# Maple integration test file: "6 Hyperbolic functions\6.5 Hyperbolic secant\6.5.2 (e x)^m (a+b sech(c+d x^n))^p.txt"

lst:=[

# Integrands of the form (e x)^m (a+b Sech[c+d x^n])^p

# Integrands of the form (e x)^m (a+b Sech[c+d x^2])^p

# Integrands of the form x^m (a+b Sech[c+d x^2])^p

# p>0
[x^5*(a+b*sech(c+d*x^2)),x,10,1/6*a*x^6+b*x^4*arctan(exp(c+d*x^2))/d-I*b*x^2*polylog(2,-I*exp(c+d*x^2))/d^2+I*b*x^2*polylog(2,I*exp(c+d*x^2))/d^2+I*b*polylog(3,-I*exp(c+d*x^2))/d^3-I*b*polylog(3,I*exp(c+d*x^2))/d^3],
[x^4*(a+b*sech(c+d*x^2)),x,2,1/5*a*x^5+b*Unintegrable(x^4*sech(c+d*x^2),x)],
[x^3*(a+b*sech(c+d*x^2)),x,8,1/4*a*x^4+b*x^2*arctan(exp(c+d*x^2))/d-1/2*I*b*polylog(2,-I*exp(c+d*x^2))/d^2+1/2*I*b*polylog(2,I*exp(c+d*x^2))/d^2],
[x^2*(a+b*sech(c+d*x^2)),x,2,1/3*a*x^3+b*Unintegrable(x^2*sech(c+d*x^2),x)],
[x*(a+b*sech(c+d*x^2)),x,4,1/2*a*x^2+1/2*b*arctan(sinh(c+d*x^2))/d],
[(a+b*sech(c+d*x^2))/x,x,2,a*log(x)+b*Unintegrable(sech(c+d*x^2)/x,x)],
[(a+b*sech(c+d*x^2))/x^2,x,2,-a/x+b*Unintegrable(sech(c+d*x^2)/x^2,x)],
[x^5*(a+b*sech(c+d*x^2))^2,x,15,1/2*b^2*x^4/d+1/6*a^2*x^6+2*a*b*x^4*arctan(exp(c+d*x^2))/d-b^2*x^2*log(1+exp(2*(c+d*x^2)))/d^2-2*I*a*b*x^2*polylog(2,-I*exp(c+d*x^2))/d^2+2*I*a*b*x^2*polylog(2,I*exp(c+d*x^2))/d^2-1/2*b^2*polylog(2,-exp(2*(c+d*x^2)))/d^3+2*I*a*b*polylog(3,-I*exp(c+d*x^2))/d^3-2*I*a*b*polylog(3,I*exp(c+d*x^2))/d^3+1/2*b^2*x^4*tanh(c+d*x^2)/d],
[x^4*(a+b*sech(c+d*x^2))^2,x,0,Unintegrable(x^4*(a+b*sech(c+d*x^2))^2,x)],
[x^3*(a+b*sech(c+d*x^2))^2,x,10,1/4*a^2*x^4+2*a*b*x^2*arctan(exp(c+d*x^2))/d-1/2*b^2*log(cosh(c+d*x^2))/d^2-I*a*b*polylog(2,-I*exp(c+d*x^2))/d^2+I*a*b*polylog(2,I*exp(c+d*x^2))/d^2+1/2*b^2*x^2*tanh(c+d*x^2)/d],
[x^2*(a+b*sech(c+d*x^2))^2,x,0,Unintegrable(x^2*(a+b*sech(c+d*x^2))^2,x)],
[x*(a+b*sech(c+d*x^2))^2,x,5,1/2*a^2*x^2+a*b*arctan(sinh(c+d*x^2))/d+1/2*b^2*tanh(c+d*x^2)/d],
[(a+b*sech(c+d*x^2))^2/x,x,0,Unintegrable((a+b*sech(c+d*x^2))^2/x,x)],
[(a+b*sech(c+d*x^2))^2/x^2,x,0,Unintegrable((a+b*sech(c+d*x^2))^2/x^2,x)],
[x*sech(a+b*x^2)^7,x,5,5/32*arctan(sinh(a+b*x^2))/b+5/32*sech(a+b*x^2)*tanh(a+b*x^2)/b+5/48*sech(a+b*x^2)^3*tanh(a+b*x^2)/b+1/12*sech(a+b*x^2)^5*tanh(a+b*x^2)/b],

# p<0
[x^5/(a+b*sech(c+d*x^2)),x,13,1/6*x^6/a-1/2*b*x^4*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+1/2*b*x^4*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-b*x^2*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+b*x^2*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+b*polylog(3,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-b*polylog(3,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))],
[x^4/(a+b*sech(c+d*x^2)),x,0,Unintegrable(x^4/(a+b*sech(c+d*x^2)),x)],
[x^3/(a+b*sech(c+d*x^2)),x,11,1/4*x^4/a-1/2*b*x^2*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+1/2*b*x^2*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-1/2*b*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+1/2*b*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))],
[x^2/(a+b*sech(c+d*x^2)),x,0,Unintegrable(x^2/(a+b*sech(c+d*x^2)),x)],
[x/(a+b*sech(c+d*x^2)),x,4,1/2*x^2/a-b*arctan(sqrt(a-b)*tanh(1/2*(c+d*x^2))/sqrt(a+b))/(a*d*sqrt(a-b)*sqrt(a+b))],
[1/(x*(a+b*sech(c+d*x^2))),x,0,Unintegrable(1/(x*(a+b*sech(c+d*x^2))),x)],
[(a+b*sech(c+d*x^2))/x^2,x,2,-a/x+b*Unintegrable(sech(c+d*x^2)/x^2,x)],
[x^5/(a+b*sech(c+d*x^2))^2,x,31,1/2*b^2*x^4/(a^2*(a^2-b^2)*d)+1/6*x^6/a^2-b^2*x^2*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)+1/2*b^3*x^4*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-b^2*x^2*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)-1/2*b^3*x^4*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-b^2*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)+b^3*x^2*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-b^2*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-b^3*x^2*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-b^3*polylog(3,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+b^3*polylog(3,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+1/2*b^2*x^4*sinh(c+d*x^2)/(a*(a^2-b^2)*d*(b+a*cosh(c+d*x^2)))-b*x^4*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+b*x^4*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-2*b*x^2*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+2*b*x^2*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+2*b*polylog(3,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-2*b*polylog(3,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))],
[x^4/(a+b*sech(c+d*x^2))^2,x,0,Unintegrable(x^4/(a+b*sech(c+d*x^2))^2,x)],
[x^3/(a+b*sech(c+d*x^2))^2,x,22,1/4*x^4/a^2-1/2*b^2*log(b+a*cosh(c+d*x^2))/(a^2*(a^2-b^2)*d^2)+1/2*b^3*x^2*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-1/2*b^3*x^2*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)+1/2*b^3*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-1/2*b^3*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)+1/2*b^2*x^2*sinh(c+d*x^2)/(a*(a^2-b^2)*d*(b+a*cosh(c+d*x^2)))-b*x^2*log(1+a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+b*x^2*log(1+a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-b*polylog(2,-a*exp(c+d*x^2)/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+b*polylog(2,-a*exp(c+d*x^2)/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))],
[x^2/(a+b*sech(c+d*x^2))^2,x,0,Unintegrable(x^2/(a+b*sech(c+d*x^2))^2,x)],
[x/(a+b*sech(c+d*x^2))^2,x,6,1/2*x^2/a^2-b*(2*a^2-b^2)*arctan(sqrt(a-b)*tanh(1/2*(c+d*x^2))/sqrt(a+b))/(a^2*(a-b)^(3/2)*(a+b)^(3/2)*d)+1/2*b^2*tanh(c+d*x^2)/(a*(a^2-b^2)*d*(a+b*sech(c+d*x^2)))],
[1/(x*(a+b*sech(c+d*x^2))^2),x,0,Unintegrable(1/(x*(a+b*sech(c+d*x^2))^2),x)],
[1/(x^2*(a+b*sech(c+d*x^2))^2),x,0,Unintegrable(1/(x^2*(a+b*sech(c+d*x^2))^2),x)],
[1/(x^3*(a+b*sech(c+d*x^2))^2),x,0,Unintegrable(1/(x^3*(a+b*sech(c+d*x^2))^2),x)],

# Integrands of the form (e x)^m (a+b Sech[c+d / x^1])^p

# Integrands of the form (e x)^m (a+b Sech[c+d / x])^p
[sech(1/x)^2/x^2,x,3,-tanh(1/x)],

# Integrands of the form (e x)^m (a+b Sech[c+d x^(1/2)])^p

# Integrands of the form x^m (a+b Sech[c+d x^(1/2)])^p

# p>0
[x^3*(a+b*sech(c+d*sqrt(x))),x,20,1/4*a*x^4+4*b*x^(7/2)*arctan(exp(c+d*sqrt(x)))/d-14*I*b*x^3*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+14*I*b*x^3*polylog(2,I*exp(c+d*sqrt(x)))/d^2+84*I*b*x^(5/2)*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-84*I*b*x^(5/2)*polylog(3,I*exp(c+d*sqrt(x)))/d^3-420*I*b*x^2*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+420*I*b*x^2*polylog(4,I*exp(c+d*sqrt(x)))/d^4+1680*I*b*x^(3/2)*polylog(5,-I*exp(c+d*sqrt(x)))/d^5-1680*I*b*x^(3/2)*polylog(5,I*exp(c+d*sqrt(x)))/d^5-5040*I*b*x*polylog(6,-I*exp(c+d*sqrt(x)))/d^6+5040*I*b*x*polylog(6,I*exp(c+d*sqrt(x)))/d^6-10080*I*b*polylog(8,-I*exp(c+d*sqrt(x)))/d^8+10080*I*b*polylog(8,I*exp(c+d*sqrt(x)))/d^8+10080*I*b*polylog(7,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^7-10080*I*b*polylog(7,I*exp(c+d*sqrt(x)))*sqrt(x)/d^7],
[x^2*(a+b*sech(c+d*sqrt(x))),x,16,1/3*a*x^3+4*b*x^(5/2)*arctan(exp(c+d*sqrt(x)))/d-10*I*b*x^2*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+10*I*b*x^2*polylog(2,I*exp(c+d*sqrt(x)))/d^2+40*I*b*x^(3/2)*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-40*I*b*x^(3/2)*polylog(3,I*exp(c+d*sqrt(x)))/d^3-120*I*b*x*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+120*I*b*x*polylog(4,I*exp(c+d*sqrt(x)))/d^4-240*I*b*polylog(6,-I*exp(c+d*sqrt(x)))/d^6+240*I*b*polylog(6,I*exp(c+d*sqrt(x)))/d^6+240*I*b*polylog(5,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^5-240*I*b*polylog(5,I*exp(c+d*sqrt(x)))*sqrt(x)/d^5],
[x*(a+b*sech(c+d*sqrt(x))),x,12,1/2*a*x^2+4*b*x^(3/2)*arctan(exp(c+d*sqrt(x)))/d-6*I*b*x*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+6*I*b*x*polylog(2,I*exp(c+d*sqrt(x)))/d^2-12*I*b*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+12*I*b*polylog(4,I*exp(c+d*sqrt(x)))/d^4+12*I*b*polylog(3,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^3-12*I*b*polylog(3,I*exp(c+d*sqrt(x)))*sqrt(x)/d^3],
[(a+b*sech(c+d*sqrt(x)))/x,x,2,a*log(x)+b*Unintegrable(sech(c+d*sqrt(x))/x,x)],
[(a+b*sech(c+d*sqrt(x)))/x^2,x,2,-a/x+b*Unintegrable(sech(c+d*sqrt(x))/x^2,x)],
[x^3*(a+b*sech(c+d*sqrt(x)))^2,x,30,2*b^2*x^(7/2)/d+1/4*a^2*x^4+8*a*b*x^(7/2)*arctan(exp(c+d*sqrt(x)))/d-14*b^2*x^3*log(1+exp(2*(c+d*sqrt(x))))/d^2-28*I*a*b*x^3*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+28*I*a*b*x^3*polylog(2,I*exp(c+d*sqrt(x)))/d^2-42*b^2*x^(5/2)*polylog(2,-exp(2*(c+d*sqrt(x))))/d^3+168*I*a*b*x^(5/2)*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-168*I*a*b*x^(5/2)*polylog(3,I*exp(c+d*sqrt(x)))/d^3+105*b^2*x^2*polylog(3,-exp(2*(c+d*sqrt(x))))/d^4-840*I*a*b*x^2*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+840*I*a*b*x^2*polylog(4,I*exp(c+d*sqrt(x)))/d^4-210*b^2*x^(3/2)*polylog(4,-exp(2*(c+d*sqrt(x))))/d^5+3360*I*a*b*x^(3/2)*polylog(5,-I*exp(c+d*sqrt(x)))/d^5-3360*I*a*b*x^(3/2)*polylog(5,I*exp(c+d*sqrt(x)))/d^5+315*b^2*x*polylog(5,-exp(2*(c+d*sqrt(x))))/d^6-10080*I*a*b*x*polylog(6,-I*exp(c+d*sqrt(x)))/d^6+10080*I*a*b*x*polylog(6,I*exp(c+d*sqrt(x)))/d^6+315/2*b^2*polylog(7,-exp(2*(c+d*sqrt(x))))/d^8-20160*I*a*b*polylog(8,-I*exp(c+d*sqrt(x)))/d^8+20160*I*a*b*polylog(8,I*exp(c+d*sqrt(x)))/d^8-315*b^2*polylog(6,-exp(2*(c+d*sqrt(x))))*sqrt(x)/d^7+20160*I*a*b*polylog(7,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^7-20160*I*a*b*polylog(7,I*exp(c+d*sqrt(x)))*sqrt(x)/d^7+2*b^2*x^(7/2)*tanh(c+d*sqrt(x))/d],
[x^2*(a+b*sech(c+d*sqrt(x)))^2,x,24,2*b^2*x^(5/2)/d+1/3*a^2*x^3+8*a*b*x^(5/2)*arctan(exp(c+d*sqrt(x)))/d-10*b^2*x^2*log(1+exp(2*(c+d*sqrt(x))))/d^2-20*I*a*b*x^2*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+20*I*a*b*x^2*polylog(2,I*exp(c+d*sqrt(x)))/d^2-20*b^2*x^(3/2)*polylog(2,-exp(2*(c+d*sqrt(x))))/d^3+80*I*a*b*x^(3/2)*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-80*I*a*b*x^(3/2)*polylog(3,I*exp(c+d*sqrt(x)))/d^3+30*b^2*x*polylog(3,-exp(2*(c+d*sqrt(x))))/d^4-240*I*a*b*x*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+240*I*a*b*x*polylog(4,I*exp(c+d*sqrt(x)))/d^4+15*b^2*polylog(5,-exp(2*(c+d*sqrt(x))))/d^6-480*I*a*b*polylog(6,-I*exp(c+d*sqrt(x)))/d^6+480*I*a*b*polylog(6,I*exp(c+d*sqrt(x)))/d^6-30*b^2*polylog(4,-exp(2*(c+d*sqrt(x))))*sqrt(x)/d^5+480*I*a*b*polylog(5,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^5-480*I*a*b*polylog(5,I*exp(c+d*sqrt(x)))*sqrt(x)/d^5+2*b^2*x^(5/2)*tanh(c+d*sqrt(x))/d],
[x*(a+b*sech(c+d*sqrt(x)))^2,x,18,2*b^2*x^(3/2)/d+1/2*a^2*x^2+8*a*b*x^(3/2)*arctan(exp(c+d*sqrt(x)))/d-6*b^2*x*log(1+exp(2*(c+d*sqrt(x))))/d^2-12*I*a*b*x*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+12*I*a*b*x*polylog(2,I*exp(c+d*sqrt(x)))/d^2+3*b^2*polylog(3,-exp(2*(c+d*sqrt(x))))/d^4-24*I*a*b*polylog(4,-I*exp(c+d*sqrt(x)))/d^4+24*I*a*b*polylog(4,I*exp(c+d*sqrt(x)))/d^4-6*b^2*polylog(2,-exp(2*(c+d*sqrt(x))))*sqrt(x)/d^3+24*I*a*b*polylog(3,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^3-24*I*a*b*polylog(3,I*exp(c+d*sqrt(x)))*sqrt(x)/d^3+2*b^2*x^(3/2)*tanh(c+d*sqrt(x))/d],
[(a+b*sech(c+d*sqrt(x)))^2/x,x,0,Unintegrable((a+b*sech(c+d*sqrt(x)))^2/x,x)],
[(a+b*sech(c+d*sqrt(x)))^2/x^2,x,0,Unintegrable((a+b*sech(c+d*sqrt(x)))^2/x^2,x)],

# p<0
[x^3/(a+b*sech(c+d*sqrt(x))),x,23,1/4*x^4/a-2*b*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+2*b*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-14*b*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+14*b*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+84*b*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-84*b*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-420*b*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))+420*b*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))+1680*b*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^5*sqrt(-a^2+b^2))-1680*b*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^5*sqrt(-a^2+b^2))-5040*b*x*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^6*sqrt(-a^2+b^2))+5040*b*x*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^6*sqrt(-a^2+b^2))-10080*b*polylog(8,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^8*sqrt(-a^2+b^2))+10080*b*polylog(8,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^8*sqrt(-a^2+b^2))+10080*b*polylog(7,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a*d^7*sqrt(-a^2+b^2))-10080*b*polylog(7,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a*d^7*sqrt(-a^2+b^2))],
[x^2/(a+b*sech(c+d*sqrt(x))),x,19,1/3*x^3/a-2*b*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+2*b*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-10*b*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+10*b*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+40*b*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-40*b*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-120*b*x*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))+120*b*x*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))-240*b*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^6*sqrt(-a^2+b^2))+240*b*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^6*sqrt(-a^2+b^2))+240*b*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a*d^5*sqrt(-a^2+b^2))-240*b*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a*d^5*sqrt(-a^2+b^2))],
[x/(a+b*sech(c+d*sqrt(x))),x,15,1/2*x^2/a-2*b*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+2*b*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-6*b*x*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+6*b*x*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))-12*b*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))+12*b*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^4*sqrt(-a^2+b^2))+12*b*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a*d^3*sqrt(-a^2+b^2))-12*b*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a*d^3*sqrt(-a^2+b^2))],
[1/(x*(a+b*sech(c+d*sqrt(x)))),x,0,Unintegrable(1/(x*(a+b*sech(c+d*sqrt(x)))),x)],
[(a+b*sech(c+d*sqrt(x)))/x^2,x,2,-a/x+b*Unintegrable(sech(c+d*sqrt(x))/x^2,x)],
[x^3/(a+b*sech(c+d*sqrt(x)))^2,x,61,2*b^2*x^(7/2)/(a^2*(a^2-b^2)*d)+1/4*x^4/a^2-14*b^2*x^3*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)+2*b^3*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-14*b^2*x^3*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)-2*b^3*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-84*b^2*x^(5/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)+14*b^3*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-84*b^2*x^(5/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-14*b^3*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)+420*b^2*x^2*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)-84*b^3*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+420*b^2*x^2*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)+84*b^3*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)-1680*b^2*x^(3/2)*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^5)+420*b^3*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)-1680*b^2*x^(3/2)*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^5)-420*b^3*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)+5040*b^2*x*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^6)-1680*b^3*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^5)+5040*b^2*x*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^6)+1680*b^3*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^5)+5040*b^3*x*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^6)-5040*b^3*x*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^6)+10080*b^2*polylog(7,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^8)+10080*b^2*polylog(7,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^8)+10080*b^3*polylog(8,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^8)-10080*b^3*polylog(8,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^8)+2*b^2*x^(7/2)*sinh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(b+a*cosh(c+d*sqrt(x))))-4*b*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+4*b*x^(7/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-28*b*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+28*b*x^3*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+168*b*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-168*b*x^(5/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-840*b*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))+840*b*x^2*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))+3360*b*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^5*sqrt(-a^2+b^2))-3360*b*x^(3/2)*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^5*sqrt(-a^2+b^2))-10080*b*x*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^6*sqrt(-a^2+b^2))+10080*b*x*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^6*sqrt(-a^2+b^2))-20160*b*polylog(8,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^8*sqrt(-a^2+b^2))+20160*b*polylog(8,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^8*sqrt(-a^2+b^2))-10080*b^2*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^7)-10080*b^2*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^7)-10080*b^3*polylog(7,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^7)+10080*b^3*polylog(7,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^7)+20160*b*polylog(7,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^7*sqrt(-a^2+b^2))-20160*b*polylog(7,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^7*sqrt(-a^2+b^2))],
[x^2/(a+b*sech(c+d*sqrt(x)))^2,x,49,2*b^2*x^(5/2)/(a^2*(a^2-b^2)*d)+1/3*x^3/a^2-10*b^2*x^2*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)+2*b^3*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-10*b^2*x^2*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)-2*b^3*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-40*b^2*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)+10*b^3*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-40*b^2*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-10*b^3*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)+120*b^2*x*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)-40*b^3*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+120*b^2*x*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)+40*b^3*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+120*b^3*x*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)-120*b^3*x*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)+240*b^2*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^6)+240*b^2*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^6)+240*b^3*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^6)-240*b^3*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^6)+2*b^2*x^(5/2)*sinh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(b+a*cosh(c+d*sqrt(x))))-4*b*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+4*b*x^(5/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-20*b*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+20*b*x^2*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+80*b*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-80*b*x^(3/2)*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-240*b*x*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))+240*b*x*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))-480*b*polylog(6,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^6*sqrt(-a^2+b^2))+480*b*polylog(6,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^6*sqrt(-a^2+b^2))-240*b^2*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^5)-240*b^2*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^5)-240*b^3*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^5)+240*b^3*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^5)+480*b*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^5*sqrt(-a^2+b^2))-480*b*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^5*sqrt(-a^2+b^2))],
[x/(a+b*sech(c+d*sqrt(x)))^2,x,37,2*b^2*x^(3/2)/(a^2*(a^2-b^2)*d)+1/2*x^2/a^2-6*b^2*x*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)+2*b^3*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-6*b^2*x*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)-2*b^3*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)+6*b^3*x*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-6*b^3*x*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)+12*b^2*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)+12*b^2*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^4)+12*b^3*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)-12*b^3*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^4)+2*b^2*x^(3/2)*sinh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(b+a*cosh(c+d*sqrt(x))))-4*b*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+4*b*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-12*b*x*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+12*b*x*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))-24*b*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))+24*b*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^4*sqrt(-a^2+b^2))-12*b^2*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^3)-12*b^2*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^3)-12*b^3*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^3)+12*b^3*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^3)+24*b*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^3*sqrt(-a^2+b^2))-24*b*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^3*sqrt(-a^2+b^2))],
[1/(x*(a+b*sech(c+d*sqrt(x)))^2),x,0,Unintegrable(1/(x*(a+b*sech(c+d*sqrt(x)))^2),x)],
[1/(x^2*(a+b*sech(c+d*sqrt(x)))^2),x,0,Unintegrable(1/(x^2*(a+b*sech(c+d*sqrt(x)))^2),x)],

# Integrands of the form (e x)^(m/2) (a+b Sech[c+d x^(1/2)])^p

# p>0
[x^(3/2)*(a+b*sech(c+d*sqrt(x))),x,14,2/5*a*x^(5/2)+4*b*x^2*arctan(exp(c+d*sqrt(x)))/d-8*I*b*x^(3/2)*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+8*I*b*x^(3/2)*polylog(2,I*exp(c+d*sqrt(x)))/d^2+24*I*b*x*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-24*I*b*x*polylog(3,I*exp(c+d*sqrt(x)))/d^3+48*I*b*polylog(5,-I*exp(c+d*sqrt(x)))/d^5-48*I*b*polylog(5,I*exp(c+d*sqrt(x)))/d^5-48*I*b*polylog(4,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^4+48*I*b*polylog(4,I*exp(c+d*sqrt(x)))*sqrt(x)/d^4],
[(a+b*sech(c+d*sqrt(x)))*sqrt(x),x,10,2/3*a*x^(3/2)+4*b*x*arctan(exp(c+d*sqrt(x)))/d+4*I*b*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-4*I*b*polylog(3,I*exp(c+d*sqrt(x)))/d^3-4*I*b*polylog(2,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^2+4*I*b*polylog(2,I*exp(c+d*sqrt(x)))*sqrt(x)/d^2],
[(a+b*sech(c+d*sqrt(x)))/sqrt(x),x,4,2*b*arctan(sinh(c+d*sqrt(x)))/d+2*a*sqrt(x)],
[(a+b*sech(c+d*sqrt(x)))/x^(3/2),x,2,-2*a/sqrt(x)+b*Unintegrable(sech(c+d*sqrt(x))/x^(3/2),x)],
[(a+b*sech(c+d*sqrt(x)))/x^(5/2),x,2,-2/3*a/x^(3/2)+b*Unintegrable(sech(c+d*sqrt(x))/x^(5/2),x)],
[x^(3/2)*(a+b*sech(c+d*sqrt(x)))^2,x,21,2*b^2*x^2/d+2/5*a^2*x^(5/2)+8*a*b*x^2*arctan(exp(c+d*sqrt(x)))/d-8*b^2*x^(3/2)*log(1+exp(2*(c+d*sqrt(x))))/d^2-16*I*a*b*x^(3/2)*polylog(2,-I*exp(c+d*sqrt(x)))/d^2+16*I*a*b*x^(3/2)*polylog(2,I*exp(c+d*sqrt(x)))/d^2-12*b^2*x*polylog(2,-exp(2*(c+d*sqrt(x))))/d^3+48*I*a*b*x*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-48*I*a*b*x*polylog(3,I*exp(c+d*sqrt(x)))/d^3-6*b^2*polylog(4,-exp(2*(c+d*sqrt(x))))/d^5+96*I*a*b*polylog(5,-I*exp(c+d*sqrt(x)))/d^5-96*I*a*b*polylog(5,I*exp(c+d*sqrt(x)))/d^5+12*b^2*polylog(3,-exp(2*(c+d*sqrt(x))))*sqrt(x)/d^4-96*I*a*b*polylog(4,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^4+96*I*a*b*polylog(4,I*exp(c+d*sqrt(x)))*sqrt(x)/d^4+2*b^2*x^2*tanh(c+d*sqrt(x))/d],
[(a+b*sech(c+d*sqrt(x)))^2*sqrt(x),x,15,2*b^2*x/d+2/3*a^2*x^(3/2)+8*a*b*x*arctan(exp(c+d*sqrt(x)))/d-2*b^2*polylog(2,-exp(2*(c+d*sqrt(x))))/d^3+8*I*a*b*polylog(3,-I*exp(c+d*sqrt(x)))/d^3-8*I*a*b*polylog(3,I*exp(c+d*sqrt(x)))/d^3-4*b^2*log(1+exp(2*(c+d*sqrt(x))))*sqrt(x)/d^2-8*I*a*b*polylog(2,-I*exp(c+d*sqrt(x)))*sqrt(x)/d^2+8*I*a*b*polylog(2,I*exp(c+d*sqrt(x)))*sqrt(x)/d^2+2*b^2*x*tanh(c+d*sqrt(x))/d],
[(a+b*sech(c+d*sqrt(x)))^2/sqrt(x),x,5,4*a*b*arctan(sinh(c+d*sqrt(x)))/d+2*a^2*sqrt(x)+2*b^2*tanh(c+d*sqrt(x))/d],
[(a+b*sech(c+d*sqrt(x)))^2/x^(3/2),x,0,Unintegrable((a+b*sech(c+d*sqrt(x)))^2/x^(3/2),x)],
[(a+b*sech(c+d*sqrt(x)))^2/x^(5/2),x,0,Unintegrable((a+b*sech(c+d*sqrt(x)))^2/x^(5/2),x)],

# p<0
[x^(3/2)/(a+b*sech(c+d*sqrt(x))),x,17,2/5*x^(5/2)/a-2*b*x^2*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+2*b*x^2*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))-8*b*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+8*b*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^2*sqrt(-a^2+b^2))+24*b*x*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-24*b*x*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))+48*b*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^5*sqrt(-a^2+b^2))-48*b*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^5*sqrt(-a^2+b^2))-48*b*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a*d^4*sqrt(-a^2+b^2))+48*b*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a*d^4*sqrt(-a^2+b^2))],
[sqrt(x)/(a+b*sech(c+d*sqrt(x))),x,13,2/3*x^(3/2)/a-2*b*x*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+2*b*x*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d*sqrt(-a^2+b^2))+4*b*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-4*b*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a*d^3*sqrt(-a^2+b^2))-4*b*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a*d^2*sqrt(-a^2+b^2))+4*b*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a*d^2*sqrt(-a^2+b^2))],
[1/((a+b*sech(c+d*sqrt(x)))*sqrt(x)),x,4,-4*b*arctan(sqrt(a-b)*tanh(1/2*(c+d*sqrt(x)))/sqrt(a+b))/(a*d*sqrt(a-b)*sqrt(a+b))+2*sqrt(x)/a],
[1/(x^(3/2)*(a+b*sech(c+d*sqrt(x)))),x,0,Unintegrable(1/(x^(3/2)*(a+b*sech(c+d*sqrt(x)))),x)],
[1/(x^(5/2)*(a+b*sech(c+d*sqrt(x)))),x,0,Unintegrable(1/(x^(5/2)*(a+b*sech(c+d*sqrt(x)))),x)],
[x^(3/2)/(a+b*sech(c+d*sqrt(x)))^2,x,43,2*b^2*x^2/(a^2*(a^2-b^2)*d)+2/5*x^(5/2)/a^2-8*b^2*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)+2*b^3*x^2*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-8*b^2*x^(3/2)*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2)-2*b^3*x^2*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-24*b^2*x*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)+8*b^3*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-24*b^2*x*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-8*b^3*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2)-24*b^3*x*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+24*b^3*x*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)-48*b^2*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^5)-48*b^2*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^5)-48*b^3*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^5)+48*b^3*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^5)+2*b^2*x^2*sinh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(b+a*cosh(c+d*sqrt(x))))-4*b*x^2*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+4*b*x^2*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))-16*b*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+16*b*x^(3/2)*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^2*sqrt(-a^2+b^2))+48*b*x*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-48*b*x*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))+96*b*polylog(5,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^5*sqrt(-a^2+b^2))-96*b*polylog(5,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^5*sqrt(-a^2+b^2))+48*b^2*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^4)+48*b^2*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^4)+48*b^3*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^4)-48*b^3*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^4)-96*b*polylog(4,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^4*sqrt(-a^2+b^2))+96*b*polylog(4,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^4*sqrt(-a^2+b^2))],
[sqrt(x)/(a+b*sech(c+d*sqrt(x)))^2,x,31,2*b^2*x/(a^2*(a^2-b^2)*d)+2/3*x^(3/2)/a^2+2*b^3*x*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-2*b^3*x*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d)-4*b^2*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-4*b^2*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3)-4*b^3*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+4*b^3*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3)+2*b^2*x*sinh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(b+a*cosh(c+d*sqrt(x))))-4*b*x*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+4*b*x*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d*sqrt(-a^2+b^2))+8*b*polylog(3,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-8*b*polylog(3,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))/(a^2*d^3*sqrt(-a^2+b^2))-4*b^2*log(1+a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^2)-4*b^2*log(1+a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(a^2-b^2)*d^2)+4*b^3*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^2)-4*b^3*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*(-a^2+b^2)^(3/2)*d^2)-8*b*polylog(2,-a*exp(c+d*sqrt(x))/(b-sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^2*sqrt(-a^2+b^2))+8*b*polylog(2,-a*exp(c+d*sqrt(x))/(b+sqrt(-a^2+b^2)))*sqrt(x)/(a^2*d^2*sqrt(-a^2+b^2))],
[1/((a+b*sech(c+d*sqrt(x)))^2*sqrt(x)),x,6,-4*b*(2*a^2-b^2)*arctan(sqrt(a-b)*tanh(1/2*(c+d*sqrt(x)))/sqrt(a+b))/(a^2*(a-b)^(3/2)*(a+b)^(3/2)*d)+2*sqrt(x)/a^2+2*b^2*tanh(c+d*sqrt(x))/(a*(a^2-b^2)*d*(a+b*sech(c+d*sqrt(x))))],
[1/(x^(3/2)*(a+b*sech(c+d*sqrt(x)))^2),x,0,Unintegrable(1/(x^(3/2)*(a+b*sech(c+d*sqrt(x)))^2),x)],
[1/(x^(5/2)*(a+b*sech(c+d*sqrt(x)))^2),x,0,Unintegrable(1/(x^(5/2)*(a+b*sech(c+d*sqrt(x)))^2),x)],

# Integrands of the form (e x)^m (a+b Sech[c+d x^n])^p
[(e*x)^m*(a+b*sech(c+d*x^n))^p,x,1,(e*x)^m*Unintegrable(x^m*(a+b*sech(c+d*x^n))^p,x)/x^m],

# p>0
[(e*x)^(-1+n)*(a+b*sech(c+d*x^n)),x,5,a*(e*x)^n/(e*n)+b*(e*x)^n*arctan(sinh(c+d*x^n))/(d*e*n*x^n)],
[(e*x)^(-1+2*n)*(a+b*sech(c+d*x^n)),x,9,1/2*a*(e*x)^(2*n)/(e*n)+2*b*(e*x)^(2*n)*arctan(exp(c+d*x^n))/(d*e*n*x^n)-I*b*(e*x)^(2*n)*polylog(2,-I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+I*b*(e*x)^(2*n)*polylog(2,I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))],
[(e*x)^(-1+3*n)*(a+b*sech(c+d*x^n)),x,11,1/3*a*(e*x)^(3*n)/(e*n)+2*b*(e*x)^(3*n)*arctan(exp(c+d*x^n))/(d*e*n*x^n)-2*I*b*(e*x)^(3*n)*polylog(2,-I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+2*I*b*(e*x)^(3*n)*polylog(2,I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+2*I*b*(e*x)^(3*n)*polylog(3,-I*exp(c+d*x^n))/(d^3*e*n*x^(3*n))-2*I*b*(e*x)^(3*n)*polylog(3,I*exp(c+d*x^n))/(d^3*e*n*x^(3*n))],
[(e*x)^(-1+n)*(a+b*sech(c+d*x^n))^2,x,6,a^2*(e*x)^n/(e*n)+2*a*b*(e*x)^n*arctan(sinh(c+d*x^n))/(d*e*n*x^n)+b^2*(e*x)^n*tanh(c+d*x^n)/(d*e*n*x^n)],
[(e*x)^(-1+2*n)*(a+b*sech(c+d*x^n))^2,x,11,1/2*a^2*(e*x)^(2*n)/(e*n)+4*a*b*(e*x)^(2*n)*arctan(exp(c+d*x^n))/(d*e*n*x^n)-b^2*(e*x)^(2*n)*log(cosh(c+d*x^n))/(d^2*e*n*x^(2*n))-2*I*a*b*(e*x)^(2*n)*polylog(2,-I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+2*I*a*b*(e*x)^(2*n)*polylog(2,I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+b^2*(e*x)^(2*n)*tanh(c+d*x^n)/(d*e*n*x^n)],
[(e*x)^(-1+3*n)*(a+b*sech(c+d*x^n))^2,x,16,1/3*a^2*(e*x)^(3*n)/(e*n)+b^2*(e*x)^(3*n)/(d*e*n*x^n)+4*a*b*(e*x)^(3*n)*arctan(exp(c+d*x^n))/(d*e*n*x^n)-2*b^2*(e*x)^(3*n)*log(1+exp(2*(c+d*x^n)))/(d^2*e*n*x^(2*n))-4*I*a*b*(e*x)^(3*n)*polylog(2,-I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))+4*I*a*b*(e*x)^(3*n)*polylog(2,I*exp(c+d*x^n))/(d^2*e*n*x^(2*n))-b^2*(e*x)^(3*n)*polylog(2,-exp(2*(c+d*x^n)))/(d^3*e*n*x^(3*n))+4*I*a*b*(e*x)^(3*n)*polylog(3,-I*exp(c+d*x^n))/(d^3*e*n*x^(3*n))-4*I*a*b*(e*x)^(3*n)*polylog(3,I*exp(c+d*x^n))/(d^3*e*n*x^(3*n))+b^2*(e*x)^(3*n)*tanh(c+d*x^n)/(d*e*n*x^n)],

# p<0
[(e*x)^(-1+n)/(a+b*sech(c+d*x^n)),x,5,(e*x)^n/(a*e*n)-2*b*(e*x)^n*arctan(sqrt(a-b)*tanh(1/2*(c+d*x^n))/sqrt(a+b))/(a*d*e*n*x^n*sqrt(a-b)*sqrt(a+b))],
[(e*x)^(-1+2*n)/(a+b*sech(c+d*x^n)),x,12,1/2*(e*x)^(2*n)/(a*e*n)-b*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a*d*e*n*x^n*sqrt(-a^2+b^2))+b*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a*d*e*n*x^n*sqrt(-a^2+b^2))-b*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+b*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))],
[(e*x)^(-1+3*n)/(a+b*sech(c+d*x^n)),x,14,1/3*(e*x)^(3*n)/(a*e*n)-b*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a*d*e*n*x^n*sqrt(-a^2+b^2))+b*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a*d*e*n*x^n*sqrt(-a^2+b^2))-2*b*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+2*b*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+2*b*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a*d^3*e*n*x^(3*n)*sqrt(-a^2+b^2))-2*b*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a*d^3*e*n*x^(3*n)*sqrt(-a^2+b^2))],
[(e*x)^(-1+n)/(a+b*sech(c+d*x^n))^2,x,7,(e*x)^n/(a^2*e*n)-2*b*(2*a^2-b^2)*(e*x)^n*arctan(sqrt(a-b)*tanh(1/2*(c+d*x^n))/sqrt(a+b))/(a^2*(a-b)^(3/2)*(a+b)^(3/2)*d*e*n*x^n)+b^2*(e*x)^n*tanh(c+d*x^n)/(a*(a^2-b^2)*d*e*n*x^n*(a+b*sech(c+d*x^n)))],
[(e*x)^(-1+2*n)/(a+b*sech(c+d*x^n))^2,x,23,1/2*(e*x)^(2*n)/(a^2*e*n)-b^2*(e*x)^(2*n)*log(b+a*cosh(c+d*x^n))/(a^2*(a^2-b^2)*d^2*e*n*x^(2*n))+b^3*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d*e*n*x^n)-b^3*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d*e*n*x^n)+b^3*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2*e*n*x^(2*n))-b^3*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2*e*n*x^(2*n))+b^2*(e*x)^(2*n)*sinh(c+d*x^n)/(a*(a^2-b^2)*d*e*n*x^n*(b+a*cosh(c+d*x^n)))-2*b*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*d*e*n*x^n*sqrt(-a^2+b^2))+2*b*(e*x)^(2*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*d*e*n*x^n*sqrt(-a^2+b^2))-2*b*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+2*b*(e*x)^(2*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))],
[(e*x)^(-1+3*n)/(a+b*sech(c+d*x^n))^2,x,32,1/3*(e*x)^(3*n)/(a^2*e*n)+b^2*(e*x)^(3*n)/(a^2*(a^2-b^2)*d*e*n*x^n)-2*b^2*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2*e*n*x^(2*n))+b^3*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d*e*n*x^n)-2*b^2*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^2*e*n*x^(2*n))-b^3*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d*e*n*x^n)-2*b^2*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3*e*n*x^(3*n))+2*b^3*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2*e*n*x^(2*n))-2*b^2*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(a^2-b^2)*d^3*e*n*x^(3*n))-2*b^3*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^2*e*n*x^(2*n))-2*b^3*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3*e*n*x^(3*n))+2*b^3*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*d^3*e*n*x^(3*n))+b^2*(e*x)^(3*n)*sinh(c+d*x^n)/(a*(a^2-b^2)*d*e*n*x^n*(b+a*cosh(c+d*x^n)))-2*b*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*d*e*n*x^n*sqrt(-a^2+b^2))+2*b*(e*x)^(3*n)*log(1+a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*d*e*n*x^n*sqrt(-a^2+b^2))-4*b*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+4*b*(e*x)^(3*n)*polylog(2,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*d^2*e*n*x^(2*n)*sqrt(-a^2+b^2))+4*b*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b-sqrt(-a^2+b^2)))/(a^2*d^3*e*n*x^(3*n)*sqrt(-a^2+b^2))-4*b*(e*x)^(3*n)*polylog(3,-a*exp(c+d*x^n)/(b+sqrt(-a^2+b^2)))/(a^2*d^3*e*n*x^(3*n)*sqrt(-a^2+b^2))]]:
