^{2}+4620 b^{3} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2790 A \,a^{3}-5544 A \,a^{2} b -7920 A a \,b^{2}-1386 A \,b^{3}-1848 a^{3} B -7920 a^{2} b B -4158 B a \,b^{2}-2310 b^{3} B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+675 A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2475 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-4851 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -2079 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{3}+2475 a^{2} b B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+1155 b^{3} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1617 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}-6237 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}\right)}{3465 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3465*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(20160*A*a^3*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^12+(-50400*A*a^3-36960*A*a^2*b-12320*B*a^3)*sin(1/2*d*x+1/2*c)^10*cos(1/2*d*x+1/2*c)+(56880*A*a^3+73920*A*a^2*b+23760*A*a*b^2+24640*B*a^3+23760*B*a^2*b)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-34920*A*a^3-68376*A*a^2*b-35640*A*a*b^2-5544*A*b^3-22792*B*a^3-35640*B*a^2*b-16632*B*a*b^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(13860*A*a^3+31416*A*a^2*b+27720*A*a*b^2+5544*A*b^3+10472*B*a^3+27720*B*a^2*b+16632*B*a*b^2+4620*B*b^3)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-2790*A*a^3-5544*A*a^2*b-7920*A*a*b^2-1386*A*b^3-1848*B*a^3-7920*B*a^2*b-4158*B*a*b^2-2310*B*b^3)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+675*A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2475*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-4851*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-2079*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^3+2475*a^2*b*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1155*b^3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1617*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3-6237*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
415,1,785,327,15.566000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \left(A b -a B \right) a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 b \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{2 \left(A b -a B \right) a \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 \left(A b -a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*(A*b-B*a)*a^3/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/5*B/b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-2*(A*b-B*a)/b^3*a*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b-B*a)/b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
416,1,466,268,11.188000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \left(A b -a B \right) a^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(A*b-B*a)*a^2/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B/b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
417,1,325,168,8.388000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \left(A b -a B \right) a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 B \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*(A*b-B*a)/b/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*B/b*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
418,1,217,145,4.437000," ","int(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \right)}{a \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b-B*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a)/a/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
419,1,295,215,4.851000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{2}-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a b \right)}{a^{2} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+A*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^2-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-B*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b)/a^2/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
420,1,786,256,4.870000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(4 A \,a^{3}-4 A \,a^{2} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 A \,a^{3}+2 A \,a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \,a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{3}-3 a^{2} b B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \,b^{2}\right)}{3 a^{3} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((4*A*a^3-4*A*a^2*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*A*a^3+2*A*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^3-3*a^2*b*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b^2)/a^3/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
421,1,1074,296,5.680000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(-24 A \,a^{4}+24 A \,a^{3} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 A \,a^{4}-44 A \,a^{3} b +20 A \,a^{2} b^{2}+20 a^{4} B -20 B \,a^{3} b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 A \,a^{4}+16 A \,a^{3} b -10 A \,a^{2} b^{2}-10 a^{4} B +10 B \,a^{3} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{4}-5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \,b^{3}+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}-5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}\right)}{15 a^{4} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((-24*A*a^4+24*A*a^3*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a^4-44*A*a^3*b+20*A*a^2*b^2+20*B*a^4-20*B*a^3*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a^4+16*A*a^3*b-10*A*a^2*b^2-10*B*a^4+10*B*a^3*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^4-5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b^3+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4-5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3)/a^4/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
422,1,1024,462,19.500000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \left(A b -2 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}-\frac{2 \left(A b -a B \right) a \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(A*b-2*B*a)/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-2*B*a)/b^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B/b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2*(A*b-B*a)*a/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
423,1,877,377,12.400000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 B \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*B/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*B/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b-B*a)/b*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
424,1,715,321,10.083000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(-A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*A/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(-A*b+B*a)/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
425,1,802,327,10.880000," ","int(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 \left(-2 A b +a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*(-2*A*b+B*a)/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)*b/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
426,1,843,347,13.447000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b \left(3 A b -2 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{2} \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{3}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a)-2/a^2*b*(3*A*b-2*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^2*(A*b-B*a)/a^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
427,1,1059,423,15.594000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\frac{8 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3}+6 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\frac{4 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-4 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{a^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(4 A b -3 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{3} \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{4}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/3/a^4*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-6*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b^2/a^3*(4*A*b-3*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^3*(A*b-B*a)/a^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
428,1,2178,627,30.140000," ","int(sec(d*x+c)^(9/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(A*b-3*B*a)/b^4/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*(A*b-B*a)*a/b^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*(A*b-3*B*a)/b^4*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B/b^3*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2*a*(A*b-2*B*a)/b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
429,1,2024,528,19.725000," ","int(sec(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*B/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)/b*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*B/b^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2*a*B/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
430,1,1768,454,16.344000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \left(-A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}+\frac{2 A \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(-A*b+B*a)/a*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*A/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
431,1,1872,454,16.602000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}+\frac{2 \left(-2 A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*A/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)*b/a^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*(-2*A*b+B*a)/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
432,1,1959,454,18.139000," ","int(sec(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*(-3*A*b+B*a)/a^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^2*(A*b-B*a)/a^3*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a^3*b*(3*A*b-2*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
433,1,2000,479,20.238000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a)-6/a^3*b*(2*A*b-B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^3*(A*b-B*a)/a^4*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-2*b^2/a^4*(4*A*b-3*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
434,1,2216,569,23.622000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/3/a^5*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+18*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-9*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+4/a^4*b^2*(5*A*b-3*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^4*(A*b-B*a)/a^5*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a^5*b^3*(5*A*b-4*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
435,1,2521,387,2.245000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b-8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a*b-B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b+4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a*b-B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+2*B*((a-b)/(a+b))^(1/2)*b^2-4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*b^2-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2+B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*b^2-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2)*(1/cos(d*x+c))^(3/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/b","C"
436,1,1431,318,2.292000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a -2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b +4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b +2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a +B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b +2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a -2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b +4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b +2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b +B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -B \sqrt{\frac{a -b}{a +b}}\, b \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-1/d*(2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b+2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b+2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-B*((a-b)/(a+b))^(1/2)*b)*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
437,1,1549,277,2.984000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(1/2),x)","-\frac{2 \left(-A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b +A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +2 B \cos \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)+A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+2 B \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -A b \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/d*(-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b+A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+2*B*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-A*b*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
438,1,1926,237,2.368000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(3/2),x)","-\frac{2 \left(-A \sqrt{\frac{a -b}{a +b}}\, a b -3 B \sqrt{\frac{a -b}{a +b}}\, a b -A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -A \sqrt{\frac{a -b}{a +b}}\, b^{2}+A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}-A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-A \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a}"," ",0,"-2/3/d*(A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-A*((a-b)/(a+b))^(1/2)*a*b-3*B*((a-b)/(a+b))^(1/2)*a*b-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+3*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-A*((a-b)/(a+b))^(1/2)*b^2+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-3*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)+2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2+A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-A*a^2*((a-b)/(a+b))^(1/2)*cos(d*x+c)-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a","B"
439,1,2737,297,2.242000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(5/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(-9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-7*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b-2*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2-5*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2-10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-2*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+5*B*a^3*((a-b)/(a+b))^(1/2)*cos(d*x+c)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b+2*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2+5*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b-5*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b+5*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*A*b^3*((a-b)/(a+b))^(1/2)+9*A*a^2*b*((a-b)/(a+b))^(1/2)+A*a*b^2*((a-b)/(a+b))^(1/2)+5*B*a^2*b*((a-b)/(a+b))^(1/2)+5*B*a*b^2*((a-b)/(a+b))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2+9*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^3-2*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3-5*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-7*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+2*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-5*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+5*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a^2","B"
440,1,3778,367,2.576000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/sec(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(-63*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+19*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b-8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-25*A*a^3*b*((a-b)/(a+b))^(1/2)-19*A*a^2*b^2*((a-b)/(a+b))^(1/2)+4*A*a*b^3*((a-b)/(a+b))^(1/2)-63*B*a^3*b*((a-b)/(a+b))^(1/2)-7*B*a^2*b^2*((a-b)/(a+b))^(1/2)+14*B*a*b^3*((a-b)/(a+b))^(1/2)+21*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4+42*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4+8*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-63*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+15*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4-8*A*b^4*((a-b)/(a+b))^(1/2)-8*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^4+25*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^4-63*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+19*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-19*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-19*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-14*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+14*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+49*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+14*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-19*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+8*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3-19*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+2*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-8*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3-63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b-14*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+14*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3+49*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+14*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+28*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b+26*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-7*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2-19*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+20*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-8*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+35*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+18*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+14*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-14*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a^3","B"
441,1,4051,466,2.289000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"-1/24/d*(3*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3+16*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3-8*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3+12*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3-30*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b-30*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b-42*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2-17*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-8*B*((a-b)/(a+b))^(1/2)*b^3-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3-22*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2+30*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2+36*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b+14*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^2*b-20*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a*b^2+3*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b-16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2+72*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-30*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+30*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+36*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+14*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b-20*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2+3*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b-16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+72*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^2*b+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a*b^2-24*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*b^3+48*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*b^3+6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^3-3*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3+16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*b^3-6*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3-24*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*b^3+48*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3+6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^3-3*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3+16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3-6*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3+30*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b+12*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2+14*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b+16*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2+30*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+6*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(3/2)/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)/b/((a-b)/(a+b))^(1/2)","C"
442,1,2947,390,1.900000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/4/d*(4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b-24*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a*b-5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b+4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-24*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a*b-5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+5*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+2*B*((a-b)/(a+b))^(1/2)*b^2-4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-5*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+7*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+8*A*sin(d*x+c)*cos(d*x+c)^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+8*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*b^2-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2+5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*b^2-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2-8*A*sin(d*x+c)*cos(d*x+c)^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-8*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
443,1,2595,337,2.311000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-1/d*(4*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^2+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^2-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2-2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-2*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b-2*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+2*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-B*((a-b)/(a+b))^(1/2)*b^2+B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^2-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b^2+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b+2*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2+4*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-2*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
444,1,2552,335,2.218000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-A*((a-b)/(a+b))^(1/2)*a*b-3*B*((a-b)/(a+b))^(1/2)*a*b+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)-4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)+4*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+6*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-4*A*((a-b)/(a+b))^(1/2)*b^2+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2*sin(d*x+c)+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-4*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-3*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-4*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)+5*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2+A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-A*a^2*((a-b)/(a+b))^(1/2)*cos(d*x+c)-4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)-3*B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^2+6*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
445,1,2915,296,2.194000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"-2/15/d*(9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+12*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+15*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*sin(d*x+c)-3*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+25*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-3*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-5*B*a^3*((a-b)/(a+b))^(1/2)*cos(d*x+c)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3-9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+15*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2-9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b+3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-20*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+20*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-20*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2+5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*b^3*((a-b)/(a+b))^(1/2)-9*A*a^2*b*((a-b)/(a+b))^(1/2)-6*A*a*b^2*((a-b)/(a+b))^(1/2)-5*B*a^2*b*((a-b)/(a+b))^(1/2)-20*B*a*b^2*((a-b)/(a+b))^(1/2)+20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-9*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^3-3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3+5*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+3*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-20*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+20*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-20*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a/((a-b)/(a+b))^(1/2)","B"
446,1,3752,366,2.447000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(-63*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+82*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b+6*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-25*A*a^3*b*((a-b)/(a+b))^(1/2)-82*A*a^2*b^2*((a-b)/(a+b))^(1/2)-3*A*a*b^3*((a-b)/(a+b))^(1/2)-63*B*a^3*b*((a-b)/(a+b))^(1/2)-42*B*a^2*b^2*((a-b)/(a+b))^(1/2)-21*B*a*b^3*((a-b)/(a+b))^(1/2)+21*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4+42*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4-6*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-63*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+15*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+6*A*b^4*((a-b)/(a+b))^(1/2)+6*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^4+25*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^4-63*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+82*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-6*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+51*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+21*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-21*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+84*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-21*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-82*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2-6*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3-82*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+51*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+6*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3-63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b+21*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2-21*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3+84*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-21*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+27*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+63*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b+68*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-3*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+63*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2-82*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+55*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+6*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3+39*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b-21*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+21*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
447,1,4846,445,3.002000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"2/315/d*(-186*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+147*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*A*a^4*b*((a-b)/(a+b))^(1/2)+88*A*a^3*b^2*((a-b)/(a+b))^(1/2)+33*A*a^2*b^3*((a-b)/(a+b))^(1/2)-4*A*a*b^4*((a-b)/(a+b))^(1/2)+75*B*a^4*b*((a-b)/(a+b))^(1/2)+246*B*a^3*b^2*((a-b)/(a+b))^(1/2)+9*B*a^2*b^3*((a-b)/(a+b))^(1/2)-18*B*a*b^4*((a-b)/(a+b))^(1/2)-45*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^5-8*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5-30*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5+75*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5-35*A*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^5-14*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5-98*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5+147*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5-246*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+246*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+18*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-18*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-147*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+8*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5-75*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-186*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+33*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-33*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+33*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+246*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-153*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-18*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8*A*b^5*((a-b)/(a+b))^(1/2)-52*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b+A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3-81*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2-68*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2-85*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b-53*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^2-117*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4-204*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b+9*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3+33*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-2*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+8*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+147*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-33*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2+33*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-8*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4+246*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-153*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-18*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3-246*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b+246*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2+18*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-18*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4+8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-75*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b+33*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2-34*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+8*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4+246*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-165*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2-18*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+18*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^3/((a-b)/(a+b))^(1/2)","B"
448,1,5392,552,2.626000," ","int(sec(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"result too large to display","C"
449,1,4258,467,2.156000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"1/24/d*(-33*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3-16*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3+8*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3-12*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3+54*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b+54*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b+66*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+59*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+8*B*((a-b)/(a+b))^(1/2)*b^3+33*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+34*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-48*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^3*a^3-48*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^4*a^3-54*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2-180*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b-26*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^2*b+44*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a*b^2-33*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^2*b+16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2-120*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a*b^2+36*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b-12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2+54*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b-54*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2-180*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b-26*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b+44*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-33*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2-120*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+36*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^2*b-12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a*b^2+24*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*b^3-48*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*b^3-18*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^4*a^3+33*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3-16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*b^3-30*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^4*a^3+24*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*b^3-48*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3-18*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^3+33*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3-16*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*b^3-30*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3-54*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b-12*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2-26*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b-16*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2-54*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2-33*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b-18*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^2/sin(d*x+c)/((a-b)/(a+b))^(1/2)","C"
450,1,3939,410,2.266000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"-1/4/d*(2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2-9*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-8*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3-2*B*((a-b)/(a+b))^(1/2)*b^3+40*A*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^2+30*B*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2*b+24*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-16*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+40*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^2-8*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3-11*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-4*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-6*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+2*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+30*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2*b-9*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+9*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-8*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^3*a^3-8*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b+9*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+24*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b-16*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-8*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b-4*A*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2-6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^2*b+2*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a*b^2-9*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^2*b+9*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a*b^2+8*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^3*a^3+8*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+4*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3+8*A*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+4*A*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3-4*B*cos(d*x+c)^3*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+8*B*cos(d*x+c)^3*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3-8*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+8*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-4*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+8*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3+4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2+9*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b+2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/cos(d*x+c)/((a-b)/(a+b))^(1/2)","C"
451,1,3663,402,2.247000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"-1/3/d*(-14*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+18*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b+16*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-3*B*((a-b)/(a+b))^(1/2)*b^3-14*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+18*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+14*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3+6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3-12*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2+14*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-14*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2+18*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b-6*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-3*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2+30*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a*b^2+30*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*a*b^2-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-14*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+18*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-12*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-6*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-3*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-14*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2+2*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-6*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+12*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*b^3-6*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3+6*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+3*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*b^3+12*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*b^3-6*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)^2*b^3+6*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^3+3*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^3+2*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-6*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
452,1,3564,395,2.380000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(5/2),x)","\text{output too large to display}"," ",0,"-2/15/d*(9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+17*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+45*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*sin(d*x+c)-23*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2-5*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b+34*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+40*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-23*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-23*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-5*B*a^3*((a-b)/(a+b))^(1/2)*cos(d*x+c)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3-9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3+23*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+45*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2-9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b+23*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-35*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+35*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-35*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2+5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-23*A*b^3*((a-b)/(a+b))^(1/2)-9*A*a^2*b*((a-b)/(a+b))^(1/2)-11*A*a*b^2*((a-b)/(a+b))^(1/2)-5*B*a^2*b*((a-b)/(a+b))^(1/2)-35*B*a*b^2*((a-b)/(a+b))^(1/2)+15*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*sin(d*x+c)-15*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+30*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-9*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^3-23*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3+5*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+17*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-23*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+23*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-35*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+35*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-35*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-15*B*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3+30*B*sin(d*x+c)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3+15*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
453,1,3980,364,2.673000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(7/2),x)","\text{output too large to display}"," ",0,"-2/105/d*(-63*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+145*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b-15*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-25*A*a^3*b*((a-b)/(a+b))^(1/2)-145*A*a^2*b^2*((a-b)/(a+b))^(1/2)-45*A*a*b^3*((a-b)/(a+b))^(1/2)-63*B*a^3*b*((a-b)/(a+b))^(1/2)-77*B*a^2*b^2*((a-b)/(a+b))^(1/2)-161*B*a*b^3*((a-b)/(a+b))^(1/2)+105*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^3+21*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4+42*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4+15*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4-63*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+15*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4+10*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-25*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4-15*A*b^4*((a-b)/(a+b))^(1/2)-15*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^4+25*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^4-63*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+145*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-145*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+15*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-145*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+135*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+161*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-161*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+119*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-161*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-145*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+15*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3-145*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+135*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-15*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3-63*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b+161*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2-161*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3+119*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-161*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+105*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*sin(d*x+c)+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+63*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+90*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2+98*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b+110*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+60*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+238*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2-145*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+55*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-15*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3-35*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+60*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b-161*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+161*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^4*(1/cos(d*x+c))^(7/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a/((a-b)/(a+b))^(1/2)","B"
454,1,4847,443,2.892000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(9/2),x)","\text{output too large to display}"," ",0,"-2/315/d*(261*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-147*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+147*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*A*a^4*b*((a-b)/(a+b))^(1/2)-163*A*a^3*b^2*((a-b)/(a+b))^(1/2)-279*A*a^2*b^3*((a-b)/(a+b))^(1/2)-5*A*a*b^4*((a-b)/(a+b))^(1/2)-75*B*a^4*b*((a-b)/(a+b))^(1/2)-435*B*a^3*b^2*((a-b)/(a+b))^(1/2)-135*B*a^2*b^3*((a-b)/(a+b))^(1/2)-45*B*a*b^4*((a-b)/(a+b))^(1/2)+45*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^5-10*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^5+30*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5-75*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5+35*A*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^5+14*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5+98*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5-147*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5+435*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-435*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+45*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-45*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+147*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^5+10*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^5+75*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+261*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-279*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+155*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-147*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+279*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-279*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-10*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-435*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+405*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-45*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+10*A*b^5*((a-b)/(a+b))^(1/2)+82*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b+80*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^3+270*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2+272*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2+130*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b+170*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^2+180*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b-5*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^4+330*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b+180*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3-279*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+155*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+10*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-147*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b+279*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2-279*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-10*A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4-435*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+405*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-45*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+435*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4*b-435*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^3*b^2+45*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2*b^3-45*B*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b^4+10*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+75*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-65*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b-279*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2+199*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+10*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4-435*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b+165*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^2-45*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^3+45*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^4)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^5*(1/cos(d*x+c))^(9/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
455,1,5946,531,3.030000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/sec(d*x+c)^(11/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
456,1,2738,395,2.330000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a*b+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b+4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a*b+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2+2*B*((a-b)/(a+b))^(1/2)*b^2-4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b-2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-8*A*sin(d*x+c)*cos(d*x+c)^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-8*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*b^2+6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^2-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*b^2+6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^2-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*b^2)*cos(d*x+c)*(1/cos(d*x+c))^(5/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/b^2/((a-b)/(a+b))^(1/2)","C"
457,1,1440,321,2.568000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b -2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b -2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a +2 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a +B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b +4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b -2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b -2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +2 B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b +B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -B \sqrt{\frac{a -b}{a +b}}\, b \right) \cos \left(d x +c \right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b}"," ",0,"-1/d*(4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a+2*B*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+2*B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-B*((a-b)/(a+b))^(1/2)*b)*cos(d*x+c)*(1/cos(d*x+c))^(3/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/b","C"
458,1,283,184,2.095000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)-B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)+2 B \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right)\right) \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \left(\sin^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(-1+\cos \left(d x +c \right)\right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))-B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))+2*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2)))*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)^2*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(-1+cos(d*x+c))/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)","C"
459,1,940,196,2.506000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a -A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b -A b \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a}"," ",0,"-2/d*(-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b-A*b*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))/((a-b)/(a+b))^(1/2)/a","B"
460,1,1731,248,2.331000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-A \sqrt{\frac{a -b}{a +b}}\, a b -3 B \sqrt{\frac{a -b}{a +b}}\, a b +2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b -2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+2 A \sqrt{\frac{a -b}{a +b}}\, b^{2}-2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+2 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2}-A \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)-A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b +2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b +A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)+2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{3 d \sin \left(d x +c \right) \left(b +a \cos \left(d x +c \right)\right) a^{2} \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/3/d*(A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-A*((a-b)/(a+b))^(1/2)*a*b-3*B*((a-b)/(a+b))^(1/2)*a*b+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)-2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+2*A*((a-b)/(a+b))^(1/2)*b^2+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-3*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2+A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2-A*a^2*((a-b)/(a+b))^(1/2)*cos(d*x+c)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^2/((a-b)/(a+b))^(1/2)","B"
461,1,2738,310,2.478000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"2/15/d*(-9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-2*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+8*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2-10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b+8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+5*B*a^3*((a-b)/(a+b))^(1/2)*cos(d*x+c)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3+9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-10*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+10*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-10*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*A*b^3*((a-b)/(a+b))^(1/2)+9*A*a^2*b*((a-b)/(a+b))^(1/2)-4*A*a*b^2*((a-b)/(a+b))^(1/2)+5*B*a^2*b*((a-b)/(a+b))^(1/2)-10*B*a*b^2*((a-b)/(a+b))^(1/2)+10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2+9*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-9*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^3+8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3-5*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-10*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+10*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-10*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^3/((a-b)/(a+b))^(1/2)","B"
462,1,2656,432,2.556000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/d*(4*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b-2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b-4*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a*b-4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b+B*((a-b)/(a+b))^(1/2)*a*b+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*cos(d*x+c)*b^2-2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-4*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+6*B*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b-4*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b+6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2-6*B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2+B*((a-b)/(a+b))^(1/2)*b^2+2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2+4*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*a^2-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2+2*A*sin(d*x+c)*cos(d*x+c)^2*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2-4*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-B*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-4*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a^2-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(5/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)/b^2","C"
463,1,1585,262,3.116000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) b -2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a -2 B \cos \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +2 B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sin \left(d x +c \right)-2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a \sin \left(d x +c \right)-2 B \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+2 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +A b \sqrt{\frac{a -b}{a +b}}-B a \sqrt{\frac{a -b}{a +b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right) \left(\frac{1}{\cos \left(d x +c \right)}\right)^{\frac{3}{2}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) b \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"2/d*(A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a-2*B*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+2*B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a+B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*sin(d*x+c)-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*sin(d*x+c)-2*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+2*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+A*b*((a-b)/(a+b))^(1/2)-B*a*((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/(b+a*cos(d*x+c))/sin(d*x+c)/b/(a+b)/((a-b)/(a+b))^(1/2)","C"
464,1,941,257,2.447000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{2 \left(A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +A \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \cos \left(d x +c \right) a +A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)+A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \sin \left(d x +c \right)-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a +A b \sqrt{\frac{a -b}{a +b}}-B a \sqrt{\frac{a -b}{a +b}}\right) \cos \left(d x +c \right) \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) a \left(a +b \right) \sqrt{\frac{a -b}{a +b}}}"," ",0,"-2/d*(A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+B*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a+A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*sin(d*x+c)-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a+A*b*((a-b)/(a+b))^(1/2)-B*a*((a-b)/(a+b))^(1/2))*cos(d*x+c)*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/a/(a+b)/((a-b)/(a+b))^(1/2)","B"
465,1,1448,277,2.360000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/sec(d*x+c)^(1/2),x)","-\frac{2 \left(A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}-A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b +B \cos \left(d x +c \right) \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2} \sin \left(d x +c \right)-A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-2 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b \sin \left(d x +c \right)+B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} \sin \left(d x +c \right)+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2}+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b -A \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right)+2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2}-B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b -A \sqrt{\frac{a -b}{a +b}}\, a b -2 A \sqrt{\frac{a -b}{a +b}}\, b^{2}+B \sqrt{\frac{a -b}{a +b}}\, a b \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{1}{\cos \left(d x +c \right)}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, \left(a +b \right) a^{2}}"," ",0,"-2/d*(A*sin(d*x+c)*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*A*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a*b+B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b+B*cos(d*x+c)*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^2+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2*sin(d*x+c)-A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b*sin(d*x+c)+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*sin(d*x+c)+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b-A*a^2*((a-b)/(a+b))^(1/2)*cos(d*x+c)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b-A*((a-b)/(a+b))^(1/2)*a*b-2*A*((a-b)/(a+b))^(1/2)*b^2+B*((a-b)/(a+b))^(1/2)*a*b)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/(1/cos(d*x+c))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/((a-b)/(a+b))^(1/2)/(a+b)/a^2","B"
466,1,2285,358,2.311000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(6*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+8*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2+4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b+8*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3-3*B*a^3*((a-b)/(a+b))^(1/2)*cos(d*x+c)-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3-5*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-6*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b-6*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-3*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*A*b^3*((a-b)/(a+b))^(1/2)-A*a^2*b*((a-b)/(a+b))^(1/2)+4*A*a*b^2*((a-b)/(a+b))^(1/2)-3*B*a^2*b*((a-b)/(a+b))^(1/2)-6*B*a*b^2*((a-b)/(a+b))^(1/2)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*sin(d*x+c)+6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b+A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3-3*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+6*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+8*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-5*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-6*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+3*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^3/(a+b)/((a-b)/(a+b))^(1/2)","B"
467,1,3156,449,2.499000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","\text{output too large to display}"," ",0,"2/15/d*(-5*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-9*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+48*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+9*A*a^3*b*((a-b)/(a+b))^(1/2)+24*A*a*b^3*((a-b)/(a+b))^(1/2)+5*B*a^3*b*((a-b)/(a+b))^(1/2)-20*B*a^2*b^2*((a-b)/(a+b))^(1/2)-40*B*a*b^3*((a-b)/(a+b))^(1/2)-5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4-3*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4-6*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4-9*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-48*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+5*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+9*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4+6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b+48*A*b^4*((a-b)/(a+b))^(1/2)-24*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2+20*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+48*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^4+9*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-5*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-24*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+36*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+48*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+25*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-40*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-30*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-40*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-24*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+12*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+36*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+48*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+25*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b-40*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3-30*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-40*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^2-5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b-6*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-24*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3+20*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2-6*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+18*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-20*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b-3*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b+40*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^3*(1/cos(d*x+c))^(5/2)/sin(d*x+c)/(b+a*cos(d*x+c))/a^4/(a+b)/((a-b)/(a+b))^(1/2)","B"
468,1,5195,452,2.365000," ","int(sec(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
469,1,3138,359,2.405000," ","int(sec(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*(2*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*sin(d*x+c)-A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a*b^2+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2+4*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b-A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3-3*B*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^2-3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b-A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-2*B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^2*b+4*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^2*b+4*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a*b^2-A*b^3*((a-b)/(a+b))^(1/2)-2*A*a^2*b*((a-b)/(a+b))^(1/2)+A*a*b^2*((a-b)/(a+b))^(1/2)-B*a^2*b*((a-b)/(a+b))^(1/2)+4*B*a*b^2*((a-b)/(a+b))^(1/2)-B*((a-b)/(a+b))^(1/2)*a^3-4*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2-A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-3*B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+4*B*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b+3*A*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3-3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*a^3-A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*b^3+B*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*a^3+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)+4*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)-3*A*cos(d*x+c)^2*sin(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+3*A*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+B*cos(d*x+c)^2*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*(1/(1+cos(d*x+c)))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^2*(1/cos(d*x+c))^(3/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/a/((a-b)/(a+b))^(1/2)","B"
470,1,3857,376,2.250000," ","int((A+B*sec(d*x+c))*sec(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(-6*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b+2*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-5*A*a^2*b^2*((a-b)/(a+b))^(1/2)+A*a*b^3*((a-b)/(a+b))^(1/2)+2*B*a^3*b*((a-b)/(a+b))^(1/2)-B*a^2*b^2*((a-b)/(a+b))^(1/2)+B*a*b^3*((a-b)/(a+b))^(1/2)+2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2*b^2+2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a*b^3+B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^3*b-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^4+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4-3*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4+2*A*b^4*((a-b)/(a+b))^(1/2)-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b+B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^2*b^2-6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^3*b+3*A*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b+2*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*b^4-3*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+3*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^4-3*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-6*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^3*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^4-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*a^4-6*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+2*A*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3+5*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+2*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+3*B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^3*b+B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a^2*b^2+B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)*a*b^3-2*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+6*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b-3*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^3-6*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+6*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^2-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^3)*cos(d*x+c)*(1/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/(b+a*cos(d*x+c))^2/(a-b)/(a+b)^2/((a-b)/(a+b))^(1/2)/a^2","B"
471,1,5169,398,2.444000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/sec(d*x+c)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
472,1,6746,496,2.630000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
473,1,8251,606,2.940000," ","int((A+B*sec(d*x+c))/sec(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
474,0,0,103,1.079000," ","int((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^(2/3)*(A+B*sec(d*x+c)),x)","F"
475,0,0,103,1.084000," ","int((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","\int \left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int((a+b*sec(d*x+c))^(1/3)*(A+B*sec(d*x+c)),x)","F"
476,0,0,103,1.116000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{1}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/3),x)","F"
477,0,0,103,1.209000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(2/3),x)","\int \frac{A +B \sec \left(d x +c \right)}{\left(a +b \sec \left(d x +c \right)\right)^{\frac{2}{3}}}\, dx"," ",0,"int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(2/3),x)","F"
478,0,0,35,3.327000," ","int((c*sec(f*x+e))^n*(a+b*sec(f*x+e))^m*(A+B*sec(f*x+e)),x)","\int \left(c \sec \left(f x +e \right)\right)^{n} \left(a +b \sec \left(f x +e \right)\right)^{m} \left(A +B \sec \left(f x +e \right)\right)\, dx"," ",0,"int((c*sec(f*x+e))^n*(a+b*sec(f*x+e))^m*(A+B*sec(f*x+e)),x)","F"
479,0,0,523,2.477000," ","int(sec(d*x+c)^m*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{4} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(a+b*sec(d*x+c))^4*(A+B*sec(d*x+c)),x)","F"
480,0,0,348,1.993000," ","int(sec(d*x+c)^m*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{3} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(a+b*sec(d*x+c))^3*(A+B*sec(d*x+c)),x)","F"
481,0,0,243,3.596000," ","int(sec(d*x+c)^m*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right)^{2} \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","F"
482,0,0,159,2.180000," ","int(sec(d*x+c)^m*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","\int \left(\sec^{m}\left(d x +c \right)\right) \left(a +b \sec \left(d x +c \right)\right) \left(A +B \sec \left(d x +c \right)\right)\, dx"," ",0,"int(sec(d*x+c)^m*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","F"
483,1,383,168,4.663000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(240 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-528 A -168 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(448 A +308 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-122 A -112 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(240*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-528*A-168*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(448*A+308*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-122*A-112*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+35*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
484,1,355,141,4.074000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(-24 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(44 A +20 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-16 A -10 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(-24*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(44*A+20*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-16*A-10*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
485,1,321,116,4.404000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(4 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(4*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
486,1,240,116,4.920000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","-\frac{2 a \left(A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*a*(A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*B*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
487,1,426,139,11.025000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(\frac{A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{2}+\frac{\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*(1/2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+(1/2*A+1/2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
488,1,661,168,12.333000," ","int((a+a*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{4 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a \left(\left(\frac{A}{2}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{2 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{10 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a*((1/2*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+1/2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-1/10*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
489,1,413,226,4.868000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-560 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(1840 A +360 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-2368 A -1044 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(1568 A +1134 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-387 A -351 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+75 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-168 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+90 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-189 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{315 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/315*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-560*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^10+(1840*A+360*B)*sin(1/2*d*x+1/2*c)^8*cos(1/2*d*x+1/2*c)+(-2368*A-1044*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(1568*A+1134*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-387*A-351*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+75*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-168*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+90*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-189*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
490,1,385,197,5.046000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(120 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-348 A -84 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(378 A +224 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-117 A -91 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-84 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(120*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-348*A-84*B)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(378*A+224*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-117*A-91*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+30*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+35*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-84*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
491,1,357,166,4.205000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{4 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(-12 A \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(32 A +10 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-13 A -5 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+10 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(-12*A*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(32*A+10*B)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-13*A-5*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-12*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+10*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
492,1,388,160,4.592000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{4 a^{2} \left(2 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A +3 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+2 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-4/3*a^2*(2*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A+3*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+2*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
493,1,513,162,4.806000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","-\frac{4 \left(6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A +2 B \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(3 A +7 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(3 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}+3 B \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) a^{2}}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)^{\frac{3}{2}} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) d}"," ",0,"-4/3*(6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A+2*B)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A+7*B)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2+3*A*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+3*B*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*a^2/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*cos(1/2*d*x+1/2*c)^2-1)^(3/2)/sin(1/2*d*x+1/2*c)/d","B"
494,1,741,195,12.757000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{8 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(\frac{A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{4 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\left(\frac{A}{4}+\frac{B}{2}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{20 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{\left(\frac{A}{2}+\frac{B}{4}\right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*(1/4*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+(1/4*A+1/2*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-1/20*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+(1/2*A+1/4*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
495,1,851,226,15.458000," ","int((a+a*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{8 \sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, a^{2} \left(\left(\frac{A}{2}+\frac{B}{4}\right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{\left(\frac{A}{4}+\frac{B}{2}\right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+\frac{A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{4 \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{4}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-8*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*a^2*((1/2*A+1/4*B)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-1/5*(1/4*A+1/2*B)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+1/4*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+1/4*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
496,1,282,195,5.240000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(25 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+63 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-25 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-45 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+48 A \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-56 A -40 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-30 A +90 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(23 A -35 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{15 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(25*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+63*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-25*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-45*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+48*A*sin(1/2*d*x+1/2*c)^8+(-56*A-40*B)*sin(1/2*d*x+1/2*c)^6+(-30*A+90*B)*sin(1/2*d*x+1/2*c)^4+(23*A-35*B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
497,1,262,168,4.322000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(5 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+9 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-8 A \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(18 A -6 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-7 A +3 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(5*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-8*A*sin(1/2*d*x+1/2*c)^6+(18*A-6*B)*sin(1/2*d*x+1/2*c)^4+(-7*A+3*B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
498,1,244,138,4.794000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c)),x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
499,1,243,133,4.669000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+\left(2 A -2 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-A +B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*sin(1/2*d*x+1/2*c)^4+(-A+B)*sin(1/2*d*x+1/2*c)^2)/a/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
500,1,318,161,8.911000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -3 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -5 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(-cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-3*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-5*B)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^3/(2*sin(1/2*d*x+1/2*c)^2-1)/cos(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
501,1,493,194,11.491000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(2 A -2 B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\left(-A +B \right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a*(2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+(2*A-2*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+(-A+B)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
502,1,465,238,5.006000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(96 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-352 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+80 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+120 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-150 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-336 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+60 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+100 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+210 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+266 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-240 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-135 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+105 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+5 A -5 B \right)}{30 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/30*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(96*A*cos(1/2*d*x+1/2*c)^10-352*A*cos(1/2*d*x+1/2*c)^8+80*B*cos(1/2*d*x+1/2*c)^8+120*A*cos(1/2*d*x+1/2*c)^6-150*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-336*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+60*B*cos(1/2*d*x+1/2*c)^6+100*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+210*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+266*A*cos(1/2*d*x+1/2*c)^4-240*B*cos(1/2*d*x+1/2*c)^4-135*A*cos(1/2*d*x+1/2*c)^2+105*B*cos(1/2*d*x+1/2*c)^2+5*A-5*B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
503,1,435,209,5.539000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(16 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+12 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+42 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-24 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-48 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+38 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+21 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-15 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(16*A*cos(1/2*d*x+1/2*c)^8+12*A*cos(1/2*d*x+1/2*c)^6+20*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+42*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-24*B*cos(1/2*d*x+1/2*c)^6-10*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-24*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-48*A*cos(1/2*d*x+1/2*c)^4+38*B*cos(1/2*d*x+1/2*c)^4+21*A*cos(1/2*d*x+1/2*c)^2-15*B*cos(1/2*d*x+1/2*c)^2-A+B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
504,1,421,179,5.153000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^2,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(24 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-4 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-38 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+15 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-9 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(24*A*cos(1/2*d*x+1/2*c)^6+10*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+24*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^6-4*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-6*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-38*A*cos(1/2*d*x+1/2*c)^4+20*B*cos(1/2*d*x+1/2*c)^4+15*A*cos(1/2*d*x+1/2*c)^2-9*B*cos(1/2*d*x+1/2*c)^2-A+B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
505,1,350,165,5.228000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^2/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-20 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+9 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-A +B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^6+4*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3+6*A*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-20*A*cos(1/2*d*x+1/2*c)^4+2*B*cos(1/2*d*x+1/2*c)^4+9*A*cos(1/2*d*x+1/2*c)^2-3*B*cos(1/2*d*x+1/2*c)^2-A+B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
506,1,350,165,4.748000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{3}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+16 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+A -B \right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/6*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-12*B*cos(1/2*d*x+1/2*c)^6+4*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^3-6*B*cos(1/2*d*x+1/2*c)^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*A*cos(1/2*d*x+1/2*c)^4+16*B*cos(1/2*d*x+1/2*c)^4-3*A*cos(1/2*d*x+1/2*c)^2-3*B*cos(1/2*d*x+1/2*c)^2+A-B)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
507,1,492,204,5.756000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^2,x)","\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-5 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(A -4 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(10 A -43 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(7 A -37 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{6 a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/6*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-5*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(A-4*B)*sin(1/2*d*x+1/2*c)^6+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(10*A-43*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(7*A-37*B)*sin(1/2*d*x+1/2*c)^2)/a^2/cos(1/2*d*x+1/2*c)^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
508,1,750,233,15.142000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{\left(-A +B \right) \left(2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-12 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+20 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(-1+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}+\frac{\left(4 A -8 B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{\left(-2 A +4 B \right) \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{2 a^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/2*(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)/a^2*(4*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+1/3*(-A+B)*(2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)-12*sin(1/2*d*x+1/2*c)^6+20*sin(1/2*d*x+1/2*c)^4-7*sin(1/2*d*x+1/2*c)^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/cos(1/2*d*x+1/2*c)/(-1+sin(1/2*d*x+1/2*c)^2)+(4*A-8*B)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+(-2*A+4*B)*(cos(1/2*d*x+1/2*c)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)/cos(1/2*d*x+1/2*c)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
509,1,465,253,5.704000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(160 A \left(\cos^{10}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+468 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+330 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+714 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-348 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-130 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-294 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-1058 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+578 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+474 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-264 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-47 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+37 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(160*A*cos(1/2*d*x+1/2*c)^10+468*A*cos(1/2*d*x+1/2*c)^8+330*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+714*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-348*B*cos(1/2*d*x+1/2*c)^8-130*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-294*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1058*A*cos(1/2*d*x+1/2*c)^6+578*B*cos(1/2*d*x+1/2*c)^6+474*A*cos(1/2*d*x+1/2*c)^4-264*B*cos(1/2*d*x+1/2*c)^4-47*A*cos(1/2*d*x+1/2*c)^2+37*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
510,1,451,224,5.371000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(348 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+130 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+294 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-54 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-578 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+198 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+264 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-114 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-37 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+27 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(348*A*cos(1/2*d*x+1/2*c)^8+130*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+294*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-108*B*cos(1/2*d*x+1/2*c)^8-30*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-54*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-578*A*cos(1/2*d*x+1/2*c)^6+198*B*cos(1/2*d*x+1/2*c)^6+264*A*cos(1/2*d*x+1/2*c)^4-114*B*cos(1/2*d*x+1/2*c)^4-37*A*cos(1/2*d*x+1/2*c)^2+27*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
511,1,451,218,5.613000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^3/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(108 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+30 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-198 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+114 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-27 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 A -3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(108*A*cos(1/2*d*x+1/2*c)^8+30*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+12*B*cos(1/2*d*x+1/2*c)^8+10*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-198*A*cos(1/2*d*x+1/2*c)^6-2*B*cos(1/2*d*x+1/2*c)^6+114*A*cos(1/2*d*x+1/2*c)^4-24*B*cos(1/2*d*x+1/2*c)^4-27*A*cos(1/2*d*x+1/2*c)^2+17*B*cos(1/2*d*x+1/2*c)^2+3*A-3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
512,1,451,214,5.324000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^3,x)","-\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-12 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+10 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+22 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-6 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+17 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-7 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^8+10*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-12*B*cos(1/2*d*x+1/2*c)^8+10*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5-6*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-2*A*cos(1/2*d*x+1/2*c)^6+22*B*cos(1/2*d*x+1/2*c)^6-24*A*cos(1/2*d*x+1/2*c)^4-6*B*cos(1/2*d*x+1/2*c)^4+17*A*cos(1/2*d*x+1/2*c)^2-7*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
513,1,451,216,5.569000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^3,x)","\frac{\sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(12 A \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-10 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+108 B \left(\cos^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-30 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+54 B \left(\cos^{5}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-22 A \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-138 B \left(\cos^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 A \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 B \left(\cos^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+7 A \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-3 A +3 B \right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(12*A*cos(1/2*d*x+1/2*c)^8-10*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+6*A*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+108*B*cos(1/2*d*x+1/2*c)^8-30*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*cos(1/2*d*x+1/2*c)^5+54*B*cos(1/2*d*x+1/2*c)^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-22*A*cos(1/2*d*x+1/2*c)^6-138*B*cos(1/2*d*x+1/2*c)^6+6*A*cos(1/2*d*x+1/2*c)^4+24*B*cos(1/2*d*x+1/2*c)^4+7*A*cos(1/2*d*x+1/2*c)^2+3*B*cos(1/2*d*x+1/2*c)^2-3*A+3*B)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
514,1,685,253,6.056000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^3,x)","\frac{-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+4 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-2 \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(15 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-27 A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-65 B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+147 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+12 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(9 A -49 B \right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(147 A -817 B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(43 A -248 B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \left(69 A -439 B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{60 a^{3} \cos \left(\frac{d x}{2}+\frac{c}{2}\right)^{5} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"1/60*(-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+4*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-2*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(15*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-27*A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-65*B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+147*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))*cos(1/2*d*x+1/2*c)+12*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(9*A-49*B)*sin(1/2*d*x+1/2*c)^8-2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(147*A-817*B)*sin(1/2*d*x+1/2*c)^6+6*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(43*A-248*B)*sin(1/2*d*x+1/2*c)^4-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(69*A-439*B)*sin(1/2*d*x+1/2*c)^2)/a^3/cos(1/2*d*x+1/2*c)^5/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
515,1,130,190,1.955000," ","int(cos(d*x+c)^(9/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(35 A \left(\cos^{4}\left(d x +c \right)\right)+40 A \left(\cos^{3}\left(d x +c \right)\right)+45 B \left(\cos^{3}\left(d x +c \right)\right)+48 A \left(\cos^{2}\left(d x +c \right)\right)+54 B \left(\cos^{2}\left(d x +c \right)\right)+64 A \cos \left(d x +c \right)+72 B \cos \left(d x +c \right)+128 A +144 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*(-1+cos(d*x+c))*(35*A*cos(d*x+c)^4+40*A*cos(d*x+c)^3+45*B*cos(d*x+c)^3+48*A*cos(d*x+c)^2+54*B*cos(d*x+c)^2+64*A*cos(d*x+c)+72*B*cos(d*x+c)+128*A+144*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
516,1,108,151,1.798000," ","int(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+18 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+24 A \cos \left(d x +c \right)+28 B \cos \left(d x +c \right)+48 A +56 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+18*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+24*A*cos(d*x+c)+28*B*cos(d*x+c)+48*A+56*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
517,1,86,112,1.786000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(3 A \left(\cos^{2}\left(d x +c \right)\right)+4 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+8 A +10 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right)}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*(-1+cos(d*x+c))*(3*A*cos(d*x+c)^2+4*A*cos(d*x+c)+5*B*cos(d*x+c)+8*A+10*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)/sin(d*x+c)","A"
518,1,65,70,1.739000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2),x)","-\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(A \cos \left(d x +c \right)+2 A +3 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3 d \sin \left(d x +c \right)}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(A*cos(d*x+c)+2*A+3*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
519,1,169,82,1.664000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 A \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"-1/d*(-1+cos(d*x+c))*(2*A*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","B"
520,1,275,84,2.408000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}+B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/2/d*(-1+cos(d*x+c))*(2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)+B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-2*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)","B"
521,1,342,127,2.238000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(-4 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+4 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-3 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+3 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(-4*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+4*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-3*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+3*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+6*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(3/2)","B"
522,1,404,166,2.294000," ","int((A+B*sec(d*x+c))*(a+a*sec(d*x+c))^(1/2)/cos(d*x+c)^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(18 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-18 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+15 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-15 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+36 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+30 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+20 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{48 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{5}{2}}}"," ",0,"-1/48/d*(-1+cos(d*x+c))*(18*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-18*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3+15*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-15*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3+36*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+30*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+20*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(5/2)","B"
523,1,153,239,2.130000," ","int(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(315 A \left(\cos^{5}\left(d x +c \right)\right)+735 A \left(\cos^{4}\left(d x +c \right)\right)+385 B \left(\cos^{4}\left(d x +c \right)\right)+840 A \left(\cos^{3}\left(d x +c \right)\right)+935 B \left(\cos^{3}\left(d x +c \right)\right)+1008 A \left(\cos^{2}\left(d x +c \right)\right)+1122 B \left(\cos^{2}\left(d x +c \right)\right)+1344 A \cos \left(d x +c \right)+1496 B \cos \left(d x +c \right)+2688 A +2992 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3465 d \sin \left(d x +c \right)}"," ",0,"-2/3465/d*a*(-1+cos(d*x+c))*(315*A*cos(d*x+c)^5+735*A*cos(d*x+c)^4+385*B*cos(d*x+c)^4+840*A*cos(d*x+c)^3+935*B*cos(d*x+c)^3+1008*A*cos(d*x+c)^2+1122*B*cos(d*x+c)^2+1344*A*cos(d*x+c)+1496*B*cos(d*x+c)+2688*A+2992*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
524,1,131,198,2.574000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(35 A \left(\cos^{4}\left(d x +c \right)\right)+85 A \left(\cos^{3}\left(d x +c \right)\right)+45 B \left(\cos^{3}\left(d x +c \right)\right)+102 A \left(\cos^{2}\left(d x +c \right)\right)+117 B \left(\cos^{2}\left(d x +c \right)\right)+136 A \cos \left(d x +c \right)+156 B \cos \left(d x +c \right)+272 A +312 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*a*(-1+cos(d*x+c))*(35*A*cos(d*x+c)^4+85*A*cos(d*x+c)^3+45*B*cos(d*x+c)^3+102*A*cos(d*x+c)^2+117*B*cos(d*x+c)^2+136*A*cos(d*x+c)+156*B*cos(d*x+c)+272*A+312*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
525,1,109,157,1.952000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+39 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+52 A \cos \left(d x +c \right)+63 B \cos \left(d x +c \right)+104 A +126 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*a*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+39*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+52*A*cos(d*x+c)+63*B*cos(d*x+c)+104*A+126*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
526,1,87,113,1.880000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a \left(-1+\cos \left(d x +c \right)\right) \left(3 A \left(\cos^{2}\left(d x +c \right)\right)+9 A \cos \left(d x +c \right)+5 B \cos \left(d x +c \right)+18 A +25 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{15 d \sin \left(d x +c \right)}"," ",0,"-2/15/d*a*(-1+cos(d*x+c))*(3*A*cos(d*x+c)^2+9*A*cos(d*x+c)+5*B*cos(d*x+c)+18*A+25*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
527,1,201,123,1.797000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","-\frac{a \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-3 B \sqrt{2}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+4 A \left(\cos^{2}\left(d x +c \right)\right)+16 A \cos \left(d x +c \right)+12 B \cos \left(d x +c \right)-20 A -12 B \right)}{6 d \sin \left(d x +c \right)}"," ",0,"-1/6/d*a*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-3*B*2^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+4*A*cos(d*x+c)^2+16*A*cos(d*x+c)+12*B*cos(d*x+c)-20*A-12*B)/sin(d*x+c)","A"
528,1,306,126,1.875000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","-\frac{a \left(-1+\cos \left(d x +c \right)\right) \left(4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}+3 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-3 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}+2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*a*(-1+cos(d*x+c))*(4*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)+3*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-3*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)+2*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)","B"
529,1,343,129,2.072000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{a \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(12 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-12 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+7 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-7 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+14 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{8 d \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/8/d*a*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(12*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-12*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+7*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-7*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+14*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)","B"
530,1,405,170,1.818000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{a \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(42 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-42 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+33 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-33 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-84 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-66 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-44 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{\frac{5}{2}} \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/48/d*a*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(42*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-42*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3+33*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-33*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-84*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-66*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-44*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/cos(d*x+c)^(5/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)","B"
531,1,467,211,1.818000," ","int((a+a*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{a \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(264 A \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-264 A \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+225 B \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-225 B \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+528 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+450 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+352 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+300 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+128 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+240 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+96 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{384 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{7}{2}} \sin \left(d x +c \right)^{2}}"," ",0,"-1/384/d*a*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(264*A*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-264*A*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+225*B*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-225*B*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+528*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+450*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+352*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+300*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+128*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+240*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+96*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(7/2)/sin(d*x+c)^2","B"
532,1,155,239,2.081000," ","int(cos(d*x+c)^(11/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(315 A \left(\cos^{5}\left(d x +c \right)\right)+1120 A \left(\cos^{4}\left(d x +c \right)\right)+385 B \left(\cos^{4}\left(d x +c \right)\right)+1775 A \left(\cos^{3}\left(d x +c \right)\right)+1430 B \left(\cos^{3}\left(d x +c \right)\right)+2130 A \left(\cos^{2}\left(d x +c \right)\right)+2409 B \left(\cos^{2}\left(d x +c \right)\right)+2840 A \cos \left(d x +c \right)+3212 B \cos \left(d x +c \right)+5680 A +6424 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{3465 d \sin \left(d x +c \right)}"," ",0,"-2/3465/d*a^2*(-1+cos(d*x+c))*(315*A*cos(d*x+c)^5+1120*A*cos(d*x+c)^4+385*B*cos(d*x+c)^4+1775*A*cos(d*x+c)^3+1430*B*cos(d*x+c)^3+2130*A*cos(d*x+c)^2+2409*B*cos(d*x+c)^2+2840*A*cos(d*x+c)+3212*B*cos(d*x+c)+5680*A+6424*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
533,1,133,198,1.914000," ","int(cos(d*x+c)^(9/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(35 A \left(\cos^{4}\left(d x +c \right)\right)+130 A \left(\cos^{3}\left(d x +c \right)\right)+45 B \left(\cos^{3}\left(d x +c \right)\right)+219 A \left(\cos^{2}\left(d x +c \right)\right)+180 B \left(\cos^{2}\left(d x +c \right)\right)+292 A \cos \left(d x +c \right)+345 B \cos \left(d x +c \right)+584 A +690 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{315 d \sin \left(d x +c \right)}"," ",0,"-2/315/d*a^2*(-1+cos(d*x+c))*(35*A*cos(d*x+c)^4+130*A*cos(d*x+c)^3+45*B*cos(d*x+c)^3+219*A*cos(d*x+c)^2+180*B*cos(d*x+c)^2+292*A*cos(d*x+c)+345*B*cos(d*x+c)+584*A+690*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
534,1,111,154,1.954000," ","int(cos(d*x+c)^(7/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{2 a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(15 A \left(\cos^{3}\left(d x +c \right)\right)+60 A \left(\cos^{2}\left(d x +c \right)\right)+21 B \left(\cos^{2}\left(d x +c \right)\right)+115 A \cos \left(d x +c \right)+98 B \cos \left(d x +c \right)+230 A +301 B \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{105 d \sin \left(d x +c \right)}"," ",0,"-2/105/d*a^2*(-1+cos(d*x+c))*(15*A*cos(d*x+c)^3+60*A*cos(d*x+c)^2+21*B*cos(d*x+c)^2+115*A*cos(d*x+c)+98*B*cos(d*x+c)+230*A+301*B)*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)","A"
535,1,225,164,1.942000," ","int(cos(d*x+c)^(5/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{a^{2} \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-15 B \sqrt{2}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+12 A \left(\cos^{3}\left(d x +c \right)\right)+44 A \left(\cos^{2}\left(d x +c \right)\right)+20 B \left(\cos^{2}\left(d x +c \right)\right)+116 A \cos \left(d x +c \right)+140 B \cos \left(d x +c \right)-172 A -160 B \right)}{30 d \sin \left(d x +c \right)}"," ",0,"-1/30/d*a^2*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-15*B*2^(1/2)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+12*A*cos(d*x+c)^3+44*A*cos(d*x+c)^2+20*B*cos(d*x+c)^2+116*A*cos(d*x+c)+140*B*cos(d*x+c)-172*A-160*B)/sin(d*x+c)","A"
536,1,368,169,2.054000," ","int(cos(d*x+c)^(3/2)*(a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","-\frac{a^{2} \left(6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-6 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+15 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-15 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sqrt{2}+8 A \left(\cos^{3}\left(d x +c \right)\right)+56 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)-64 A \cos \left(d x +c \right)-12 B \cos \left(d x +c \right)-12 B \right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{12 d \sin \left(d x +c \right) \sqrt{\cos \left(d x +c \right)}}"," ",0,"-1/12/d*a^2*(6*A*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-6*A*cos(d*x+c)*sin(d*x+c)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*2^(1/2)+15*B*cos(d*x+c)*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-15*B*cos(d*x+c)*sin(d*x+c)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*2^(1/2)+8*A*cos(d*x+c)^3+56*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2-64*A*cos(d*x+c)-12*B*cos(d*x+c)-12*B)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)/cos(d*x+c)^(1/2)","B"
537,1,376,170,2.250000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","-\frac{a^{2} \left(-1+\cos \left(d x +c \right)\right) \left(16 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-20 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+20 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-19 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+19 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+22 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{8 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/8/d*a^2*(-1+cos(d*x+c))*(16*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-20*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+20*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-19*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+19*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+22*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(3/2)/(-2/(1+cos(d*x+c)))^(1/2)","B"
538,1,407,170,2.509000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{a^{2} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(114 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-114 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)+75 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-75 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}\, \left(\cos^{3}\left(d x +c \right)\right)-132 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-150 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-24 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-68 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{48 d \cos \left(d x +c \right)^{\frac{5}{2}} \sin \left(d x +c \right)^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/48/d*a^2*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(114*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-114*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3+75*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-75*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)*cos(d*x+c)^3-132*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-150*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-24*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-68*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-16*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/cos(d*x+c)^(5/2)/sin(d*x+c)^2/(-2/(1+cos(d*x+c)))^(1/2)","B"
539,1,469,211,2.169000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\frac{a^{2} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(600 A \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-600 A \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+489 B \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-489 B \left(\cos^{4}\left(d x +c \right)\right) \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-1200 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-978 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-544 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-652 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-128 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-368 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-96 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{384 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{7}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/384/d*a^2*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(600*A*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)-600*A*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)+489*B*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)-489*B*cos(d*x+c)^4*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-1200*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-978*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-544*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-652*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)-128*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-368*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-96*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/sin(d*x+c)^2/cos(d*x+c)^(7/2)/(-2/(1+cos(d*x+c)))^(1/2)","B"
540,1,531,252,2.122000," ","int((a+a*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(5/2),x)","-\frac{a^{2} \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(-4890 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+4890 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}-4245 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+4245 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{5}\left(d x +c \right)\right) \sqrt{2}+9780 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+8490 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{4}\left(d x +c \right)\right) \sin \left(d x +c \right)+6520 A \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+5660 B \left(\cos^{3}\left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+3680 A \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+4528 B \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+960 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+2784 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+768 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{3840 d \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{9}{2}} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/3840/d*a^2*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(-4890*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+4890*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)-4245*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+4245*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^5*2^(1/2)+9780*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)+8490*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*sin(d*x+c)+6520*A*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+5660*B*cos(d*x+c)^3*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+3680*A*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+4528*B*sin(d*x+c)*cos(d*x+c)^2*(-2/(1+cos(d*x+c)))^(1/2)+960*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+2784*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+768*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/sin(d*x+c)^2/cos(d*x+c)^(9/2)/(-2/(1+cos(d*x+c)))^(1/2)","B"
541,1,217,211,2.071000," ","int(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(30 A \left(\cos^{4}\left(d x +c \right)\right)+105 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-36 A \left(\cos^{3}\left(d x +c \right)\right)-105 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+42 B \left(\cos^{3}\left(d x +c \right)\right)+68 A \left(\cos^{2}\left(d x +c \right)\right)-56 B \left(\cos^{2}\left(d x +c \right)\right)-148 A \cos \left(d x +c \right)+196 B \cos \left(d x +c \right)+86 A -182 B \right)}{105 d a \sin \left(d x +c \right)}"," ",0,"-1/105/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(30*A*cos(d*x+c)^4+105*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-36*A*cos(d*x+c)^3-105*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+42*B*cos(d*x+c)^3+68*A*cos(d*x+c)^2-56*B*cos(d*x+c)^2-148*A*cos(d*x+c)+196*B*cos(d*x+c)+86*A-182*B)/a/sin(d*x+c)","A"
542,1,195,174,2.351000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-6 A \left(\cos^{3}\left(d x +c \right)\right)-15 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+8 A \left(\cos^{2}\left(d x +c \right)\right)-10 B \left(\cos^{2}\left(d x +c \right)\right)-28 A \cos \left(d x +c \right)+20 B \cos \left(d x +c \right)+26 A -10 B \right)}{15 d a \sin \left(d x +c \right)}"," ",0,"1/15/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-6*A*cos(d*x+c)^3-15*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+8*A*cos(d*x+c)^2-10*B*cos(d*x+c)^2-28*A*cos(d*x+c)+20*B*cos(d*x+c)+26*A-10*B)/a/sin(d*x+c)","A"
543,1,173,135,2.548000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-3 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+2 A \left(\cos^{2}\left(d x +c \right)\right)-4 A \cos \left(d x +c \right)+6 B \cos \left(d x +c \right)+2 A -6 B \right)}{3 d a \sin \left(d x +c \right)}"," ",0,"-1/3/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-3*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+2*A*cos(d*x+c)^2-4*A*cos(d*x+c)+6*B*cos(d*x+c)+2*A-6*B)/a/sin(d*x+c)","A"
544,1,142,100,2.268000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(-A \sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d a \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2}}"," ",0,"2/d*(-1+cos(d*x+c))*(-A*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/a/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2","A"
545,1,201,115,2.401000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sqrt{2}+2 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-2 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{d \sin \left(d x +c \right)^{2} a \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/d*(-1+cos(d*x+c))*(B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*2^(1/2)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*2^(1/2)+2*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-2*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^2/a/(-2/(1+cos(d*x+c)))^(1/2)","A"
546,1,342,152,2.337000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-2 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}-B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}+B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \cos \left(d x +c \right) \sqrt{2}+4 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right)-2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-4 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{\cos \left(d x +c \right)}\, \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} a}"," ",0,"1/2/d*(-1+cos(d*x+c))*(2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-2*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)-B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)+B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)*2^(1/2)+4*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)-2*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-4*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/a","B"
547,1,413,191,2.314000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(4 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-4 A \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}-7 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+7 B \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{2}+8 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+16 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-16 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)\right)}{8 d a \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{2} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/8/d*(-1+cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(4*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-4*A*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)-7*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+7*B*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*cos(d*x+c)^2*2^(1/2)+8*A*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)+16*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-2*B*sin(d*x+c)*cos(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2)-16*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+4*B*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c))/a/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^2/cos(d*x+c)^(3/2)","B"
548,1,329,229,2.372000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(225 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-24 A \left(\cos^{4}\left(d x +c \right)\right)-165 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+225 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)+48 A \left(\cos^{3}\left(d x +c \right)\right)-165 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-40 B \left(\cos^{3}\left(d x +c \right)\right)-240 A \left(\cos^{2}\left(d x +c \right)\right)+160 B \left(\cos^{2}\left(d x +c \right)\right)-78 A \cos \left(d x +c \right)+70 B \cos \left(d x +c \right)+294 A -190 B \right)}{60 d \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/60/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(225*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-24*A*cos(d*x+c)^4-165*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+225*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)+48*A*cos(d*x+c)^3-165*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-40*B*cos(d*x+c)^3-240*A*cos(d*x+c)^2+160*B*cos(d*x+c)^2-78*A*cos(d*x+c)+70*B*cos(d*x+c)+294*A-190*B)/sin(d*x+c)^3/a^2","A"
549,1,307,188,2.242000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(33 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-21 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+33 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)+8 A \left(\cos^{3}\left(d x +c \right)\right)-21 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)-32 A \left(\cos^{2}\left(d x +c \right)\right)+24 B \left(\cos^{2}\left(d x +c \right)\right)-14 A \cos \left(d x +c \right)+6 B \cos \left(d x +c \right)+38 A -30 B \right)}{12 d \,a^{2} \sin \left(d x +c \right)^{3}}"," ",0,"1/12/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(33*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-21*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+33*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)+8*A*cos(d*x+c)^3-21*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)-32*A*cos(d*x+c)^2+24*B*cos(d*x+c)^2-14*A*cos(d*x+c)+6*B*cos(d*x+c)+38*A-30*B)/a^2/sin(d*x+c)^3","A"
550,1,235,147,2.323000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+7 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-3 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \,a^{2} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"1/2/d*(-1+cos(d*x+c))*(4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+7*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*A*(-2/(1+cos(d*x+c)))^(1/2)+B*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/a^2/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","A"
551,1,209,104,2.112000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(3 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \,a^{2} \sin \left(d x +c \right)^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"-1/2/d*(-1+cos(d*x+c))*(3*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)+B*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/a^2/sin(d*x+c)^3/(-2/(1+cos(d*x+c)))^(1/2)","A"
552,1,303,152,2.219000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(3/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(2 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-2 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)+A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} a^{2}}"," ",0,"-1/2/d*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(2*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-2*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)+A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+A*(-2/(1+cos(d*x+c)))^(1/2)-B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/a^2","A"
553,1,468,198,2.243000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+5 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-9 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+3 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-2 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{2 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{2}}"," ",0,"1/2/d*(-1+cos(d*x+c))*(2*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-2*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-3*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+3*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+5*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-9*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+3*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-2*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^3/(-2/(1+cos(d*x+c)))^(1/2)/a^2","B"
554,1,531,240,2.036000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(3/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-12 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+12 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+19 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-19 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+12 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-36 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-14 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+52 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+8 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-8 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+10 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right)}{8 d \,a^{2} \sin \left(d x +c \right)^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/8/d*(-1+cos(d*x+c))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-12*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+12*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+19*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-19*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+12*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-36*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-14*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+52*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+8*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-8*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+10*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-4*B*(-2/(1+cos(d*x+c)))^(1/2))/a^2/sin(d*x+c)^3/(-2/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)","B"
555,1,461,270,2.297000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(4245 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-192 A \left(\cos^{5}\left(d x +c \right)\right)-2445 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+8490 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+512 A \left(\cos^{4}\left(d x +c \right)\right)-4890 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)-320 B \left(\cos^{4}\left(d x +c \right)\right)+4245 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-3456 A \left(\cos^{3}\left(d x +c \right)\right)-2445 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+1920 B \left(\cos^{3}\left(d x +c \right)\right)-5974 A \left(\cos^{2}\left(d x +c \right)\right)+3430 B \left(\cos^{2}\left(d x +c \right)\right)+3768 A \cos \left(d x +c \right)-2040 B \cos \left(d x +c \right)+5342 A -2990 B \right)}{480 d \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/480/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(4245*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-192*A*cos(d*x+c)^5-2445*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+8490*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+512*A*cos(d*x+c)^4-4890*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)-320*B*cos(d*x+c)^4+4245*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-3456*A*cos(d*x+c)^3-2445*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+1920*B*cos(d*x+c)^3-5974*A*cos(d*x+c)^2+3430*B*cos(d*x+c)^2+3768*A*cos(d*x+c)-2040*B*cos(d*x+c)+5342*A-2990*B)/sin(d*x+c)^5/a^3","A"
556,1,439,229,2.286000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right)^{2} \left(489 A \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)-225 B \left(\cos^{2}\left(d x +c \right)\right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)+978 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+64 A \left(\cos^{4}\left(d x +c \right)\right)-450 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right) \sin \left(d x +c \right)+489 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, A \sin \left(d x +c \right)-384 A \left(\cos^{3}\left(d x +c \right)\right)-225 \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, B \sin \left(d x +c \right)+192 B \left(\cos^{3}\left(d x +c \right)\right)-686 A \left(\cos^{2}\left(d x +c \right)\right)+318 B \left(\cos^{2}\left(d x +c \right)\right)+408 A \cos \left(d x +c \right)-216 B \cos \left(d x +c \right)+598 A -294 B \right)}{96 d \,a^{3} \sin \left(d x +c \right)^{5}}"," ",0,"-1/96/d*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))^2*(489*A*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)-225*B*cos(d*x+c)^2*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*sin(d*x+c)+978*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+64*A*cos(d*x+c)^4-450*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)*sin(d*x+c)+489*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*A*sin(d*x+c)-384*A*cos(d*x+c)^3-225*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*(-2/(1+cos(d*x+c)))^(1/2)*B*sin(d*x+c)+192*B*cos(d*x+c)^3-686*A*cos(d*x+c)^2+318*B*cos(d*x+c)^2+408*A*cos(d*x+c)-216*B*cos(d*x+c)+598*A-294*B)/a^3/sin(d*x+c)^5","A"
557,1,365,188,2.088000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(32 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+53 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+75 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-13 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-19 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-36 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+75 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-19 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-49 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+9 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \,a^{3} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5}}"," ",0,"-1/16/d*(-1+cos(d*x+c))^2*(32*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+53*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+75*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-13*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-19*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-36*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+75*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-19*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-49*A*(-2/(1+cos(d*x+c)))^(1/2)+9*B*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/a^3/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5","A"
558,1,339,188,2.241000," ","int((A+B*sec(d*x+c))/(a+a*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(13 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+19 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-5 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+5 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+19 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+5 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-9 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}+B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \,a^{3} \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(13*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+19*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-5*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+5*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+19*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+5*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-9*A*(-2/(1+cos(d*x+c)))^(1/2)+B*(-2/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/a^3/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)","A"
559,1,340,147,2.226000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+a*sec(d*x+c))^(5/2),x)","-\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(5 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-5 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+3 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-3 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-5 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-3 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-7 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"-1/16/d*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))^2*(5*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-5*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+3*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-3*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-5*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-3*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-A*(-2/(1+cos(d*x+c)))^(1/2)-7*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
560,1,540,195,2.270000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right)^{2} \left(16 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-16 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+3 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-3 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+16 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-16 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right)-43 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)+11 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+3 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)-4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)-43 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right)+4 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+7 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}-15 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{5} a^{3}}"," ",0,"1/16/d*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))^2*(16*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-16*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+3*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-3*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+16*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)-16*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)-43*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))+11*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+3*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)-4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)-43*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)+4*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+7*A*(-2/(1+cos(d*x+c)))^(1/2)-15*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/(-2/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^5/a^3","B"
561,1,821,241,2.744000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+a*sec(d*x+c))^(5/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right)^{2} \left(-16 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+16 A \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+40 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-40 B \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+11 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)-43 A \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)-16 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+16 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-35 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right)+115 B \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right)+40 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1-\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)-40 B \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{2}\, \arctan \left(\frac{\sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos \left(d x +c \right)+1+\sin \left(d x +c \right)\right) \sqrt{2}}{4}\right)+4 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)-43 A \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-20 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \left(\cos^{2}\left(d x +c \right)\right)+115 B \cos \left(d x +c \right) \sin \left(d x +c \right) \arctan \left(\frac{\sin \left(d x +c \right) \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}}{2}\right)-15 A \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+39 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)+16 B \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a \left(1+\cos \left(d x +c \right)\right)}{\cos \left(d x +c \right)}}}{16 d \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{5} \sqrt{-\frac{2}{1+\cos \left(d x +c \right)}}\, a^{3}}"," ",0,"1/16/d*(-1+cos(d*x+c))^2*(-16*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+16*A*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+40*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2-40*B*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))*sin(d*x+c)*cos(d*x+c)^2+11*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3-43*A*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2-16*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))+16*A*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))-35*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3+115*B*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))*sin(d*x+c)*cos(d*x+c)^2+40*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1-sin(d*x+c))*2^(1/2))-40*B*cos(d*x+c)*sin(d*x+c)*2^(1/2)*arctan(1/4*(-2/(1+cos(d*x+c)))^(1/2)*(cos(d*x+c)+1+sin(d*x+c))*2^(1/2))+4*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2-43*A*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-20*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2+115*B*cos(d*x+c)*sin(d*x+c)*arctan(1/2*sin(d*x+c)*(-2/(1+cos(d*x+c)))^(1/2))-15*A*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+39*B*(-2/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)+16*B*(-2/(1+cos(d*x+c)))^(1/2))*(a*(1+cos(d*x+c))/cos(d*x+c))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^5/(-2/(1+cos(d*x+c)))^(1/2)/a^3","B"
562,1,413,176,5.284000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a A -168 A b -168 a B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a A +168 A b +168 a B +140 B b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a A -42 A b -42 a B -70 B b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +35 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*A*a-168*A*b-168*B*a)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a+168*A*b+168*B*a+140*B*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*A*a-42*A*b-42*B*a-70*B*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b+35*B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
563,1,371,148,4.406000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a A +20 A b +20 a B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a A -10 A b -10 a B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a -15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a+20*A*b+20*B*a)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a-10*A*b-10*B*a)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+5*A*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a+5*a*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
564,1,326,121,4.675000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(4 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b -2 A a \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+3 B b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(4*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b-2*A*a*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+3*B*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
565,1,244,121,5.326000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))*(A+B*sec(d*x+c)),x)","-\frac{2 \left(A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, a +B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b -2 B b \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*(A*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a+a*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b-2*B*b*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
566,1,428,147,9.894000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 B b \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*(A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B*b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
567,1,663,176,13.225000," ","int((a+b*sec(d*x+c))*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 \left(A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)-\frac{2 B b \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2/5*B*b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
568,1,548,218,4.833000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(240 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{8}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-360 a^{2} A -336 A a b -168 a^{2} B \right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(280 a^{2} A +336 A a b +140 A \,b^{2}+168 a^{2} B +280 B a b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-80 a^{2} A -84 A a b -70 A \,b^{2}-42 a^{2} B -140 B a b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+25 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+35 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-126 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +70 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-63 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-105 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{2}\right)}{105 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/105*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(240*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^8+(-360*A*a^2-336*A*a*b-168*B*a^2)*sin(1/2*d*x+1/2*c)^6*cos(1/2*d*x+1/2*c)+(280*A*a^2+336*A*a*b+140*A*b^2+168*B*a^2+280*B*a*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-80*A*a^2-84*A*a*b-70*A*b^2-42*B*a^2-140*B*a*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+25*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+35*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-126*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+70*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-63*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-105*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
569,1,487,180,5.316000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-24 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 a^{2} A +40 A a b +20 a^{2} B \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 a^{2} A -20 A a b -10 a^{2} B \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+10 A a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+5 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+15 b^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-30 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b \right)}{15 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-24*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a^2+40*A*a*b+20*B*a^2)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a^2-20*A*a*b-10*B*a^2)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+10*A*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+5*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+15*b^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-30*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
570,1,404,165,5.301000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{2 \left(4 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-6 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -2 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+3 B \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, b^{2}-6 B \,b^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{3 \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-6*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2+6*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+3*B*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*b^2-6*B*b^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
571,1,677,170,10.267000," ","int(cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^2*(A+B*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(\EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-\EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{4 A a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b \left(A b +2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 b^{2} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-EllipticE(cos(1/2*d*x+1/2*c),2^(1/2)))-2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+4*A*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a^2*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*b*(A*b+2*B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*b^2*B*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
572,1,750,208,14.557000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 a \left(2 A b +a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}-\frac{2 b^{2} B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+2 b \left(A b +2 a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+2*a*(2*A*b+B*a)*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2/5*b^2*B/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b*(A*b+2*B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
573,1,859,246,16.099000," ","int((a+b*sec(d*x+c))^2*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 b \left(A b +2 a B \right) \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}+2 b^{2} B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{56 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{4}}-\frac{5 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{42 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{5 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{21 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)+\frac{2 a^{2} A \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+2 a \left(2 A b +a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/5*b*(A*b+2*B*a)/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b^2*B*(-1/56*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^4-5/42*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+5/21*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*a^2*A*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*a*(2*A*b+B*a)*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
574,1,1074,248,5.943000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(-24 A \,a^{4}+24 A \,a^{3} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(24 A \,a^{4}-44 A \,a^{3} b +20 A \,a^{2} b^{2}+20 a^{4} B -20 B \,a^{3} b \right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+\left(-6 A \,a^{4}+16 A \,a^{3} b -10 A \,a^{2} b^{2}-10 a^{4} B +10 B \,a^{3} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)-9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}+9 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{4}-5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +5 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}+15 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{4}+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b -15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}+15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \,b^{3}+5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{4}-5 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3} b +15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b^{2}-15 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{3}\right)}{15 a^{4} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/15*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((-24*A*a^4+24*A*a^3*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6+(24*A*a^4-44*A*a^3*b+20*A*a^2*b^2+20*B*a^4-20*B*a^3*b)*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+(-6*A*a^4+16*A*a^3*b-10*A*a^2*b^2-10*B*a^4+10*B*a^3*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)-9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^4+9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^4-5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+5*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3+15*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^4+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b^3+5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^4-5*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^3*b+15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b^2-15*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^3)/a^4/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
575,1,786,208,5.595000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\left(4 A \,a^{3}-4 A \,a^{2} b \right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\left(-2 A \,a^{3}+2 A \,a^{2} b \right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+A \,a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-A \,a^{2} b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 A \,b^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \,b^{2}+3 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{3}-3 a^{2} b B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+3 B a \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{3}+3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2} b -3 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \,b^{2}\right)}{3 a^{3} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2/3*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*((4*A*a^3-4*A*a^2*b)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+(-2*A*a^3+2*A*a^2*b)*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c)+A*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-A*a^2*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*A*b^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b^2+3*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^3-3*a^2*b*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3*B*a*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^3+3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2*b-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b^2)/a^3/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
576,1,295,167,5.162000," ","int(cos(d*x+c)^(1/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c)),x)","\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b^{2}+A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}-A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b +A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b^{2}-B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}+B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a b \right)}{a^{2} \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b^2+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b+A*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b^2-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2+B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-B*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a*b)/a^2/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
577,1,217,113,5.049000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c)),x)","-\frac{2 \sqrt{\left(2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \left(A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +A \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) b -B \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right) a \right)}{a \left(a -b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-2*((2*cos(1/2*d*x+1/2*c)^2-1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)*(A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a-A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*b-B*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))*a)/a/(a-b)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","A"
578,1,325,136,8.678000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \left(A b -a B \right) a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 B \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*(A*b-B*a)/b/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*B/b*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
579,1,466,220,11.585000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \left(A b -a B \right) a^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(A*b-B*a)*a^2/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B/b*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
580,1,785,279,15.598000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c)),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \left(A b -a B \right) a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 B \left(12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-24 \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+24 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)+3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-8 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right)\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{5 b \left(8 \left(\sin^{6}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-12 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+6 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right) \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2}}-\frac{2 \left(A b -a B \right) a \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 \left(A b -a B \right) \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*(A*b-B*a)*a^3/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2/5*B/b/(8*sin(1/2*d*x+1/2*c)^6-12*sin(1/2*d*x+1/2*c)^4+6*sin(1/2*d*x+1/2*c)^2-1)/sin(1/2*d*x+1/2*c)^2*(12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^4-24*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^6-12*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*sin(1/2*d*x+1/2*c)^2+24*sin(1/2*d*x+1/2*c)^4*cos(1/2*d*x+1/2*c)+3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-8*sin(1/2*d*x+1/2*c)^2*cos(1/2*d*x+1/2*c))*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)-2*(A*b-B*a)/b^3*a*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b-B*a)/b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
581,1,1059,375,15.997000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{\frac{8 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}+\frac{2 a^{2} A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3}+6 A \,b^{2} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+4 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a b -\frac{4 A \,a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}{3}-4 B a b \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)-2 B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{a^{4} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{2} \left(4 A b -3 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 b^{3} \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{4}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/3/a^4*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+6*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-6*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+2*b^2/a^3*(4*A*b-3*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^3*(A*b-B*a)/a^4*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
582,1,843,299,13.830000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \left(2 A \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) b +A \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a -B \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a \right)}{a^{3} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b \left(3 A b -2 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 b^{2} \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{3}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^3/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(2*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a)-2/a^2*b*(3*A*b-2*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^2*(A*b-B*a)/a^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
583,1,802,279,11.822000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^2/cos(d*x+c)^(1/2),x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{a^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{2 \left(-2 A b +a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*(-2*A*b+B*a)/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)*b/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
584,1,715,273,11.371000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{\left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(-A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*A/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(-A*b+B*a)/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
585,1,877,329,14.906000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} B \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 B \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{2} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 \left(A b -a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*B/b^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*B/b^2*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*(A*b-B*a)/b*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
586,1,1024,414,20.449000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^2,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 a^{2} \left(A b -2 a B \right) \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{b^{3} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -2 a B \right) \left(-\sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)+2 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}\, \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)\right)}{b^{3} \sin \left(\frac{d x}{2}+\frac{c}{2}\right)^{2} \left(2 \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1\right)}+\frac{2 B \left(-\frac{\cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{6 \left(-\frac{1}{2}+\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)^{2}}+\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{3 \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}-\frac{2 \left(A b -a B \right) a \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{b^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(A*b-2*B*a)/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-2*B*a)/b^3*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)+2*B/b^2*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))-2*(A*b-B*a)*a/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
587,1,2216,521,22.695000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2/3/a^5*(4*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^4+a^2*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+18*A*b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+9*A*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a*b-2*A*a^2*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2-9*B*a*b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3*B*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a^2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)+4/a^4*b^2*(5*A*b-3*B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^4*(A*b-B*a)/a^5*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a^5*b^3*(5*A*b-4*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
588,1,2000,431,21.886000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2/a^4/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*(3*A*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*b+A*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))*a-B*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a)-6/a^3*b*(2*A*b-B*a)/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*b^3*(A*b-B*a)/a^4*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))-2*b^2/a^4*(4*A*b-3*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
589,1,1959,410,19.949000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^3/cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*A/a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-2*(-3*A*b+B*a)/a^2/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*b^2*(A*b-B*a)/a^3*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/a^3*b*(3*A*b-2*B*a)*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
590,1,1872,402,20.359000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(-\frac{2 A \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{a \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{2 \left(A b -a B \right) b \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}+\frac{2 \left(-2 A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a^{2}}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*A/a/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)*b/a^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*(-2*A*b+B*a)/a^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
591,1,1768,406,19.436000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^3,x)","-\frac{\sqrt{-\left(-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1\right) \left(\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)}\, \left(\frac{2 \left(-A b +a B \right) \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{2 b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)^{2}}+\frac{3 a^{2} \left(a^{2}-3 b^{2}\right) \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{4 b^{2} \left(a^{2}-b^{2}\right)^{2} \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{3 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a^{2}}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right) a}{4 \left(a +b \right) \left(a^{2}-b^{2}\right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{7 \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a +b \right) \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 b^{2} \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{9 a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{8 \left(a^{2}-b^{2}\right)^{2} \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{3 a^{5} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) b^{2} \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{4 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{15 b^{2} a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{8 \left(a -b \right) \left(a +b \right) \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}+\frac{2 A \left(\frac{a^{2} \cos \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}{b \left(a^{2}-b^{2}\right) \left(2 a \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-a +b \right)}-\frac{\sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 \left(a +b \right) b \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticF \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticE \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}-\frac{a^{3} \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 b \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}+\frac{3 b a \sqrt{\frac{1}{2}-\frac{\cos \left(d x +c \right)}{2}}\, \sqrt{-2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+1}\, \EllipticPi \left(\cos \left(\frac{d x}{2}+\frac{c}{2}\right), \frac{2 a}{a -b}, \sqrt{2}\right)}{2 \left(a^{2}-b^{2}\right) \left(a^{2}-a b \right) \sqrt{-2 \left(\sin^{4}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)+\sin^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)}}\right)}{a}\right)}{\sin \left(\frac{d x}{2}+\frac{c}{2}\right) \sqrt{2 \left(\cos^{2}\left(\frac{d x}{2}+\frac{c}{2}\right)\right)-1}\, d}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*(-A*b+B*a)/a*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*A/a*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
592,1,2024,480,23.806000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*B/b^3/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+2*(A*b-B*a)/b*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2/b^3*B*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2*a*B/b^2*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
593,1,2178,579,35.259000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(9/2)/(a+b*sec(d*x+c))^3,x)","\text{Expression too large to display}"," ",0,"-(-(-2*cos(1/2*d*x+1/2*c)^2+1)*sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*a^2*(A*b-3*B*a)/b^4/(a^2-a*b)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-2*a*(A*b-B*a)/b^2*(1/2*a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)^2+3/4*a^2*(a^2-3*b^2)/b^2/(a^2-b^2)^2*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-3/8/(a+b)/(a^2-b^2)/b^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a^2-1/4/(a+b)/(a^2-b^2)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))*a+7/8/(a+b)/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-3/8*a^3/b^2/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+9/8*a/(a^2-b^2)^2*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-3/8/(a-b)/(a+b)/(a^2-b^2)/b^2/(a^2-a*b)*a^5*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/4/(a-b)/(a+b)/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))-15/8/(a-b)/(a+b)/(a^2-b^2)*b^2/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2)))+2*B/b^3*(-1/6*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(-1/2+cos(1/2*d*x+1/2*c)^2)^2+1/3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2)))+2*(A*b-3*B*a)/b^4*(-(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(2*sin(1/2*d*x+1/2*c)^2-1)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))+2*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*cos(1/2*d*x+1/2*c)*sin(1/2*d*x+1/2*c)^2)/sin(1/2*d*x+1/2*c)^2/(2*sin(1/2*d*x+1/2*c)^2-1)-2*a*(A*b-2*B*a)/b^3*(a^2/b/(a^2-b^2)*cos(1/2*d*x+1/2*c)*(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)/(2*a*cos(1/2*d*x+1/2*c)^2-a+b)-1/2/(a+b)/b*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))+1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticF(cos(1/2*d*x+1/2*c),2^(1/2))-1/2*a/b/(a^2-b^2)*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticE(cos(1/2*d*x+1/2*c),2^(1/2))-1/2/b/(a^2-b^2)/(a^2-a*b)*a^3*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))+3/2*b/(a^2-b^2)/(a^2-a*b)*a*(sin(1/2*d*x+1/2*c)^2)^(1/2)*(-2*cos(1/2*d*x+1/2*c)^2+1)^(1/2)/(-2*sin(1/2*d*x+1/2*c)^4+sin(1/2*d*x+1/2*c)^2)^(1/2)*EllipticPi(cos(1/2*d*x+1/2*c),2*a/(a-b),2^(1/2))))/sin(1/2*d*x+1/2*c)/(2*cos(1/2*d*x+1/2*c)^2-1)^(1/2)/d","B"
594,1,2364,367,2.872000," ","int(cos(d*x+c)^(7/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\text{Expression too large to display}"," ",0,"2/105/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(18*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-14*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-8*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)+14*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+49*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+14*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-19*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-8*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+19*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-19*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+28*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+26*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-7*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-19*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+20*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+14*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-14*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4-8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+21*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*(1/(1+cos(d*x+c)))^(1/2)+42*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-19*A*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-7*B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+14*B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)+63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-63*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4+15*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^4*(1/(1+cos(d*x+c)))^(1/2))/a^3/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
595,1,1699,297,2.102000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(-5 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}+9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +2 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-10 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}-3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -5 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +5 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-7 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -4 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+9 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-2 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}+9 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{15 d \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"-2/15/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-5*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-7*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-2*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-5*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)+9*A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+9*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3)/a^2/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)","B"
596,1,1162,237,2.603000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{2}+A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}+3 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -A \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{3 d a \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"2/3/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^2+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2+3*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-A*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2))/a/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)","B"
597,1,822,277,2.232000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)*(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a -A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b +A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b +B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b +2 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b -A \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"2/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*a-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*a+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b-A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b+B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b-A*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b)*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","C"
598,1,789,318,2.863000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(1/2),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b +4 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b +B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 B \cos \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -B \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \sqrt{\frac{a -b}{a +b}}\, b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b+4*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*b*(1/(1+cos(d*x+c)))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^(1/2)","C"
599,1,1475,387,1.966000," ","int((A+B*sec(d*x+c))*(a+b*sec(d*x+c))^(1/2)/cos(d*x+c)^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}-8 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -4 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b +4 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}-B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b +2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}-8 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}-B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 B \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{4 d b \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b-4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^2-8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+4*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a^2-B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b+2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2-8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2-B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/b/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^(3/2)","C"
600,1,3069,445,3.375000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"2/315/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-246*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+165*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-8*A*((a-b)/(a+b))^(1/2)*b^5*(1/(1+cos(d*x+c)))^(1/2)+81*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+68*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+204*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-9*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-33*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+34*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+85*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+53*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+117*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+52*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-147*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+33*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2-33*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3+8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4-246*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+153*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+18*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+246*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b-246*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2-18*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3+18*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4+186*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-33*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+2*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3-8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+30*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^5*(1/(1+cos(d*x+c)))^(1/2)-75*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^5*(1/(1+cos(d*x+c)))^(1/2)+75*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-147*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^5*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^5*(1/(1+cos(d*x+c)))^(1/2)-147*A*((a-b)/(a+b))^(1/2)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-88*A*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-33*A*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)-75*B*((a-b)/(a+b))^(1/2)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-246*B*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-9*B*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+18*B*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+45*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^5*(1/(1+cos(d*x+c)))^(1/2)+35*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^6*a^5*(1/(1+cos(d*x+c)))^(1/2)+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^5*(1/(1+cos(d*x+c)))^(1/2)+98*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^5*(1/(1+cos(d*x+c)))^(1/2)+147*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5-147*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5+18*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-18*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2))/a^3/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
601,1,2326,366,2.148000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(21 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+42 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+10 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 A \sqrt{\frac{a -b}{a +b}}\, b^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-82 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+55 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-21 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+21 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+21 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-21 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a \,b^{3}+84 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{3} b -21 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2} b^{2}-82 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{3} b +51 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2} b^{2}+6 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a \,b^{3}+82 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{3} b +25 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{4}+6 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{4}+63 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{4}-63 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4}+15 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{5}\left(d x +c \right)\right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-63 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-25 A \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-82 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-63 B \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-42 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-21 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-25 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-82 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-6 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a \,b^{3}-63 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{3} b +39 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+27 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+63 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+68 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+63 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{105 d \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"2/105/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(39*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+21*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+6*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-21*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+84*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-21*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+27*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-82*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+51*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+6*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+82*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-82*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+63*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+68*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+63*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-82*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+55*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-21*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+21*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4+6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+21*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*(1/(1+cos(d*x+c)))^(1/2)+42*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-82*A*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-42*B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-21*B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)+63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-63*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4+15*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^4*(1/(1+cos(d*x+c)))^(1/2))/a^2/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
602,1,1749,296,2.793000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(-9 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-3 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}-9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +3 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+25 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}+6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+20 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+20 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -20 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+12 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +9 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-9 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-9 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -3 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}+15 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}\right)}{15 d a \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"2/15/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(25*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-20*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+20*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-20*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+12*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+3*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+5*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-20*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-9*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-3*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3+15*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2)/a/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
603,1,1429,335,2.198000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c)),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -4 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{2}+A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-4 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b +3 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}+6 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -3 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}+6 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}-3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{3 d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+5*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^2+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-4*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b+3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2+6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2+6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2))/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","C"
604,1,1410,337,2.834000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(-2 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2}+2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+2 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}-2 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}-6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a b -B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+B \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\cos \left(d x +c \right)}\, \sin \left(d x +c \right)^{3}}"," ",0,"-1/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-2*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-2*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2+2*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-4*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*a^2-2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2-6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b^2+B*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)/sin(d*x+c)^3","C"
605,1,1659,390,2.555000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","\frac{\sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(4 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+24 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b +8 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}-8 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b +4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+5 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}+8 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+2 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}+2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -4 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-5 B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}+5 B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-7 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}\right)}{4 d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3} \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"1/4/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+24*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+8*A*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2-8*A*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b+4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^2+5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2+8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+2*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2+2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b-4*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-5*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a^2+5*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-7*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^(3/2)","C"
606,1,2351,466,3.862000," ","int((a+b*sec(d*x+c))^(3/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\text{Expression too large to display}"," ",0,"1/24/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-17*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+48*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*b^3-8*B*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-22*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-30*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-42*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)+16*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-8*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-3*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)+16*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^3+12*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-24*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^3+30*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+6*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+30*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+12*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+14*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+16*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^3+6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^3-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^3+72*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a*b^2+14*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b-20*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b-16*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2+36*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^2*b+12*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b+12*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2-30*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b+30*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2)/b/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(5/2)/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","C"
607,1,3816,531,4.773000," ","int(cos(d*x+c)^(11/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"2/3465/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(2992*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)+1535*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-40*A*((a-b)/(a+b))^(1/2)*b^6*(1/(1+cos(d*x+c)))^(1/2)-40*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^6-3069*B*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-55*B*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+110*B*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+315*A*cos(d*x+c)^7*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)+90*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)+270*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)-675*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)-1617*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6+385*B*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)+154*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)+1078*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)+40*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^6*(1/(1+cos(d*x+c)))^(1/2)-1617*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)-675*A*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)-3705*A*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-1025*A*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-255*A*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+20*A*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)-1617*B*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)-1793*B*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)+675*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6-255*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+260*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)-40*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)-715*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)-3069*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)+2189*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+110*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)-110*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+1430*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+430*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+580*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+1870*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-3705*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+3315*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-255*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+10*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-40*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+3705*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b-3705*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2+255*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3-255*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+40*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5+1120*A*cos(d*x+c)^6*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+2871*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-3069*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+1705*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+110*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-1617*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b+3069*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2-3069*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3-110*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+110*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5+1370*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)+800*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+902*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+880*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+1617*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6+2830*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+700*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+20*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)-55*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)-3705*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2))/a^3/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
608,1,3069,443,2.774000," ","int(cos(d*x+c)^(9/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{output too large to display}"," ",0,"2/315/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-435*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+165*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*b^5*(1/(1+cos(d*x+c)))^(1/2)+270*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+272*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+330*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+180*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-65*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-279*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+199*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+130*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+170*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+180*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+82*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+80*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-147*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b+279*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2-279*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3-10*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4-435*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b+405*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-45*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+435*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b-435*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2+45*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3-45*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4+261*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-279*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+155*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+10*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4+30*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^5*(1/(1+cos(d*x+c)))^(1/2)-75*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^5*(1/(1+cos(d*x+c)))^(1/2)+75*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5-147*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^5*(1/(1+cos(d*x+c)))^(1/2)-10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^5*(1/(1+cos(d*x+c)))^(1/2)-147*A*((a-b)/(a+b))^(1/2)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-163*A*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-279*A*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-5*A*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)-75*B*((a-b)/(a+b))^(1/2)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-435*B*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-135*B*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-45*B*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+45*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^5*(1/(1+cos(d*x+c)))^(1/2)+35*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^6*a^5*(1/(1+cos(d*x+c)))^(1/2)+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^5*(1/(1+cos(d*x+c)))^(1/2)+98*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^5*(1/(1+cos(d*x+c)))^(1/2)+147*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5+10*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5-147*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5-45*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+45*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2))/a^2/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
609,1,2450,364,3.026000," ","int(cos(d*x+c)^(7/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\text{Expression too large to display}"," ",0,"2/105/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(60*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+161*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-15*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-161*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+119*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-161*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+90*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-145*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+135*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-15*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+145*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-145*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+15*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+98*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+110*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+60*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+238*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-145*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+55*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-15*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-161*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+161*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+105*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+25*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4-15*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+21*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*(1/(1+cos(d*x+c)))^(1/2)+42*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*(1/(1+cos(d*x+c)))^(1/2)+15*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-145*A*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-45*A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-63*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-77*B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-161*B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*(1/(1+cos(d*x+c)))^(1/2)-25*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)+63*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-63*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4+15*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^5*a^4*(1/(1+cos(d*x+c)))^(1/2))/a/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
610,1,2052,395,2.177000," ","int(cos(d*x+c)^(5/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(-9 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}-23 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}-5 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +23 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+40 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}+6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-23 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-35 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+35 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+35 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -35 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+17 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +14 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+34 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-23 A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-15 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{3}+15 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{3}+30 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{3}-5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-9 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+23 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-9 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-11 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-35 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-35 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -23 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}+45 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}\right)}{15 d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"2/15/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(40*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-5*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-23*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+35*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-35*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+35*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-35*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+17*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-23*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+23*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+34*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-23*A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+5*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)-15*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+30*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3+15*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+23*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-11*A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-35*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-9*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3-23*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3+45*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)","C"
611,1,2073,402,2.847000," ","int(cos(d*x+c)^(3/2)*(a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c)),x)","\frac{\left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(-3 B \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}-2 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-14 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+16 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+14 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-12 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}-6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -3 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+18 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}+14 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -14 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-14 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +18 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +30 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a \,b^{2}+2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-6 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{3}-6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+3 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}+12 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{3}-14 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{3 d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/3/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-3*B*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+16*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+14*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+6*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)-12*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-3*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+30*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b^2+18*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+14*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-14*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-14*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+18*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-6*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^3+12*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^3-14*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+3*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)","C"
612,1,2216,410,2.317000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))*cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-9*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-11*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-4*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3-8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3+8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-8*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3+4*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3+30*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-9*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+9*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+40*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2+24*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-16*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-8*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+9*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+9*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/cos(d*x+c)^(3/2)/(1/(1+cos(d*x+c)))^(1/2)","C"
613,1,2441,467,2.870000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/24/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-59*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+48*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*b^3-8*B*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-34*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-54*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-66*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+33*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)+16*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-8*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-33*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)+16*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^3+12*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+48*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^3*a^3-24*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*b^3+54*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+33*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+18*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+54*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+12*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+26*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+16*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+30*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^3+18*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^3-33*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^3+120*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a*b^2+26*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b-44*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2+33*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b-16*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2+180*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^3*a^2*b-36*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b+12*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2-54*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a^2*b+54*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^3*a*b^2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/cos(d*x+c)^(5/2)/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)","C"
614,1,3175,552,2.327000," ","int((a+b*sec(d*x+c))^(5/2)*(A+B*sec(d*x+c))/cos(d*x+c)^(3/2),x)","\text{output too large to display}"," ",0,"1/192/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(-264*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+288*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*b^4-48*B*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-472*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-133*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-272*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-254*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-184*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+264*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+208*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+128*A*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+118*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+284*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+72*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+128*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+264*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+144*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+15*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-30*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+284*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-172*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+30*B*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4-144*B*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4-15*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4-30*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^4+15*B*cos(d*x+c)^5*((a-b)/(a+b))^(1/2)*a^4*(1/(1+cos(d*x+c)))^(1/2)+128*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-64*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)+72*B*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-24*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)+960*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^3+118*B*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-76*B*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+72*B*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+15*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-284*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+284*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+720*B*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2+144*A*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+208*A*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-352*A*cos(d*x+c)^4*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3-264*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+264*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2-128*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+240*A*cos(d*x+c)^4*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b-15*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^4*(1/(1+cos(d*x+c)))^(1/2)-64*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2))/b/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3/cos(d*x+c)^(7/2)","C"
615,1,1700,310,3.356000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(9 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+8 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}-10 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -8 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+5 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3}-6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+8 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-10 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+10 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+10 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -10 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-2 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+8 A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+9 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-8 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-10 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-10 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +8 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}\right)}{15 d \,a^{3} \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"-2/15/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-10*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+10*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-10*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+10*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-10*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-2*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+8*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2+9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-5*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-5*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)+9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)+9*A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-10*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+9*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3)/a^3/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
616,1,1080,248,2.414000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}+2 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b +2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{2}-A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}+3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}-3 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{3 d \,a^{2} \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))*(A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^2-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+2*A*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2))/a^2/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)/sin(d*x+c)^3","B"
617,1,564,196,3.277000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right) \left(A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a -A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a +A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -A \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b \right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}}{d a \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"2/d*(-1+cos(d*x+c))*(1+cos(d*x+c))*(A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*a+A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a-A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*a+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b+B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-A*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b)*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)/a/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)","B"
618,1,257,184,2.373000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{2 \left(A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)-B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right)+2 B \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right)\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}}{d \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}"," ",0,"-2/d*(A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))-B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))+2*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2)))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/(1/(1+cos(d*x+c)))^(1/2)","C"
619,1,776,321,3.306000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(2 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -4 A \cos \left(d x +c \right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b -B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a +2 B \cos \left(d x +c \right) \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -B \cos \left(d x +c \right) \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \sqrt{\frac{a -b}{a +b}}\, b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right)}{d b \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \sqrt{\cos \left(d x +c \right)}}"," ",0,"1/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(2*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-4*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)-2*B*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a+2*B*cos(d*x+c)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-B*cos(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*b*(1/(1+cos(d*x+c)))^(1/2))/b/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)/(1/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(1/2)","C"
620,1,1569,395,2.357000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(1/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right) \left(4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -4 A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+8 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -8 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b -4 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}+3 B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b -6 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a^{2}-8 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) b^{2}+6 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-2 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) a b +4 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}+3 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 B \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}\right)}{4 d \,b^{2} \sqrt{\frac{a -b}{a +b}}\, \left(b +a \cos \left(d x +c \right)\right) \sin \left(d x +c \right)^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \cos \left(d x +c \right)^{\frac{3}{2}}}"," ",0,"-1/4/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))*(4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b-4*A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*b^2+8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b-8*A*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b-4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-3*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a^2+3*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)^2*a*b-6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a^2-8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*b^2+6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*a*b+4*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2)/b^2/((a-b)/(a+b))^(1/2)/(b+a*cos(d*x+c))/sin(d*x+c)^3/(1/(1+cos(d*x+c)))^(1/2)/cos(d*x+c)^(3/2)","C"
621,1,2084,449,3.183000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(5 B \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{4}+3 A \left(\cos^{4}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-48 A \sqrt{\frac{a -b}{a +b}}\, b^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-18 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+20 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-40 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+40 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a \,b^{3}+30 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{3} b +40 B \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2} b^{2}-12 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{3} b -36 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2} b^{2}-48 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a \,b^{3}-9 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{4}-48 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{4}+5 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{4}+24 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 A \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+9 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{4}+48 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-9 A \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-24 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 B \sqrt{\frac{a -b}{a +b}}\, a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+20 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+40 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-9 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{4} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+24 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2} b^{2}-25 B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{3} b +3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{4}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+5 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+6 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+24 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-20 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{15 d \,a^{4} \left(b +a \cos \left(d x +c \right)\right) \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"2/15/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^4*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-48*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)+40*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3+30*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+40*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-12*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-36*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-48*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+24*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+24*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-18*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+20*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-40*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-25*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b+9*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^4+5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*a^4+3*A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*(1/(1+cos(d*x+c)))^(1/2)+6*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*(1/(1+cos(d*x+c)))^(1/2)+24*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-20*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-9*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4-48*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+48*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-24*A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-5*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+20*B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+40*B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-9*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)+5*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^4/(b+a*cos(d*x+c))/(a-b)/sin(d*x+c)^3","B"
622,1,1460,358,2.369000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(\sqrt{\cos}\left(d x +c \right)\right) \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}+8 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}+4 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-5 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b +3 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{3}+6 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+6 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{3}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+8 A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-8 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-6 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, \left(\cos^{3}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3}-6 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +8 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{3 d \,a^{3} \left(b +a \cos \left(d x +c \right)\right) \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-6*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+6*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+8*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-5*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)-3*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-6*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3+A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3-4*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2))*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^3/(b+a*cos(d*x+c))/(a-b)/sin(d*x+c)^3","B"
623,1,889,277,3.136000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, a^{2}+A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-2 A \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) b^{2}-A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a^{2}-2 A \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) a b -A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a b +B \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{2}-B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sqrt{\frac{a -b}{a +b}}\, b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{d \,a^{2} \left(b +a \cos \left(d x +c \right)\right) \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"2/d*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*(1/(1+cos(d*x+c)))^(1/2)*a^2+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+A*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^2-A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2-2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b-A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^2/(b+a*cos(d*x+c))/(a-b)/sin(d*x+c)^3","B"
624,1,564,257,2.437000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(3/2)/cos(d*x+c)^(1/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \left(1+\cos \left(d x +c \right)\right)^{2} \left(A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b -B \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{d a \left(b +a \cos \left(d x +c \right)\right) \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"2/d*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b+B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b-B*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a/(b+a*cos(d*x+c))/(a-b)/sin(d*x+c)^3","B"
625,1,840,262,2.954000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(3/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b -A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b -B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a -B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b +B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a +2 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a +2 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b -A \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b +B \sqrt{\frac{a -b}{a +b}}\, a \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{d b \left(b +a \cos \left(d x +c \right)\right) \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"2/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b+A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b-A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b-B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2)-2*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a-B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b+B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a+2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b-A*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b+B*((a-b)/(a+b))^(1/2)*a*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/b/(b+a*cos(d*x+c))/(a-b)/sin(d*x+c)^3","C"
626,1,1441,432,2.283000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(3/2),x)","-\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(2 A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a b -4 A \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) a b -4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) b^{2}+4 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b +2 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, b^{2}-3 B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) a^{2}-B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{2}+6 B \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \sin \left(d x +c \right) \cos \left(d x +c \right) a^{2}+6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticPi \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \frac{a +b}{a -b}, \frac{i}{\sqrt{\frac{a -b}{a +b}}}\right) a b -6 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2}-4 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a b -2 A \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 B \cos \left(d x +c \right) \sqrt{\frac{a -b}{a +b}}\, a^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}+B \sqrt{\frac{a -b}{a +b}}\, a b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}\, b^{2}\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{d \,b^{2} \left(b +a \cos \left(d x +c \right)\right) \sqrt{\cos \left(d x +c \right)}\, \left(a -b \right) \sin \left(d x +c \right)^{3}}"," ",0,"-1/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(2*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)-2*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b-4*A*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a*b-4*A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*b^2+4*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b+2*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^2-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^2-B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^2+6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*cos(d*x+c)*a^2+6*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*a*b-6*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2-4*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b-2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*(1/(1+cos(d*x+c)))^(1/2)*b^2+B*((a-b)/(a+b))^(1/2)*a*b*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)*b^2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/b^2/(b+a*cos(d*x+c))/cos(d*x+c)^(1/2)/(a-b)/sin(d*x+c)^3","C"
627,1,2295,534,2.924000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(3/2),x)","\text{Expression too large to display}"," ",0,"1/4/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-2*B*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+5*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)-30*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^3-4*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+8*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*b^3+15*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)-15*B*(1/(1+cos(d*x+c)))^(1/2)*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^3-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-2*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*b^3+30*B*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3+15*B*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3-24*A*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b+8*B*cos(d*x+c)^2*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a*b^2+30*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-7*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-20*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-24*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-12*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+24*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a^2*b+16*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)^2*sin(d*x+c)*a*b^2-12*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-5*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-5*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+2*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2))*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/b^3/(b+a*cos(d*x+c))/cos(d*x+c)^(3/2)/(a-b)/sin(d*x+c)^3","C"
628,1,5675,606,2.651000," ","int(cos(d*x+c)^(5/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
629,1,4480,496,3.245000," ","int(cos(d*x+c)^(3/2)*(A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"-2/3/d*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*cos(d*x+c)^(1/2)*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(-18*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-14*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-3*B*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^6+3*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6+A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^6-3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+4*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)-6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)+6*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-8*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+16*A*((a-b)/(a+b))^(1/2)*b^6*(1/(1+cos(d*x+c)))^(1/2)-8*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3+16*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+8*A*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-28*A*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-9*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b+16*A*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+15*B*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2+16*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^6+11*B*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-4*B*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)-8*B*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)-16*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*b^6*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-7*A*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-20*A*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+3*B*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^6+A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^6-3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^6*(1/(1+cos(d*x+c)))^(1/2)-22*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)+34*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+16*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+6*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+12*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-18*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-8*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+8*B*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)-A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+A*cos(d*x+c)^4*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b-9*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-16*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3+12*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+16*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^5+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2-28*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^4+3*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^5*b+9*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b^2-6*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^3-8*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b+15*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3-8*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^5+6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^4*b^2*(1/(1+cos(d*x+c)))^(1/2)-6*A*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)-3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-7*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)+34*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^3*(1/(1+cos(d*x+c)))^(1/2)-24*A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a*b^5*(1/(1+cos(d*x+c)))^(1/2)+12*B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^4*(1/(1+cos(d*x+c)))^(1/2)+2*A*cos(d*x+c)*((a-b)/(a+b))^(1/2)*a^5*b*(1/(1+cos(d*x+c)))^(1/2)-8*B*cos(d*x+c)*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^4+9*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^5*b-6*B*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2-16*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b^2+12*A*cos(d*x+c)*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^3)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^4/(a+b)/(a-b)^2/(b+a*cos(d*x+c))^2/sin(d*x+c)^3","B"
630,1,3337,398,2.689000," ","int((A+B*sec(d*x+c))*cos(d*x+c)^(1/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^3*b^2-6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*b^5*(1/(1+cos(d*x+c)))^(1/2)+3*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^4*b-4*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^3-3*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^5+3*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^5+B*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b^2+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^5+18*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^4*(1/(1+cos(d*x+c)))^(1/2)-6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*b*(1/(1+cos(d*x+c)))^(1/2)+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-12*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)+18*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^4*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^3*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+3*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^4*b-15*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b^3+3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-3*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2-2*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+6*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3*b^2-2*B*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^4-3*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^4*b-9*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^3*b^2+6*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b^3+8*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^4-8*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^5*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-11*A*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)-9*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^4*b+6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3*b^2+8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b^3-15*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3*b^2+8*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a*b^4-3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^4*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^3*b^2+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^4*b-2*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*cos(d*x+c)*a^2*b^3+3*A*(1/(1+cos(d*x+c)))^(1/2)*cos(d*x+c)^3*((a-b)/(a+b))^(1/2)*a^5+5*B*((a-b)/(a+b))^(1/2)*a^3*b^2*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)-2*B*((a-b)/(a+b))^(1/2)*a*b^4*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^5*(1/(1+cos(d*x+c)))^(1/2)+8*A*sin(d*x+c)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*b^5-2*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^3*(1/(1+cos(d*x+c)))^(1/2)+2*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^4*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^3/(a+b)/(a-b)^2/(b+a*cos(d*x+c))^2/sin(d*x+c)^3","B"
631,1,2416,376,3.169000," ","int((A+B*sec(d*x+c))/(a+b*sec(d*x+c))^(5/2)/cos(d*x+c)^(1/2),x)","\text{Expression too large to display}"," ",0,"-2/3/d*(-1+cos(d*x+c))*(1+cos(d*x+c))^2*(-3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^4+2*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3-3*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2-3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3-6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^2*b^2+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+6*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-3*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-6*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^3*b+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^3+B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b+B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^2+3*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b+2*A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^2*b^2+2*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-5*A*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+2*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a^2/(a+b)/(a-b)^2/(b+a*cos(d*x+c))^2/sin(d*x+c)^3","B"
632,1,1925,359,2.292000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(3/2)/(a+b*sec(d*x+c))^(5/2),x)","\frac{2 \left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\cos \left(d x +c \right)}}\, \left(1+\cos \left(d x +c \right)\right)^{2} \left(-A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) b^{3}+3 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -3 B \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+3 A \sqrt{\frac{a -b}{a +b}}\, \left(\cos^{2}\left(d x +c \right)\right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-4 B \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 B \sin \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}+3 A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -B \sqrt{\frac{a -b}{a +b}}\, a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \sqrt{\frac{a -b}{a +b}}\, b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-A \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-3 A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{a -b}{a +b}}\, \cos \left(d x +c \right) b^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-2 A \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+A \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}-B \sqrt{\frac{a -b}{a +b}}\, a^{2} b \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+4 B \sqrt{\frac{a -b}{a +b}}\, a \,b^{2} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \left(\cos^{2}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, a^{3} \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}+B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b -3 B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +4 B \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a^{2} b -A \sin \left(d x +c \right) \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) a \,b^{2}-A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{2} b +3 A \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-3 B \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}-3 A \cos \left(d x +c \right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, \EllipticE \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sin \left(d x +c \right) a^{3}+B \sin \left(d x +c \right) \cos \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a^{3}-A \sin \left(d x +c \right) \EllipticF \left(\frac{\left(-1+\cos \left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}}{\sin \left(d x +c \right)}, \sqrt{-\frac{a +b}{a -b}}\right) \sqrt{\frac{b +a \cos \left(d x +c \right)}{\left(1+\cos \left(d x +c \right)\right) \left(a +b \right)}}\, a \,b^{2}\right) \left(\sqrt{\cos}\left(d x +c \right)\right) \sqrt{\frac{a -b}{a +b}}\, \sqrt{\frac{1}{1+\cos \left(d x +c \right)}}}{3 d a \left(a +b \right) \left(a -b \right)^{2} \left(b +a \cos \left(d x +c \right)\right)^{2} \sin \left(d x +c \right)^{3}}"," ",0,"2/3/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+3*A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-4*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)+B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+4*B*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2+3*A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b-A*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-3*A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-B*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*b^3*(1/(1+cos(d*x+c)))^(1/2)+B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*(1/(1+cos(d*x+c)))^(1/2)+3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^3*(1/(1+cos(d*x+c)))^(1/2)-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^3*(1/(1+cos(d*x+c)))^(1/2)-2*A*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+A*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-B*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)+4*B*((a-b)/(a+b))^(1/2)*a*b^2*(1/(1+cos(d*x+c)))^(1/2)-A*sin(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*b^3-3*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^2-3*B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b+4*B*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a^2*b-3*A*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3+B*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^3-A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b*(1/(1+cos(d*x+c)))^(1/2)-A*sin(d*x+c)*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*a*b^2-A*sin(d*x+c)*cos(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a^2*b)*cos(d*x+c)^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/a/(a+b)/(a-b)^2/(b+a*cos(d*x+c))^2/sin(d*x+c)^3","B"
633,1,3159,452,3.038000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(5/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"2/3/d*(-1+cos(d*x+c))*((b+a*cos(d*x+c))/cos(d*x+c))^(1/2)*(1+cos(d*x+c))^2*(-3*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^3+6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b-6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^2-6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a*b^3+9*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^2+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^3+4*A*((a-b)/(a+b))^(1/2)*b^4*(1/(1+cos(d*x+c)))^(1/2)-7*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a*b^3-6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^3*b-4*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^2*b^2+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3-3*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+6*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-7*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)+7*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*a^3*b-6*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a^4+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^4+A*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-B*cos(d*x+c)^2*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)-3*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4-6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*b^4+3*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a*b^3-4*B*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^3*b-7*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*cos(d*x+c)*sin(d*x+c)*a^2*b^2+A*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^2*b^2+9*B*sin(d*x+c)*EllipticF((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*a*b^3+6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*cos(d*x+c)*sin(d*x+c)*a^4+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^3*b+6*B*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*sin(d*x+c)*a^2*b^2-6*B*EllipticPi((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(a+b)/(a-b),I/((a-b)/(a+b))^(1/2))*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*sin(d*x+c)*a*b^3+4*A*((b+a*cos(d*x+c))/(1+cos(d*x+c))/(a+b))^(1/2)*EllipticE((-1+cos(d*x+c))*((a-b)/(a+b))^(1/2)/sin(d*x+c),(-(a+b)/(a-b))^(1/2))*sin(d*x+c)*b^4-3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)^2*a^4*(1/(1+cos(d*x+c)))^(1/2)-4*A*((a-b)/(a+b))^(1/2)*cos(d*x+c)*b^4*(1/(1+cos(d*x+c)))^(1/2)+3*B*((a-b)/(a+b))^(1/2)*cos(d*x+c)*a^4*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-A*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2)+4*B*((a-b)/(a+b))^(1/2)*a^3*b*(1/(1+cos(d*x+c)))^(1/2)+B*((a-b)/(a+b))^(1/2)*a^2*b^2*(1/(1+cos(d*x+c)))^(1/2)-7*B*((a-b)/(a+b))^(1/2)*a*b^3*(1/(1+cos(d*x+c)))^(1/2))*cos(d*x+c)^(1/2)*((a-b)/(a+b))^(1/2)*(1/(1+cos(d*x+c)))^(1/2)/b^2/(a+b)/(a-b)^2/(b+a*cos(d*x+c))^2/sin(d*x+c)^3","C"
634,1,5358,573,2.481000," ","int((A+B*sec(d*x+c))/cos(d*x+c)^(7/2)/(a+b*sec(d*x+c))^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"