1,1,179,0,0.463059," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{480 \, a^{2} c^{5} f x \cos\left(f x + e\right)^{6} - 285 \, a^{2} c^{5} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) + 285 \, a^{2} c^{5} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(176 \, a^{2} c^{5} \cos\left(f x + e\right)^{5} - 435 \, a^{2} c^{5} \cos\left(f x + e\right)^{4} + 208 \, a^{2} c^{5} \cos\left(f x + e\right)^{3} + 110 \, a^{2} c^{5} \cos\left(f x + e\right)^{2} - 144 \, a^{2} c^{5} \cos\left(f x + e\right) + 40 \, a^{2} c^{5}\right)} \sin\left(f x + e\right)}{480 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/480*(480*a^2*c^5*f*x*cos(f*x + e)^6 - 285*a^2*c^5*cos(f*x + e)^6*log(sin(f*x + e) + 1) + 285*a^2*c^5*cos(f*x + e)^6*log(-sin(f*x + e) + 1) - 2*(176*a^2*c^5*cos(f*x + e)^5 - 435*a^2*c^5*cos(f*x + e)^4 + 208*a^2*c^5*cos(f*x + e)^3 + 110*a^2*c^5*cos(f*x + e)^2 - 144*a^2*c^5*cos(f*x + e) + 40*a^2*c^5)*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
2,1,163,0,0.518111," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{120 \, a^{2} c^{4} f x \cos\left(f x + e\right)^{5} - 45 \, a^{2} c^{4} \cos\left(f x + e\right)^{5} \log\left(\sin\left(f x + e\right) + 1\right) + 45 \, a^{2} c^{4} \cos\left(f x + e\right)^{5} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(68 \, a^{2} c^{4} \cos\left(f x + e\right)^{4} - 75 \, a^{2} c^{4} \cos\left(f x + e\right)^{3} + 4 \, a^{2} c^{4} \cos\left(f x + e\right)^{2} + 30 \, a^{2} c^{4} \cos\left(f x + e\right) - 12 \, a^{2} c^{4}\right)} \sin\left(f x + e\right)}{120 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/120*(120*a^2*c^4*f*x*cos(f*x + e)^5 - 45*a^2*c^4*cos(f*x + e)^5*log(sin(f*x + e) + 1) + 45*a^2*c^4*cos(f*x + e)^5*log(-sin(f*x + e) + 1) - 2*(68*a^2*c^4*cos(f*x + e)^4 - 75*a^2*c^4*cos(f*x + e)^3 + 4*a^2*c^4*cos(f*x + e)^2 + 30*a^2*c^4*cos(f*x + e) - 12*a^2*c^4)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
3,1,147,0,0.488223," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{48 \, a^{2} c^{3} f x \cos\left(f x + e\right)^{4} - 9 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) + 9 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(32 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} - 15 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} - 8 \, a^{2} c^{3} \cos\left(f x + e\right) + 6 \, a^{2} c^{3}\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(48*a^2*c^3*f*x*cos(f*x + e)^4 - 9*a^2*c^3*cos(f*x + e)^4*log(sin(f*x + e) + 1) + 9*a^2*c^3*cos(f*x + e)^4*log(-sin(f*x + e) + 1) - 2*(32*a^2*c^3*cos(f*x + e)^3 - 15*a^2*c^3*cos(f*x + e)^2 - 8*a^2*c^3*cos(f*x + e) + 6*a^2*c^3)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
4,1,65,0,0.432822," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} c^{2} f x \cos\left(f x + e\right)^{3} - {\left(4 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - a^{2} c^{2}\right)} \sin\left(f x + e\right)}{3 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/3*(3*a^2*c^2*f*x*cos(f*x + e)^3 - (4*a^2*c^2*cos(f*x + e)^2 - a^2*c^2)*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
5,1,103,0,0.476384," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, a^{2} c f x \cos\left(f x + e\right)^{2} + a^{2} c \cos\left(f x + e\right)^{2} \log\left(\sin\left(f x + e\right) + 1\right) - a^{2} c \cos\left(f x + e\right)^{2} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a^{2} c \cos\left(f x + e\right) + a^{2} c\right)} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{2}}"," ",0,"1/4*(4*a^2*c*f*x*cos(f*x + e)^2 + a^2*c*cos(f*x + e)^2*log(sin(f*x + e) + 1) - a^2*c*cos(f*x + e)^2*log(-sin(f*x + e) + 1) - 2*(2*a^2*c*cos(f*x + e) + a^2*c)*sin(f*x + e))/(f*cos(f*x + e)^2)","B",0
6,1,87,0,0.483969," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, a^{2} f x \sin\left(f x + e\right) - a^{2} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + a^{2} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 8 \, a^{2} \cos\left(f x + e\right) + 8 \, a^{2}}{2 \, c f \sin\left(f x + e\right)}"," ",0,"1/2*(2*a^2*f*x*sin(f*x + e) - a^2*log(sin(f*x + e) + 1)*sin(f*x + e) + a^2*log(-sin(f*x + e) + 1)*sin(f*x + e) + 8*a^2*cos(f*x + e) + 8*a^2)/(c*f*sin(f*x + e))","A",0
7,1,88,0,0.457921," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{8 \, a^{2} \cos\left(f x + e\right)^{2} + 4 \, a^{2} \cos\left(f x + e\right) - 4 \, a^{2} + 3 \, {\left(a^{2} f x \cos\left(f x + e\right) - a^{2} f x\right)} \sin\left(f x + e\right)}{3 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(8*a^2*cos(f*x + e)^2 + 4*a^2*cos(f*x + e) - 4*a^2 + 3*(a^2*f*x*cos(f*x + e) - a^2*f*x)*sin(f*x + e))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))","A",0
8,1,128,0,0.425455," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{43 \, a^{2} \cos\left(f x + e\right)^{3} - 11 \, a^{2} \cos\left(f x + e\right)^{2} - 31 \, a^{2} \cos\left(f x + e\right) + 23 \, a^{2} + 15 \, {\left(a^{2} f x \cos\left(f x + e\right)^{2} - 2 \, a^{2} f x \cos\left(f x + e\right) + a^{2} f x\right)} \sin\left(f x + e\right)}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(43*a^2*cos(f*x + e)^3 - 11*a^2*cos(f*x + e)^2 - 31*a^2*cos(f*x + e) + 23*a^2 + 15*(a^2*f*x*cos(f*x + e)^2 - 2*a^2*f*x*cos(f*x + e) + a^2*f*x)*sin(f*x + e))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","A",0
9,1,172,0,0.434857," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{319 \, a^{2} \cos\left(f x + e\right)^{4} - 327 \, a^{2} \cos\left(f x + e\right)^{3} - 95 \, a^{2} \cos\left(f x + e\right)^{2} + 387 \, a^{2} \cos\left(f x + e\right) - 164 \, a^{2} + 105 \, {\left(a^{2} f x \cos\left(f x + e\right)^{3} - 3 \, a^{2} f x \cos\left(f x + e\right)^{2} + 3 \, a^{2} f x \cos\left(f x + e\right) - a^{2} f x\right)} \sin\left(f x + e\right)}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/105*(319*a^2*cos(f*x + e)^4 - 327*a^2*cos(f*x + e)^3 - 95*a^2*cos(f*x + e)^2 + 387*a^2*cos(f*x + e) - 164*a^2 + 105*(a^2*f*x*cos(f*x + e)^3 - 3*a^2*f*x*cos(f*x + e)^2 + 3*a^2*f*x*cos(f*x + e) - a^2*f*x)*sin(f*x + e))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","A",0
10,1,212,0,0.463112," ","integrate((a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{1004 \, a^{2} \cos\left(f x + e\right)^{5} - 1811 \, a^{2} \cos\left(f x + e\right)^{4} + 797 \, a^{2} \cos\left(f x + e\right)^{3} + 1457 \, a^{2} \cos\left(f x + e\right)^{2} - 1661 \, a^{2} \cos\left(f x + e\right) + 494 \, a^{2} + 315 \, {\left(a^{2} f x \cos\left(f x + e\right)^{4} - 4 \, a^{2} f x \cos\left(f x + e\right)^{3} + 6 \, a^{2} f x \cos\left(f x + e\right)^{2} - 4 \, a^{2} f x \cos\left(f x + e\right) + a^{2} f x\right)} \sin\left(f x + e\right)}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(1004*a^2*cos(f*x + e)^5 - 1811*a^2*cos(f*x + e)^4 + 797*a^2*cos(f*x + e)^3 + 1457*a^2*cos(f*x + e)^2 - 1661*a^2*cos(f*x + e) + 494*a^2 + 315*(a^2*f*x*cos(f*x + e)^4 - 4*a^2*f*x*cos(f*x + e)^3 + 6*a^2*f*x*cos(f*x + e)^2 - 4*a^2*f*x*cos(f*x + e) + a^2*f*x)*sin(f*x + e))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
11,1,195,0,0.484869," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{1680 \, a^{3} c^{5} f x \cos\left(f x + e\right)^{7} - 525 \, a^{3} c^{5} \cos\left(f x + e\right)^{7} \log\left(\sin\left(f x + e\right) + 1\right) + 525 \, a^{3} c^{5} \cos\left(f x + e\right)^{7} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(1168 \, a^{3} c^{5} \cos\left(f x + e\right)^{6} - 1155 \, a^{3} c^{5} \cos\left(f x + e\right)^{5} - 256 \, a^{3} c^{5} \cos\left(f x + e\right)^{4} + 910 \, a^{3} c^{5} \cos\left(f x + e\right)^{3} - 192 \, a^{3} c^{5} \cos\left(f x + e\right)^{2} - 280 \, a^{3} c^{5} \cos\left(f x + e\right) + 120 \, a^{3} c^{5}\right)} \sin\left(f x + e\right)}{1680 \, f \cos\left(f x + e\right)^{7}}"," ",0,"1/1680*(1680*a^3*c^5*f*x*cos(f*x + e)^7 - 525*a^3*c^5*cos(f*x + e)^7*log(sin(f*x + e) + 1) + 525*a^3*c^5*cos(f*x + e)^7*log(-sin(f*x + e) + 1) - 2*(1168*a^3*c^5*cos(f*x + e)^6 - 1155*a^3*c^5*cos(f*x + e)^5 - 256*a^3*c^5*cos(f*x + e)^4 + 910*a^3*c^5*cos(f*x + e)^3 - 192*a^3*c^5*cos(f*x + e)^2 - 280*a^3*c^5*cos(f*x + e) + 120*a^3*c^5)*sin(f*x + e))/(f*cos(f*x + e)^7)","A",0
12,1,179,0,0.525949," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{480 \, a^{3} c^{4} f x \cos\left(f x + e\right)^{6} - 75 \, a^{3} c^{4} \cos\left(f x + e\right)^{6} \log\left(\sin\left(f x + e\right) + 1\right) + 75 \, a^{3} c^{4} \cos\left(f x + e\right)^{6} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(368 \, a^{3} c^{4} \cos\left(f x + e\right)^{5} - 165 \, a^{3} c^{4} \cos\left(f x + e\right)^{4} - 176 \, a^{3} c^{4} \cos\left(f x + e\right)^{3} + 130 \, a^{3} c^{4} \cos\left(f x + e\right)^{2} + 48 \, a^{3} c^{4} \cos\left(f x + e\right) - 40 \, a^{3} c^{4}\right)} \sin\left(f x + e\right)}{480 \, f \cos\left(f x + e\right)^{6}}"," ",0,"1/480*(480*a^3*c^4*f*x*cos(f*x + e)^6 - 75*a^3*c^4*cos(f*x + e)^6*log(sin(f*x + e) + 1) + 75*a^3*c^4*cos(f*x + e)^6*log(-sin(f*x + e) + 1) - 2*(368*a^3*c^4*cos(f*x + e)^5 - 165*a^3*c^4*cos(f*x + e)^4 - 176*a^3*c^4*cos(f*x + e)^3 + 130*a^3*c^4*cos(f*x + e)^2 + 48*a^3*c^4*cos(f*x + e) - 40*a^3*c^4)*sin(f*x + e))/(f*cos(f*x + e)^6)","A",0
13,1,81,0,0.464692," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, a^{3} c^{3} f x \cos\left(f x + e\right)^{5} - {\left(23 \, a^{3} c^{3} \cos\left(f x + e\right)^{4} - 11 \, a^{3} c^{3} \cos\left(f x + e\right)^{2} + 3 \, a^{3} c^{3}\right)} \sin\left(f x + e\right)}{15 \, f \cos\left(f x + e\right)^{5}}"," ",0,"1/15*(15*a^3*c^3*f*x*cos(f*x + e)^5 - (23*a^3*c^3*cos(f*x + e)^4 - 11*a^3*c^3*cos(f*x + e)^2 + 3*a^3*c^3)*sin(f*x + e))/(f*cos(f*x + e)^5)","A",0
14,1,147,0,0.496330," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{48 \, a^{3} c^{2} f x \cos\left(f x + e\right)^{4} + 9 \, a^{3} c^{2} \cos\left(f x + e\right)^{4} \log\left(\sin\left(f x + e\right) + 1\right) - 9 \, a^{3} c^{2} \cos\left(f x + e\right)^{4} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(32 \, a^{3} c^{2} \cos\left(f x + e\right)^{3} + 15 \, a^{3} c^{2} \cos\left(f x + e\right)^{2} - 8 \, a^{3} c^{2} \cos\left(f x + e\right) - 6 \, a^{3} c^{2}\right)} \sin\left(f x + e\right)}{48 \, f \cos\left(f x + e\right)^{4}}"," ",0,"1/48*(48*a^3*c^2*f*x*cos(f*x + e)^4 + 9*a^3*c^2*cos(f*x + e)^4*log(sin(f*x + e) + 1) - 9*a^3*c^2*cos(f*x + e)^4*log(-sin(f*x + e) + 1) - 2*(32*a^3*c^2*cos(f*x + e)^3 + 15*a^3*c^2*cos(f*x + e)^2 - 8*a^3*c^2*cos(f*x + e) - 6*a^3*c^2)*sin(f*x + e))/(f*cos(f*x + e)^4)","A",0
15,1,118,0,0.447995," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{6 \, a^{3} c f x \cos\left(f x + e\right)^{3} + 3 \, a^{3} c \cos\left(f x + e\right)^{3} \log\left(\sin\left(f x + e\right) + 1\right) - 3 \, a^{3} c \cos\left(f x + e\right)^{3} \log\left(-\sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, a^{3} c \cos\left(f x + e\right)^{2} + 3 \, a^{3} c \cos\left(f x + e\right) + a^{3} c\right)} \sin\left(f x + e\right)}{6 \, f \cos\left(f x + e\right)^{3}}"," ",0,"1/6*(6*a^3*c*f*x*cos(f*x + e)^3 + 3*a^3*c*cos(f*x + e)^3*log(sin(f*x + e) + 1) - 3*a^3*c*cos(f*x + e)^3*log(-sin(f*x + e) + 1) - 2*(2*a^3*c*cos(f*x + e)^2 + 3*a^3*c*cos(f*x + e) + a^3*c)*sin(f*x + e))/(f*cos(f*x + e)^3)","A",0
16,1,125,0,0.514699," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{a^{3} f x \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} \cos\left(f x + e\right) \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 2 \, a^{3} \cos\left(f x + e\right) \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 9 \, a^{3} \cos\left(f x + e\right)^{2} + 8 \, a^{3} \cos\left(f x + e\right) - a^{3}}{c f \cos\left(f x + e\right) \sin\left(f x + e\right)}"," ",0,"(a^3*f*x*cos(f*x + e)*sin(f*x + e) - 2*a^3*cos(f*x + e)*log(sin(f*x + e) + 1)*sin(f*x + e) + 2*a^3*cos(f*x + e)*log(-sin(f*x + e) + 1)*sin(f*x + e) + 9*a^3*cos(f*x + e)^2 + 8*a^3*cos(f*x + e) - a^3)/(c*f*cos(f*x + e)*sin(f*x + e))","A",0
17,1,156,0,0.454709," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{8 \, a^{3} \cos\left(f x + e\right)^{2} + 16 \, a^{3} \cos\left(f x + e\right) + 8 \, a^{3} + 3 \, {\left(a^{3} \cos\left(f x + e\right) - a^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 3 \, {\left(a^{3} \cos\left(f x + e\right) - a^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + 6 \, {\left(a^{3} f x \cos\left(f x + e\right) - a^{3} f x\right)} \sin\left(f x + e\right)}{6 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/6*(8*a^3*cos(f*x + e)^2 + 16*a^3*cos(f*x + e) + 8*a^3 + 3*(a^3*cos(f*x + e) - a^3)*log(sin(f*x + e) + 1)*sin(f*x + e) - 3*(a^3*cos(f*x + e) - a^3)*log(-sin(f*x + e) + 1)*sin(f*x + e) + 6*(a^3*f*x*cos(f*x + e) - a^3*f*x)*sin(f*x + e))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))","A",0
18,1,128,0,0.429488," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{46 \, a^{3} \cos\left(f x + e\right)^{3} - 2 \, a^{3} \cos\left(f x + e\right)^{2} - 22 \, a^{3} \cos\left(f x + e\right) + 26 \, a^{3} + 15 \, {\left(a^{3} f x \cos\left(f x + e\right)^{2} - 2 \, a^{3} f x \cos\left(f x + e\right) + a^{3} f x\right)} \sin\left(f x + e\right)}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(46*a^3*cos(f*x + e)^3 - 2*a^3*cos(f*x + e)^2 - 22*a^3*cos(f*x + e) + 26*a^3 + 15*(a^3*f*x*cos(f*x + e)^2 - 2*a^3*f*x*cos(f*x + e) + a^3*f*x)*sin(f*x + e))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))","A",0
19,1,172,0,0.453001," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{337 \, a^{3} \cos\left(f x + e\right)^{4} - 276 \, a^{3} \cos\left(f x + e\right)^{3} - 50 \, a^{3} \cos\left(f x + e\right)^{2} + 396 \, a^{3} \cos\left(f x + e\right) - 167 \, a^{3} + 105 \, {\left(a^{3} f x \cos\left(f x + e\right)^{3} - 3 \, a^{3} f x \cos\left(f x + e\right)^{2} + 3 \, a^{3} f x \cos\left(f x + e\right) - a^{3} f x\right)} \sin\left(f x + e\right)}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/105*(337*a^3*cos(f*x + e)^4 - 276*a^3*cos(f*x + e)^3 - 50*a^3*cos(f*x + e)^2 + 396*a^3*cos(f*x + e) - 167*a^3 + 105*(a^3*f*x*cos(f*x + e)^3 - 3*a^3*f*x*cos(f*x + e)^2 + 3*a^3*f*x*cos(f*x + e) - a^3*f*x)*sin(f*x + e))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))","A",0
20,1,212,0,0.438024," ","integrate((a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{1051 \, a^{3} \cos\left(f x + e\right)^{5} - 1684 \, a^{3} \cos\left(f x + e\right)^{4} + 898 \, a^{3} \cos\left(f x + e\right)^{3} + 1468 \, a^{3} \cos\left(f x + e\right)^{2} - 1669 \, a^{3} \cos\left(f x + e\right) + 496 \, a^{3} + 315 \, {\left(a^{3} f x \cos\left(f x + e\right)^{4} - 4 \, a^{3} f x \cos\left(f x + e\right)^{3} + 6 \, a^{3} f x \cos\left(f x + e\right)^{2} - 4 \, a^{3} f x \cos\left(f x + e\right) + a^{3} f x\right)} \sin\left(f x + e\right)}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(1051*a^3*cos(f*x + e)^5 - 1684*a^3*cos(f*x + e)^4 + 898*a^3*cos(f*x + e)^3 + 1468*a^3*cos(f*x + e)^2 - 1669*a^3*cos(f*x + e) + 496*a^3 + 315*(a^3*f*x*cos(f*x + e)^4 - 4*a^3*f*x*cos(f*x + e)^3 + 6*a^3*f*x*cos(f*x + e)^2 - 4*a^3*f*x*cos(f*x + e) + a^3*f*x)*sin(f*x + e))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))","A",0
21,1,242,0,0.458540," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{12 \, c^{5} f x \cos\left(f x + e\right)^{4} + 24 \, c^{5} f x \cos\left(f x + e\right)^{3} + 12 \, c^{5} f x \cos\left(f x + e\right)^{2} - 141 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 2 \, c^{5} \cos\left(f x + e\right)^{3} + c^{5} \cos\left(f x + e\right)^{2}\right)} \log\left(\sin\left(f x + e\right) + 1\right) + 141 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 2 \, c^{5} \cos\left(f x + e\right)^{3} + c^{5} \cos\left(f x + e\right)^{2}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + 2 \, {\left(202 \, c^{5} \cos\left(f x + e\right)^{3} + 305 \, c^{5} \cos\left(f x + e\right)^{2} + 36 \, c^{5} \cos\left(f x + e\right) - 3 \, c^{5}\right)} \sin\left(f x + e\right)}{12 \, {\left(a^{2} f \cos\left(f x + e\right)^{4} + 2 \, a^{2} f \cos\left(f x + e\right)^{3} + a^{2} f \cos\left(f x + e\right)^{2}\right)}}"," ",0,"1/12*(12*c^5*f*x*cos(f*x + e)^4 + 24*c^5*f*x*cos(f*x + e)^3 + 12*c^5*f*x*cos(f*x + e)^2 - 141*(c^5*cos(f*x + e)^4 + 2*c^5*cos(f*x + e)^3 + c^5*cos(f*x + e)^2)*log(sin(f*x + e) + 1) + 141*(c^5*cos(f*x + e)^4 + 2*c^5*cos(f*x + e)^3 + c^5*cos(f*x + e)^2)*log(-sin(f*x + e) + 1) + 2*(202*c^5*cos(f*x + e)^3 + 305*c^5*cos(f*x + e)^2 + 36*c^5*cos(f*x + e) - 3*c^5)*sin(f*x + e))/(a^2*f*cos(f*x + e)^4 + 2*a^2*f*cos(f*x + e)^3 + a^2*f*cos(f*x + e)^2)","A",0
22,1,220,0,0.488347," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, c^{4} f x \cos\left(f x + e\right)^{3} + 6 \, c^{4} f x \cos\left(f x + e\right)^{2} + 3 \, c^{4} f x \cos\left(f x + e\right) - 9 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 2 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) + 9 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 2 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + {\left(19 \, c^{4} \cos\left(f x + e\right)^{2} + 38 \, c^{4} \cos\left(f x + e\right) + 3 \, c^{4}\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"1/3*(3*c^4*f*x*cos(f*x + e)^3 + 6*c^4*f*x*cos(f*x + e)^2 + 3*c^4*f*x*cos(f*x + e) - 9*(c^4*cos(f*x + e)^3 + 2*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*log(sin(f*x + e) + 1) + 9*(c^4*cos(f*x + e)^3 + 2*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*log(-sin(f*x + e) + 1) + (19*c^4*cos(f*x + e)^2 + 38*c^4*cos(f*x + e) + 3*c^4)*sin(f*x + e))/(a^2*f*cos(f*x + e)^3 + 2*a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e))","B",0
23,1,173,0,0.462600," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{6 \, c^{3} f x \cos\left(f x + e\right)^{2} + 12 \, c^{3} f x \cos\left(f x + e\right) + 6 \, c^{3} f x - 3 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \log\left(\sin\left(f x + e\right) + 1\right) + 3 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 8 \, {\left(c^{3} \cos\left(f x + e\right) - c^{3}\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/6*(6*c^3*f*x*cos(f*x + e)^2 + 12*c^3*f*x*cos(f*x + e) + 6*c^3*f*x - 3*(c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*log(sin(f*x + e) + 1) + 3*(c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*log(-sin(f*x + e) + 1) - 8*(c^3*cos(f*x + e) - c^3)*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","B",0
24,1,94,0,0.450198," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, c^{2} f x \cos\left(f x + e\right)^{2} + 6 \, c^{2} f x \cos\left(f x + e\right) + 3 \, c^{2} f x - 4 \, {\left(2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/3*(3*c^2*f*x*cos(f*x + e)^2 + 6*c^2*f*x*cos(f*x + e) + 3*c^2*f*x - 4*(2*c^2*cos(f*x + e) + c^2)*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
25,1,86,0,0.469975," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, c f x \cos\left(f x + e\right)^{2} + 6 \, c f x \cos\left(f x + e\right) + 3 \, c f x - {\left(7 \, c \cos\left(f x + e\right) + 5 \, c\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}"," ",0,"1/3*(3*c*f*x*cos(f*x + e)^2 + 6*c*f*x*cos(f*x + e) + 3*c*f*x - (7*c*cos(f*x + e) + 5*c)*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)","A",0
26,1,70,0,0.425202," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, \cos\left(f x + e\right)^{2} + 3 \, {\left(f x \cos\left(f x + e\right) + f x\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) - 2}{3 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(4*cos(f*x + e)^2 + 3*(f*x*cos(f*x + e) + f*x)*sin(f*x + e) + cos(f*x + e) - 2)/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e))","A",0
27,1,81,0,0.413577," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{4 \, \cos\left(f x + e\right)^{3} + 3 \, {\left(f x \cos\left(f x + e\right)^{2} - f x\right)} \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)}{3 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3*(4*cos(f*x + e)^3 + 3*(f*x*cos(f*x + e)^2 - f*x)*sin(f*x + e) - 3*cos(f*x + e))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))","A",0
28,1,154,0,0.423588," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{23 \, \cos\left(f x + e\right)^{4} - 8 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)^{2} + 15 \, {\left(f x \cos\left(f x + e\right)^{3} - f x \cos\left(f x + e\right)^{2} - f x \cos\left(f x + e\right) + f x\right)} \sin\left(f x + e\right) + 7 \, \cos\left(f x + e\right) + 8}{15 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(23*cos(f*x + e)^4 - 8*cos(f*x + e)^3 - 27*cos(f*x + e)^2 + 15*(f*x*cos(f*x + e)^3 - f*x*cos(f*x + e)^2 - f*x*cos(f*x + e) + f*x)*sin(f*x + e) + 7*cos(f*x + e) + 8)/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e))","A",0
29,1,166,0,0.490355," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{191 \, \cos\left(f x + e\right)^{5} - 172 \, \cos\left(f x + e\right)^{4} - 253 \, \cos\left(f x + e\right)^{3} + 258 \, \cos\left(f x + e\right)^{2} + 105 \, {\left(f x \cos\left(f x + e\right)^{4} - 2 \, f x \cos\left(f x + e\right)^{3} + 2 \, f x \cos\left(f x + e\right) - f x\right)} \sin\left(f x + e\right) + 87 \, \cos\left(f x + e\right) - 96}{105 \, {\left(a^{2} c^{4} f \cos\left(f x + e\right)^{4} - 2 \, a^{2} c^{4} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} c^{4} f \cos\left(f x + e\right) - a^{2} c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/105*(191*cos(f*x + e)^5 - 172*cos(f*x + e)^4 - 253*cos(f*x + e)^3 + 258*cos(f*x + e)^2 + 105*(f*x*cos(f*x + e)^4 - 2*f*x*cos(f*x + e)^3 + 2*f*x*cos(f*x + e) - f*x)*sin(f*x + e) + 87*cos(f*x + e) - 96)/((a^2*c^4*f*cos(f*x + e)^4 - 2*a^2*c^4*f*cos(f*x + e)^3 + 2*a^2*c^4*f*cos(f*x + e) - a^2*c^4*f)*sin(f*x + e))","A",0
30,1,232,0,0.424230," ","integrate(1/(a+a*sec(f*x+e))^2/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{668 \, \cos\left(f x + e\right)^{6} - 1059 \, \cos\left(f x + e\right)^{5} - 573 \, \cos\left(f x + e\right)^{4} + 1813 \, \cos\left(f x + e\right)^{3} - 393 \, \cos\left(f x + e\right)^{2} + 315 \, {\left(f x \cos\left(f x + e\right)^{5} - 3 \, f x \cos\left(f x + e\right)^{4} + 2 \, f x \cos\left(f x + e\right)^{3} + 2 \, f x \cos\left(f x + e\right)^{2} - 3 \, f x \cos\left(f x + e\right) + f x\right)} \sin\left(f x + e\right) - 789 \, \cos\left(f x + e\right) + 368}{315 \, {\left(a^{2} c^{5} f \cos\left(f x + e\right)^{5} - 3 \, a^{2} c^{5} f \cos\left(f x + e\right)^{4} + 2 \, a^{2} c^{5} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} c^{5} f \cos\left(f x + e\right)^{2} - 3 \, a^{2} c^{5} f \cos\left(f x + e\right) + a^{2} c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(668*cos(f*x + e)^6 - 1059*cos(f*x + e)^5 - 573*cos(f*x + e)^4 + 1813*cos(f*x + e)^3 - 393*cos(f*x + e)^2 + 315*(f*x*cos(f*x + e)^5 - 3*f*x*cos(f*x + e)^4 + 2*f*x*cos(f*x + e)^3 + 2*f*x*cos(f*x + e)^2 - 3*f*x*cos(f*x + e) + f*x)*sin(f*x + e) - 789*cos(f*x + e) + 368)/((a^2*c^5*f*cos(f*x + e)^5 - 3*a^2*c^5*f*cos(f*x + e)^4 + 2*a^2*c^5*f*cos(f*x + e)^3 + 2*a^2*c^5*f*cos(f*x + e)^2 - 3*a^2*c^5*f*cos(f*x + e) + a^2*c^5*f)*sin(f*x + e))","A",0
31,1,289,0,0.452241," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, c^{5} f x \cos\left(f x + e\right)^{4} + 45 \, c^{5} f x \cos\left(f x + e\right)^{3} + 45 \, c^{5} f x \cos\left(f x + e\right)^{2} + 15 \, c^{5} f x \cos\left(f x + e\right) + 60 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + 3 \, c^{5} \cos\left(f x + e\right)^{2} + c^{5} \cos\left(f x + e\right)\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 60 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + 3 \, c^{5} \cos\left(f x + e\right)^{2} + c^{5} \cos\left(f x + e\right)\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - {\left(239 \, c^{5} \cos\left(f x + e\right)^{3} + 477 \, c^{5} \cos\left(f x + e\right)^{2} + 349 \, c^{5} \cos\left(f x + e\right) + 15 \, c^{5}\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"1/15*(15*c^5*f*x*cos(f*x + e)^4 + 45*c^5*f*x*cos(f*x + e)^3 + 45*c^5*f*x*cos(f*x + e)^2 + 15*c^5*f*x*cos(f*x + e) + 60*(c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + 3*c^5*cos(f*x + e)^2 + c^5*cos(f*x + e))*log(sin(f*x + e) + 1) - 60*(c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + 3*c^5*cos(f*x + e)^2 + c^5*cos(f*x + e))*log(-sin(f*x + e) + 1) - (239*c^5*cos(f*x + e)^3 + 477*c^5*cos(f*x + e)^2 + 349*c^5*cos(f*x + e) + 15*c^5)*sin(f*x + e))/(a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + a^3*f*cos(f*x + e))","A",0
32,1,242,0,0.480407," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{10 \, c^{4} f x \cos\left(f x + e\right)^{3} + 30 \, c^{4} f x \cos\left(f x + e\right)^{2} + 30 \, c^{4} f x \cos\left(f x + e\right) + 10 \, c^{4} f x + 5 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \log\left(\sin\left(f x + e\right) + 1\right) - 5 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \log\left(-\sin\left(f x + e\right) + 1\right) - 16 \, {\left(3 \, c^{4} \cos\left(f x + e\right)^{2} + 4 \, c^{4} \cos\left(f x + e\right) + 3 \, c^{4}\right)} \sin\left(f x + e\right)}{10 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/10*(10*c^4*f*x*cos(f*x + e)^3 + 30*c^4*f*x*cos(f*x + e)^2 + 30*c^4*f*x*cos(f*x + e) + 10*c^4*f*x + 5*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*log(sin(f*x + e) + 1) - 5*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*log(-sin(f*x + e) + 1) - 16*(3*c^4*cos(f*x + e)^2 + 4*c^4*cos(f*x + e) + 3*c^4)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
33,1,138,0,0.438829," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, c^{3} f x \cos\left(f x + e\right)^{3} + 45 \, c^{3} f x \cos\left(f x + e\right)^{2} + 45 \, c^{3} f x \cos\left(f x + e\right) + 15 \, c^{3} f x - 2 \, {\left(23 \, c^{3} \cos\left(f x + e\right)^{2} + 24 \, c^{3} \cos\left(f x + e\right) + 13 \, c^{3}\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*(15*c^3*f*x*cos(f*x + e)^3 + 45*c^3*f*x*cos(f*x + e)^2 + 45*c^3*f*x*cos(f*x + e) + 15*c^3*f*x - 2*(23*c^3*cos(f*x + e)^2 + 24*c^3*cos(f*x + e) + 13*c^3)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
34,1,138,0,0.442206," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, c^{2} f x \cos\left(f x + e\right)^{3} + 45 \, c^{2} f x \cos\left(f x + e\right)^{2} + 45 \, c^{2} f x \cos\left(f x + e\right) + 15 \, c^{2} f x - {\left(43 \, c^{2} \cos\left(f x + e\right)^{2} + 54 \, c^{2} \cos\left(f x + e\right) + 23 \, c^{2}\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/15*(15*c^2*f*x*cos(f*x + e)^3 + 45*c^2*f*x*cos(f*x + e)^2 + 45*c^2*f*x*cos(f*x + e) + 15*c^2*f*x - (43*c^2*cos(f*x + e)^2 + 54*c^2*cos(f*x + e) + 23*c^2)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
35,1,124,0,0.426560," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{5 \, c f x \cos\left(f x + e\right)^{3} + 15 \, c f x \cos\left(f x + e\right)^{2} + 15 \, c f x \cos\left(f x + e\right) + 5 \, c f x - {\left(13 \, c \cos\left(f x + e\right)^{2} + 19 \, c \cos\left(f x + e\right) + 8 \, c\right)} \sin\left(f x + e\right)}{5 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}"," ",0,"1/5*(5*c*f*x*cos(f*x + e)^3 + 15*c*f*x*cos(f*x + e)^2 + 15*c*f*x*cos(f*x + e) + 5*c*f*x - (13*c*cos(f*x + e)^2 + 19*c*cos(f*x + e) + 8*c)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)","A",0
36,1,109,0,0.427760," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\frac{26 \, \cos\left(f x + e\right)^{3} + 22 \, \cos\left(f x + e\right)^{2} + 15 \, {\left(f x \cos\left(f x + e\right)^{2} + 2 \, f x \cos\left(f x + e\right) + f x\right)} \sin\left(f x + e\right) - 17 \, \cos\left(f x + e\right) - 16}{15 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(26*cos(f*x + e)^3 + 22*cos(f*x + e)^2 + 15*(f*x*cos(f*x + e)^2 + 2*f*x*cos(f*x + e) + f*x)*sin(f*x + e) - 17*cos(f*x + e) - 16)/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e))","A",0
37,1,154,0,0.425906," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\frac{23 \, \cos\left(f x + e\right)^{4} + 8 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)^{2} + 15 \, {\left(f x \cos\left(f x + e\right)^{3} + f x \cos\left(f x + e\right)^{2} - f x \cos\left(f x + e\right) - f x\right)} \sin\left(f x + e\right) - 7 \, \cos\left(f x + e\right) + 8}{15 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(23*cos(f*x + e)^4 + 8*cos(f*x + e)^3 - 27*cos(f*x + e)^2 + 15*(f*x*cos(f*x + e)^3 + f*x*cos(f*x + e)^2 - f*x*cos(f*x + e) - f*x)*sin(f*x + e) - 7*cos(f*x + e) + 8)/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e))","A",0
38,1,118,0,0.448205," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\frac{23 \, \cos\left(f x + e\right)^{5} - 35 \, \cos\left(f x + e\right)^{3} + 15 \, {\left(f x \cos\left(f x + e\right)^{4} - 2 \, f x \cos\left(f x + e\right)^{2} + f x\right)} \sin\left(f x + e\right) + 15 \, \cos\left(f x + e\right)}{15 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}"," ",0,"1/15*(23*cos(f*x + e)^5 - 35*cos(f*x + e)^3 + 15*(f*x*cos(f*x + e)^4 - 2*f*x*cos(f*x + e)^2 + f*x)*sin(f*x + e) + 15*cos(f*x + e))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e))","A",0
39,1,232,0,0.447115," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\frac{176 \, \cos\left(f x + e\right)^{6} - 71 \, \cos\left(f x + e\right)^{5} - 335 \, \cos\left(f x + e\right)^{4} + 125 \, \cos\left(f x + e\right)^{3} + 225 \, \cos\left(f x + e\right)^{2} + 105 \, {\left(f x \cos\left(f x + e\right)^{5} - f x \cos\left(f x + e\right)^{4} - 2 \, f x \cos\left(f x + e\right)^{3} + 2 \, f x \cos\left(f x + e\right)^{2} + f x \cos\left(f x + e\right) - f x\right)} \sin\left(f x + e\right) - 57 \, \cos\left(f x + e\right) - 48}{105 \, {\left(a^{3} c^{4} f \cos\left(f x + e\right)^{5} - a^{3} c^{4} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{4} f \cos\left(f x + e\right)^{3} + 2 \, a^{3} c^{4} f \cos\left(f x + e\right)^{2} + a^{3} c^{4} f \cos\left(f x + e\right) - a^{3} c^{4} f\right)} \sin\left(f x + e\right)}"," ",0,"1/105*(176*cos(f*x + e)^6 - 71*cos(f*x + e)^5 - 335*cos(f*x + e)^4 + 125*cos(f*x + e)^3 + 225*cos(f*x + e)^2 + 105*(f*x*cos(f*x + e)^5 - f*x*cos(f*x + e)^4 - 2*f*x*cos(f*x + e)^3 + 2*f*x*cos(f*x + e)^2 + f*x*cos(f*x + e) - f*x)*sin(f*x + e) - 57*cos(f*x + e) - 48)/((a^3*c^4*f*cos(f*x + e)^5 - a^3*c^4*f*cos(f*x + e)^4 - 2*a^3*c^4*f*cos(f*x + e)^3 + 2*a^3*c^4*f*cos(f*x + e)^2 + a^3*c^4*f*cos(f*x + e) - a^3*c^4*f)*sin(f*x + e))","A",0
40,1,271,0,0.461779," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\frac{598 \, \cos\left(f x + e\right)^{7} - 566 \, \cos\left(f x + e\right)^{6} - 1212 \, \cos\left(f x + e\right)^{5} + 1310 \, \cos\left(f x + e\right)^{4} + 860 \, \cos\left(f x + e\right)^{3} - 1014 \, \cos\left(f x + e\right)^{2} + 315 \, {\left(f x \cos\left(f x + e\right)^{6} - 2 \, f x \cos\left(f x + e\right)^{5} - f x \cos\left(f x + e\right)^{4} + 4 \, f x \cos\left(f x + e\right)^{3} - f x \cos\left(f x + e\right)^{2} - 2 \, f x \cos\left(f x + e\right) + f x\right)} \sin\left(f x + e\right) - 197 \, \cos\left(f x + e\right) + 256}{315 \, {\left(a^{3} c^{5} f \cos\left(f x + e\right)^{6} - 2 \, a^{3} c^{5} f \cos\left(f x + e\right)^{5} - a^{3} c^{5} f \cos\left(f x + e\right)^{4} + 4 \, a^{3} c^{5} f \cos\left(f x + e\right)^{3} - a^{3} c^{5} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} c^{5} f \cos\left(f x + e\right) + a^{3} c^{5} f\right)} \sin\left(f x + e\right)}"," ",0,"1/315*(598*cos(f*x + e)^7 - 566*cos(f*x + e)^6 - 1212*cos(f*x + e)^5 + 1310*cos(f*x + e)^4 + 860*cos(f*x + e)^3 - 1014*cos(f*x + e)^2 + 315*(f*x*cos(f*x + e)^6 - 2*f*x*cos(f*x + e)^5 - f*x*cos(f*x + e)^4 + 4*f*x*cos(f*x + e)^3 - f*x*cos(f*x + e)^2 - 2*f*x*cos(f*x + e) + f*x)*sin(f*x + e) - 197*cos(f*x + e) + 256)/((a^3*c^5*f*cos(f*x + e)^6 - 2*a^3*c^5*f*cos(f*x + e)^5 - a^3*c^5*f*cos(f*x + e)^4 + 4*a^3*c^5*f*cos(f*x + e)^3 - a^3*c^5*f*cos(f*x + e)^2 - 2*a^3*c^5*f*cos(f*x + e) + a^3*c^5*f)*sin(f*x + e))","A",0
41,1,310,0,0.454606," ","integrate(1/(a+a*sec(f*x+e))^3/(c-c*sec(f*x+e))^6,x, algorithm=""fricas"")","\frac{7453 \, \cos\left(f x + e\right)^{8} - 11964 \, \cos\left(f x + e\right)^{7} - 11866 \, \cos\left(f x + e\right)^{6} + 30542 \, \cos\left(f x + e\right)^{5} + 90 \, \cos\left(f x + e\right)^{4} - 26438 \, \cos\left(f x + e\right)^{3} + 8539 \, \cos\left(f x + e\right)^{2} + 3465 \, {\left(f x \cos\left(f x + e\right)^{7} - 3 \, f x \cos\left(f x + e\right)^{6} + f x \cos\left(f x + e\right)^{5} + 5 \, f x \cos\left(f x + e\right)^{4} - 5 \, f x \cos\left(f x + e\right)^{3} - f x \cos\left(f x + e\right)^{2} + 3 \, f x \cos\left(f x + e\right) - f x\right)} \sin\left(f x + e\right) + 7671 \, \cos\left(f x + e\right) - 3712}{3465 \, {\left(a^{3} c^{6} f \cos\left(f x + e\right)^{7} - 3 \, a^{3} c^{6} f \cos\left(f x + e\right)^{6} + a^{3} c^{6} f \cos\left(f x + e\right)^{5} + 5 \, a^{3} c^{6} f \cos\left(f x + e\right)^{4} - 5 \, a^{3} c^{6} f \cos\left(f x + e\right)^{3} - a^{3} c^{6} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} c^{6} f \cos\left(f x + e\right) - a^{3} c^{6} f\right)} \sin\left(f x + e\right)}"," ",0,"1/3465*(7453*cos(f*x + e)^8 - 11964*cos(f*x + e)^7 - 11866*cos(f*x + e)^6 + 30542*cos(f*x + e)^5 + 90*cos(f*x + e)^4 - 26438*cos(f*x + e)^3 + 8539*cos(f*x + e)^2 + 3465*(f*x*cos(f*x + e)^7 - 3*f*x*cos(f*x + e)^6 + f*x*cos(f*x + e)^5 + 5*f*x*cos(f*x + e)^4 - 5*f*x*cos(f*x + e)^3 - f*x*cos(f*x + e)^2 + 3*f*x*cos(f*x + e) - f*x)*sin(f*x + e) + 7671*cos(f*x + e) - 3712)/((a^3*c^6*f*cos(f*x + e)^7 - 3*a^3*c^6*f*cos(f*x + e)^6 + a^3*c^6*f*cos(f*x + e)^5 + 5*a^3*c^6*f*cos(f*x + e)^4 - 5*a^3*c^6*f*cos(f*x + e)^3 - a^3*c^6*f*cos(f*x + e)^2 + 3*a^3*c^6*f*cos(f*x + e) - a^3*c^6*f)*sin(f*x + e))","A",0
42,1,373,0,0.506520," ","integrate((c-c*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(176 \, c^{4} \cos\left(f x + e\right)^{3} - 122 \, c^{4} \cos\left(f x + e\right)^{2} + 66 \, c^{4} \cos\left(f x + e\right) - 15 \, c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(176 \, c^{4} \cos\left(f x + e\right)^{3} - 122 \, c^{4} \cos\left(f x + e\right)^{2} + 66 \, c^{4} \cos\left(f x + e\right) - 15 \, c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(176*c^4*cos(f*x + e)^3 - 122*c^4*cos(f*x + e)^2 + 66*c^4*cos(f*x + e) - 15*c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (176*c^4*cos(f*x + e)^3 - 122*c^4*cos(f*x + e)^2 + 66*c^4*cos(f*x + e) - 15*c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
43,1,347,0,0.480804," ","integrate((c-c*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(23 \, c^{3} \cos\left(f x + e\right)^{2} - 11 \, c^{3} \cos\left(f x + e\right) + 3 \, c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(23 \, c^{3} \cos\left(f x + e\right)^{2} - 11 \, c^{3} \cos\left(f x + e\right) + 3 \, c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(23*c^3*cos(f*x + e)^2 - 11*c^3*cos(f*x + e) + 3*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/15*(15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (23*c^3*cos(f*x + e)^2 - 11*c^3*cos(f*x + e) + 3*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
44,1,313,0,0.493811," ","integrate((c-c*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(4 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(4 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(4*c^2*cos(f*x + e) - c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), -2/3*(3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (4*c^2*cos(f*x + e) - c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
45,1,234,0,0.443694," ","integrate((c-c*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{f \cos\left(f x + e\right) + f}, -\frac{2 \, {\left({\left(c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{f \cos\left(f x + e\right) + f}\right]"," ",0,"[((c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e) + f), -2*((c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e) + f)]","A",0
46,1,266,0,0.588991," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, c f \sin\left(f x + e\right)}, \frac{\sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{c f \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e)), (sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e))]","A",0
47,1,339,0,0.545378," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{-a} {\left(\cos\left(f x + e\right) - 1\right)} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(4 \, \cos\left(f x + e\right)^{2} - 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{6 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{a} {\left(\cos\left(f x + e\right) - 1\right)} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(4 \, \cos\left(f x + e\right)^{2} - 3 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{3 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/6*(3*sqrt(-a)*(cos(f*x + e) - 1)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(4*cos(f*x + e)^2 - 3*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), 1/3*(3*sqrt(a)*(cos(f*x + e) - 1)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(4*cos(f*x + e)^2 - 3*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","A",0
48,1,405,0,0.580436," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(23 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)^{2} + 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{30 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, \frac{15 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(23 \, \cos\left(f x + e\right)^{3} - 35 \, \cos\left(f x + e\right)^{2} + 15 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/30*(15*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(23*cos(f*x + e)^3 - 35*cos(f*x + e)^2 + 15*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), 1/15*(15*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(23*cos(f*x + e)^3 - 35*cos(f*x + e)^2 + 15*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","A",0
49,1,475,0,0.638926," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) - 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(176 \, \cos\left(f x + e\right)^{4} - 406 \, \cos\left(f x + e\right)^{3} + 350 \, \cos\left(f x + e\right)^{2} - 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{210 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}, \frac{105 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)^{2} + 3 \, \cos\left(f x + e\right) - 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(176 \, \cos\left(f x + e\right)^{4} - 406 \, \cos\left(f x + e\right)^{3} + 350 \, \cos\left(f x + e\right)^{2} - 105 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/210*(105*(cos(f*x + e)^3 - 3*cos(f*x + e)^2 + 3*cos(f*x + e) - 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(176*cos(f*x + e)^4 - 406*cos(f*x + e)^3 + 350*cos(f*x + e)^2 - 105*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e)), 1/105*(105*(cos(f*x + e)^3 - 3*cos(f*x + e)^2 + 3*cos(f*x + e) - 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(176*cos(f*x + e)^4 - 406*cos(f*x + e)^3 + 350*cos(f*x + e)^2 - 105*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))]","A",0
50,1,385,0,0.483459," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a c^{3} \cos\left(f x + e\right)^{4} + a c^{3} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(146 \, a c^{3} \cos\left(f x + e\right)^{3} - 32 \, a c^{3} \cos\left(f x + e\right)^{2} - 24 \, a c^{3} \cos\left(f x + e\right) + 15 \, a c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(a c^{3} \cos\left(f x + e\right)^{4} + a c^{3} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(146 \, a c^{3} \cos\left(f x + e\right)^{3} - 32 \, a c^{3} \cos\left(f x + e\right)^{2} - 24 \, a c^{3} \cos\left(f x + e\right) + 15 \, a c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(a*c^3*cos(f*x + e)^4 + a*c^3*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(146*a*c^3*cos(f*x + e)^3 - 32*a*c^3*cos(f*x + e)^2 - 24*a*c^3*cos(f*x + e) + 15*a*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(a*c^3*cos(f*x + e)^4 + a*c^3*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (146*a*c^3*cos(f*x + e)^3 - 32*a*c^3*cos(f*x + e)^2 - 24*a*c^3*cos(f*x + e) + 15*a*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
51,1,355,0,0.461914," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(17 \, a c^{2} \cos\left(f x + e\right)^{2} + a c^{2} \cos\left(f x + e\right) - 3 \, a c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(17 \, a c^{2} \cos\left(f x + e\right)^{2} + a c^{2} \cos\left(f x + e\right) - 3 \, a c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(17*a*c^2*cos(f*x + e)^2 + a*c^2*cos(f*x + e) - 3*a*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/15*(15*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (17*a*c^2*cos(f*x + e)^2 + a*c^2*cos(f*x + e) - 3*a*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
52,1,303,0,0.459095," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c \cos\left(f x + e\right)^{2} + a c \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(2 \, a c \cos\left(f x + e\right) + a c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(a c \cos\left(f x + e\right)^{2} + a c \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(2 \, a c \cos\left(f x + e\right) + a c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(3*(a*c*cos(f*x + e)^2 + a*c*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(2*a*c*cos(f*x + e) + a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), -2/3*(3*(a*c*cos(f*x + e)^2 + a*c*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (2*a*c*cos(f*x + e) + a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
53,1,269,0,0.540210," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} a \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 8 \, a \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, c f \sin\left(f x + e\right)}, \frac{a^{\frac{3}{2}} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 4 \, a \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{c f \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(-a)*a*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 8*a*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e)), (a^(3/2)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 4*a*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(c*f*sin(f*x + e))]","A",0
54,1,351,0,0.548615," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a \cos\left(f x + e\right) - a\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(5 \, a \cos\left(f x + e\right)^{2} - 3 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{6 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, \frac{3 \, {\left(a \cos\left(f x + e\right) - a\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(5 \, a \cos\left(f x + e\right)^{2} - 3 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{3 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/6*(3*(a*cos(f*x + e) - a)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(5*a*cos(f*x + e)^2 - 3*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), 1/3*(3*(a*cos(f*x + e) - a)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(5*a*cos(f*x + e)^2 - 3*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","A",0
55,1,417,0,0.560123," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(26 \, a \cos\left(f x + e\right)^{3} - 35 \, a \cos\left(f x + e\right)^{2} + 15 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{30 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, \frac{15 \, {\left(a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(26 \, a \cos\left(f x + e\right)^{3} - 35 \, a \cos\left(f x + e\right)^{2} + 15 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/30*(15*(a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(26*a*cos(f*x + e)^3 - 35*a*cos(f*x + e)^2 + 15*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), 1/15*(15*(a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(26*a*cos(f*x + e)^3 - 35*a*cos(f*x + e)^2 + 15*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","A",0
56,1,495,0,0.602919," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a \cos\left(f x + e\right)^{3} - 3 \, a \cos\left(f x + e\right)^{2} + 3 \, a \cos\left(f x + e\right) - a\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(191 \, a \cos\left(f x + e\right)^{4} - 406 \, a \cos\left(f x + e\right)^{3} + 350 \, a \cos\left(f x + e\right)^{2} - 105 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{210 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}, \frac{105 \, {\left(a \cos\left(f x + e\right)^{3} - 3 \, a \cos\left(f x + e\right)^{2} + 3 \, a \cos\left(f x + e\right) - a\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(191 \, a \cos\left(f x + e\right)^{4} - 406 \, a \cos\left(f x + e\right)^{3} + 350 \, a \cos\left(f x + e\right)^{2} - 105 \, a \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/210*(105*(a*cos(f*x + e)^3 - 3*a*cos(f*x + e)^2 + 3*a*cos(f*x + e) - a)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(191*a*cos(f*x + e)^4 - 406*a*cos(f*x + e)^3 + 350*a*cos(f*x + e)^2 - 105*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e)), 1/105*(105*(a*cos(f*x + e)^3 - 3*a*cos(f*x + e)^2 + 3*a*cos(f*x + e) - a)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(191*a*cos(f*x + e)^4 - 406*a*cos(f*x + e)^3 + 350*a*cos(f*x + e)^2 - 105*a*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))]","A",0
57,1,441,0,0.525333," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} c^{3} \cos\left(f x + e\right)^{5} + a^{2} c^{3} \cos\left(f x + e\right)^{4}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(383 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} + 34 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} - 132 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} - 5 \, a^{2} c^{3} \cos\left(f x + e\right) + 35 \, a^{2} c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{315 \, {\left(f \cos\left(f x + e\right)^{5} + f \cos\left(f x + e\right)^{4}\right)}}, -\frac{2 \, {\left(315 \, {\left(a^{2} c^{3} \cos\left(f x + e\right)^{5} + a^{2} c^{3} \cos\left(f x + e\right)^{4}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(383 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} + 34 \, a^{2} c^{3} \cos\left(f x + e\right)^{3} - 132 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} - 5 \, a^{2} c^{3} \cos\left(f x + e\right) + 35 \, a^{2} c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{315 \, {\left(f \cos\left(f x + e\right)^{5} + f \cos\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[1/315*(315*(a^2*c^3*cos(f*x + e)^5 + a^2*c^3*cos(f*x + e)^4)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(383*a^2*c^3*cos(f*x + e)^4 + 34*a^2*c^3*cos(f*x + e)^3 - 132*a^2*c^3*cos(f*x + e)^2 - 5*a^2*c^3*cos(f*x + e) + 35*a^2*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5 + f*cos(f*x + e)^4), -2/315*(315*(a^2*c^3*cos(f*x + e)^5 + a^2*c^3*cos(f*x + e)^4)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (383*a^2*c^3*cos(f*x + e)^4 + 34*a^2*c^3*cos(f*x + e)^3 - 132*a^2*c^3*cos(f*x + e)^2 - 5*a^2*c^3*cos(f*x + e) + 35*a^2*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5 + f*cos(f*x + e)^4)]","A",0
58,1,409,0,0.489682," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{4} + a^{2} c^{2} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(92 \, a^{2} c^{2} \cos\left(f x + e\right)^{3} + 46 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - 18 \, a^{2} c^{2} \cos\left(f x + e\right) - 15 \, a^{2} c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{4} + a^{2} c^{2} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(92 \, a^{2} c^{2} \cos\left(f x + e\right)^{3} + 46 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - 18 \, a^{2} c^{2} \cos\left(f x + e\right) - 15 \, a^{2} c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(a^2*c^2*cos(f*x + e)^4 + a^2*c^2*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(92*a^2*c^2*cos(f*x + e)^3 + 46*a^2*c^2*cos(f*x + e)^2 - 18*a^2*c^2*cos(f*x + e) - 15*a^2*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(a^2*c^2*cos(f*x + e)^4 + a^2*c^2*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (92*a^2*c^2*cos(f*x + e)^3 + 46*a^2*c^2*cos(f*x + e)^2 - 18*a^2*c^2*cos(f*x + e) - 15*a^2*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
59,1,353,0,0.500125," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(a^{2} c \cos\left(f x + e\right)^{2} + 3 \, a^{2} c \cos\left(f x + e\right) + a^{2} c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{5 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(5 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(a^{2} c \cos\left(f x + e\right)^{2} + 3 \, a^{2} c \cos\left(f x + e\right) + a^{2} c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{5 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/5*(5*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(a^2*c*cos(f*x + e)^2 + 3*a^2*c*cos(f*x + e) + a^2*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/5*(5*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (a^2*c*cos(f*x + e)^2 + 3*a^2*c*cos(f*x + e) + a^2*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
60,1,291,0,0.577419," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a} a^{2} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(5 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{2 \, c f \sin\left(f x + e\right)}, \frac{a^{\frac{5}{2}} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(5 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{c f \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(-a)*a^2*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(5*a^2*cos(f*x + e) - a^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/(c*f*sin(f*x + e)), (a^(5/2)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(5*a^2*cos(f*x + e) - a^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/(c*f*sin(f*x + e))]","A",0
61,1,339,0,0.566808," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{16 \, a^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right)}{6 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, \frac{8 \, a^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)^{2} + 3 \, {\left(a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right)}{3 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/6*(16*a^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)^2 + 3*(a^2*cos(f*x + e) - a^2)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), 1/3*(8*a^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)^2 + 3*(a^2*cos(f*x + e) - a^2)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","B",0
62,1,441,0,0.570032," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{5 \, {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(9 \, a^{2} \cos\left(f x + e\right)^{3} - 10 \, a^{2} \cos\left(f x + e\right)^{2} + 5 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{10 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}, \frac{5 \, {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(9 \, a^{2} \cos\left(f x + e\right)^{3} - 10 \, a^{2} \cos\left(f x + e\right)^{2} + 5 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{5 \, {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) + c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/10*(5*(a^2*cos(f*x + e)^2 - 2*a^2*cos(f*x + e) + a^2)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(9*a^2*cos(f*x + e)^3 - 10*a^2*cos(f*x + e)^2 + 5*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e)), 1/5*(5*(a^2*cos(f*x + e)^2 - 2*a^2*cos(f*x + e) + a^2)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(9*a^2*cos(f*x + e)^3 - 10*a^2*cos(f*x + e)^2 + 5*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) + c^3*f)*sin(f*x + e))]","B",0
63,1,527,0,0.567441," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{21 \, {\left(a^{2} \cos\left(f x + e\right)^{3} - 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(40 \, a^{2} \cos\left(f x + e\right)^{4} - 77 \, a^{2} \cos\left(f x + e\right)^{3} + 70 \, a^{2} \cos\left(f x + e\right)^{2} - 21 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{42 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}, \frac{21 \, {\left(a^{2} \cos\left(f x + e\right)^{3} - 3 \, a^{2} \cos\left(f x + e\right)^{2} + 3 \, a^{2} \cos\left(f x + e\right) - a^{2}\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(40 \, a^{2} \cos\left(f x + e\right)^{4} - 77 \, a^{2} \cos\left(f x + e\right)^{3} + 70 \, a^{2} \cos\left(f x + e\right)^{2} - 21 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{21 \, {\left(c^{4} f \cos\left(f x + e\right)^{3} - 3 \, c^{4} f \cos\left(f x + e\right)^{2} + 3 \, c^{4} f \cos\left(f x + e\right) - c^{4} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/42*(21*(a^2*cos(f*x + e)^3 - 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) - a^2)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(40*a^2*cos(f*x + e)^4 - 77*a^2*cos(f*x + e)^3 + 70*a^2*cos(f*x + e)^2 - 21*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e)), 1/21*(21*(a^2*cos(f*x + e)^3 - 3*a^2*cos(f*x + e)^2 + 3*a^2*cos(f*x + e) - a^2)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(40*a^2*cos(f*x + e)^4 - 77*a^2*cos(f*x + e)^3 + 70*a^2*cos(f*x + e)^2 - 21*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^4*f*cos(f*x + e)^3 - 3*c^4*f*cos(f*x + e)^2 + 3*c^4*f*cos(f*x + e) - c^4*f)*sin(f*x + e))]","B",0
64,1,601,0,0.576093," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^5,x, algorithm=""fricas"")","\left[\frac{45 \, {\left(a^{2} \cos\left(f x + e\right)^{4} - 4 \, a^{2} \cos\left(f x + e\right)^{3} + 6 \, a^{2} \cos\left(f x + e\right)^{2} - 4 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} - 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, {\left(89 \, a^{2} \cos\left(f x + e\right)^{5} - 243 \, a^{2} \cos\left(f x + e\right)^{4} + 324 \, a^{2} \cos\left(f x + e\right)^{3} - 195 \, a^{2} \cos\left(f x + e\right)^{2} + 45 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{90 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}, \frac{45 \, {\left(a^{2} \cos\left(f x + e\right)^{4} - 4 \, a^{2} \cos\left(f x + e\right)^{3} + 6 \, a^{2} \cos\left(f x + e\right)^{2} - 4 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(89 \, a^{2} \cos\left(f x + e\right)^{5} - 243 \, a^{2} \cos\left(f x + e\right)^{4} + 324 \, a^{2} \cos\left(f x + e\right)^{3} - 195 \, a^{2} \cos\left(f x + e\right)^{2} + 45 \, a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{45 \, {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} + 6 \, c^{5} f \cos\left(f x + e\right)^{2} - 4 \, c^{5} f \cos\left(f x + e\right) + c^{5} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/90*(45*(a^2*cos(f*x + e)^4 - 4*a^2*cos(f*x + e)^3 + 6*a^2*cos(f*x + e)^2 - 4*a^2*cos(f*x + e) + a^2)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 - 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*(89*a^2*cos(f*x + e)^5 - 243*a^2*cos(f*x + e)^4 + 324*a^2*cos(f*x + e)^3 - 195*a^2*cos(f*x + e)^2 + 45*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e)), 1/45*(45*(a^2*cos(f*x + e)^4 - 4*a^2*cos(f*x + e)^3 + 6*a^2*cos(f*x + e)^2 - 4*a^2*cos(f*x + e) + a^2)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(89*a^2*cos(f*x + e)^5 - 243*a^2*cos(f*x + e)^4 + 324*a^2*cos(f*x + e)^3 - 195*a^2*cos(f*x + e)^2 + 45*a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 + 6*c^5*f*cos(f*x + e)^2 - 4*c^5*f*cos(f*x + e) + c^5*f)*sin(f*x + e))]","A",0
65,1,552,0,1.256740," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{40 \, \sqrt{2} {\left(a c^{4} \cos\left(f x + e\right)^{3} + a c^{4} \cos\left(f x + e\right)^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 5 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + c^{4} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(41 \, c^{4} \cos\left(f x + e\right)^{2} - 7 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{5 \, {\left(a f \cos\left(f x + e\right)^{3} + a f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(5 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + c^{4} \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(41 \, c^{4} \cos\left(f x + e\right)^{2} - 7 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \frac{40 \, \sqrt{2} {\left(a c^{4} \cos\left(f x + e\right)^{3} + a c^{4} \cos\left(f x + e\right)^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}\right)}}{5 \, {\left(a f \cos\left(f x + e\right)^{3} + a f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/5*(40*sqrt(2)*(a*c^4*cos(f*x + e)^3 + a*c^4*cos(f*x + e)^2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 5*(c^4*cos(f*x + e)^3 + c^4*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(41*c^4*cos(f*x + e)^2 - 7*c^4*cos(f*x + e) + c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^3 + a*f*cos(f*x + e)^2), -2/5*(5*(c^4*cos(f*x + e)^3 + c^4*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (41*c^4*cos(f*x + e)^2 - 7*c^4*cos(f*x + e) + c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 40*sqrt(2)*(a*c^4*cos(f*x + e)^3 + a*c^4*cos(f*x + e)^2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f*cos(f*x + e)^3 + a*f*cos(f*x + e)^2)]","A",0
66,1,518,0,1.028718," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{12 \, \sqrt{2} {\left(a c^{3} \cos\left(f x + e\right)^{2} + a c^{3} \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 3 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(10 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(10 \, c^{3} \cos\left(f x + e\right) - c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \frac{12 \, \sqrt{2} {\left(a c^{3} \cos\left(f x + e\right)^{2} + a c^{3} \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}\right)}}{3 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(12*sqrt(2)*(a*c^3*cos(f*x + e)^2 + a*c^3*cos(f*x + e))*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 3*(c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(10*c^3*cos(f*x + e) - c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e)), -2/3*(3*(c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (10*c^3*cos(f*x + e) - c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 12*sqrt(2)*(a*c^3*cos(f*x + e)^2 + a*c^3*cos(f*x + e))*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e))]","A",0
67,1,438,0,0.725354," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 2 \, \sqrt{2} {\left(a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - {\left(c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{a f \cos\left(f x + e\right) + a f}, \frac{2 \, {\left(c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - {\left(c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + \frac{2 \, \sqrt{2} {\left(a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}\right)}}{a f \cos\left(f x + e\right) + a f}\right]"," ",0,"[(2*c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + 2*sqrt(2)*(a*c^2*cos(f*x + e) + a*c^2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - (c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a*f*cos(f*x + e) + a*f), 2*(c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - (c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 2*sqrt(2)*(a*c^2*cos(f*x + e) + a*c^2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f*cos(f*x + e) + a*f)]","A",0
68,1,298,0,0.597224," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a c \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - \sqrt{-a} c \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{a f}, \frac{2 \, {\left(\sqrt{2} \sqrt{a} c \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - \sqrt{a} c \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)\right)}}{a f}\right]"," ",0,"[(sqrt(2)*a*c*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - sqrt(-a)*c*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a*f), 2*(sqrt(2)*sqrt(a)*c*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - sqrt(a)*c*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(a*f)]","A",0
69,1,436,0,0.618208," ","integrate(1/(c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 2 \, \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 4 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{4 \, a c f \sin\left(f x + e\right)}, \frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 2 \, \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{2 \, a c f \sin\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(2)*a*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) - 2*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) + 4*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e)), 1/2*(sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 2*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e))/(a*c*f*sin(f*x + e))]","A",0
70,1,520,0,0.603855," ","integrate(1/(c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} \sqrt{-a} {\left(\cos\left(f x + e\right) - 1\right)} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 12 \, \sqrt{-a} {\left(\cos\left(f x + e\right) - 1\right)} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(11 \, \cos\left(f x + e\right)^{2} - 9 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{24 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}, \frac{3 \, \sqrt{2} \sqrt{a} {\left(\cos\left(f x + e\right) - 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 12 \, \sqrt{a} {\left(\cos\left(f x + e\right) - 1\right)} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(11 \, \cos\left(f x + e\right)^{2} - 9 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{12 \, {\left(a c^{2} f \cos\left(f x + e\right) - a c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/24*(3*sqrt(2)*sqrt(-a)*(cos(f*x + e) - 1)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 12*sqrt(-a)*(cos(f*x + e) - 1)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(11*cos(f*x + e)^2 - 9*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e)), 1/12*(3*sqrt(2)*sqrt(a)*(cos(f*x + e) - 1)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 12*sqrt(a)*(cos(f*x + e) - 1)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(11*cos(f*x + e)^2 - 9*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a*c^2*f*cos(f*x + e) - a*c^2*f)*sin(f*x + e))]","A",0
71,1,608,0,0.610485," ","integrate(1/(c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{5 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 40 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(49 \, \cos\left(f x + e\right)^{3} - 80 \, \cos\left(f x + e\right)^{2} + 35 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{80 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}, \frac{5 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 40 \, {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(49 \, \cos\left(f x + e\right)^{3} - 80 \, \cos\left(f x + e\right)^{2} + 35 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{40 \, {\left(a c^{3} f \cos\left(f x + e\right)^{2} - 2 \, a c^{3} f \cos\left(f x + e\right) + a c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/80*(5*sqrt(2)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 40*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(49*cos(f*x + e)^3 - 80*cos(f*x + e)^2 + 35*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e)), 1/40*(5*sqrt(2)*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 40*(cos(f*x + e)^2 - 2*cos(f*x + e) + 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(49*cos(f*x + e)^3 - 80*cos(f*x + e)^2 + 35*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a*c^3*f*cos(f*x + e)^2 - 2*a*c^3*f*cos(f*x + e) + a*c^3*f)*sin(f*x + e))]","A",0
72,1,634,0,1.869050," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{18 \, \sqrt{2} {\left(a c^{4} \cos\left(f x + e\right)^{3} + 2 \, a c^{4} \cos\left(f x + e\right)^{2} + a c^{4} \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 3 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 2 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(28 \, c^{4} \cos\left(f x + e\right)^{2} + 15 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 2 \, c^{4} \cos\left(f x + e\right)^{2} + c^{4} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(28 \, c^{4} \cos\left(f x + e\right)^{2} + 15 \, c^{4} \cos\left(f x + e\right) - c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + \frac{18 \, \sqrt{2} {\left(a c^{4} \cos\left(f x + e\right)^{3} + 2 \, a c^{4} \cos\left(f x + e\right)^{2} + a c^{4} \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}\right)}}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{3} + 2 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(18*sqrt(2)*(a*c^4*cos(f*x + e)^3 + 2*a*c^4*cos(f*x + e)^2 + a*c^4*cos(f*x + e))*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 3*(c^4*cos(f*x + e)^3 + 2*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(28*c^4*cos(f*x + e)^2 + 15*c^4*cos(f*x + e) - c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^3 + 2*a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e)), -2/3*(3*(c^4*cos(f*x + e)^3 + 2*c^4*cos(f*x + e)^2 + c^4*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (28*c^4*cos(f*x + e)^2 + 15*c^4*cos(f*x + e) - c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + 18*sqrt(2)*(a*c^4*cos(f*x + e)^3 + 2*a*c^4*cos(f*x + e)^2 + a*c^4*cos(f*x + e))*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a^2*f*cos(f*x + e)^3 + 2*a^2*f*cos(f*x + e)^2 + a^2*f*cos(f*x + e))]","A",0
73,1,550,0,1.018237," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(a c^{3} \cos\left(f x + e\right)^{2} + 2 \, a c^{3} \cos\left(f x + e\right) + a c^{3}\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - {\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f}, -\frac{2 \, {\left({\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + \frac{\sqrt{2} {\left(a c^{3} \cos\left(f x + e\right)^{2} + 2 \, a c^{3} \cos\left(f x + e\right) + a c^{3}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}\right)}}{a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f}\right]"," ",0,"[(sqrt(2)*(a*c^3*cos(f*x + e)^2 + 2*a*c^3*cos(f*x + e) + a*c^3)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - (c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(3*c^3*cos(f*x + e) + c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -2*((c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (3*c^3*cos(f*x + e) + c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + sqrt(2)*(a*c^3*cos(f*x + e)^2 + 2*a*c^3*cos(f*x + e) + a*c^3)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","A",0
74,1,542,0,0.934289," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - \sqrt{2} {\left(a c^{2} \cos\left(f x + e\right)^{2} + 2 \, a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, -\frac{2 \, c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - \frac{\sqrt{2} {\left(a c^{2} \cos\left(f x + e\right)^{2} + 2 \, a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f}\right]"," ",0,"[-1/2*(4*c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - sqrt(2)*(a*c^2*cos(f*x + e)^2 + 2*a*c^2*cos(f*x + e) + a*c^2)*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -(2*c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 2*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - sqrt(2)*(a*c^2*cos(f*x + e)^2 + 2*a*c^2*cos(f*x + e) + a*c^2)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","B",0
75,1,505,0,0.665736," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \sqrt{2} {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 4 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{4 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, -\frac{2 \, c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \sqrt{2} {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 4 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{2 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[-1/4*(4*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*sqrt(2)*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 4*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -1/2*(2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*sqrt(2)*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 4*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","B",0
76,1,514,0,0.630846," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{7 \, \sqrt{2} \sqrt{-a} {\left(\cos\left(f x + e\right) + 1\right)} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 8 \, \sqrt{-a} {\left(\cos\left(f x + e\right) + 1\right)} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(3 \, \cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{16 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}, \frac{7 \, \sqrt{2} \sqrt{a} {\left(\cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 8 \, \sqrt{a} {\left(\cos\left(f x + e\right) + 1\right)} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(3 \, \cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{8 \, {\left(a^{2} c f \cos\left(f x + e\right) + a^{2} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/16*(7*sqrt(2)*sqrt(-a)*(cos(f*x + e) + 1)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 8*sqrt(-a)*(cos(f*x + e) + 1)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(3*cos(f*x + e)^2 + cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e)), 1/8*(7*sqrt(2)*sqrt(a)*(cos(f*x + e) + 1)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 8*sqrt(a)*(cos(f*x + e) + 1)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(3*cos(f*x + e)^2 + cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c*f*cos(f*x + e) + a^2*c*f)*sin(f*x + e))]","A",0
77,1,560,0,0.651598," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{27 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 48 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(31 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} - 21 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{96 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{27 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 48 \, {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(31 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} - 21 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{48 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/96*(27*sqrt(2)*(cos(f*x + e)^2 - 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 48*(cos(f*x + e)^2 - 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(31*cos(f*x + e)^3 - 2*cos(f*x + e)^2 - 21*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e)), 1/48*(27*sqrt(2)*(cos(f*x + e)^2 - 1)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 48*(cos(f*x + e)^2 - 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(31*cos(f*x + e)^3 - 2*cos(f*x + e)^2 - 21*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))]","A",0
78,1,714,0,0.693435," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{165 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 480 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(449 \, \cos\left(f x + e\right)^{4} - 351 \, \cos\left(f x + e\right)^{3} - 365 \, \cos\left(f x + e\right)^{2} + 315 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{960 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}, \frac{165 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 480 \, {\left(\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(449 \, \cos\left(f x + e\right)^{4} - 351 \, \cos\left(f x + e\right)^{3} - 365 \, \cos\left(f x + e\right)^{2} + 315 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{480 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} - a^{2} c^{3} f \cos\left(f x + e\right)^{2} - a^{2} c^{3} f \cos\left(f x + e\right) + a^{2} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/960*(165*sqrt(2)*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 480*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(449*cos(f*x + e)^4 - 351*cos(f*x + e)^3 - 365*cos(f*x + e)^2 + 315*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e)), 1/480*(165*sqrt(2)*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 480*(cos(f*x + e)^3 - cos(f*x + e)^2 - cos(f*x + e) + 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(449*cos(f*x + e)^4 - 351*cos(f*x + e)^3 - 365*cos(f*x + e)^2 + 315*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^2*c^3*f*cos(f*x + e)^3 - a^2*c^3*f*cos(f*x + e)^2 - a^2*c^3*f*cos(f*x + e) + a^2*c^3*f)*sin(f*x + e))]","A",0
79,1,742,0,2.963469," ","integrate((c-c*sec(f*x+e))^5/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{69 \, \sqrt{2} {\left(a c^{5} \cos\left(f x + e\right)^{4} + 3 \, a c^{5} \cos\left(f x + e\right)^{3} + 3 \, a c^{5} \cos\left(f x + e\right)^{2} + a c^{5} \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 6 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + 3 \, c^{5} \cos\left(f x + e\right)^{2} + c^{5} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 4 \, {\left(37 \, c^{5} \cos\left(f x + e\right)^{3} + 70 \, c^{5} \cos\left(f x + e\right)^{2} + 20 \, c^{5} \cos\left(f x + e\right) - c^{5}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{6 \, {\left(a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + a^{3} f \cos\left(f x + e\right)\right)}}, -\frac{6 \, {\left(c^{5} \cos\left(f x + e\right)^{4} + 3 \, c^{5} \cos\left(f x + e\right)^{3} + 3 \, c^{5} \cos\left(f x + e\right)^{2} + c^{5} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(37 \, c^{5} \cos\left(f x + e\right)^{3} + 70 \, c^{5} \cos\left(f x + e\right)^{2} + 20 \, c^{5} \cos\left(f x + e\right) - c^{5}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \frac{69 \, \sqrt{2} {\left(a c^{5} \cos\left(f x + e\right)^{4} + 3 \, a c^{5} \cos\left(f x + e\right)^{3} + 3 \, a c^{5} \cos\left(f x + e\right)^{2} + a c^{5} \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{3 \, {\left(a^{3} f \cos\left(f x + e\right)^{4} + 3 \, a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + a^{3} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(69*sqrt(2)*(a*c^5*cos(f*x + e)^4 + 3*a*c^5*cos(f*x + e)^3 + 3*a*c^5*cos(f*x + e)^2 + a*c^5*cos(f*x + e))*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 6*(c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + 3*c^5*cos(f*x + e)^2 + c^5*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 4*(37*c^5*cos(f*x + e)^3 + 70*c^5*cos(f*x + e)^2 + 20*c^5*cos(f*x + e) - c^5)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + a^3*f*cos(f*x + e)), -1/3*(6*(c^5*cos(f*x + e)^4 + 3*c^5*cos(f*x + e)^3 + 3*c^5*cos(f*x + e)^2 + c^5*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(37*c^5*cos(f*x + e)^3 + 70*c^5*cos(f*x + e)^2 + 20*c^5*cos(f*x + e) - c^5)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 69*sqrt(2)*(a*c^5*cos(f*x + e)^4 + 3*a*c^5*cos(f*x + e)^3 + 3*a*c^5*cos(f*x + e)^2 + a*c^5*cos(f*x + e))*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a^3*f*cos(f*x + e)^4 + 3*a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + a^3*f*cos(f*x + e))]","A",0
80,1,655,0,2.475955," ","integrate((c-c*sec(f*x+e))^4/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{11 \, \sqrt{2} {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left(3 \, c^{4} \cos\left(f x + e\right)^{2} + 9 \, c^{4} \cos\left(f x + e\right) + 2 \, c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{11 \, \sqrt{2} {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 4 \, {\left(c^{4} \cos\left(f x + e\right)^{3} + 3 \, c^{4} \cos\left(f x + e\right)^{2} + 3 \, c^{4} \cos\left(f x + e\right) + c^{4}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 2 \, {\left(3 \, c^{4} \cos\left(f x + e\right)^{2} + 9 \, c^{4} \cos\left(f x + e\right) + 2 \, c^{4}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{2 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/4*(11*sqrt(2)*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 4*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*(3*c^4*cos(f*x + e)^2 + 9*c^4*cos(f*x + e) + 2*c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/2*(11*sqrt(2)*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 4*(c^4*cos(f*x + e)^3 + 3*c^4*cos(f*x + e)^2 + 3*c^4*cos(f*x + e) + c^4)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 2*(3*c^4*cos(f*x + e)^2 + 9*c^4*cos(f*x + e) + 2*c^4)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","A",0
81,1,645,0,1.982262," ","integrate((c-c*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{7 \, \sqrt{2} {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 4 \, {\left(3 \, c^{3} \cos\left(f x + e\right)^{2} - c^{3} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{7 \, \sqrt{2} {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 8 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(3 \, c^{3} \cos\left(f x + e\right)^{2} - c^{3} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/8*(7*sqrt(2)*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 4*(3*c^3*cos(f*x + e)^2 - c^3*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/4*(7*sqrt(2)*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 8*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(3*c^3*cos(f*x + e)^2 - c^3*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","A",0
82,1,645,0,1.528985," ","integrate((c-c*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{11 \, \sqrt{2} {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 16 \, {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 4 \, {\left(7 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{16 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{11 \, \sqrt{2} {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 16 \, {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(7 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/16*(11*sqrt(2)*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 16*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 4*(7*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/8*(11*sqrt(2)*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 16*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(7*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","A",0
83,1,605,0,1.034507," ","integrate((c-c*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{23 \, \sqrt{2} {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 32 \, {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 4 \, {\left(11 \, c \cos\left(f x + e\right)^{2} + 7 \, c \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{23 \, \sqrt{2} {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 32 \, {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(11 \, c \cos\left(f x + e\right)^{2} + 7 \, c \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{16 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[-1/32*(23*sqrt(2)*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 32*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 4*(11*c*cos(f*x + e)^2 + 7*c*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/16*(23*sqrt(2)*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 32*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(11*c*cos(f*x + e)^2 + 7*c*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","B",0
84,1,608,0,0.658393," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{71 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 64 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(27 \, \cos\left(f x + e\right)^{3} + 12 \, \cos\left(f x + e\right)^{2} - 7 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{128 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}, \frac{71 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 64 \, {\left(\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(27 \, \cos\left(f x + e\right)^{3} + 12 \, \cos\left(f x + e\right)^{2} - 7 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{64 \, {\left(a^{3} c f \cos\left(f x + e\right)^{2} + 2 \, a^{3} c f \cos\left(f x + e\right) + a^{3} c f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/128*(71*sqrt(2)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 64*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(27*cos(f*x + e)^3 + 12*cos(f*x + e)^2 - 7*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e)), 1/64*(71*sqrt(2)*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 64*(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(27*cos(f*x + e)^3 + 12*cos(f*x + e)^2 - 7*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^3*c*f*cos(f*x + e)^2 + 2*a^3*c*f*cos(f*x + e) + a^3*c*f)*sin(f*x + e))]","A",0
85,1,706,0,0.674739," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{321 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) + 384 \, {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{-a} \log\left(-\frac{8 \, a \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right)\right)} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 7 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right) + 1}\right) \sin\left(f x + e\right) - 4 \, {\left(205 \, \cos\left(f x + e\right)^{4} + 71 \, \cos\left(f x + e\right)^{3} - 149 \, \cos\left(f x + e\right)^{2} - 63 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{768 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}, \frac{321 \, \sqrt{2} {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + 384 \, {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} - \cos\left(f x + e\right) - 1\right)} \sqrt{a} \arctan\left(\frac{2 \, \sqrt{a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{2 \, a \cos\left(f x + e\right)^{2} + a \cos\left(f x + e\right) - a}\right) \sin\left(f x + e\right) + 2 \, {\left(205 \, \cos\left(f x + e\right)^{4} + 71 \, \cos\left(f x + e\right)^{3} - 149 \, \cos\left(f x + e\right)^{2} - 63 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}}}{384 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} + a^{3} c^{2} f \cos\left(f x + e\right)^{2} - a^{3} c^{2} f \cos\left(f x + e\right) - a^{3} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/768*(321*sqrt(2)*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1))*sin(f*x + e) + 384*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(-a)*log(-(8*a*cos(f*x + e)^3 + 4*(2*cos(f*x + e)^2 - cos(f*x + e))*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 7*a*cos(f*x + e) + a)/(cos(f*x + e) + 1))*sin(f*x + e) - 4*(205*cos(f*x + e)^4 + 71*cos(f*x + e)^3 - 149*cos(f*x + e)^2 - 63*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e)), 1/384*(321*sqrt(2)*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))*sin(f*x + e) + 384*(cos(f*x + e)^3 + cos(f*x + e)^2 - cos(f*x + e) - 1)*sqrt(a)*arctan(2*sqrt(a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(2*a*cos(f*x + e)^2 + a*cos(f*x + e) - a))*sin(f*x + e) + 2*(205*cos(f*x + e)^4 + 71*cos(f*x + e)^3 - 149*cos(f*x + e)^2 - 63*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e)))/((a^3*c^2*f*cos(f*x + e)^3 + a^3*c^2*f*cos(f*x + e)^2 - a^3*c^2*f*cos(f*x + e) - a^3*c^2*f)*sin(f*x + e))]","A",0
86,1,459,0,0.591986," ","integrate((c-c*sec(f*x+e))^(7/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(11 \, c^{3} \cos\left(f x + e\right)^{2} - 7 \, c^{3} \cos\left(f x + e\right) + 2 \, c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 3 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{{\left(11 \, c^{3} \cos\left(f x + e\right)^{2} - 7 \, c^{3} \cos\left(f x + e\right) + 2 \, c^{3}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 6 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/6*((11*c^3*cos(f*x + e)^2 - 7*c^3*cos(f*x + e) + 2*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - 3*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -1/6*((11*c^3*cos(f*x + e)^2 - 7*c^3*cos(f*x + e) + 2*c^3)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - 6*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
87,1,425,0,0.565912," ","integrate((c-c*sec(f*x+e))^(5/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, -\frac{{\left(3 \, c^{2} \cos\left(f x + e\right) - c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 2 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{2 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[-1/2*((3*c^2*cos(f*x + e) - c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - (c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), -1/2*((3*c^2*cos(f*x + e) - c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - 2*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
88,1,350,0,0.569055," ","integrate((c-c*sec(f*x+e))^(3/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \sqrt{-a c} {\left(c \cos\left(f x + e\right) + c\right)} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(f \cos\left(f x + e\right) + f\right)}}, -\frac{c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \sqrt{a c} {\left(c \cos\left(f x + e\right) + c\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{f \cos\left(f x + e\right) + f}\right]"," ",0,"[-1/2*(2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - sqrt(-a*c)*(c*cos(f*x + e) + c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e) + f), -(c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - sqrt(a*c)*(c*cos(f*x + e) + c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e) + f)]","A",0
89,1,200,0,0.570815," ","integrate((c-c*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, f}, \frac{\sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{f}\right]"," ",0,"[1/2*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2)/f, sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c))/f]","B",0
90,0,0,0,0.567429," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c*sec(f*x + e) - c), x)","F",0
91,0,0,0,0.545142," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
92,0,0,0,0.552484," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3), x)","F",0
93,0,0,0,0.563921," ","integrate((a+a*sec(f*x+e))^(1/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{4} \sec\left(f x + e\right)^{4} - 4 \, c^{4} \sec\left(f x + e\right)^{3} + 6 \, c^{4} \sec\left(f x + e\right)^{2} - 4 \, c^{4} \sec\left(f x + e\right) + c^{4}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^4*sec(f*x + e)^4 - 4*c^4*sec(f*x + e)^3 + 6*c^4*sec(f*x + e)^2 - 4*c^4*sec(f*x + e) + c^4), x)","F",0
94,1,467,0,0.571486," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left(7 \, a c^{2} \cos\left(f x + e\right)^{2} + a c^{2} \cos\left(f x + e\right) - 2 \, a c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 3 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{{\left(7 \, a c^{2} \cos\left(f x + e\right)^{2} + a c^{2} \cos\left(f x + e\right) - 2 \, a c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 6 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/6*((7*a*c^2*cos(f*x + e)^2 + a*c^2*cos(f*x + e) - 2*a*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - 3*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -1/6*((7*a*c^2*cos(f*x + e)^2 + a*c^2*cos(f*x + e) - 2*a*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) - 6*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
95,1,346,0,0.586972," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a c} a c \cos\left(f x + e\right) \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right) - a c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{2 \, f \cos\left(f x + e\right)}, \frac{2 \, \sqrt{a c} a c \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right) \cos\left(f x + e\right) - a c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{2 \, f \cos\left(f x + e\right)}\right]"," ",0,"[1/2*(sqrt(-a*c)*a*c*cos(f*x + e)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2) - a*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)), 1/2*(2*sqrt(a*c)*a*c*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c))*cos(f*x + e) - a*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e))]","A",0
96,1,347,0,0.565799," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, a \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{-a c} {\left(a \cos\left(f x + e\right) + a\right)} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(f \cos\left(f x + e\right) + f\right)}}, \frac{a \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{a c} {\left(a \cos\left(f x + e\right) + a\right)} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{f \cos\left(f x + e\right) + f}\right]"," ",0,"[1/2*(2*a*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + sqrt(-a*c)*(a*cos(f*x + e) + a)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e) + f), (a*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + sqrt(a*c)*(a*cos(f*x + e) + a)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e) + f)]","A",0
97,0,0,0,0.631856," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sec\left(f x + e\right) + c}}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a*sec(f*x + e) + a)^(3/2)*sqrt(-c*sec(f*x + e) + c)/(c*sec(f*x + e) - c), x)","F",0
98,0,0,0,0.567160," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*sqrt(-c*sec(f*x + e) + c)/(c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2), x)","F",0
99,0,0,0,0.569163," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}}, x\right)"," ",0,"integral(-(a*sec(f*x + e) + a)^(3/2)*sqrt(-c*sec(f*x + e) + c)/(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3), x)","F",0
100,0,0,0,0.613660," ","integrate((a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{4} \sec\left(f x + e\right)^{4} - 4 \, c^{4} \sec\left(f x + e\right)^{3} + 6 \, c^{4} \sec\left(f x + e\right)^{2} - 4 \, c^{4} \sec\left(f x + e\right) + c^{4}}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*sqrt(-c*sec(f*x + e) + c)/(c^4*sec(f*x + e)^4 - 4*c^4*sec(f*x + e)^3 + 6*c^4*sec(f*x + e)^2 - 4*c^4*sec(f*x + e) + c^4), x)","F",0
101,1,405,0,0.599028," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-a c} a^{2} c^{2} \cos\left(f x + e\right)^{3} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right) - {\left(3 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - a^{2} c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{3}}, \frac{4 \, \sqrt{a c} a^{2} c^{2} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right) \cos\left(f x + e\right)^{3} - {\left(3 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} - a^{2} c^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, f \cos\left(f x + e\right)^{3}}\right]"," ",0,"[1/4*(2*sqrt(-a*c)*a^2*c^2*cos(f*x + e)^3*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2) - (3*a^2*c^2*cos(f*x + e)^2 - a^2*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3), 1/4*(4*sqrt(a*c)*a^2*c^2*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c))*cos(f*x + e)^3 - (3*a^2*c^2*cos(f*x + e)^2 - a^2*c^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3)]","A",0
102,1,467,0,0.578965," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c \cos\left(f x + e\right)^{2} - 5 \, a^{2} c \cos\left(f x + e\right) - 2 \, a^{2} c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 3 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, \frac{{\left(a^{2} c \cos\left(f x + e\right)^{2} - 5 \, a^{2} c \cos\left(f x + e\right) - 2 \, a^{2} c\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 6 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{6 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/6*((a^2*c*cos(f*x + e)^2 - 5*a^2*c*cos(f*x + e) - 2*a^2*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + 3*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), 1/6*((a^2*c*cos(f*x + e)^2 - 5*a^2*c*cos(f*x + e) - 2*a^2*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + 6*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
103,1,420,0,0.559812," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(5 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right)\right)} \sqrt{-a c} \log\left(\frac{a c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, \frac{{\left(5 \, a^{2} \cos\left(f x + e\right) + a^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 2 \, {\left(a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right)\right)} \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a c \cos\left(f x + e\right)^{2} + a c}\right)}{2 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/2*((5*a^2*cos(f*x + e) + a^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + (a^2*cos(f*x + e)^2 + a^2*cos(f*x + e))*sqrt(-a*c)*log(1/2*(a*c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a*c)/cos(f*x + e)^2))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), 1/2*((5*a^2*cos(f*x + e) + a^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + 2*(a^2*cos(f*x + e)^2 + a^2*cos(f*x + e))*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*c*cos(f*x + e)^2 + a*c)))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
104,0,0,0,0.616183," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c \sec\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c*sec(f*x + e) - c), x)","F",0
105,1,442,0,0.584922," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} c \cos\left(f x + e\right) - a^{2} c\right)} \sqrt{-\frac{a}{c}} \log\left(\frac{a \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + a}{2 \, \cos\left(f x + e\right)^{2}}\right) \sin\left(f x + e\right) + 4 \, {\left(a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{2 \, {\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}, \frac{{\left(a^{2} c \cos\left(f x + e\right) - a^{2} c\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{\sqrt{\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{a \cos\left(f x + e\right)^{2} + a}\right) \sin\left(f x + e\right) + 2 \, {\left(a^{2} \cos\left(f x + e\right)^{2} + a^{2} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(c^{2} f \cos\left(f x + e\right) - c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/2*((a^2*c*cos(f*x + e) - a^2*c)*sqrt(-a/c)*log(1/2*(a*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + a)/cos(f*x + e)^2)*sin(f*x + e) + 4*(a^2*cos(f*x + e)^2 + a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e)), ((a^2*c*cos(f*x + e) - a^2*c)*sqrt(a/c)*arctan(sqrt(a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(a*cos(f*x + e)^2 + a))*sin(f*x + e) + 2*(a^2*cos(f*x + e)^2 + a^2*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((c^2*f*cos(f*x + e) - c^2*f)*sin(f*x + e))]","B",0
106,0,0,0,0.558081," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}}, x\right)"," ",0,"integral(-(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3), x)","F",0
107,0,0,0,0.570518," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{4} \sec\left(f x + e\right)^{4} - 4 \, c^{4} \sec\left(f x + e\right)^{3} + 6 \, c^{4} \sec\left(f x + e\right)^{2} - 4 \, c^{4} \sec\left(f x + e\right) + c^{4}}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^4*sec(f*x + e)^4 - 4*c^4*sec(f*x + e)^3 + 6*c^4*sec(f*x + e)^2 - 4*c^4*sec(f*x + e) + c^4), x)","F",0
108,0,0,0,0.615696," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{5} \sec\left(f x + e\right)^{5} - 5 \, c^{5} \sec\left(f x + e\right)^{4} + 10 \, c^{5} \sec\left(f x + e\right)^{3} - 10 \, c^{5} \sec\left(f x + e\right)^{2} + 5 \, c^{5} \sec\left(f x + e\right) - c^{5}}, x\right)"," ",0,"integral(-(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^5*sec(f*x + e)^5 - 5*c^5*sec(f*x + e)^4 + 10*c^5*sec(f*x + e)^3 - 10*c^5*sec(f*x + e)^2 + 5*c^5*sec(f*x + e) - c^5), x)","F",0
109,0,0,0,0.613174," ","integrate((a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{c^{6} \sec\left(f x + e\right)^{6} - 6 \, c^{6} \sec\left(f x + e\right)^{5} + 15 \, c^{6} \sec\left(f x + e\right)^{4} - 20 \, c^{6} \sec\left(f x + e\right)^{3} + 15 \, c^{6} \sec\left(f x + e\right)^{2} - 6 \, c^{6} \sec\left(f x + e\right) + c^{6}}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(c^6*sec(f*x + e)^6 - 6*c^6*sec(f*x + e)^5 + 15*c^6*sec(f*x + e)^4 - 20*c^6*sec(f*x + e)^3 + 15*c^6*sec(f*x + e)^2 - 6*c^6*sec(f*x + e) + c^6), x)","F",0
110,0,0,0,0.632773," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}\right)} \sqrt{-c \sec\left(f x + e\right) + c}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3)*sqrt(-c*sec(f*x + e) + c)/sqrt(a*sec(f*x + e) + a), x)","F",0
111,0,0,0,0.615117," ","integrate((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}\right)} \sqrt{-c \sec\left(f x + e\right) + c}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2)*sqrt(-c*sec(f*x + e) + c)/sqrt(a*sec(f*x + e) + a), x)","F",0
112,0,0,0,0.618409," ","integrate((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((-c*sec(f*x + e) + c)^(3/2)/sqrt(a*sec(f*x + e) + a), x)","F",0
113,0,0,0,0.522657," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c \sec\left(f x + e\right) + c}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(sqrt(-c*sec(f*x + e) + c)/sqrt(a*sec(f*x + e) + a), x)","F",0
114,1,272,0,0.725152," ","integrate(1/(c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a c} \log\left(-\frac{8 \, {\left({\left(256 \, \cos\left(f x + e\right)^{5} - 512 \, \cos\left(f x + e\right)^{3} + 175 \, \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} - {\left(256 \, a c \cos\left(f x + e\right)^{4} - 512 \, a c \cos\left(f x + e\right)^{2} + 337 \, a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right)}{2 \, a c f}, -\frac{\sqrt{a c} \arctan\left(\frac{{\left(16 \, \cos\left(f x + e\right)^{3} - 7 \, \cos\left(f x + e\right)\right)} \sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(16 \, a c \cos\left(f x + e\right)^{2} - 25 \, a c\right)} \sin\left(f x + e\right)}\right)}{a c f}\right]"," ",0,"[-1/2*sqrt(-a*c)*log(-8*((256*cos(f*x + e)^5 - 512*cos(f*x + e)^3 + 175*cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) - (256*a*c*cos(f*x + e)^4 - 512*a*c*cos(f*x + e)^2 + 337*a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))/(a*c*f), -sqrt(a*c)*arctan((16*cos(f*x + e)^3 - 7*cos(f*x + e))*sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((16*a*c*cos(f*x + e)^2 - 25*a*c)*sin(f*x + e)))/(a*c*f)]","B",0
115,0,0,0,0.649550," ","integrate(1/(c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a c^{2} \sec\left(f x + e\right)^{3} - a c^{2} \sec\left(f x + e\right)^{2} - a c^{2} \sec\left(f x + e\right) + a c^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a*c^2*sec(f*x + e)^3 - a*c^2*sec(f*x + e)^2 - a*c^2*sec(f*x + e) + a*c^2), x)","F",0
116,0,0,0,1.018244," ","integrate(1/(c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a c^{3} \sec\left(f x + e\right)^{4} - 2 \, a c^{3} \sec\left(f x + e\right)^{3} + 2 \, a c^{3} \sec\left(f x + e\right) - a c^{3}}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a*c^3*sec(f*x + e)^4 - 2*a*c^3*sec(f*x + e)^3 + 2*a*c^3*sec(f*x + e) - a*c^3), x)","F",0
117,0,0,0,0.735619," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(-(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
118,1,453,0,0.575953," ","integrate((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} \cos\left(f x + e\right)^{2} + 2 \, a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \sqrt{-\frac{c}{a}} \log\left(\frac{c \cos\left(f x + e\right)^{4} - {\left(\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)\right)} \sqrt{-\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + c}{2 \, \cos\left(f x + e\right)^{2}}\right)}{2 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, -\frac{2 \, c^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} \cos\left(f x + e\right)^{2} + 2 \, a c^{2} \cos\left(f x + e\right) + a c^{2}\right)} \sqrt{\frac{c}{a}} \arctan\left(\frac{\sqrt{\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + c}\right)}{a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f}\right]"," ",0,"[-1/2*(4*c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (a*c^2*cos(f*x + e)^2 + 2*a*c^2*cos(f*x + e) + a*c^2)*sqrt(-c/a)*log(1/2*(c*cos(f*x + e)^4 - (cos(f*x + e)^3 + cos(f*x + e))*sqrt(-c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*sin(f*x + e) + c)/cos(f*x + e)^2))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -(2*c^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (a*c^2*cos(f*x + e)^2 + 2*a*c^2*cos(f*x + e) + a*c^2)*sqrt(c/a)*arctan(sqrt(c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e)/(c*cos(f*x + e)^2 + c)))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","B",0
119,0,0,0,0.525907," ","integrate((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^(3/2)/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
120,0,0,0,0.550858," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
121,0,0,0,0.806158," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} c \sec\left(f x + e\right)^{3} + a^{2} c \sec\left(f x + e\right)^{2} - a^{2} c \sec\left(f x + e\right) - a^{2} c}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*c*sec(f*x + e)^3 + a^2*c*sec(f*x + e)^2 - a^2*c*sec(f*x + e) - a^2*c), x)","F",0
122,1,492,0,0.863193," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{9 \, \sqrt{-a c} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \log\left(-\frac{8 \, {\left({\left(256 \, \cos\left(f x + e\right)^{5} - 512 \, \cos\left(f x + e\right)^{3} + 175 \, \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} - {\left(256 \, a c \cos\left(f x + e\right)^{4} - 512 \, a c \cos\left(f x + e\right)^{2} + 337 \, a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(16 \, \cos\left(f x + e\right)^{3} - 25 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{18 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}, -\frac{18 \, \sqrt{a c} {\left(\cos\left(f x + e\right)^{2} - 1\right)} \arctan\left(\frac{{\left(16 \, \cos\left(f x + e\right)^{3} - 7 \, \cos\left(f x + e\right)\right)} \sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(16 \, a c \cos\left(f x + e\right)^{2} - 25 \, a c\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(16 \, \cos\left(f x + e\right)^{3} - 25 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{18 \, {\left(a^{2} c^{2} f \cos\left(f x + e\right)^{2} - a^{2} c^{2} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/18*(9*sqrt(-a*c)*(cos(f*x + e)^2 - 1)*log(-8*((256*cos(f*x + e)^5 - 512*cos(f*x + e)^3 + 175*cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) - (256*a*c*cos(f*x + e)^4 - 512*a*c*cos(f*x + e)^2 + 337*a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) + (16*cos(f*x + e)^3 - 25*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e)), -1/18*(18*sqrt(a*c)*(cos(f*x + e)^2 - 1)*arctan((16*cos(f*x + e)^3 - 7*cos(f*x + e))*sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((16*a*c*cos(f*x + e)^2 - 25*a*c)*sin(f*x + e)))*sin(f*x + e) + (16*cos(f*x + e)^3 - 25*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^2*c^2*f*cos(f*x + e)^2 - a^2*c^2*f)*sin(f*x + e))]","B",0
123,0,0,0,0.800705," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{2} c^{3} \sec\left(f x + e\right)^{5} - a^{2} c^{3} \sec\left(f x + e\right)^{4} - 2 \, a^{2} c^{3} \sec\left(f x + e\right)^{3} + 2 \, a^{2} c^{3} \sec\left(f x + e\right)^{2} + a^{2} c^{3} \sec\left(f x + e\right) - a^{2} c^{3}}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^2*c^3*sec(f*x + e)^5 - a^2*c^3*sec(f*x + e)^4 - 2*a^2*c^3*sec(f*x + e)^3 + 2*a^2*c^3*sec(f*x + e)^2 + a^2*c^3*sec(f*x + e) - a^2*c^3), x)","F",0
124,0,0,0,0.691934," ","integrate((c-c*sec(f*x+e))^(7/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{3} \sec\left(f x + e\right)^{3} - 3 \, c^{3} \sec\left(f x + e\right)^{2} + 3 \, c^{3} \sec\left(f x + e\right) - c^{3}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral(-(c^3*sec(f*x + e)^3 - 3*c^3*sec(f*x + e)^2 + 3*c^3*sec(f*x + e) - c^3)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3), x)","F",0
125,0,0,0,0.558527," ","integrate((c-c*sec(f*x+e))^(5/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \sec\left(f x + e\right)^{2} - 2 \, c^{2} \sec\left(f x + e\right) + c^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral((c^2*sec(f*x + e)^2 - 2*c^2*sec(f*x + e) + c^2)*sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3), x)","F",0
126,0,0,0,0.556993," ","integrate((c-c*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^(3/2)/(a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3), x)","F",0
127,0,0,0,0.573692," ","integrate((c-c*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3), x)","F",0
128,0,0,0,0.770571," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} c \sec\left(f x + e\right)^{4} + 2 \, a^{3} c \sec\left(f x + e\right)^{3} - 2 \, a^{3} c \sec\left(f x + e\right) - a^{3} c}, x\right)"," ",0,"integral(-sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*c*sec(f*x + e)^4 + 2*a^3*c*sec(f*x + e)^3 - 2*a^3*c*sec(f*x + e) - a^3*c), x)","F",0
129,0,0,0,0.795203," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} \sqrt{-c \sec\left(f x + e\right) + c}}{a^{3} c^{2} \sec\left(f x + e\right)^{5} + a^{3} c^{2} \sec\left(f x + e\right)^{4} - 2 \, a^{3} c^{2} \sec\left(f x + e\right)^{3} - 2 \, a^{3} c^{2} \sec\left(f x + e\right)^{2} + a^{3} c^{2} \sec\left(f x + e\right) + a^{3} c^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*sqrt(-c*sec(f*x + e) + c)/(a^3*c^2*sec(f*x + e)^5 + a^3*c^2*sec(f*x + e)^4 - 2*a^3*c^2*sec(f*x + e)^3 - 2*a^3*c^2*sec(f*x + e)^2 + a^3*c^2*sec(f*x + e) + a^3*c^2), x)","F",0
130,1,564,0,1.021935," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c-c*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{162 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{-a c} \log\left(-\frac{8 \, {\left({\left(256 \, \cos\left(f x + e\right)^{5} - 512 \, \cos\left(f x + e\right)^{3} + 175 \, \cos\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}} - {\left(256 \, a c \cos\left(f x + e\right)^{4} - 512 \, a c \cos\left(f x + e\right)^{2} + 337 \, a c\right)} \sin\left(f x + e\right)\right)}}{{\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(832 \, \cos\left(f x + e\right)^{5} - 1988 \, \cos\left(f x + e\right)^{3} + 1075 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{324 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}, -\frac{324 \, {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sqrt{a c} \arctan\left(\frac{{\left(16 \, \cos\left(f x + e\right)^{3} - 7 \, \cos\left(f x + e\right)\right)} \sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{{\left(16 \, a c \cos\left(f x + e\right)^{2} - 25 \, a c\right)} \sin\left(f x + e\right)}\right) \sin\left(f x + e\right) + {\left(832 \, \cos\left(f x + e\right)^{5} - 1988 \, \cos\left(f x + e\right)^{3} + 1075 \, \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) - c}{\cos\left(f x + e\right)}}}{324 \, {\left(a^{3} c^{3} f \cos\left(f x + e\right)^{4} - 2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{2} + a^{3} c^{3} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[-1/324*(162*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(-a*c)*log(-8*((256*cos(f*x + e)^5 - 512*cos(f*x + e)^3 + 175*cos(f*x + e))*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)) - (256*a*c*cos(f*x + e)^4 - 512*a*c*cos(f*x + e)^2 + 337*a*c)*sin(f*x + e))/((cos(f*x + e)^2 - 1)*sin(f*x + e)))*sin(f*x + e) + (832*cos(f*x + e)^5 - 1988*cos(f*x + e)^3 + 1075*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e)), -1/324*(324*(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sqrt(a*c)*arctan((16*cos(f*x + e)^3 - 7*cos(f*x + e))*sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e))/((16*a*c*cos(f*x + e)^2 - 25*a*c)*sin(f*x + e)))*sin(f*x + e) + (832*cos(f*x + e)^5 - 1988*cos(f*x + e)^3 + 1075*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) - c)/cos(f*x + e)))/((a^3*c^3*f*cos(f*x + e)^4 - 2*a^3*c^3*f*cos(f*x + e)^2 + a^3*c^3*f)*sin(f*x + e))]","A",0
131,0,0,0,0.477930," ","integrate((1+sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(-c \sec\left(f x + e\right) + c\right)}^{n} {\left(\sec\left(f x + e\right) + 1\right)}^{m}, x\right)"," ",0,"integral((-c*sec(f*x + e) + c)^n*(sec(f*x + e) + 1)^m, x)","F",0
132,0,0,0,0.506824," ","integrate((a+a*sec(f*x+e))^m*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{m} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^m*(-c*sec(f*x + e) + c)^n, x)","F",0
133,0,0,0,0.451759," ","integrate((a+a*sec(f*x+e))^3*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3)*(-c*sec(f*x + e) + c)^n, x)","F",0
134,0,0,0,0.459685," ","integrate((a+a*sec(f*x+e))^2*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*(-c*sec(f*x + e) + c)^n, x)","F",0
135,0,0,0,0.431180," ","integrate((a+a*sec(f*x+e))*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n, x)","F",0
136,0,0,0,0.432965," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((-c*sec(f*x + e) + c)^n/(a*sec(f*x + e) + a), x)","F",0
137,0,0,0,0.442450," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((-c*sec(f*x + e) + c)^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
138,0,0,0,0.452783," ","integrate((a+a*sec(f*x+e))^(5/2)*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n, x)","F",0
139,0,0,0,0.466166," ","integrate((a+a*sec(f*x+e))^(3/2)*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)^(3/2)*(-c*sec(f*x + e) + c)^n, x)","F",0
140,0,0,0,0.454917," ","integrate((a+a*sec(f*x+e))^(1/2)*(c-c*sec(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n, x)","F",0
141,0,0,0,0.447199," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{\sqrt{a \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((-c*sec(f*x + e) + c)^n/sqrt(a*sec(f*x + e) + a), x)","F",0
142,0,0,0,0.460955," ","integrate((c-c*sec(f*x+e))^n/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sec\left(f x + e\right) + a} {\left(-c \sec\left(f x + e\right) + c\right)}^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*sec(f*x + e) + a)*(-c*sec(f*x + e) + c)^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
143,1,293,0,0.555657," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+c*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, c f}, \frac{\sqrt{2} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{c f}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*f), (sqrt(2)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(c*f)]","A",0
144,0,0,0,0.825597," ","integrate((c+d*sec(f*x+e))^(3/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sec\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sec(f*x + e) + c)^(3/2)/(a*sec(f*x + e) + a), x)","F",0
145,0,0,0,22.527398," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right) + c}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e) + c)/(a*sec(f*x + e) + a), x)","F",0
146,0,0,0,0.818175," ","integrate(1/(a+a*sec(f*x+e))/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right) + c}}{a d \sec\left(f x + e\right)^{2} + a c + {\left(a c + a d\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e) + c)/(a*d*sec(f*x + e)^2 + a*c + (a*c + a*d)*sec(f*x + e)), x)","F",0
147,1,472,0,0.511513," ","integrate((c+d*sec(f*x+e))^4*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(15 \, d^{4} + 4 \, {\left(105 \, c^{3} d + 105 \, c^{2} d^{2} + 56 \, c d^{3} + 12 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(105 \, c^{2} d^{2} + 56 \, c d^{3} + 12 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(14 \, c d^{3} + 3 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(c^{4} \cos\left(f x + e\right)^{4} + c^{4} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(15 \, d^{4} + 4 \, {\left(105 \, c^{3} d + 105 \, c^{2} d^{2} + 56 \, c d^{3} + 12 \, d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(105 \, c^{2} d^{2} + 56 \, c d^{3} + 12 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(14 \, c d^{3} + 3 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(15*d^4 + 4*(105*c^3*d + 105*c^2*d^2 + 56*c*d^3 + 12*d^4)*cos(f*x + e)^3 + 2*(105*c^2*d^2 + 56*c*d^3 + 12*d^4)*cos(f*x + e)^2 + 6*(14*c*d^3 + 3*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(c^4*cos(f*x + e)^4 + c^4*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (15*d^4 + 4*(105*c^3*d + 105*c^2*d^2 + 56*c*d^3 + 12*d^4)*cos(f*x + e)^3 + 2*(105*c^2*d^2 + 56*c*d^3 + 12*d^4)*cos(f*x + e)^2 + 6*(14*c*d^3 + 3*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
148,1,392,0,0.482860," ","integrate((c+d*sec(f*x+e))^3*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(3 \, d^{3} + {\left(45 \, c^{2} d + 30 \, c d^{2} + 8 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, c d^{2} + 4 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + c^{3} \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(3 \, d^{3} + {\left(45 \, c^{2} d + 30 \, c d^{2} + 8 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, c d^{2} + 4 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(3*d^3 + (45*c^2*d + 30*c*d^2 + 8*d^3)*cos(f*x + e)^2 + (15*c*d^2 + 4*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/15*(15*(c^3*cos(f*x + e)^3 + c^3*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (3*d^3 + (45*c^2*d + 30*c*d^2 + 8*d^3)*cos(f*x + e)^2 + (15*c*d^2 + 4*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
149,1,320,0,0.477565," ","integrate((c+d*sec(f*x+e))^2*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(d^{2} + 2 \, {\left(3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + c^{2} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(d^{2} + 2 \, {\left(3 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(d^2 + 2*(3*c*d + d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), -2/3*(3*(c^2*cos(f*x + e)^2 + c^2*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (d^2 + 2*(3*c*d + d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
150,1,235,0,0.501335," ","integrate((c+d*sec(f*x+e))*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{f \cos\left(f x + e\right) + f}, -\frac{2 \, {\left({\left(c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{f \cos\left(f x + e\right) + f}\right]"," ",0,"[((c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e) + f), -2*((c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e) + f)]","A",0
151,1,669,0,0.868173," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c f}, -\frac{2 \, \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - \sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{c f}, \frac{2 \, \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right) + \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c f}, -\frac{2 \, {\left(\sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right)\right)}}{c f}\right]"," ",0,"[(sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*f), -(2*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/(c*f), (2*sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))) + sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*f), -2*(sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))))/(c*f)]","A",0
152,1,1413,0,2.865398," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, c d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left({\left(3 \, c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + 3 \, c d + 2 \, d^{2} + {\left(3 \, c^{2} + 5 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left({\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f\right)}}, -\frac{2 \, c d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 4 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left({\left(3 \, c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + 3 \, c d + 2 \, d^{2} + {\left(3 \, c^{2} + 5 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{2 \, {\left({\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f\right)}}, -\frac{c d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left({\left(3 \, c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + 3 \, c d + 2 \, d^{2} + {\left(3 \, c^{2} + 5 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right) - {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{{\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f}, -\frac{c d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left({\left(3 \, c^{2} + 2 \, c d\right)} \cos\left(f x + e\right)^{2} + 3 \, c d + 2 \, d^{2} + {\left(3 \, c^{2} + 5 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right)}{{\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f}\right]"," ",0,"[-1/2*(2*c*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - ((3*c^2 + 2*c*d)*cos(f*x + e)^2 + 3*c*d + 2*d^2 + (3*c^2 + 5*c*d + 2*d^2)*cos(f*x + e))*sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - 2*((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), -1/2*(2*c*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 4*((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - ((3*c^2 + 2*c*d)*cos(f*x + e)^2 + 3*c*d + 2*d^2 + (3*c^2 + 5*c*d + 2*d^2)*cos(f*x + e))*sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), -(c*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - ((3*c^2 + 2*c*d)*cos(f*x + e)^2 + 3*c*d + 2*d^2 + (3*c^2 + 5*c*d + 2*d^2)*cos(f*x + e))*sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))) - ((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), -(c*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 2*((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - ((3*c^2 + 2*c*d)*cos(f*x + e)^2 + 3*c*d + 2*d^2 + (3*c^2 + 5*c*d + 2*d^2)*cos(f*x + e))*sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f)]","A",0
153,1,2368,0,7.737870," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{{\left(15 \, c^{2} d^{2} + 20 \, c d^{3} + 8 \, d^{4} + {\left(15 \, c^{4} + 20 \, c^{3} d + 8 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(15 \, c^{4} + 50 \, c^{3} d + 48 \, c^{2} d^{2} + 16 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(30 \, c^{3} d + 55 \, c^{2} d^{2} + 36 \, c d^{3} + 8 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + 8 \, {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{4} + 4 \, c^{3} d + 5 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{3} d + 5 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left(3 \, {\left(3 \, c^{3} d + 2 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(7 \, c^{2} d^{2} + 4 \, c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, -\frac{16 \, {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{4} + 4 \, c^{3} d + 5 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{3} d + 5 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(15 \, c^{2} d^{2} + 20 \, c d^{3} + 8 \, d^{4} + {\left(15 \, c^{4} + 20 \, c^{3} d + 8 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(15 \, c^{4} + 50 \, c^{3} d + 48 \, c^{2} d^{2} + 16 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(30 \, c^{3} d + 55 \, c^{2} d^{2} + 36 \, c d^{3} + 8 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a d}{c + d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + 2 \, {\left(3 \, {\left(3 \, c^{3} d + 2 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(7 \, c^{2} d^{2} + 4 \, c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, \frac{{\left(15 \, c^{2} d^{2} + 20 \, c d^{3} + 8 \, d^{4} + {\left(15 \, c^{4} + 20 \, c^{3} d + 8 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(15 \, c^{4} + 50 \, c^{3} d + 48 \, c^{2} d^{2} + 16 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(30 \, c^{3} d + 55 \, c^{2} d^{2} + 36 \, c d^{3} + 8 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right) + 4 \, {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{4} + 4 \, c^{3} d + 5 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{3} d + 5 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - {\left(3 \, {\left(3 \, c^{3} d + 2 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(7 \, c^{2} d^{2} + 4 \, c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, -\frac{8 \, {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(c^{4} + 4 \, c^{3} d + 5 \, c^{2} d^{2} + 2 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, c^{3} d + 5 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(15 \, c^{2} d^{2} + 20 \, c d^{3} + 8 \, d^{4} + {\left(15 \, c^{4} + 20 \, c^{3} d + 8 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(15 \, c^{4} + 50 \, c^{3} d + 48 \, c^{2} d^{2} + 16 \, c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(30 \, c^{3} d + 55 \, c^{2} d^{2} + 36 \, c d^{3} + 8 \, d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a d}{c + d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a d}{c + d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right) + {\left(3 \, {\left(3 \, c^{3} d + 2 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(7 \, c^{2} d^{2} + 4 \, c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}\right]"," ",0,"[1/8*((15*c^2*d^2 + 20*c*d^3 + 8*d^4 + (15*c^4 + 20*c^3*d + 8*c^2*d^2)*cos(f*x + e)^3 + (15*c^4 + 50*c^3*d + 48*c^2*d^2 + 16*c*d^3)*cos(f*x + e)^2 + (30*c^3*d + 55*c^2*d^2 + 36*c*d^3 + 8*d^4)*cos(f*x + e))*sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + 8*(c^2*d^2 + 2*c*d^3 + d^4 + (c^4 + 2*c^3*d + c^2*d^2)*cos(f*x + e)^3 + (c^4 + 4*c^3*d + 5*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^2 + (2*c^3*d + 5*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*(3*(3*c^3*d + 2*c^2*d^2)*cos(f*x + e)^2 + (7*c^2*d^2 + 4*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), -1/8*(16*(c^2*d^2 + 2*c*d^3 + d^4 + (c^4 + 2*c^3*d + c^2*d^2)*cos(f*x + e)^3 + (c^4 + 4*c^3*d + 5*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^2 + (2*c^3*d + 5*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (15*c^2*d^2 + 20*c*d^3 + 8*d^4 + (15*c^4 + 20*c^3*d + 8*c^2*d^2)*cos(f*x + e)^3 + (15*c^4 + 50*c^3*d + 48*c^2*d^2 + 16*c*d^3)*cos(f*x + e)^2 + (30*c^3*d + 55*c^2*d^2 + 36*c*d^3 + 8*d^4)*cos(f*x + e))*sqrt(-a*d/(c + d))*log((2*(c + d)*sqrt(-a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + 2*(3*(3*c^3*d + 2*c^2*d^2)*cos(f*x + e)^2 + (7*c^2*d^2 + 4*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), 1/4*((15*c^2*d^2 + 20*c*d^3 + 8*d^4 + (15*c^4 + 20*c^3*d + 8*c^2*d^2)*cos(f*x + e)^3 + (15*c^4 + 50*c^3*d + 48*c^2*d^2 + 16*c*d^3)*cos(f*x + e)^2 + (30*c^3*d + 55*c^2*d^2 + 36*c*d^3 + 8*d^4)*cos(f*x + e))*sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))) + 4*(c^2*d^2 + 2*c*d^3 + d^4 + (c^4 + 2*c^3*d + c^2*d^2)*cos(f*x + e)^3 + (c^4 + 4*c^3*d + 5*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^2 + (2*c^3*d + 5*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - (3*(3*c^3*d + 2*c^2*d^2)*cos(f*x + e)^2 + (7*c^2*d^2 + 4*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), -1/4*(8*(c^2*d^2 + 2*c*d^3 + d^4 + (c^4 + 2*c^3*d + c^2*d^2)*cos(f*x + e)^3 + (c^4 + 4*c^3*d + 5*c^2*d^2 + 2*c*d^3)*cos(f*x + e)^2 + (2*c^3*d + 5*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (15*c^2*d^2 + 20*c*d^3 + 8*d^4 + (15*c^4 + 20*c^3*d + 8*c^2*d^2)*cos(f*x + e)^3 + (15*c^4 + 50*c^3*d + 48*c^2*d^2 + 16*c*d^3)*cos(f*x + e)^2 + (30*c^3*d + 55*c^2*d^2 + 36*c*d^3 + 8*d^4)*cos(f*x + e))*sqrt(a*d/(c + d))*arctan((c + d)*sqrt(a*d/(c + d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))) + (3*(3*c^3*d + 2*c^2*d^2)*cos(f*x + e)^2 + (7*c^2*d^2 + 4*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f)]","B",0
154,1,482,0,0.502190," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a c^{3} \cos\left(f x + e\right)^{4} + a c^{3} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(15 \, a d^{3} + {\left(105 \, a c^{3} + 525 \, a c^{2} d + 378 \, a c d^{2} + 104 \, a d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(105 \, a c^{2} d + 189 \, a c d^{2} + 52 \, a d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(21 \, a c d^{2} + 13 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(a c^{3} \cos\left(f x + e\right)^{4} + a c^{3} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(15 \, a d^{3} + {\left(105 \, a c^{3} + 525 \, a c^{2} d + 378 \, a c d^{2} + 104 \, a d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(105 \, a c^{2} d + 189 \, a c d^{2} + 52 \, a d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(21 \, a c d^{2} + 13 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(a*c^3*cos(f*x + e)^4 + a*c^3*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(15*a*d^3 + (105*a*c^3 + 525*a*c^2*d + 378*a*c*d^2 + 104*a*d^3)*cos(f*x + e)^3 + (105*a*c^2*d + 189*a*c*d^2 + 52*a*d^3)*cos(f*x + e)^2 + 3*(21*a*c*d^2 + 13*a*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(a*c^3*cos(f*x + e)^4 + a*c^3*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (15*a*d^3 + (105*a*c^3 + 525*a*c^2*d + 378*a*c*d^2 + 104*a*d^3)*cos(f*x + e)^3 + (105*a*c^2*d + 189*a*c*d^2 + 52*a*d^3)*cos(f*x + e)^2 + 3*(21*a*c*d^2 + 13*a*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
155,1,398,0,0.504069," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(3 \, a d^{2} + {\left(15 \, a c^{2} + 50 \, a c d + 18 \, a d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(10 \, a c d + 9 \, a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(a c^{2} \cos\left(f x + e\right)^{3} + a c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(3 \, a d^{2} + {\left(15 \, a c^{2} + 50 \, a c d + 18 \, a d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(10 \, a c d + 9 \, a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(3*a*d^2 + (15*a*c^2 + 50*a*c*d + 18*a*d^2)*cos(f*x + e)^2 + (10*a*c*d + 9*a*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/15*(15*(a*c^2*cos(f*x + e)^3 + a*c^2*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (3*a*d^2 + (15*a*c^2 + 50*a*c*d + 18*a*d^2)*cos(f*x + e)^2 + (10*a*c*d + 9*a*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
156,1,316,0,0.510833," ","integrate((a+a*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a c \cos\left(f x + e\right)^{2} + a c \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(a d + {\left(3 \, a c + 5 \, a d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}, -\frac{2 \, {\left(3 \, {\left(a c \cos\left(f x + e\right)^{2} + a c \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(a d + {\left(3 \, a c + 5 \, a d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{3 \, {\left(f \cos\left(f x + e\right)^{2} + f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/3*(3*(a*c*cos(f*x + e)^2 + a*c*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(a*d + (3*a*c + 5*a*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e)), -2/3*(3*(a*c*cos(f*x + e)^2 + a*c*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (a*d + (3*a*c + 5*a*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^2 + f*cos(f*x + e))]","A",0
157,1,731,0,1.625499," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{{\left(a c - a d\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - \sqrt{-a} a \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c f}, -\frac{2 \, a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(a c - a d\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{c f}, -\frac{2 \, {\left(a c - a d\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - \sqrt{-a} a \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c f}, -\frac{2 \, {\left({\left(a c - a d\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + a^{\frac{3}{2}} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)\right)}}{c f}\right]"," ",0,"[-((a*c - a*d)*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - sqrt(-a)*a*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*f), -(2*a^(3/2)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (a*c - a*d)*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/(c*f), -(2*(a*c - a*d)*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - sqrt(-a)*a*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*f), -2*((a*c - a*d)*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + a^(3/2)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(c*f)]","A",0
158,1,1640,0,7.403063," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a c^{2} - a c d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - 3 \, a c d^{2} - 2 \, a d^{3} + {\left(a c^{3} - 3 \, a c^{2} d - 2 \, a c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 2 \, a c^{2} d - 5 \, a c d^{2} - 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + 2 \, {\left(a c d + a d^{2} + {\left(a c^{2} + a c d\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left({\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f\right)}}, \frac{2 \, {\left(a c^{2} - a c d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 4 \, {\left(a c d + a d^{2} + {\left(a c^{2} + a c d\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(a c^{2} d - 3 \, a c d^{2} - 2 \, a d^{3} + {\left(a c^{3} - 3 \, a c^{2} d - 2 \, a c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 2 \, a c^{2} d - 5 \, a c d^{2} - 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{2 \, {\left({\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f\right)}}, \frac{{\left(a c^{2} - a c d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - 3 \, a c d^{2} - 2 \, a d^{3} + {\left(a c^{3} - 3 \, a c^{2} d - 2 \, a c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 2 \, a c^{2} d - 5 \, a c d^{2} - 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + {\left(a c d + a d^{2} + {\left(a c^{2} + a c d\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{{\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f}, \frac{{\left(a c^{2} - a c d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - 3 \, a c d^{2} - 2 \, a d^{3} + {\left(a c^{3} - 3 \, a c^{2} d - 2 \, a c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 2 \, a c^{2} d - 5 \, a c d^{2} - 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - 2 \, {\left(a c d + a d^{2} + {\left(a c^{2} + a c d\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{2} + 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{{\left(c^{4} + c^{3} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} + 2 \, c^{3} d + c^{2} d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d + c^{2} d^{2}\right)} f}\right]"," ",0,"[1/2*(2*(a*c^2 - a*c*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - 3*a*c*d^2 - 2*a*d^3 + (a*c^3 - 3*a*c^2*d - 2*a*c*d^2)*cos(f*x + e)^2 + (a*c^3 - 2*a*c^2*d - 5*a*c*d^2 - 2*a*d^3)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + 2*(a*c*d + a*d^2 + (a*c^2 + a*c*d)*cos(f*x + e)^2 + (a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), 1/2*(2*(a*c^2 - a*c*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 4*(a*c*d + a*d^2 + (a*c^2 + a*c*d)*cos(f*x + e)^2 + (a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (a*c^2*d - 3*a*c*d^2 - 2*a*d^3 + (a*c^3 - 3*a*c^2*d - 2*a*c*d^2)*cos(f*x + e)^2 + (a*c^3 - 2*a*c^2*d - 5*a*c*d^2 - 2*a*d^3)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), ((a*c^2 - a*c*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - 3*a*c*d^2 - 2*a*d^3 + (a*c^3 - 3*a*c^2*d - 2*a*c*d^2)*cos(f*x + e)^2 + (a*c^3 - 2*a*c^2*d - 5*a*c*d^2 - 2*a*d^3)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + (a*c*d + a*d^2 + (a*c^2 + a*c*d)*cos(f*x + e)^2 + (a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f), ((a*c^2 - a*c*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - 3*a*c*d^2 - 2*a*d^3 + (a*c^3 - 3*a*c^2*d - 2*a*c*d^2)*cos(f*x + e)^2 + (a*c^3 - 2*a*c^2*d - 5*a*c*d^2 - 2*a*d^3)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - 2*(a*c*d + a*d^2 + (a*c^2 + a*c*d)*cos(f*x + e)^2 + (a*c^2 + 2*a*c*d + a*d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/((c^4 + c^3*d)*f*cos(f*x + e)^2 + (c^4 + 2*c^3*d + c^2*d^2)*f*cos(f*x + e) + (c^3*d + c^2*d^2)*f)]","A",0
159,1,2729,0,20.444306," ","integrate((a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, a c^{3} d^{2} - 15 \, a c^{2} d^{3} - 20 \, a c d^{4} - 8 \, a d^{5} + {\left(3 \, a c^{5} - 15 \, a c^{4} d - 20 \, a c^{3} d^{2} - 8 \, a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(3 \, a c^{5} - 9 \, a c^{4} d - 50 \, a c^{3} d^{2} - 48 \, a c^{2} d^{3} - 16 \, a c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, a c^{4} d - 27 \, a c^{3} d^{2} - 55 \, a c^{2} d^{3} - 36 \, a c d^{4} - 8 \, a d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - 8 \, {\left(a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4} + {\left(a c^{4} + 2 \, a c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(a c^{4} + 4 \, a c^{3} d + 5 \, a c^{2} d^{2} + 2 \, a c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{3} d + 5 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 2 \, {\left({\left(5 \, a c^{4} - 7 \, a c^{3} d - 6 \, a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, a c^{3} d - 7 \, a c^{2} d^{2} - 4 \, a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, -\frac{16 \, {\left(a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4} + {\left(a c^{4} + 2 \, a c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(a c^{4} + 4 \, a c^{3} d + 5 \, a c^{2} d^{2} + 2 \, a c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{3} d + 5 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(3 \, a c^{3} d^{2} - 15 \, a c^{2} d^{3} - 20 \, a c d^{4} - 8 \, a d^{5} + {\left(3 \, a c^{5} - 15 \, a c^{4} d - 20 \, a c^{3} d^{2} - 8 \, a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(3 \, a c^{5} - 9 \, a c^{4} d - 50 \, a c^{3} d^{2} - 48 \, a c^{2} d^{3} - 16 \, a c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, a c^{4} d - 27 \, a c^{3} d^{2} - 55 \, a c^{2} d^{3} - 36 \, a c d^{4} - 8 \, a d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - 2 \, {\left({\left(5 \, a c^{4} - 7 \, a c^{3} d - 6 \, a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, a c^{3} d - 7 \, a c^{2} d^{2} - 4 \, a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, -\frac{{\left(3 \, a c^{3} d^{2} - 15 \, a c^{2} d^{3} - 20 \, a c d^{4} - 8 \, a d^{5} + {\left(3 \, a c^{5} - 15 \, a c^{4} d - 20 \, a c^{3} d^{2} - 8 \, a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(3 \, a c^{5} - 9 \, a c^{4} d - 50 \, a c^{3} d^{2} - 48 \, a c^{2} d^{3} - 16 \, a c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, a c^{4} d - 27 \, a c^{3} d^{2} - 55 \, a c^{2} d^{3} - 36 \, a c d^{4} - 8 \, a d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - 4 \, {\left(a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4} + {\left(a c^{4} + 2 \, a c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(a c^{4} + 4 \, a c^{3} d + 5 \, a c^{2} d^{2} + 2 \, a c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{3} d + 5 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - {\left({\left(5 \, a c^{4} - 7 \, a c^{3} d - 6 \, a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, a c^{3} d - 7 \, a c^{2} d^{2} - 4 \, a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}, -\frac{{\left(3 \, a c^{3} d^{2} - 15 \, a c^{2} d^{3} - 20 \, a c d^{4} - 8 \, a d^{5} + {\left(3 \, a c^{5} - 15 \, a c^{4} d - 20 \, a c^{3} d^{2} - 8 \, a c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(3 \, a c^{5} - 9 \, a c^{4} d - 50 \, a c^{3} d^{2} - 48 \, a c^{2} d^{3} - 16 \, a c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, a c^{4} d - 27 \, a c^{3} d^{2} - 55 \, a c^{2} d^{3} - 36 \, a c d^{4} - 8 \, a d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + 8 \, {\left(a c^{2} d^{2} + 2 \, a c d^{3} + a d^{4} + {\left(a c^{4} + 2 \, a c^{3} d + a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(a c^{4} + 4 \, a c^{3} d + 5 \, a c^{2} d^{2} + 2 \, a c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a c^{3} d + 5 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left({\left(5 \, a c^{4} - 7 \, a c^{3} d - 6 \, a c^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, a c^{3} d - 7 \, a c^{2} d^{2} - 4 \, a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} + 2 \, c^{6} d + c^{5} d^{2}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} + 4 \, c^{6} d + 5 \, c^{5} d^{2} + 2 \, c^{4} d^{3}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d + 5 \, c^{5} d^{2} + 4 \, c^{4} d^{3} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{2} + 2 \, c^{4} d^{3} + c^{3} d^{4}\right)} f\right)}}\right]"," ",0,"[-1/8*((3*a*c^3*d^2 - 15*a*c^2*d^3 - 20*a*c*d^4 - 8*a*d^5 + (3*a*c^5 - 15*a*c^4*d - 20*a*c^3*d^2 - 8*a*c^2*d^3)*cos(f*x + e)^3 + (3*a*c^5 - 9*a*c^4*d - 50*a*c^3*d^2 - 48*a*c^2*d^3 - 16*a*c*d^4)*cos(f*x + e)^2 + (6*a*c^4*d - 27*a*c^3*d^2 - 55*a*c^2*d^3 - 36*a*c*d^4 - 8*a*d^5)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - 8*(a*c^2*d^2 + 2*a*c*d^3 + a*d^4 + (a*c^4 + 2*a*c^3*d + a*c^2*d^2)*cos(f*x + e)^3 + (a*c^4 + 4*a*c^3*d + 5*a*c^2*d^2 + 2*a*c*d^3)*cos(f*x + e)^2 + (2*a*c^3*d + 5*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 2*((5*a*c^4 - 7*a*c^3*d - 6*a*c^2*d^2)*cos(f*x + e)^2 + (3*a*c^3*d - 7*a*c^2*d^2 - 4*a*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), -1/8*(16*(a*c^2*d^2 + 2*a*c*d^3 + a*d^4 + (a*c^4 + 2*a*c^3*d + a*c^2*d^2)*cos(f*x + e)^3 + (a*c^4 + 4*a*c^3*d + 5*a*c^2*d^2 + 2*a*c*d^3)*cos(f*x + e)^2 + (2*a*c^3*d + 5*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (3*a*c^3*d^2 - 15*a*c^2*d^3 - 20*a*c*d^4 - 8*a*d^5 + (3*a*c^5 - 15*a*c^4*d - 20*a*c^3*d^2 - 8*a*c^2*d^3)*cos(f*x + e)^3 + (3*a*c^5 - 9*a*c^4*d - 50*a*c^3*d^2 - 48*a*c^2*d^3 - 16*a*c*d^4)*cos(f*x + e)^2 + (6*a*c^4*d - 27*a*c^3*d^2 - 55*a*c^2*d^3 - 36*a*c*d^4 - 8*a*d^5)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - 2*((5*a*c^4 - 7*a*c^3*d - 6*a*c^2*d^2)*cos(f*x + e)^2 + (3*a*c^3*d - 7*a*c^2*d^2 - 4*a*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), -1/4*((3*a*c^3*d^2 - 15*a*c^2*d^3 - 20*a*c*d^4 - 8*a*d^5 + (3*a*c^5 - 15*a*c^4*d - 20*a*c^3*d^2 - 8*a*c^2*d^3)*cos(f*x + e)^3 + (3*a*c^5 - 9*a*c^4*d - 50*a*c^3*d^2 - 48*a*c^2*d^3 - 16*a*c*d^4)*cos(f*x + e)^2 + (6*a*c^4*d - 27*a*c^3*d^2 - 55*a*c^2*d^3 - 36*a*c*d^4 - 8*a*d^5)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - 4*(a*c^2*d^2 + 2*a*c*d^3 + a*d^4 + (a*c^4 + 2*a*c^3*d + a*c^2*d^2)*cos(f*x + e)^3 + (a*c^4 + 4*a*c^3*d + 5*a*c^2*d^2 + 2*a*c*d^3)*cos(f*x + e)^2 + (2*a*c^3*d + 5*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - ((5*a*c^4 - 7*a*c^3*d - 6*a*c^2*d^2)*cos(f*x + e)^2 + (3*a*c^3*d - 7*a*c^2*d^2 - 4*a*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f), -1/4*((3*a*c^3*d^2 - 15*a*c^2*d^3 - 20*a*c*d^4 - 8*a*d^5 + (3*a*c^5 - 15*a*c^4*d - 20*a*c^3*d^2 - 8*a*c^2*d^3)*cos(f*x + e)^3 + (3*a*c^5 - 9*a*c^4*d - 50*a*c^3*d^2 - 48*a*c^2*d^3 - 16*a*c*d^4)*cos(f*x + e)^2 + (6*a*c^4*d - 27*a*c^3*d^2 - 55*a*c^2*d^3 - 36*a*c*d^4 - 8*a*d^5)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + 8*(a*c^2*d^2 + 2*a*c*d^3 + a*d^4 + (a*c^4 + 2*a*c^3*d + a*c^2*d^2)*cos(f*x + e)^3 + (a*c^4 + 4*a*c^3*d + 5*a*c^2*d^2 + 2*a*c*d^3)*cos(f*x + e)^2 + (2*a*c^3*d + 5*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - ((5*a*c^4 - 7*a*c^3*d - 6*a*c^2*d^2)*cos(f*x + e)^2 + (3*a*c^3*d - 7*a*c^2*d^2 - 4*a*c*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7 + 2*c^6*d + c^5*d^2)*f*cos(f*x + e)^3 + (c^7 + 4*c^6*d + 5*c^5*d^2 + 2*c^4*d^3)*f*cos(f*x + e)^2 + (2*c^6*d + 5*c^5*d^2 + 4*c^4*d^3 + c^3*d^4)*f*cos(f*x + e) + (c^5*d^2 + 2*c^4*d^3 + c^3*d^4)*f)]","B",0
160,1,620,0,0.522178," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{315 \, {\left(a^{2} c^{3} \cos\left(f x + e\right)^{5} + a^{2} c^{3} \cos\left(f x + e\right)^{4}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(35 \, a^{2} d^{3} + {\left(840 \, a^{2} c^{3} + 2709 \, a^{2} c^{2} d + 2070 \, a^{2} c d^{2} + 584 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{4} + {\left(105 \, a^{2} c^{3} + 882 \, a^{2} c^{2} d + 1035 \, a^{2} c d^{2} + 292 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(63 \, a^{2} c^{2} d + 180 \, a^{2} c d^{2} + 73 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 5 \, {\left(27 \, a^{2} c d^{2} + 26 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{315 \, {\left(f \cos\left(f x + e\right)^{5} + f \cos\left(f x + e\right)^{4}\right)}}, -\frac{2 \, {\left(315 \, {\left(a^{2} c^{3} \cos\left(f x + e\right)^{5} + a^{2} c^{3} \cos\left(f x + e\right)^{4}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(35 \, a^{2} d^{3} + {\left(840 \, a^{2} c^{3} + 2709 \, a^{2} c^{2} d + 2070 \, a^{2} c d^{2} + 584 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{4} + {\left(105 \, a^{2} c^{3} + 882 \, a^{2} c^{2} d + 1035 \, a^{2} c d^{2} + 292 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(63 \, a^{2} c^{2} d + 180 \, a^{2} c d^{2} + 73 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 5 \, {\left(27 \, a^{2} c d^{2} + 26 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{315 \, {\left(f \cos\left(f x + e\right)^{5} + f \cos\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[1/315*(315*(a^2*c^3*cos(f*x + e)^5 + a^2*c^3*cos(f*x + e)^4)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(35*a^2*d^3 + (840*a^2*c^3 + 2709*a^2*c^2*d + 2070*a^2*c*d^2 + 584*a^2*d^3)*cos(f*x + e)^4 + (105*a^2*c^3 + 882*a^2*c^2*d + 1035*a^2*c*d^2 + 292*a^2*d^3)*cos(f*x + e)^3 + 3*(63*a^2*c^2*d + 180*a^2*c*d^2 + 73*a^2*d^3)*cos(f*x + e)^2 + 5*(27*a^2*c*d^2 + 26*a^2*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5 + f*cos(f*x + e)^4), -2/315*(315*(a^2*c^3*cos(f*x + e)^5 + a^2*c^3*cos(f*x + e)^4)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (35*a^2*d^3 + (840*a^2*c^3 + 2709*a^2*c^2*d + 2070*a^2*c*d^2 + 584*a^2*d^3)*cos(f*x + e)^4 + (105*a^2*c^3 + 882*a^2*c^2*d + 1035*a^2*c*d^2 + 292*a^2*d^3)*cos(f*x + e)^3 + 3*(63*a^2*c^2*d + 180*a^2*c*d^2 + 73*a^2*d^3)*cos(f*x + e)^2 + 5*(27*a^2*c*d^2 + 26*a^2*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^5 + f*cos(f*x + e)^4)]","A",0
161,1,500,0,0.538785," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{4} + a^{2} c^{2} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(15 \, a^{2} d^{2} + 2 \, {\left(140 \, a^{2} c^{2} + 301 \, a^{2} c d + 115 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(35 \, a^{2} c^{2} + 196 \, a^{2} c d + 115 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(7 \, a^{2} c d + 10 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}, -\frac{2 \, {\left(105 \, {\left(a^{2} c^{2} \cos\left(f x + e\right)^{4} + a^{2} c^{2} \cos\left(f x + e\right)^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(15 \, a^{2} d^{2} + 2 \, {\left(140 \, a^{2} c^{2} + 301 \, a^{2} c d + 115 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(35 \, a^{2} c^{2} + 196 \, a^{2} c d + 115 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(7 \, a^{2} c d + 10 \, a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{105 \, {\left(f \cos\left(f x + e\right)^{4} + f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/105*(105*(a^2*c^2*cos(f*x + e)^4 + a^2*c^2*cos(f*x + e)^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(15*a^2*d^2 + 2*(140*a^2*c^2 + 301*a^2*c*d + 115*a^2*d^2)*cos(f*x + e)^3 + (35*a^2*c^2 + 196*a^2*c*d + 115*a^2*d^2)*cos(f*x + e)^2 + 6*(7*a^2*c*d + 10*a^2*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3), -2/105*(105*(a^2*c^2*cos(f*x + e)^4 + a^2*c^2*cos(f*x + e)^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (15*a^2*d^2 + 2*(140*a^2*c^2 + 301*a^2*c*d + 115*a^2*d^2)*cos(f*x + e)^3 + (35*a^2*c^2 + 196*a^2*c*d + 115*a^2*d^2)*cos(f*x + e)^2 + 6*(7*a^2*c*d + 10*a^2*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^4 + f*cos(f*x + e)^3)]","A",0
162,1,390,0,0.460927," ","integrate((a+a*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left(3 \, a^{2} d + {\left(40 \, a^{2} c + 43 \, a^{2} d\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, a^{2} c + 14 \, a^{2} d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(15 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - {\left(3 \, a^{2} d + {\left(40 \, a^{2} c + 43 \, a^{2} d\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, a^{2} c + 14 \, a^{2} d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)\right)}}{15 \, {\left(f \cos\left(f x + e\right)^{3} + f \cos\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/15*(15*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*(3*a^2*d + (40*a^2*c + 43*a^2*d)*cos(f*x + e)^2 + (5*a^2*c + 14*a^2*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2), -2/15*(15*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e)^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - (3*a^2*d + (40*a^2*c + 43*a^2*d)*cos(f*x + e)^2 + (5*a^2*c + 14*a^2*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(f*cos(f*x + e)^3 + f*cos(f*x + e)^2)]","A",0
163,1,1140,0,5.105308," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + {\left(a^{2} d \cos\left(f x + e\right) + a^{2} d\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c d f \cos\left(f x + e\right) + c d f}, \frac{2 \, a^{2} c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 2 \, {\left(a^{2} d \cos\left(f x + e\right) + a^{2} d\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{c d f \cos\left(f x + e\right) + c d f}, \frac{2 \, a^{2} c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + 2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + {\left(a^{2} d \cos\left(f x + e\right) + a^{2} d\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{c d f \cos\left(f x + e\right) + c d f}, \frac{2 \, {\left(a^{2} c \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2} + {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - {\left(a^{2} d \cos\left(f x + e\right) + a^{2} d\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)\right)}}{c d f \cos\left(f x + e\right) + c d f}\right]"," ",0,"[(2*a^2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + (a^2*c^2 - 2*a^2*c*d + a^2*d^2 + (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + (a^2*d*cos(f*x + e) + a^2*d)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*d*f*cos(f*x + e) + c*d*f), (2*a^2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 2*(a^2*d*cos(f*x + e) + a^2*d)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (a^2*c^2 - 2*a^2*c*d + a^2*d^2 + (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/(c*d*f*cos(f*x + e) + c*d*f), (2*a^2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2 + (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + (a^2*d*cos(f*x + e) + a^2*d)*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(c*d*f*cos(f*x + e) + c*d*f), 2*(a^2*c*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + (a^2*c^2 - 2*a^2*c*d + a^2*d^2 + (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - (a^2*d*cos(f*x + e) + a^2*d)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(c*d*f*cos(f*x + e) + c*d*f)]","A",0
164,1,2031,0,23.656283," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} c^{3} - 2 \, a^{2} c^{2} d + a^{2} c d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a^{2} c^{3} d + 4 \, a^{2} c^{2} d^{2} - 3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(a^{2} c^{4} + 4 \, a^{2} c^{3} d - 3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{4} + 5 \, a^{2} c^{3} d + a^{2} c^{2} d^{2} - 5 \, a^{2} c d^{3} - 2 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - 2 \, {\left(a^{2} c d^{2} + a^{2} d^{3} + {\left(a^{2} c^{2} d + a^{2} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{2} d + 2 \, a^{2} c d^{2} + a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left({\left(c^{4} d + c^{3} d^{2}\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d^{2} + c^{2} d^{3}\right)} f\right)}}, -\frac{2 \, {\left(a^{2} c^{3} - 2 \, a^{2} c^{2} d + a^{2} c d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 4 \, {\left(a^{2} c d^{2} + a^{2} d^{3} + {\left(a^{2} c^{2} d + a^{2} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{2} d + 2 \, a^{2} c d^{2} + a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(a^{2} c^{3} d + 4 \, a^{2} c^{2} d^{2} - 3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(a^{2} c^{4} + 4 \, a^{2} c^{3} d - 3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{4} + 5 \, a^{2} c^{3} d + a^{2} c^{2} d^{2} - 5 \, a^{2} c d^{3} - 2 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right)}{2 \, {\left({\left(c^{4} d + c^{3} d^{2}\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d^{2} + c^{2} d^{3}\right)} f\right)}}, -\frac{{\left(a^{2} c^{3} - 2 \, a^{2} c^{2} d + a^{2} c d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a^{2} c^{3} d + 4 \, a^{2} c^{2} d^{2} - 3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(a^{2} c^{4} + 4 \, a^{2} c^{3} d - 3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{4} + 5 \, a^{2} c^{3} d + a^{2} c^{2} d^{2} - 5 \, a^{2} c d^{3} - 2 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - {\left(a^{2} c d^{2} + a^{2} d^{3} + {\left(a^{2} c^{2} d + a^{2} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{2} d + 2 \, a^{2} c d^{2} + a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{{\left(c^{4} d + c^{3} d^{2}\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d^{2} + c^{2} d^{3}\right)} f}, -\frac{{\left(a^{2} c^{3} - 2 \, a^{2} c^{2} d + a^{2} c d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a^{2} c^{3} d + 4 \, a^{2} c^{2} d^{2} - 3 \, a^{2} c d^{3} - 2 \, a^{2} d^{4} + {\left(a^{2} c^{4} + 4 \, a^{2} c^{3} d - 3 \, a^{2} c^{2} d^{2} - 2 \, a^{2} c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{4} + 5 \, a^{2} c^{3} d + a^{2} c^{2} d^{2} - 5 \, a^{2} c d^{3} - 2 \, a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + 2 \, {\left(a^{2} c d^{2} + a^{2} d^{3} + {\left(a^{2} c^{2} d + a^{2} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{2} d + 2 \, a^{2} c d^{2} + a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{{\left(c^{4} d + c^{3} d^{2}\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{4} d + 2 \, c^{3} d^{2} + c^{2} d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{3} d^{2} + c^{2} d^{3}\right)} f}\right]"," ",0,"[-1/2*(2*(a^2*c^3 - 2*a^2*c^2*d + a^2*c*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a^2*c^3*d + 4*a^2*c^2*d^2 - 3*a^2*c*d^3 - 2*a^2*d^4 + (a^2*c^4 + 4*a^2*c^3*d - 3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e)^2 + (a^2*c^4 + 5*a^2*c^3*d + a^2*c^2*d^2 - 5*a^2*c*d^3 - 2*a^2*d^4)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - 2*(a^2*c*d^2 + a^2*d^3 + (a^2*c^2*d + a^2*c*d^2)*cos(f*x + e)^2 + (a^2*c^2*d + 2*a^2*c*d^2 + a^2*d^3)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4*d + c^3*d^2)*f*cos(f*x + e)^2 + (c^4*d + 2*c^3*d^2 + c^2*d^3)*f*cos(f*x + e) + (c^3*d^2 + c^2*d^3)*f), -1/2*(2*(a^2*c^3 - 2*a^2*c^2*d + a^2*c*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 4*(a^2*c*d^2 + a^2*d^3 + (a^2*c^2*d + a^2*c*d^2)*cos(f*x + e)^2 + (a^2*c^2*d + 2*a^2*c*d^2 + a^2*d^3)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (a^2*c^3*d + 4*a^2*c^2*d^2 - 3*a^2*c*d^3 - 2*a^2*d^4 + (a^2*c^4 + 4*a^2*c^3*d - 3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e)^2 + (a^2*c^4 + 5*a^2*c^3*d + a^2*c^2*d^2 - 5*a^2*c*d^3 - 2*a^2*d^4)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)))/((c^4*d + c^3*d^2)*f*cos(f*x + e)^2 + (c^4*d + 2*c^3*d^2 + c^2*d^3)*f*cos(f*x + e) + (c^3*d^2 + c^2*d^3)*f), -((a^2*c^3 - 2*a^2*c^2*d + a^2*c*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a^2*c^3*d + 4*a^2*c^2*d^2 - 3*a^2*c*d^3 - 2*a^2*d^4 + (a^2*c^4 + 4*a^2*c^3*d - 3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e)^2 + (a^2*c^4 + 5*a^2*c^3*d + a^2*c^2*d^2 - 5*a^2*c*d^3 - 2*a^2*d^4)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - (a^2*c*d^2 + a^2*d^3 + (a^2*c^2*d + a^2*c*d^2)*cos(f*x + e)^2 + (a^2*c^2*d + 2*a^2*c*d^2 + a^2*d^3)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((c^4*d + c^3*d^2)*f*cos(f*x + e)^2 + (c^4*d + 2*c^3*d^2 + c^2*d^3)*f*cos(f*x + e) + (c^3*d^2 + c^2*d^3)*f), -((a^2*c^3 - 2*a^2*c^2*d + a^2*c*d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a^2*c^3*d + 4*a^2*c^2*d^2 - 3*a^2*c*d^3 - 2*a^2*d^4 + (a^2*c^4 + 4*a^2*c^3*d - 3*a^2*c^2*d^2 - 2*a^2*c*d^3)*cos(f*x + e)^2 + (a^2*c^4 + 5*a^2*c^3*d + a^2*c^2*d^2 - 5*a^2*c*d^3 - 2*a^2*d^4)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + 2*(a^2*c*d^2 + a^2*d^3 + (a^2*c^2*d + a^2*c*d^2)*cos(f*x + e)^2 + (a^2*c^2*d + 2*a^2*c*d^2 + a^2*d^3)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/((c^4*d + c^3*d^2)*f*cos(f*x + e)^2 + (c^4*d + 2*c^3*d^2 + c^2*d^3)*f*cos(f*x + e) + (c^3*d^2 + c^2*d^3)*f)]","A",0
165,1,3351,0,40.754723," ","integrate((a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} c^{4} d^{2} + 10 \, a^{2} c^{3} d^{3} - 15 \, a^{2} c^{2} d^{4} - 20 \, a^{2} c d^{5} - 8 \, a^{2} d^{6} + {\left(a^{2} c^{6} + 10 \, a^{2} c^{5} d - 15 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 8 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{6} + 12 \, a^{2} c^{5} d + 5 \, a^{2} c^{4} d^{2} - 50 \, a^{2} c^{3} d^{3} - 48 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{5} d + 21 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 55 \, a^{2} c^{2} d^{4} - 36 \, a^{2} c d^{5} - 8 \, a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - 8 \, {\left(a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4} + a^{2} d^{5} + {\left(a^{2} c^{4} d + 2 \, a^{2} c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{4} d + 4 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 4 \, a^{2} c d^{4} + a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + 2 \, {\left({\left(a^{2} c^{5} - 12 \, a^{2} c^{4} d + 5 \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} d + 10 \, a^{2} c^{3} d^{2} - 7 \, a^{2} c^{2} d^{3} - 4 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} d + 2 \, c^{6} d^{2} + c^{5} d^{3}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} d + 4 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 2 \, c^{4} d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 4 \, c^{4} d^{4} + c^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{4} d^{4} + c^{3} d^{5}\right)} f\right)}}, -\frac{16 \, {\left(a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4} + a^{2} d^{5} + {\left(a^{2} c^{4} d + 2 \, a^{2} c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{4} d + 4 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 4 \, a^{2} c d^{4} + a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left(a^{2} c^{4} d^{2} + 10 \, a^{2} c^{3} d^{3} - 15 \, a^{2} c^{2} d^{4} - 20 \, a^{2} c d^{5} - 8 \, a^{2} d^{6} + {\left(a^{2} c^{6} + 10 \, a^{2} c^{5} d - 15 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 8 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{6} + 12 \, a^{2} c^{5} d + 5 \, a^{2} c^{4} d^{2} - 50 \, a^{2} c^{3} d^{3} - 48 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{5} d + 21 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 55 \, a^{2} c^{2} d^{4} - 36 \, a^{2} c d^{5} - 8 \, a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \log\left(\frac{2 \, {\left(c d + d^{2}\right)} \sqrt{-\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c + 2 \, a d\right)} \cos\left(f x + e\right)^{2} - a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + 2 \, {\left({\left(a^{2} c^{5} - 12 \, a^{2} c^{4} d + 5 \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} d + 10 \, a^{2} c^{3} d^{2} - 7 \, a^{2} c^{2} d^{3} - 4 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left({\left(c^{7} d + 2 \, c^{6} d^{2} + c^{5} d^{3}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} d + 4 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 2 \, c^{4} d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 4 \, c^{4} d^{4} + c^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{4} d^{4} + c^{3} d^{5}\right)} f\right)}}, -\frac{{\left(a^{2} c^{4} d^{2} + 10 \, a^{2} c^{3} d^{3} - 15 \, a^{2} c^{2} d^{4} - 20 \, a^{2} c d^{5} - 8 \, a^{2} d^{6} + {\left(a^{2} c^{6} + 10 \, a^{2} c^{5} d - 15 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 8 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{6} + 12 \, a^{2} c^{5} d + 5 \, a^{2} c^{4} d^{2} - 50 \, a^{2} c^{3} d^{3} - 48 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{5} d + 21 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 55 \, a^{2} c^{2} d^{4} - 36 \, a^{2} c d^{5} - 8 \, a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) - 4 \, {\left(a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4} + a^{2} d^{5} + {\left(a^{2} c^{4} d + 2 \, a^{2} c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{4} d + 4 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 4 \, a^{2} c d^{4} + a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) + {\left({\left(a^{2} c^{5} - 12 \, a^{2} c^{4} d + 5 \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} d + 10 \, a^{2} c^{3} d^{2} - 7 \, a^{2} c^{2} d^{3} - 4 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} d + 2 \, c^{6} d^{2} + c^{5} d^{3}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} d + 4 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 2 \, c^{4} d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 4 \, c^{4} d^{4} + c^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{4} d^{4} + c^{3} d^{5}\right)} f\right)}}, -\frac{{\left(a^{2} c^{4} d^{2} + 10 \, a^{2} c^{3} d^{3} - 15 \, a^{2} c^{2} d^{4} - 20 \, a^{2} c d^{5} - 8 \, a^{2} d^{6} + {\left(a^{2} c^{6} + 10 \, a^{2} c^{5} d - 15 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 8 \, a^{2} c^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{6} + 12 \, a^{2} c^{5} d + 5 \, a^{2} c^{4} d^{2} - 50 \, a^{2} c^{3} d^{3} - 48 \, a^{2} c^{2} d^{4} - 16 \, a^{2} c d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{5} d + 21 \, a^{2} c^{4} d^{2} - 20 \, a^{2} c^{3} d^{3} - 55 \, a^{2} c^{2} d^{4} - 36 \, a^{2} c d^{5} - 8 \, a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{a}{c d + d^{2}}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right) + 8 \, {\left(a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4} + a^{2} d^{5} + {\left(a^{2} c^{4} d + 2 \, a^{2} c^{3} d^{2} + a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{4} d + 4 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 2 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, a^{2} c^{3} d^{2} + 5 \, a^{2} c^{2} d^{3} + 4 \, a^{2} c d^{4} + a^{2} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + {\left({\left(a^{2} c^{5} - 12 \, a^{2} c^{4} d + 5 \, a^{2} c^{3} d^{2} + 6 \, a^{2} c^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} d + 10 \, a^{2} c^{3} d^{2} - 7 \, a^{2} c^{2} d^{3} - 4 \, a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{7} d + 2 \, c^{6} d^{2} + c^{5} d^{3}\right)} f \cos\left(f x + e\right)^{3} + {\left(c^{7} d + 4 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 2 \, c^{4} d^{4}\right)} f \cos\left(f x + e\right)^{2} + {\left(2 \, c^{6} d^{2} + 5 \, c^{5} d^{3} + 4 \, c^{4} d^{4} + c^{3} d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{5} d^{3} + 2 \, c^{4} d^{4} + c^{3} d^{5}\right)} f\right)}}\right]"," ",0,"[-1/8*((a^2*c^4*d^2 + 10*a^2*c^3*d^3 - 15*a^2*c^2*d^4 - 20*a^2*c*d^5 - 8*a^2*d^6 + (a^2*c^6 + 10*a^2*c^5*d - 15*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 8*a^2*c^2*d^4)*cos(f*x + e)^3 + (a^2*c^6 + 12*a^2*c^5*d + 5*a^2*c^4*d^2 - 50*a^2*c^3*d^3 - 48*a^2*c^2*d^4 - 16*a^2*c*d^5)*cos(f*x + e)^2 + (2*a^2*c^5*d + 21*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 55*a^2*c^2*d^4 - 36*a^2*c*d^5 - 8*a^2*d^6)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - 8*(a^2*c^2*d^3 + 2*a^2*c*d^4 + a^2*d^5 + (a^2*c^4*d + 2*a^2*c^3*d^2 + a^2*c^2*d^3)*cos(f*x + e)^3 + (a^2*c^4*d + 4*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 2*a^2*c*d^4)*cos(f*x + e)^2 + (2*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 4*a^2*c*d^4 + a^2*d^5)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + 2*((a^2*c^5 - 12*a^2*c^4*d + 5*a^2*c^3*d^2 + 6*a^2*c^2*d^3)*cos(f*x + e)^2 - (a^2*c^4*d + 10*a^2*c^3*d^2 - 7*a^2*c^2*d^3 - 4*a^2*c*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7*d + 2*c^6*d^2 + c^5*d^3)*f*cos(f*x + e)^3 + (c^7*d + 4*c^6*d^2 + 5*c^5*d^3 + 2*c^4*d^4)*f*cos(f*x + e)^2 + (2*c^6*d^2 + 5*c^5*d^3 + 4*c^4*d^4 + c^3*d^5)*f*cos(f*x + e) + (c^5*d^3 + 2*c^4*d^4 + c^3*d^5)*f), -1/8*(16*(a^2*c^2*d^3 + 2*a^2*c*d^4 + a^2*d^5 + (a^2*c^4*d + 2*a^2*c^3*d^2 + a^2*c^2*d^3)*cos(f*x + e)^3 + (a^2*c^4*d + 4*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 2*a^2*c*d^4)*cos(f*x + e)^2 + (2*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 4*a^2*c*d^4 + a^2*d^5)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + (a^2*c^4*d^2 + 10*a^2*c^3*d^3 - 15*a^2*c^2*d^4 - 20*a^2*c*d^5 - 8*a^2*d^6 + (a^2*c^6 + 10*a^2*c^5*d - 15*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 8*a^2*c^2*d^4)*cos(f*x + e)^3 + (a^2*c^6 + 12*a^2*c^5*d + 5*a^2*c^4*d^2 - 50*a^2*c^3*d^3 - 48*a^2*c^2*d^4 - 16*a^2*c*d^5)*cos(f*x + e)^2 + (2*a^2*c^5*d + 21*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 55*a^2*c^2*d^4 - 36*a^2*c*d^5 - 8*a^2*d^6)*cos(f*x + e))*sqrt(-a/(c*d + d^2))*log((2*(c*d + d^2)*sqrt(-a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c + 2*a*d)*cos(f*x + e)^2 - a*d + (a*c + a*d)*cos(f*x + e))/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + 2*((a^2*c^5 - 12*a^2*c^4*d + 5*a^2*c^3*d^2 + 6*a^2*c^2*d^3)*cos(f*x + e)^2 - (a^2*c^4*d + 10*a^2*c^3*d^2 - 7*a^2*c^2*d^3 - 4*a^2*c*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7*d + 2*c^6*d^2 + c^5*d^3)*f*cos(f*x + e)^3 + (c^7*d + 4*c^6*d^2 + 5*c^5*d^3 + 2*c^4*d^4)*f*cos(f*x + e)^2 + (2*c^6*d^2 + 5*c^5*d^3 + 4*c^4*d^4 + c^3*d^5)*f*cos(f*x + e) + (c^5*d^3 + 2*c^4*d^4 + c^3*d^5)*f), -1/4*((a^2*c^4*d^2 + 10*a^2*c^3*d^3 - 15*a^2*c^2*d^4 - 20*a^2*c*d^5 - 8*a^2*d^6 + (a^2*c^6 + 10*a^2*c^5*d - 15*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 8*a^2*c^2*d^4)*cos(f*x + e)^3 + (a^2*c^6 + 12*a^2*c^5*d + 5*a^2*c^4*d^2 - 50*a^2*c^3*d^3 - 48*a^2*c^2*d^4 - 16*a^2*c*d^5)*cos(f*x + e)^2 + (2*a^2*c^5*d + 21*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 55*a^2*c^2*d^4 - 36*a^2*c*d^5 - 8*a^2*d^6)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) - 4*(a^2*c^2*d^3 + 2*a^2*c*d^4 + a^2*d^5 + (a^2*c^4*d + 2*a^2*c^3*d^2 + a^2*c^2*d^3)*cos(f*x + e)^3 + (a^2*c^4*d + 4*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 2*a^2*c*d^4)*cos(f*x + e)^2 + (2*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 4*a^2*c*d^4 + a^2*d^5)*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 - 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) + ((a^2*c^5 - 12*a^2*c^4*d + 5*a^2*c^3*d^2 + 6*a^2*c^2*d^3)*cos(f*x + e)^2 - (a^2*c^4*d + 10*a^2*c^3*d^2 - 7*a^2*c^2*d^3 - 4*a^2*c*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7*d + 2*c^6*d^2 + c^5*d^3)*f*cos(f*x + e)^3 + (c^7*d + 4*c^6*d^2 + 5*c^5*d^3 + 2*c^4*d^4)*f*cos(f*x + e)^2 + (2*c^6*d^2 + 5*c^5*d^3 + 4*c^4*d^4 + c^3*d^5)*f*cos(f*x + e) + (c^5*d^3 + 2*c^4*d^4 + c^3*d^5)*f), -1/4*((a^2*c^4*d^2 + 10*a^2*c^3*d^3 - 15*a^2*c^2*d^4 - 20*a^2*c*d^5 - 8*a^2*d^6 + (a^2*c^6 + 10*a^2*c^5*d - 15*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 8*a^2*c^2*d^4)*cos(f*x + e)^3 + (a^2*c^6 + 12*a^2*c^5*d + 5*a^2*c^4*d^2 - 50*a^2*c^3*d^3 - 48*a^2*c^2*d^4 - 16*a^2*c*d^5)*cos(f*x + e)^2 + (2*a^2*c^5*d + 21*a^2*c^4*d^2 - 20*a^2*c^3*d^3 - 55*a^2*c^2*d^4 - 36*a^2*c*d^5 - 8*a^2*d^6)*cos(f*x + e))*sqrt(a/(c*d + d^2))*arctan((c + d)*sqrt(a/(c*d + d^2))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))) + 8*(a^2*c^2*d^3 + 2*a^2*c*d^4 + a^2*d^5 + (a^2*c^4*d + 2*a^2*c^3*d^2 + a^2*c^2*d^3)*cos(f*x + e)^3 + (a^2*c^4*d + 4*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 2*a^2*c*d^4)*cos(f*x + e)^2 + (2*a^2*c^3*d^2 + 5*a^2*c^2*d^3 + 4*a^2*c*d^4 + a^2*d^5)*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + ((a^2*c^5 - 12*a^2*c^4*d + 5*a^2*c^3*d^2 + 6*a^2*c^2*d^3)*cos(f*x + e)^2 - (a^2*c^4*d + 10*a^2*c^3*d^2 - 7*a^2*c^2*d^3 - 4*a^2*c*d^4)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/((c^7*d + 2*c^6*d^2 + c^5*d^3)*f*cos(f*x + e)^3 + (c^7*d + 4*c^6*d^2 + 5*c^5*d^3 + 2*c^4*d^4)*f*cos(f*x + e)^2 + (2*c^6*d^2 + 5*c^5*d^3 + 4*c^4*d^4 + c^3*d^5)*f*cos(f*x + e) + (c^5*d^3 + 2*c^4*d^4 + c^3*d^5)*f)]","A",0
166,1,619,0,13.682258," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{2} {\left({\left(a c^{3} - 3 \, a c^{2} d + 3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 3 \, a c^{2} d + 3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 6 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left(d^{3} + {\left(9 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{6 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}, -\frac{6 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + c^{3} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(d^{3} + {\left(9 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - \frac{3 \, \sqrt{2} {\left({\left(a c^{3} - 3 \, a c^{2} d + 3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a c^{3} - 3 \, a c^{2} d + 3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{3 \, {\left(a f \cos\left(f x + e\right)^{2} + a f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[-1/6*(3*sqrt(2)*((a*c^3 - 3*a*c^2*d + 3*a*c*d^2 - a*d^3)*cos(f*x + e)^2 + (a*c^3 - 3*a*c^2*d + 3*a*c*d^2 - a*d^3)*cos(f*x + e))*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 6*(c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*(d^3 + (9*c*d^2 - d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e)), -1/3*(6*(c^3*cos(f*x + e)^2 + c^3*cos(f*x + e))*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(d^3 + (9*c*d^2 - d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 3*sqrt(2)*((a*c^3 - 3*a*c^2*d + 3*a*c*d^2 - a*d^3)*cos(f*x + e)^2 + (a*c^3 - 3*a*c^2*d + 3*a*c*d^2 - a*d^3)*cos(f*x + e))*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f*cos(f*x + e)^2 + a*f*cos(f*x + e))]","A",0
167,1,481,0,3.346471," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, d^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) + \sqrt{2} {\left(a c^{2} - 2 \, a c d + a d^{2} + {\left(a c^{2} - 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{1}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, \cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) - 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 2 \, {\left(c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left(a f \cos\left(f x + e\right) + a f\right)}}, \frac{2 \, d^{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right) - 2 \, {\left(c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + \frac{\sqrt{2} {\left(a c^{2} - 2 \, a c d + a d^{2} + {\left(a c^{2} - 2 \, a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{a f \cos\left(f x + e\right) + a f}\right]"," ",0,"[1/2*(4*d^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) + sqrt(2)*(a*c^2 - 2*a*c*d + a*d^2 + (a*c^2 - 2*a*c*d + a*d^2)*cos(f*x + e))*sqrt(-1/a)*log((2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) + 3*cos(f*x + e)^2 + 2*cos(f*x + e) - 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 2*(c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a*f*cos(f*x + e) + a*f), (2*d^2*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e) - 2*(c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + sqrt(2)*(a*c^2 - 2*a*c*d + a*d^2 + (a*c^2 - 2*a*c*d + a*d^2)*cos(f*x + e))*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f*cos(f*x + e) + a*f)]","A",0
168,1,314,0,1.226042," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(a c - a d\right)} \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{-a} c \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, a f}, -\frac{2 \, \sqrt{a} c \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - \frac{\sqrt{2} {\left(a c - a d\right)} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{\sqrt{a}}}{a f}\right]"," ",0,"[-1/2*(sqrt(2)*(a*c - a*d)*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(-a)*c*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a*f), -(2*sqrt(a)*c*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - sqrt(2)*(a*c - a*d)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e)))/sqrt(a))/(a*f)]","A",0
169,1,1050,0,18.622679," ","integrate(1/(c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} a c \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, a d \sqrt{-\frac{d}{a c + a d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) - d}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) + 2 \, \sqrt{-a} {\left(c - d\right)} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left(a c^{2} - a c d\right)} f}, -\frac{\sqrt{2} a c \sqrt{-\frac{1}{a}} \log\left(-\frac{2 \, \sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, \cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 4 \, a d \sqrt{\frac{d}{a c + a d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{d \sin\left(f x + e\right)}\right) + 2 \, \sqrt{-a} {\left(c - d\right)} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{2 \, {\left(a c^{2} - a c d\right)} f}, -\frac{a d \sqrt{-\frac{d}{a c + a d}} \log\left(\frac{2 \, {\left(c + d\right)} \sqrt{-\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c + 2 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) - d}{c \cos\left(f x + e\right)^{2} + {\left(c + d\right)} \cos\left(f x + e\right) + d}\right) - \sqrt{2} \sqrt{a} c \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 2 \, \sqrt{a} {\left(c - d\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{{\left(a c^{2} - a c d\right)} f}, -\frac{2 \, a d \sqrt{\frac{d}{a c + a d}} \arctan\left(\frac{{\left(c + d\right)} \sqrt{\frac{d}{a c + a d}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{d \sin\left(f x + e\right)}\right) - \sqrt{2} \sqrt{a} c \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 2 \, \sqrt{a} {\left(c - d\right)} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{{\left(a c^{2} - a c d\right)} f}\right]"," ",0,"[-1/2*(sqrt(2)*a*c*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*a*d*sqrt(-d/(a*c + a*d))*log((2*(c + d)*sqrt(-d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (c + 2*d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) - d)/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) + 2*sqrt(-a)*(c - d)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((a*c^2 - a*c*d)*f), -1/2*(sqrt(2)*a*c*sqrt(-1/a)*log(-(2*sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt(-1/a)*cos(f*x + e)*sin(f*x + e) - 3*cos(f*x + e)^2 - 2*cos(f*x + e) + 1)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 4*a*d*sqrt(d/(a*c + a*d))*arctan((c + d)*sqrt(d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(d*sin(f*x + e))) + 2*sqrt(-a)*(c - d)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/((a*c^2 - a*c*d)*f), -(a*d*sqrt(-d/(a*c + a*d))*log((2*(c + d)*sqrt(-d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (c + 2*d)*cos(f*x + e)^2 + (c + d)*cos(f*x + e) - d)/(c*cos(f*x + e)^2 + (c + d)*cos(f*x + e) + d)) - sqrt(2)*sqrt(a)*c*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 2*sqrt(a)*(c - d)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/((a*c^2 - a*c*d)*f), -(2*a*d*sqrt(d/(a*c + a*d))*arctan((c + d)*sqrt(d/(a*c + a*d))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(d*sin(f*x + e))) - sqrt(2)*sqrt(a)*c*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 2*sqrt(a)*(c - d)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/((a*c^2 - a*c*d)*f)]","A",0
170,-1,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,1,701,0,34.523294," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3} + {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(-\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left(4 \, d^{3} - {\left(c^{3} - 3 \, c^{2} d + 3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{8 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, \frac{\sqrt{2} {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3} + {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, c^{3} - 3 \, c^{2} d - 9 \, c d^{2} + 7 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 8 \, {\left(c^{3} \cos\left(f x + e\right)^{2} + 2 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 2 \, {\left(4 \, d^{3} - {\left(c^{3} - 3 \, c^{2} d + 3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{4 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[-1/8*(sqrt(2)*(5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3 + (5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3)*cos(f*x + e)^2 + 2*(5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3)*cos(f*x + e))*sqrt(-a)*log(-(2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 3*a*cos(f*x + e)^2 - 2*a*cos(f*x + e) + a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*(4*d^3 - (c^3 - 3*c^2*d + 3*c*d^2 - 5*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), 1/4*(sqrt(2)*(5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3 + (5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3)*cos(f*x + e)^2 + 2*(5*c^3 - 3*c^2*d - 9*c*d^2 + 7*d^3)*cos(f*x + e))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 8*(c^3*cos(f*x + e)^2 + 2*c^3*cos(f*x + e) + c^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 2*(4*d^3 - (c^3 - 3*c^2*d + 3*c*d^2 - 5*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","A",0
173,1,620,0,12.896447," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(c^{2} - 2 \, c d + d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - \sqrt{2} {\left({\left(5 \, c^{2} - 2 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 5 \, c^{2} - 2 \, c d - 3 \, d^{2} + 2 \, {\left(5 \, c^{2} - 2 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{8 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, -\frac{2 \, {\left(c^{2} - 2 \, c d + d^{2}\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - \sqrt{2} {\left({\left(5 \, c^{2} - 2 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 5 \, c^{2} - 2 \, c d - 3 \, d^{2} + 2 \, {\left(5 \, c^{2} - 2 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 8 \, {\left(c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{4 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[-1/8*(4*(c^2 - 2*c*d + d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - sqrt(2)*((5*c^2 - 2*c*d - 3*d^2)*cos(f*x + e)^2 + 5*c^2 - 2*c*d - 3*d^2 + 2*(5*c^2 - 2*c*d - 3*d^2)*cos(f*x + e))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -1/4*(2*(c^2 - 2*c*d + d^2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - sqrt(2)*((5*c^2 - 2*c*d - 3*d^2)*cos(f*x + e)^2 + 5*c^2 - 2*c*d - 3*d^2 + 2*(5*c^2 - 2*c*d - 3*d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 8*(c^2*cos(f*x + e)^2 + 2*c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","A",0
174,1,548,0,3.182475," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - \sqrt{2} {\left({\left(5 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, c - d\right)} \cos\left(f x + e\right) + 5 \, c - d\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 8 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right)}{8 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}, -\frac{2 \, {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - \sqrt{2} {\left({\left(5 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, c - d\right)} \cos\left(f x + e\right) + 5 \, c - d\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) + 8 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right)}{4 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} + 2 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)}}\right]"," ",0,"[-1/8*(4*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - sqrt(2)*((5*c - d)*cos(f*x + e)^2 + 2*(5*c - d)*cos(f*x + e) + 5*c - d)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 8*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f), -1/4*(2*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - sqrt(2)*((5*c - d)*cos(f*x + e)^2 + 2*(5*c - d)*cos(f*x + e) + 5*c - d)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) + 8*(c*cos(f*x + e)^2 + 2*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))))/(a^2*f*cos(f*x + e)^2 + 2*a^2*f*cos(f*x + e) + a^2*f)]","B",0
175,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,1,880,0,56.606597," ","integrate((c+d*sec(f*x+e))^3/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)^{3} + 43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3} + 3 \, {\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 64 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left(3 \, {\left(5 \, c^{3} - 7 \, c^{2} d - c d^{2} + 3 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{\sqrt{2} {\left({\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)^{3} + 43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3} + 3 \, {\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(43 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} - 19 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 64 \, {\left(c^{3} \cos\left(f x + e\right)^{3} + 3 \, c^{3} \cos\left(f x + e\right)^{2} + 3 \, c^{3} \cos\left(f x + e\right) + c^{3}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left(3 \, {\left(5 \, c^{3} - 7 \, c^{2} d - c d^{2} + 3 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c^{3} - 9 \, c^{2} d - 15 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e)^3 + 43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3 + 3*(43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e)^2 + 3*(43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 64*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*(3*(5*c^3 - 7*c^2*d - c*d^2 + 3*d^3)*cos(f*x + e)^2 + (11*c^3 - 9*c^2*d - 15*c*d^2 + 13*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/32*(sqrt(2)*((43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e)^3 + 43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3 + 3*(43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e)^2 + 3*(43*c^3 - 9*c^2*d - 15*c*d^2 - 19*d^3)*cos(f*x + e))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 64*(c^3*cos(f*x + e)^3 + 3*c^3*cos(f*x + e)^2 + 3*c^3*cos(f*x + e) + c^3)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*(3*(5*c^3 - 7*c^2*d - c*d^2 + 3*d^3)*cos(f*x + e)^2 + (11*c^3 - 9*c^2*d - 15*c*d^2 + 13*d^3)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","A",0
179,1,782,0,23.943625," ","integrate((c+d*sec(f*x+e))^2/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 43 \, c^{2} - 6 \, c d - 5 \, d^{2} + 3 \, {\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 64 \, {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left({\left(15 \, c^{2} - 14 \, c d - d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{\sqrt{2} {\left({\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 43 \, c^{2} - 6 \, c d - 5 \, d^{2} + 3 \, {\left(43 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 64 \, {\left(c^{2} \cos\left(f x + e\right)^{3} + 3 \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) + c^{2}\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left({\left(15 \, c^{2} - 14 \, c d - d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c^{2} - 6 \, c d - 5 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e)^3 + 3*(43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e)^2 + 43*c^2 - 6*c*d - 5*d^2 + 3*(43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e))*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 64*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*((15*c^2 - 14*c*d - d^2)*cos(f*x + e)^2 + (11*c^2 - 6*c*d - 5*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/32*(sqrt(2)*((43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e)^3 + 3*(43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e)^2 + 43*c^2 - 6*c*d - 5*d^2 + 3*(43*c^2 - 6*c*d - 5*d^2)*cos(f*x + e))*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 64*(c^2*cos(f*x + e)^3 + 3*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e) + c^2)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*((15*c^2 - 14*c*d - d^2)*cos(f*x + e)^2 + (11*c^2 - 6*c*d - 5*d^2)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","A",0
180,1,670,0,6.363122," ","integrate((c+d*sec(f*x+e))/(a+a*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right) + 43 \, c - 3 \, d\right)} \sqrt{-a} \log\left(\frac{2 \, \sqrt{2} \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, a \cos\left(f x + e\right)^{2} + 2 \, a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 64 \, {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{-a} \log\left(\frac{2 \, a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + a \cos\left(f x + e\right) - a}{\cos\left(f x + e\right) + 1}\right) - 4 \, {\left({\left(15 \, c - 7 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c - 3 \, d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}, \frac{\sqrt{2} {\left({\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(43 \, c - 3 \, d\right)} \cos\left(f x + e\right) + 43 \, c - 3 \, d\right)} \sqrt{a} \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 64 \, {\left(c \cos\left(f x + e\right)^{3} + 3 \, c \cos\left(f x + e\right)^{2} + 3 \, c \cos\left(f x + e\right) + c\right)} \sqrt{a} \arctan\left(\frac{\sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a} \sin\left(f x + e\right)}\right) - 2 \, {\left({\left(15 \, c - 7 \, d\right)} \cos\left(f x + e\right)^{2} + {\left(11 \, c - 3 \, d\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sin\left(f x + e\right)}{32 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} + 3 \, a^{3} f \cos\left(f x + e\right) + a^{3} f\right)}}\right]"," ",0,"[1/64*(sqrt(2)*((43*c - 3*d)*cos(f*x + e)^3 + 3*(43*c - 3*d)*cos(f*x + e)^2 + 3*(43*c - 3*d)*cos(f*x + e) + 43*c - 3*d)*sqrt(-a)*log((2*sqrt(2)*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + 3*a*cos(f*x + e)^2 + 2*a*cos(f*x + e) - a)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 64*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(-a)*log((2*a*cos(f*x + e)^2 + 2*sqrt(-a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + a*cos(f*x + e) - a)/(cos(f*x + e) + 1)) - 4*((15*c - 7*d)*cos(f*x + e)^2 + (11*c - 3*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f), 1/32*(sqrt(2)*((43*c - 3*d)*cos(f*x + e)^3 + 3*(43*c - 3*d)*cos(f*x + e)^2 + 3*(43*c - 3*d)*cos(f*x + e) + 43*c - 3*d)*sqrt(a)*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 64*(c*cos(f*x + e)^3 + 3*c*cos(f*x + e)^2 + 3*c*cos(f*x + e) + c)*sqrt(a)*arctan(sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*cos(f*x + e)/(sqrt(a)*sin(f*x + e))) - 2*((15*c - 7*d)*cos(f*x + e)^2 + (11*c - 3*d)*cos(f*x + e))*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 + 3*a^3*f*cos(f*x + e) + a^3*f)]","B",0
181,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(1/(a+a*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,1,806,0,1.469027," ","integrate((c+d*sec(f*x+e))^(1/2)*(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a d} \log\left(\frac{2 \, \sqrt{a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c - a d\right)} \cos\left(f x + e\right)^{2} + 2 \, a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)}\right) + \sqrt{-a c} \log\left(\frac{2 \, a c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - a c + a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{f}, -\frac{2 \, \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a c \sin\left(f x + e\right)}\right) - \sqrt{a d} \log\left(\frac{2 \, \sqrt{a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(a c - a d\right)} \cos\left(f x + e\right)^{2} + 2 \, a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} + \cos\left(f x + e\right)}\right)}{f}, -\frac{2 \, \sqrt{-a d} \arctan\left(\frac{\sqrt{-a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right) - \sqrt{-a c} \log\left(\frac{2 \, a c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - a c + a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{f}, -\frac{2 \, {\left(\sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a c \sin\left(f x + e\right)}\right) + \sqrt{-a d} \arctan\left(\frac{\sqrt{-a d} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a d \sin\left(f x + e\right)}\right)\right)}}{f}\right]"," ",0,"[(sqrt(a*d)*log((2*sqrt(a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c - a*d)*cos(f*x + e)^2 + 2*a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e)^2 + cos(f*x + e))) + sqrt(-a*c)*log((2*a*c*cos(f*x + e)^2 - 2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - a*c + a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1)))/f, -(2*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*c*sin(f*x + e))) - sqrt(a*d)*log((2*sqrt(a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (a*c - a*d)*cos(f*x + e)^2 + 2*a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e)^2 + cos(f*x + e))))/f, -(2*sqrt(-a*d)*arctan(sqrt(-a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))) - sqrt(-a*c)*log((2*a*c*cos(f*x + e)^2 - 2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - a*c + a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1)))/f, -2*(sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*c*sin(f*x + e))) + sqrt(-a*d)*arctan(sqrt(-a*d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*d*sin(f*x + e))))/f]","A",0
185,1,206,0,0.591002," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{c}} \log\left(-\frac{2 \, c \sqrt{-\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c \cos\left(f x + e\right)^{2} + a c - a d - {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{f}, -\frac{2 \, \sqrt{\frac{a}{c}} \arctan\left(\frac{\sqrt{\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right)}{f}\right]"," ",0,"[sqrt(-a/c)*log(-(2*c*sqrt(-a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 2*a*c*cos(f*x + e)^2 + a*c - a*d - (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1))/f, -2*sqrt(a/c)*arctan(sqrt(a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e)))/f]","A",0
186,1,517,0,0.600543," ","integrate((a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[-\frac{2 \, d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{a}{c}} \log\left(-\frac{2 \, c \sqrt{-\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c \cos\left(f x + e\right)^{2} + a c - a d - {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{{\left(c^{3} + c^{2} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{3} + 2 \, c^{2} d + c d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d + c d^{2}\right)} f}, -\frac{2 \, {\left(d \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right)^{2} + c d + d^{2} + {\left(c^{2} + 2 \, c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{\frac{a}{c}} \arctan\left(\frac{\sqrt{\frac{a}{c}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a \sin\left(f x + e\right)}\right)\right)}}{{\left(c^{3} + c^{2} d\right)} f \cos\left(f x + e\right)^{2} + {\left(c^{3} + 2 \, c^{2} d + c d^{2}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d + c d^{2}\right)} f}\right]"," ",0,"[-(2*d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - ((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(-a/c)*log(-(2*c*sqrt(-a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 2*a*c*cos(f*x + e)^2 + a*c - a*d - (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1)))/((c^3 + c^2*d)*f*cos(f*x + e)^2 + (c^3 + 2*c^2*d + c*d^2)*f*cos(f*x + e) + (c^2*d + c*d^2)*f), -2*(d*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + ((c^2 + c*d)*cos(f*x + e)^2 + c*d + d^2 + (c^2 + 2*c*d + d^2)*cos(f*x + e))*sqrt(a/c)*arctan(sqrt(a/c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*sin(f*x + e))))/((c^3 + c^2*d)*f*cos(f*x + e)^2 + (c^3 + 2*c^2*d + c*d^2)*f*cos(f*x + e) + (c^2*d + c*d^2)*f)]","B",0
187,1,883,0,1.003824," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+a*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{-\frac{c - d}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) + 2 \, \sqrt{-\frac{c}{a}} \log\left(-\frac{2 \, \sqrt{-\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c \cos\left(f x + e\right)^{2} - {\left(c + d\right)} \cos\left(f x + e\right) + c - d}{\cos\left(f x + e\right) + 1}\right)}{2 \, f}, \frac{\sqrt{2} \sqrt{-\frac{c - d}{a}} \log\left(\frac{2 \, \sqrt{2} \sqrt{-\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 4 \, \sqrt{\frac{c}{a}} \arctan\left(\frac{\sqrt{\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{c \sin\left(f x + e\right)}\right)}{2 \, f}, -\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) - \sqrt{-\frac{c}{a}} \log\left(-\frac{2 \, \sqrt{-\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c \cos\left(f x + e\right)^{2} - {\left(c + d\right)} \cos\left(f x + e\right) + c - d}{\cos\left(f x + e\right) + 1}\right)}{f}, -\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \arctan\left(-\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{{\left(c - d\right)} \sin\left(f x + e\right)}\right) + 2 \, \sqrt{\frac{c}{a}} \arctan\left(\frac{\sqrt{\frac{c}{a}} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{c \sin\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*(sqrt(2)*sqrt(-(c - d)/a)*log((2*sqrt(2)*sqrt(-(c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) + 2*sqrt(-c/a)*log(-(2*sqrt(-c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 2*c*cos(f*x + e)^2 - (c + d)*cos(f*x + e) + c - d)/(cos(f*x + e) + 1)))/f, 1/2*(sqrt(2)*sqrt(-(c - d)/a)*log((2*sqrt(2)*sqrt(-(c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 4*sqrt(c/a)*arctan(sqrt(c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(c*sin(f*x + e))))/f, -(sqrt(2)*sqrt((c - d)/a)*arctan(-sqrt(2)*sqrt((c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/((c - d)*sin(f*x + e))) - sqrt(-c/a)*log(-(2*sqrt(-c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - 2*c*cos(f*x + e)^2 - (c + d)*cos(f*x + e) + c - d)/(cos(f*x + e) + 1)))/f, -(sqrt(2)*sqrt((c - d)/a)*arctan(-sqrt(2)*sqrt((c - d)/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/((c - d)*sin(f*x + e))) + 2*sqrt(c/a)*arctan(sqrt(c/a)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(c*sin(f*x + e))))/f]","A",0
188,1,913,0,1.688228," ","integrate(1/(a+a*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a c \sqrt{-\frac{1}{a c - a d}} \log\left(\frac{2 \, \sqrt{2} {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a c - a d}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 2 \, \sqrt{-a c} \log\left(\frac{2 \, a c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - a c + a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{2 \, a c f}, \frac{\sqrt{2} a c \sqrt{-\frac{1}{a c - a d}} \log\left(\frac{2 \, \sqrt{2} {\left(c - d\right)} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \sqrt{-\frac{1}{a c - a d}} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(3 \, c - d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c + d\right)} \cos\left(f x + e\right) - c + 3 \, d}{\cos\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1}\right) - 4 \, \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a c \sin\left(f x + e\right)}\right)}{2 \, a c f}, \frac{\frac{\sqrt{2} a c \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a c - a d} \sin\left(f x + e\right)}\right)}{\sqrt{a c - a d}} - \sqrt{-a c} \log\left(\frac{2 \, a c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{-a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right) \sin\left(f x + e\right) - a c + a d + {\left(a c + a d\right)} \cos\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{a c f}, \frac{\frac{\sqrt{2} a c \arctan\left(\frac{\sqrt{2} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{\sqrt{a c - a d} \sin\left(f x + e\right)}\right)}{\sqrt{a c - a d}} - 2 \, \sqrt{a c} \arctan\left(\frac{\sqrt{a c} \sqrt{\frac{a \cos\left(f x + e\right) + a}{\cos\left(f x + e\right)}} \sqrt{\frac{c \cos\left(f x + e\right) + d}{\cos\left(f x + e\right)}} \cos\left(f x + e\right)}{a c \sin\left(f x + e\right)}\right)}{a c f}\right]"," ",0,"[1/2*(sqrt(2)*a*c*sqrt(-1/(a*c - a*d))*log((2*sqrt(2)*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sqrt(-1/(a*c - a*d))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 2*sqrt(-a*c)*log((2*a*c*cos(f*x + e)^2 + 2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - a*c + a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1)))/(a*c*f), 1/2*(sqrt(2)*a*c*sqrt(-1/(a*c - a*d))*log((2*sqrt(2)*(c - d)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*sqrt(-1/(a*c - a*d))*cos(f*x + e)*sin(f*x + e) + (3*c - d)*cos(f*x + e)^2 + 2*(c + d)*cos(f*x + e) - c + 3*d)/(cos(f*x + e)^2 + 2*cos(f*x + e) + 1)) - 4*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*c*sin(f*x + e))))/(a*c*f), (sqrt(2)*a*c*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(sqrt(a*c - a*d)*sin(f*x + e)))/sqrt(a*c - a*d) - sqrt(-a*c)*log((2*a*c*cos(f*x + e)^2 + 2*sqrt(-a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)*sin(f*x + e) - a*c + a*d + (a*c + a*d)*cos(f*x + e))/(cos(f*x + e) + 1)))/(a*c*f), (sqrt(2)*a*c*arctan(sqrt(2)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(sqrt(a*c - a*d)*sin(f*x + e)))/sqrt(a*c - a*d) - 2*sqrt(a*c)*arctan(sqrt(a*c)*sqrt((a*cos(f*x + e) + a)/cos(f*x + e))*sqrt((c*cos(f*x + e) + d)/cos(f*x + e))*cos(f*x + e)/(a*c*sin(f*x + e))))/(a*c*f)]","A",0
189,1,250,0,0.476247," ","integrate((a+b*sec(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a c^{2} - a d^{2}\right)} f x - {\left(b c - a d\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right)}{2 \, {\left(c^{3} - c d^{2}\right)} f}, \frac{{\left(a c^{2} - a d^{2}\right)} f x + {\left(b c - a d\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right)}{{\left(c^{3} - c d^{2}\right)} f}\right]"," ",0,"[1/2*(2*(a*c^2 - a*d^2)*f*x - (b*c - a*d)*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)))/((c^3 - c*d^2)*f), ((a*c^2 - a*d^2)*f*x + (b*c - a*d)*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))))/((c^3 - c*d^2)*f)]","A",0
190,1,561,0,0.495304," ","integrate((a+b*sec(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a c^{5} - 2 \, a c^{3} d^{2} + a c d^{4}\right)} f x \cos\left(f x + e\right) + 2 \, {\left(a c^{4} d - 2 \, a c^{2} d^{3} + a d^{5}\right)} f x - {\left(b c^{3} d - 2 \, a c^{2} d^{2} + a d^{4} + {\left(b c^{4} - 2 \, a c^{3} d + a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(b c^{4} d - a c^{3} d^{2} - b c^{2} d^{3} + a c d^{4}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{7} - 2 \, c^{5} d^{2} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d - 2 \, c^{4} d^{3} + c^{2} d^{5}\right)} f\right)}}, \frac{{\left(a c^{5} - 2 \, a c^{3} d^{2} + a c d^{4}\right)} f x \cos\left(f x + e\right) + {\left(a c^{4} d - 2 \, a c^{2} d^{3} + a d^{5}\right)} f x + {\left(b c^{3} d - 2 \, a c^{2} d^{2} + a d^{4} + {\left(b c^{4} - 2 \, a c^{3} d + a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(b c^{4} d - a c^{3} d^{2} - b c^{2} d^{3} + a c d^{4}\right)} \sin\left(f x + e\right)}{{\left(c^{7} - 2 \, c^{5} d^{2} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d - 2 \, c^{4} d^{3} + c^{2} d^{5}\right)} f}\right]"," ",0,"[1/2*(2*(a*c^5 - 2*a*c^3*d^2 + a*c*d^4)*f*x*cos(f*x + e) + 2*(a*c^4*d - 2*a*c^2*d^3 + a*d^5)*f*x - (b*c^3*d - 2*a*c^2*d^2 + a*d^4 + (b*c^4 - 2*a*c^3*d + a*c*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(b*c^4*d - a*c^3*d^2 - b*c^2*d^3 + a*c*d^4)*sin(f*x + e))/((c^7 - 2*c^5*d^2 + c^3*d^4)*f*cos(f*x + e) + (c^6*d - 2*c^4*d^3 + c^2*d^5)*f), ((a*c^5 - 2*a*c^3*d^2 + a*c*d^4)*f*x*cos(f*x + e) + (a*c^4*d - 2*a*c^2*d^3 + a*d^5)*f*x + (b*c^3*d - 2*a*c^2*d^2 + a*d^4 + (b*c^4 - 2*a*c^3*d + a*c*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (b*c^4*d - a*c^3*d^2 - b*c^2*d^3 + a*c*d^4)*sin(f*x + e))/((c^7 - 2*c^5*d^2 + c^3*d^4)*f*cos(f*x + e) + (c^6*d - 2*c^4*d^3 + c^2*d^5)*f)]","B",0
191,1,1152,0,0.588966," ","integrate((a+b*sec(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a c^{8} - 3 \, a c^{6} d^{2} + 3 \, a c^{4} d^{4} - a c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 8 \, {\left(a c^{7} d - 3 \, a c^{5} d^{3} + 3 \, a c^{3} d^{5} - a c d^{7}\right)} f x \cos\left(f x + e\right) + 4 \, {\left(a c^{6} d^{2} - 3 \, a c^{4} d^{4} + 3 \, a c^{2} d^{6} - a d^{8}\right)} f x - {\left(2 \, b c^{5} d^{2} - 6 \, a c^{4} d^{3} + b c^{3} d^{4} + 5 \, a c^{2} d^{5} - 2 \, a d^{7} + {\left(2 \, b c^{7} - 6 \, a c^{6} d + b c^{5} d^{2} + 5 \, a c^{4} d^{3} - 2 \, a c^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, b c^{6} d - 6 \, a c^{5} d^{2} + b c^{4} d^{3} + 5 \, a c^{3} d^{4} - 2 \, a c d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) - 2 \, {\left(3 \, b c^{6} d^{2} - 5 \, a c^{5} d^{3} - 3 \, b c^{4} d^{4} + 7 \, a c^{3} d^{5} - 2 \, a c d^{7} + {\left(4 \, b c^{7} d - 6 \, a c^{6} d^{2} - 5 \, b c^{5} d^{3} + 9 \, a c^{4} d^{4} + b c^{3} d^{5} - 3 \, a c^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}, \frac{2 \, {\left(a c^{8} - 3 \, a c^{6} d^{2} + 3 \, a c^{4} d^{4} - a c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 4 \, {\left(a c^{7} d - 3 \, a c^{5} d^{3} + 3 \, a c^{3} d^{5} - a c d^{7}\right)} f x \cos\left(f x + e\right) + 2 \, {\left(a c^{6} d^{2} - 3 \, a c^{4} d^{4} + 3 \, a c^{2} d^{6} - a d^{8}\right)} f x + {\left(2 \, b c^{5} d^{2} - 6 \, a c^{4} d^{3} + b c^{3} d^{4} + 5 \, a c^{2} d^{5} - 2 \, a d^{7} + {\left(2 \, b c^{7} - 6 \, a c^{6} d + b c^{5} d^{2} + 5 \, a c^{4} d^{3} - 2 \, a c^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, b c^{6} d - 6 \, a c^{5} d^{2} + b c^{4} d^{3} + 5 \, a c^{3} d^{4} - 2 \, a c d^{6}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) - {\left(3 \, b c^{6} d^{2} - 5 \, a c^{5} d^{3} - 3 \, b c^{4} d^{4} + 7 \, a c^{3} d^{5} - 2 \, a c d^{7} + {\left(4 \, b c^{7} d - 6 \, a c^{6} d^{2} - 5 \, b c^{5} d^{3} + 9 \, a c^{4} d^{4} + b c^{3} d^{5} - 3 \, a c^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}\right]"," ",0,"[1/4*(4*(a*c^8 - 3*a*c^6*d^2 + 3*a*c^4*d^4 - a*c^2*d^6)*f*x*cos(f*x + e)^2 + 8*(a*c^7*d - 3*a*c^5*d^3 + 3*a*c^3*d^5 - a*c*d^7)*f*x*cos(f*x + e) + 4*(a*c^6*d^2 - 3*a*c^4*d^4 + 3*a*c^2*d^6 - a*d^8)*f*x - (2*b*c^5*d^2 - 6*a*c^4*d^3 + b*c^3*d^4 + 5*a*c^2*d^5 - 2*a*d^7 + (2*b*c^7 - 6*a*c^6*d + b*c^5*d^2 + 5*a*c^4*d^3 - 2*a*c^2*d^5)*cos(f*x + e)^2 + 2*(2*b*c^6*d - 6*a*c^5*d^2 + b*c^4*d^3 + 5*a*c^3*d^4 - 2*a*c*d^6)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) - 2*(3*b*c^6*d^2 - 5*a*c^5*d^3 - 3*b*c^4*d^4 + 7*a*c^3*d^5 - 2*a*c*d^7 + (4*b*c^7*d - 6*a*c^6*d^2 - 5*b*c^5*d^3 + 9*a*c^4*d^4 + b*c^3*d^5 - 3*a*c^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f), 1/2*(2*(a*c^8 - 3*a*c^6*d^2 + 3*a*c^4*d^4 - a*c^2*d^6)*f*x*cos(f*x + e)^2 + 4*(a*c^7*d - 3*a*c^5*d^3 + 3*a*c^3*d^5 - a*c*d^7)*f*x*cos(f*x + e) + 2*(a*c^6*d^2 - 3*a*c^4*d^4 + 3*a*c^2*d^6 - a*d^8)*f*x + (2*b*c^5*d^2 - 6*a*c^4*d^3 + b*c^3*d^4 + 5*a*c^2*d^5 - 2*a*d^7 + (2*b*c^7 - 6*a*c^6*d + b*c^5*d^2 + 5*a*c^4*d^3 - 2*a*c^2*d^5)*cos(f*x + e)^2 + 2*(2*b*c^6*d - 6*a*c^5*d^2 + b*c^4*d^3 + 5*a*c^3*d^4 - 2*a*c*d^6)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) - (3*b*c^6*d^2 - 5*a*c^5*d^3 - 3*b*c^4*d^4 + 7*a*c^3*d^5 - 2*a*c*d^7 + (4*b*c^7*d - 6*a*c^6*d^2 - 5*b*c^5*d^3 + 9*a*c^4*d^4 + b*c^3*d^5 - 3*a*c^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f)]","B",0
192,1,671,0,0.530734," ","integrate((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} c^{5} - 2 \, a^{2} c^{3} d^{2} + a^{2} c d^{4}\right)} f x \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{4} d - 2 \, a^{2} c^{2} d^{3} + a^{2} d^{5}\right)} f x + {\left(2 \, a b c^{3} d + a^{2} d^{4} - {\left(2 \, a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(2 \, a b c^{4} + a^{2} c d^{3} - {\left(2 \, a^{2} + b^{2}\right)} c^{3} d\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + 2 \, a b c^{2} d^{3} - a^{2} c d^{4} + {\left(a^{2} - b^{2}\right)} c^{3} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{7} - 2 \, c^{5} d^{2} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d - 2 \, c^{4} d^{3} + c^{2} d^{5}\right)} f\right)}}, \frac{{\left(a^{2} c^{5} - 2 \, a^{2} c^{3} d^{2} + a^{2} c d^{4}\right)} f x \cos\left(f x + e\right) + {\left(a^{2} c^{4} d - 2 \, a^{2} c^{2} d^{3} + a^{2} d^{5}\right)} f x + {\left(2 \, a b c^{3} d + a^{2} d^{4} - {\left(2 \, a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(2 \, a b c^{4} + a^{2} c d^{3} - {\left(2 \, a^{2} + b^{2}\right)} c^{3} d\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b^{2} c^{5} - 2 \, a b c^{4} d + 2 \, a b c^{2} d^{3} - a^{2} c d^{4} + {\left(a^{2} - b^{2}\right)} c^{3} d^{2}\right)} \sin\left(f x + e\right)}{{\left(c^{7} - 2 \, c^{5} d^{2} + c^{3} d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{6} d - 2 \, c^{4} d^{3} + c^{2} d^{5}\right)} f}\right]"," ",0,"[1/2*(2*(a^2*c^5 - 2*a^2*c^3*d^2 + a^2*c*d^4)*f*x*cos(f*x + e) + 2*(a^2*c^4*d - 2*a^2*c^2*d^3 + a^2*d^5)*f*x + (2*a*b*c^3*d + a^2*d^4 - (2*a^2 + b^2)*c^2*d^2 + (2*a*b*c^4 + a^2*c*d^3 - (2*a^2 + b^2)*c^3*d)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 + 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b^2*c^5 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - a^2*c*d^4 + (a^2 - b^2)*c^3*d^2)*sin(f*x + e))/((c^7 - 2*c^5*d^2 + c^3*d^4)*f*cos(f*x + e) + (c^6*d - 2*c^4*d^3 + c^2*d^5)*f), ((a^2*c^5 - 2*a^2*c^3*d^2 + a^2*c*d^4)*f*x*cos(f*x + e) + (a^2*c^4*d - 2*a^2*c^2*d^3 + a^2*d^5)*f*x + (2*a*b*c^3*d + a^2*d^4 - (2*a^2 + b^2)*c^2*d^2 + (2*a*b*c^4 + a^2*c*d^3 - (2*a^2 + b^2)*c^3*d)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b^2*c^5 - 2*a*b*c^4*d + 2*a*b*c^2*d^3 - a^2*c*d^4 + (a^2 - b^2)*c^3*d^2)*sin(f*x + e))/((c^7 - 2*c^5*d^2 + c^3*d^4)*f*cos(f*x + e) + (c^6*d - 2*c^4*d^3 + c^2*d^5)*f)]","B",0
193,1,1409,0,0.581849," ","integrate((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} c^{8} - 3 \, a^{2} c^{6} d^{2} + 3 \, a^{2} c^{4} d^{4} - a^{2} c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 8 \, {\left(a^{2} c^{7} d - 3 \, a^{2} c^{5} d^{3} + 3 \, a^{2} c^{3} d^{5} - a^{2} c d^{7}\right)} f x \cos\left(f x + e\right) + 4 \, {\left(a^{2} c^{6} d^{2} - 3 \, a^{2} c^{4} d^{4} + 3 \, a^{2} c^{2} d^{6} - a^{2} d^{8}\right)} f x - {\left(4 \, a b c^{5} d^{2} + 2 \, a b c^{3} d^{4} + 5 \, a^{2} c^{2} d^{5} - 2 \, a^{2} d^{7} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{4} d^{3} + {\left(4 \, a b c^{7} + 2 \, a b c^{5} d^{2} + 5 \, a^{2} c^{4} d^{3} - 2 \, a^{2} c^{2} d^{5} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{6} d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(4 \, a b c^{6} d + 2 \, a b c^{4} d^{3} + 5 \, a^{2} c^{3} d^{4} - 2 \, a^{2} c d^{6} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{5} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b^{2} c^{7} d - 6 \, a b c^{6} d^{2} + 6 \, a b c^{4} d^{4} + 2 \, a^{2} c d^{7} + {\left(5 \, a^{2} + b^{2}\right)} c^{5} d^{3} - {\left(7 \, a^{2} + 2 \, b^{2}\right)} c^{3} d^{5} + {\left(2 \, b^{2} c^{8} - 8 \, a b c^{7} d + 10 \, a b c^{5} d^{3} - 2 \, a b c^{3} d^{5} + 3 \, a^{2} c^{2} d^{6} + {\left(6 \, a^{2} - b^{2}\right)} c^{6} d^{2} - {\left(9 \, a^{2} + b^{2}\right)} c^{4} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}, \frac{2 \, {\left(a^{2} c^{8} - 3 \, a^{2} c^{6} d^{2} + 3 \, a^{2} c^{4} d^{4} - a^{2} c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 4 \, {\left(a^{2} c^{7} d - 3 \, a^{2} c^{5} d^{3} + 3 \, a^{2} c^{3} d^{5} - a^{2} c d^{7}\right)} f x \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{6} d^{2} - 3 \, a^{2} c^{4} d^{4} + 3 \, a^{2} c^{2} d^{6} - a^{2} d^{8}\right)} f x + {\left(4 \, a b c^{5} d^{2} + 2 \, a b c^{3} d^{4} + 5 \, a^{2} c^{2} d^{5} - 2 \, a^{2} d^{7} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{4} d^{3} + {\left(4 \, a b c^{7} + 2 \, a b c^{5} d^{2} + 5 \, a^{2} c^{4} d^{3} - 2 \, a^{2} c^{2} d^{5} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{6} d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(4 \, a b c^{6} d + 2 \, a b c^{4} d^{3} + 5 \, a^{2} c^{3} d^{4} - 2 \, a^{2} c d^{6} - 3 \, {\left(2 \, a^{2} + b^{2}\right)} c^{5} d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b^{2} c^{7} d - 6 \, a b c^{6} d^{2} + 6 \, a b c^{4} d^{4} + 2 \, a^{2} c d^{7} + {\left(5 \, a^{2} + b^{2}\right)} c^{5} d^{3} - {\left(7 \, a^{2} + 2 \, b^{2}\right)} c^{3} d^{5} + {\left(2 \, b^{2} c^{8} - 8 \, a b c^{7} d + 10 \, a b c^{5} d^{3} - 2 \, a b c^{3} d^{5} + 3 \, a^{2} c^{2} d^{6} + {\left(6 \, a^{2} - b^{2}\right)} c^{6} d^{2} - {\left(9 \, a^{2} + b^{2}\right)} c^{4} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}\right]"," ",0,"[1/4*(4*(a^2*c^8 - 3*a^2*c^6*d^2 + 3*a^2*c^4*d^4 - a^2*c^2*d^6)*f*x*cos(f*x + e)^2 + 8*(a^2*c^7*d - 3*a^2*c^5*d^3 + 3*a^2*c^3*d^5 - a^2*c*d^7)*f*x*cos(f*x + e) + 4*(a^2*c^6*d^2 - 3*a^2*c^4*d^4 + 3*a^2*c^2*d^6 - a^2*d^8)*f*x - (4*a*b*c^5*d^2 + 2*a*b*c^3*d^4 + 5*a^2*c^2*d^5 - 2*a^2*d^7 - 3*(2*a^2 + b^2)*c^4*d^3 + (4*a*b*c^7 + 2*a*b*c^5*d^2 + 5*a^2*c^4*d^3 - 2*a^2*c^2*d^5 - 3*(2*a^2 + b^2)*c^6*d)*cos(f*x + e)^2 + 2*(4*a*b*c^6*d + 2*a*b*c^4*d^3 + 5*a^2*c^3*d^4 - 2*a^2*c*d^6 - 3*(2*a^2 + b^2)*c^5*d^2)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b^2*c^7*d - 6*a*b*c^6*d^2 + 6*a*b*c^4*d^4 + 2*a^2*c*d^7 + (5*a^2 + b^2)*c^5*d^3 - (7*a^2 + 2*b^2)*c^3*d^5 + (2*b^2*c^8 - 8*a*b*c^7*d + 10*a*b*c^5*d^3 - 2*a*b*c^3*d^5 + 3*a^2*c^2*d^6 + (6*a^2 - b^2)*c^6*d^2 - (9*a^2 + b^2)*c^4*d^4)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f), 1/2*(2*(a^2*c^8 - 3*a^2*c^6*d^2 + 3*a^2*c^4*d^4 - a^2*c^2*d^6)*f*x*cos(f*x + e)^2 + 4*(a^2*c^7*d - 3*a^2*c^5*d^3 + 3*a^2*c^3*d^5 - a^2*c*d^7)*f*x*cos(f*x + e) + 2*(a^2*c^6*d^2 - 3*a^2*c^4*d^4 + 3*a^2*c^2*d^6 - a^2*d^8)*f*x + (4*a*b*c^5*d^2 + 2*a*b*c^3*d^4 + 5*a^2*c^2*d^5 - 2*a^2*d^7 - 3*(2*a^2 + b^2)*c^4*d^3 + (4*a*b*c^7 + 2*a*b*c^5*d^2 + 5*a^2*c^4*d^3 - 2*a^2*c^2*d^5 - 3*(2*a^2 + b^2)*c^6*d)*cos(f*x + e)^2 + 2*(4*a*b*c^6*d + 2*a*b*c^4*d^3 + 5*a^2*c^3*d^4 - 2*a^2*c*d^6 - 3*(2*a^2 + b^2)*c^5*d^2)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b^2*c^7*d - 6*a*b*c^6*d^2 + 6*a*b*c^4*d^4 + 2*a^2*c*d^7 + (5*a^2 + b^2)*c^5*d^3 - (7*a^2 + 2*b^2)*c^3*d^5 + (2*b^2*c^8 - 8*a*b*c^7*d + 10*a*b*c^5*d^3 - 2*a*b*c^3*d^5 + 3*a^2*c^2*d^6 + (6*a^2 - b^2)*c^6*d^2 - (9*a^2 + b^2)*c^4*d^4)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f)]","B",0
194,1,2362,0,0.730859," ","integrate((a+b*sec(f*x+e))^2/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{2} c^{11} - 4 \, a^{2} c^{9} d^{2} + 6 \, a^{2} c^{7} d^{4} - 4 \, a^{2} c^{5} d^{6} + a^{2} c^{3} d^{8}\right)} f x \cos\left(f x + e\right)^{3} + 36 \, {\left(a^{2} c^{10} d - 4 \, a^{2} c^{8} d^{3} + 6 \, a^{2} c^{6} d^{5} - 4 \, a^{2} c^{4} d^{7} + a^{2} c^{2} d^{9}\right)} f x \cos\left(f x + e\right)^{2} + 36 \, {\left(a^{2} c^{9} d^{2} - 4 \, a^{2} c^{7} d^{4} + 6 \, a^{2} c^{5} d^{6} - 4 \, a^{2} c^{3} d^{8} + a^{2} c d^{10}\right)} f x \cos\left(f x + e\right) + 12 \, {\left(a^{2} c^{8} d^{3} - 4 \, a^{2} c^{6} d^{5} + 6 \, a^{2} c^{4} d^{7} - 4 \, a^{2} c^{2} d^{9} + a^{2} d^{11}\right)} f x - 3 \, {\left(4 \, a b c^{7} d^{3} + 6 \, a b c^{5} d^{5} - 7 \, a^{2} c^{2} d^{8} + 2 \, a^{2} d^{10} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{6} d^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} d^{6} + {\left(4 \, a b c^{10} + 6 \, a b c^{8} d^{2} - 7 \, a^{2} c^{5} d^{5} + 2 \, a^{2} c^{3} d^{7} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{9} d + {\left(8 \, a^{2} - b^{2}\right)} c^{7} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, a b c^{9} d + 6 \, a b c^{7} d^{3} - 7 \, a^{2} c^{4} d^{6} + 2 \, a^{2} c^{2} d^{8} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{8} d^{2} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(4 \, a b c^{8} d^{2} + 6 \, a b c^{6} d^{4} - 7 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c d^{9} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{7} d^{3} + {\left(8 \, a^{2} - b^{2}\right)} c^{5} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, b^{2} c^{9} d^{2} - 22 \, a b c^{8} d^{3} + 14 \, a b c^{6} d^{5} + 8 \, a b c^{4} d^{7} + 23 \, a^{2} c^{3} d^{8} - 6 \, a^{2} c d^{10} + {\left(26 \, a^{2} + 11 \, b^{2}\right)} c^{7} d^{4} - {\left(43 \, a^{2} + 13 \, b^{2}\right)} c^{5} d^{6} + {\left(6 \, b^{2} c^{11} - 36 \, a b c^{10} d + 46 \, a b c^{8} d^{3} - 14 \, a b c^{6} d^{5} + 4 \, a b c^{4} d^{7} - 11 \, a^{2} c^{3} d^{8} + 4 \, {\left(9 \, a^{2} + b^{2}\right)} c^{9} d^{2} - {\left(68 \, a^{2} + 11 \, b^{2}\right)} c^{7} d^{4} + {\left(43 \, a^{2} + b^{2}\right)} c^{5} d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, b^{2} c^{10} d - 18 \, a b c^{9} d^{2} + 16 \, a b c^{7} d^{4} + 2 \, a b c^{5} d^{6} - 5 \, a^{2} c^{2} d^{9} + {\left(20 \, a^{2} + 7 \, b^{2}\right)} c^{8} d^{3} - 5 \, {\left(7 \, a^{2} + 2 \, b^{2}\right)} c^{6} d^{5} + {\left(20 \, a^{2} + b^{2}\right)} c^{4} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{15} - 4 \, c^{13} d^{2} + 6 \, c^{11} d^{4} - 4 \, c^{9} d^{6} + c^{7} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{14} d - 4 \, c^{12} d^{3} + 6 \, c^{10} d^{5} - 4 \, c^{8} d^{7} + c^{6} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{13} d^{2} - 4 \, c^{11} d^{4} + 6 \, c^{9} d^{6} - 4 \, c^{7} d^{8} + c^{5} d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{12} d^{3} - 4 \, c^{10} d^{5} + 6 \, c^{8} d^{7} - 4 \, c^{6} d^{9} + c^{4} d^{11}\right)} f\right)}}, \frac{6 \, {\left(a^{2} c^{11} - 4 \, a^{2} c^{9} d^{2} + 6 \, a^{2} c^{7} d^{4} - 4 \, a^{2} c^{5} d^{6} + a^{2} c^{3} d^{8}\right)} f x \cos\left(f x + e\right)^{3} + 18 \, {\left(a^{2} c^{10} d - 4 \, a^{2} c^{8} d^{3} + 6 \, a^{2} c^{6} d^{5} - 4 \, a^{2} c^{4} d^{7} + a^{2} c^{2} d^{9}\right)} f x \cos\left(f x + e\right)^{2} + 18 \, {\left(a^{2} c^{9} d^{2} - 4 \, a^{2} c^{7} d^{4} + 6 \, a^{2} c^{5} d^{6} - 4 \, a^{2} c^{3} d^{8} + a^{2} c d^{10}\right)} f x \cos\left(f x + e\right) + 6 \, {\left(a^{2} c^{8} d^{3} - 4 \, a^{2} c^{6} d^{5} + 6 \, a^{2} c^{4} d^{7} - 4 \, a^{2} c^{2} d^{9} + a^{2} d^{11}\right)} f x + 3 \, {\left(4 \, a b c^{7} d^{3} + 6 \, a b c^{5} d^{5} - 7 \, a^{2} c^{2} d^{8} + 2 \, a^{2} d^{10} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{6} d^{4} + {\left(8 \, a^{2} - b^{2}\right)} c^{4} d^{6} + {\left(4 \, a b c^{10} + 6 \, a b c^{8} d^{2} - 7 \, a^{2} c^{5} d^{5} + 2 \, a^{2} c^{3} d^{7} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{9} d + {\left(8 \, a^{2} - b^{2}\right)} c^{7} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, a b c^{9} d + 6 \, a b c^{7} d^{3} - 7 \, a^{2} c^{4} d^{6} + 2 \, a^{2} c^{2} d^{8} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{8} d^{2} + {\left(8 \, a^{2} - b^{2}\right)} c^{6} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(4 \, a b c^{8} d^{2} + 6 \, a b c^{6} d^{4} - 7 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c d^{9} - 4 \, {\left(2 \, a^{2} + b^{2}\right)} c^{7} d^{3} + {\left(8 \, a^{2} - b^{2}\right)} c^{5} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, b^{2} c^{9} d^{2} - 22 \, a b c^{8} d^{3} + 14 \, a b c^{6} d^{5} + 8 \, a b c^{4} d^{7} + 23 \, a^{2} c^{3} d^{8} - 6 \, a^{2} c d^{10} + {\left(26 \, a^{2} + 11 \, b^{2}\right)} c^{7} d^{4} - {\left(43 \, a^{2} + 13 \, b^{2}\right)} c^{5} d^{6} + {\left(6 \, b^{2} c^{11} - 36 \, a b c^{10} d + 46 \, a b c^{8} d^{3} - 14 \, a b c^{6} d^{5} + 4 \, a b c^{4} d^{7} - 11 \, a^{2} c^{3} d^{8} + 4 \, {\left(9 \, a^{2} + b^{2}\right)} c^{9} d^{2} - {\left(68 \, a^{2} + 11 \, b^{2}\right)} c^{7} d^{4} + {\left(43 \, a^{2} + b^{2}\right)} c^{5} d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, b^{2} c^{10} d - 18 \, a b c^{9} d^{2} + 16 \, a b c^{7} d^{4} + 2 \, a b c^{5} d^{6} - 5 \, a^{2} c^{2} d^{9} + {\left(20 \, a^{2} + 7 \, b^{2}\right)} c^{8} d^{3} - 5 \, {\left(7 \, a^{2} + 2 \, b^{2}\right)} c^{6} d^{5} + {\left(20 \, a^{2} + b^{2}\right)} c^{4} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{15} - 4 \, c^{13} d^{2} + 6 \, c^{11} d^{4} - 4 \, c^{9} d^{6} + c^{7} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{14} d - 4 \, c^{12} d^{3} + 6 \, c^{10} d^{5} - 4 \, c^{8} d^{7} + c^{6} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{13} d^{2} - 4 \, c^{11} d^{4} + 6 \, c^{9} d^{6} - 4 \, c^{7} d^{8} + c^{5} d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{12} d^{3} - 4 \, c^{10} d^{5} + 6 \, c^{8} d^{7} - 4 \, c^{6} d^{9} + c^{4} d^{11}\right)} f\right)}}\right]"," ",0,"[1/12*(12*(a^2*c^11 - 4*a^2*c^9*d^2 + 6*a^2*c^7*d^4 - 4*a^2*c^5*d^6 + a^2*c^3*d^8)*f*x*cos(f*x + e)^3 + 36*(a^2*c^10*d - 4*a^2*c^8*d^3 + 6*a^2*c^6*d^5 - 4*a^2*c^4*d^7 + a^2*c^2*d^9)*f*x*cos(f*x + e)^2 + 36*(a^2*c^9*d^2 - 4*a^2*c^7*d^4 + 6*a^2*c^5*d^6 - 4*a^2*c^3*d^8 + a^2*c*d^10)*f*x*cos(f*x + e) + 12*(a^2*c^8*d^3 - 4*a^2*c^6*d^5 + 6*a^2*c^4*d^7 - 4*a^2*c^2*d^9 + a^2*d^11)*f*x - 3*(4*a*b*c^7*d^3 + 6*a*b*c^5*d^5 - 7*a^2*c^2*d^8 + 2*a^2*d^10 - 4*(2*a^2 + b^2)*c^6*d^4 + (8*a^2 - b^2)*c^4*d^6 + (4*a*b*c^10 + 6*a*b*c^8*d^2 - 7*a^2*c^5*d^5 + 2*a^2*c^3*d^7 - 4*(2*a^2 + b^2)*c^9*d + (8*a^2 - b^2)*c^7*d^3)*cos(f*x + e)^3 + 3*(4*a*b*c^9*d + 6*a*b*c^7*d^3 - 7*a^2*c^4*d^6 + 2*a^2*c^2*d^8 - 4*(2*a^2 + b^2)*c^8*d^2 + (8*a^2 - b^2)*c^6*d^4)*cos(f*x + e)^2 + 3*(4*a*b*c^8*d^2 + 6*a*b*c^6*d^4 - 7*a^2*c^3*d^7 + 2*a^2*c*d^9 - 4*(2*a^2 + b^2)*c^7*d^3 + (8*a^2 - b^2)*c^5*d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*b^2*c^9*d^2 - 22*a*b*c^8*d^3 + 14*a*b*c^6*d^5 + 8*a*b*c^4*d^7 + 23*a^2*c^3*d^8 - 6*a^2*c*d^10 + (26*a^2 + 11*b^2)*c^7*d^4 - (43*a^2 + 13*b^2)*c^5*d^6 + (6*b^2*c^11 - 36*a*b*c^10*d + 46*a*b*c^8*d^3 - 14*a*b*c^6*d^5 + 4*a*b*c^4*d^7 - 11*a^2*c^3*d^8 + 4*(9*a^2 + b^2)*c^9*d^2 - (68*a^2 + 11*b^2)*c^7*d^4 + (43*a^2 + b^2)*c^5*d^6)*cos(f*x + e)^2 + 3*(2*b^2*c^10*d - 18*a*b*c^9*d^2 + 16*a*b*c^7*d^4 + 2*a*b*c^5*d^6 - 5*a^2*c^2*d^9 + (20*a^2 + 7*b^2)*c^8*d^3 - 5*(7*a^2 + 2*b^2)*c^6*d^5 + (20*a^2 + b^2)*c^4*d^7)*cos(f*x + e))*sin(f*x + e))/((c^15 - 4*c^13*d^2 + 6*c^11*d^4 - 4*c^9*d^6 + c^7*d^8)*f*cos(f*x + e)^3 + 3*(c^14*d - 4*c^12*d^3 + 6*c^10*d^5 - 4*c^8*d^7 + c^6*d^9)*f*cos(f*x + e)^2 + 3*(c^13*d^2 - 4*c^11*d^4 + 6*c^9*d^6 - 4*c^7*d^8 + c^5*d^10)*f*cos(f*x + e) + (c^12*d^3 - 4*c^10*d^5 + 6*c^8*d^7 - 4*c^6*d^9 + c^4*d^11)*f), 1/6*(6*(a^2*c^11 - 4*a^2*c^9*d^2 + 6*a^2*c^7*d^4 - 4*a^2*c^5*d^6 + a^2*c^3*d^8)*f*x*cos(f*x + e)^3 + 18*(a^2*c^10*d - 4*a^2*c^8*d^3 + 6*a^2*c^6*d^5 - 4*a^2*c^4*d^7 + a^2*c^2*d^9)*f*x*cos(f*x + e)^2 + 18*(a^2*c^9*d^2 - 4*a^2*c^7*d^4 + 6*a^2*c^5*d^6 - 4*a^2*c^3*d^8 + a^2*c*d^10)*f*x*cos(f*x + e) + 6*(a^2*c^8*d^3 - 4*a^2*c^6*d^5 + 6*a^2*c^4*d^7 - 4*a^2*c^2*d^9 + a^2*d^11)*f*x + 3*(4*a*b*c^7*d^3 + 6*a*b*c^5*d^5 - 7*a^2*c^2*d^8 + 2*a^2*d^10 - 4*(2*a^2 + b^2)*c^6*d^4 + (8*a^2 - b^2)*c^4*d^6 + (4*a*b*c^10 + 6*a*b*c^8*d^2 - 7*a^2*c^5*d^5 + 2*a^2*c^3*d^7 - 4*(2*a^2 + b^2)*c^9*d + (8*a^2 - b^2)*c^7*d^3)*cos(f*x + e)^3 + 3*(4*a*b*c^9*d + 6*a*b*c^7*d^3 - 7*a^2*c^4*d^6 + 2*a^2*c^2*d^8 - 4*(2*a^2 + b^2)*c^8*d^2 + (8*a^2 - b^2)*c^6*d^4)*cos(f*x + e)^2 + 3*(4*a*b*c^8*d^2 + 6*a*b*c^6*d^4 - 7*a^2*c^3*d^7 + 2*a^2*c*d^9 - 4*(2*a^2 + b^2)*c^7*d^3 + (8*a^2 - b^2)*c^5*d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*b^2*c^9*d^2 - 22*a*b*c^8*d^3 + 14*a*b*c^6*d^5 + 8*a*b*c^4*d^7 + 23*a^2*c^3*d^8 - 6*a^2*c*d^10 + (26*a^2 + 11*b^2)*c^7*d^4 - (43*a^2 + 13*b^2)*c^5*d^6 + (6*b^2*c^11 - 36*a*b*c^10*d + 46*a*b*c^8*d^3 - 14*a*b*c^6*d^5 + 4*a*b*c^4*d^7 - 11*a^2*c^3*d^8 + 4*(9*a^2 + b^2)*c^9*d^2 - (68*a^2 + 11*b^2)*c^7*d^4 + (43*a^2 + b^2)*c^5*d^6)*cos(f*x + e)^2 + 3*(2*b^2*c^10*d - 18*a*b*c^9*d^2 + 16*a*b*c^7*d^4 + 2*a*b*c^5*d^6 - 5*a^2*c^2*d^9 + (20*a^2 + 7*b^2)*c^8*d^3 - 5*(7*a^2 + 2*b^2)*c^6*d^5 + (20*a^2 + b^2)*c^4*d^7)*cos(f*x + e))*sin(f*x + e))/((c^15 - 4*c^13*d^2 + 6*c^11*d^4 - 4*c^9*d^6 + c^7*d^8)*f*cos(f*x + e)^3 + 3*(c^14*d - 4*c^12*d^3 + 6*c^10*d^5 - 4*c^8*d^7 + c^6*d^9)*f*cos(f*x + e)^2 + 3*(c^13*d^2 - 4*c^11*d^4 + 6*c^9*d^6 - 4*c^7*d^8 + c^5*d^10)*f*cos(f*x + e) + (c^12*d^3 - 4*c^10*d^5 + 6*c^8*d^7 - 4*c^6*d^9 + c^4*d^11)*f)]","B",0
195,1,1629,0,0.679680," ","integrate((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} c^{8} - 3 \, a^{3} c^{6} d^{2} + 3 \, a^{3} c^{4} d^{4} - a^{3} c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 8 \, {\left(a^{3} c^{7} d - 3 \, a^{3} c^{5} d^{3} + 3 \, a^{3} c^{3} d^{5} - a^{3} c d^{7}\right)} f x \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{6} d^{2} - 3 \, a^{3} c^{4} d^{4} + 3 \, a^{3} c^{2} d^{6} - a^{3} d^{8}\right)} f x - {\left(5 \, a^{3} c^{2} d^{5} - 2 \, a^{3} d^{7} + {\left(6 \, a^{2} b + b^{3}\right)} c^{5} d^{2} - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{4} d^{3} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{3} d^{4} + {\left(5 \, a^{3} c^{4} d^{3} - 2 \, a^{3} c^{2} d^{5} + {\left(6 \, a^{2} b + b^{3}\right)} c^{7} - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{6} d + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, a^{3} c^{3} d^{4} - 2 \, a^{3} c d^{6} + {\left(6 \, a^{2} b + b^{3}\right)} c^{6} d - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{2} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{4} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b^{3} c^{8} + 3 \, a b^{2} c^{7} d + 2 \, a^{3} c d^{7} - {\left(9 \, a^{2} b + 5 \, b^{3}\right)} c^{6} d^{2} + {\left(5 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{3} + {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{4} d^{4} - {\left(7 \, a^{3} + 6 \, a b^{2}\right)} c^{3} d^{5} + 3 \, {\left(2 \, a b^{2} c^{8} - a^{2} b c^{3} d^{5} + a^{3} c^{2} d^{6} - {\left(4 \, a^{2} b + b^{3}\right)} c^{7} d + {\left(2 \, a^{3} - a b^{2}\right)} c^{6} d^{2} + {\left(5 \, a^{2} b + b^{3}\right)} c^{5} d^{3} - {\left(3 \, a^{3} + a b^{2}\right)} c^{4} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}, \frac{2 \, {\left(a^{3} c^{8} - 3 \, a^{3} c^{6} d^{2} + 3 \, a^{3} c^{4} d^{4} - a^{3} c^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} + 4 \, {\left(a^{3} c^{7} d - 3 \, a^{3} c^{5} d^{3} + 3 \, a^{3} c^{3} d^{5} - a^{3} c d^{7}\right)} f x \cos\left(f x + e\right) + 2 \, {\left(a^{3} c^{6} d^{2} - 3 \, a^{3} c^{4} d^{4} + 3 \, a^{3} c^{2} d^{6} - a^{3} d^{8}\right)} f x + {\left(5 \, a^{3} c^{2} d^{5} - 2 \, a^{3} d^{7} + {\left(6 \, a^{2} b + b^{3}\right)} c^{5} d^{2} - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{4} d^{3} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{3} d^{4} + {\left(5 \, a^{3} c^{4} d^{3} - 2 \, a^{3} c^{2} d^{5} + {\left(6 \, a^{2} b + b^{3}\right)} c^{7} - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{6} d + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, a^{3} c^{3} d^{4} - 2 \, a^{3} c d^{6} + {\left(6 \, a^{2} b + b^{3}\right)} c^{6} d - 3 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{2} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{4} d^{3}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b^{3} c^{8} + 3 \, a b^{2} c^{7} d + 2 \, a^{3} c d^{7} - {\left(9 \, a^{2} b + 5 \, b^{3}\right)} c^{6} d^{2} + {\left(5 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{3} + {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{4} d^{4} - {\left(7 \, a^{3} + 6 \, a b^{2}\right)} c^{3} d^{5} + 3 \, {\left(2 \, a b^{2} c^{8} - a^{2} b c^{3} d^{5} + a^{3} c^{2} d^{6} - {\left(4 \, a^{2} b + b^{3}\right)} c^{7} d + {\left(2 \, a^{3} - a b^{2}\right)} c^{6} d^{2} + {\left(5 \, a^{2} b + b^{3}\right)} c^{5} d^{3} - {\left(3 \, a^{3} + a b^{2}\right)} c^{4} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{11} - 3 \, c^{9} d^{2} + 3 \, c^{7} d^{4} - c^{5} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(c^{10} d - 3 \, c^{8} d^{3} + 3 \, c^{6} d^{5} - c^{4} d^{7}\right)} f \cos\left(f x + e\right) + {\left(c^{9} d^{2} - 3 \, c^{7} d^{4} + 3 \, c^{5} d^{6} - c^{3} d^{8}\right)} f\right)}}\right]"," ",0,"[1/4*(4*(a^3*c^8 - 3*a^3*c^6*d^2 + 3*a^3*c^4*d^4 - a^3*c^2*d^6)*f*x*cos(f*x + e)^2 + 8*(a^3*c^7*d - 3*a^3*c^5*d^3 + 3*a^3*c^3*d^5 - a^3*c*d^7)*f*x*cos(f*x + e) + 4*(a^3*c^6*d^2 - 3*a^3*c^4*d^4 + 3*a^3*c^2*d^6 - a^3*d^8)*f*x - (5*a^3*c^2*d^5 - 2*a^3*d^7 + (6*a^2*b + b^3)*c^5*d^2 - 3*(2*a^3 + 3*a*b^2)*c^4*d^3 + (3*a^2*b + 2*b^3)*c^3*d^4 + (5*a^3*c^4*d^3 - 2*a^3*c^2*d^5 + (6*a^2*b + b^3)*c^7 - 3*(2*a^3 + 3*a*b^2)*c^6*d + (3*a^2*b + 2*b^3)*c^5*d^2)*cos(f*x + e)^2 + 2*(5*a^3*c^3*d^4 - 2*a^3*c*d^6 + (6*a^2*b + b^3)*c^6*d - 3*(2*a^3 + 3*a*b^2)*c^5*d^2 + (3*a^2*b + 2*b^3)*c^4*d^3)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b^3*c^8 + 3*a*b^2*c^7*d + 2*a^3*c*d^7 - (9*a^2*b + 5*b^3)*c^6*d^2 + (5*a^3 + 3*a*b^2)*c^5*d^3 + (9*a^2*b + 4*b^3)*c^4*d^4 - (7*a^3 + 6*a*b^2)*c^3*d^5 + 3*(2*a*b^2*c^8 - a^2*b*c^3*d^5 + a^3*c^2*d^6 - (4*a^2*b + b^3)*c^7*d + (2*a^3 - a*b^2)*c^6*d^2 + (5*a^2*b + b^3)*c^5*d^3 - (3*a^3 + a*b^2)*c^4*d^4)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f), 1/2*(2*(a^3*c^8 - 3*a^3*c^6*d^2 + 3*a^3*c^4*d^4 - a^3*c^2*d^6)*f*x*cos(f*x + e)^2 + 4*(a^3*c^7*d - 3*a^3*c^5*d^3 + 3*a^3*c^3*d^5 - a^3*c*d^7)*f*x*cos(f*x + e) + 2*(a^3*c^6*d^2 - 3*a^3*c^4*d^4 + 3*a^3*c^2*d^6 - a^3*d^8)*f*x + (5*a^3*c^2*d^5 - 2*a^3*d^7 + (6*a^2*b + b^3)*c^5*d^2 - 3*(2*a^3 + 3*a*b^2)*c^4*d^3 + (3*a^2*b + 2*b^3)*c^3*d^4 + (5*a^3*c^4*d^3 - 2*a^3*c^2*d^5 + (6*a^2*b + b^3)*c^7 - 3*(2*a^3 + 3*a*b^2)*c^6*d + (3*a^2*b + 2*b^3)*c^5*d^2)*cos(f*x + e)^2 + 2*(5*a^3*c^3*d^4 - 2*a^3*c*d^6 + (6*a^2*b + b^3)*c^6*d - 3*(2*a^3 + 3*a*b^2)*c^5*d^2 + (3*a^2*b + 2*b^3)*c^4*d^3)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b^3*c^8 + 3*a*b^2*c^7*d + 2*a^3*c*d^7 - (9*a^2*b + 5*b^3)*c^6*d^2 + (5*a^3 + 3*a*b^2)*c^5*d^3 + (9*a^2*b + 4*b^3)*c^4*d^4 - (7*a^3 + 6*a*b^2)*c^3*d^5 + 3*(2*a*b^2*c^8 - a^2*b*c^3*d^5 + a^3*c^2*d^6 - (4*a^2*b + b^3)*c^7*d + (2*a^3 - a*b^2)*c^6*d^2 + (5*a^2*b + b^3)*c^5*d^3 - (3*a^3 + a*b^2)*c^4*d^4)*cos(f*x + e))*sin(f*x + e))/((c^11 - 3*c^9*d^2 + 3*c^7*d^4 - c^5*d^6)*f*cos(f*x + e)^2 + 2*(c^10*d - 3*c^8*d^3 + 3*c^6*d^5 - c^4*d^7)*f*cos(f*x + e) + (c^9*d^2 - 3*c^7*d^4 + 3*c^5*d^6 - c^3*d^8)*f)]","B",0
196,1,2776,0,0.809415," ","integrate((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^4,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{3} c^{11} - 4 \, a^{3} c^{9} d^{2} + 6 \, a^{3} c^{7} d^{4} - 4 \, a^{3} c^{5} d^{6} + a^{3} c^{3} d^{8}\right)} f x \cos\left(f x + e\right)^{3} + 36 \, {\left(a^{3} c^{10} d - 4 \, a^{3} c^{8} d^{3} + 6 \, a^{3} c^{6} d^{5} - 4 \, a^{3} c^{4} d^{7} + a^{3} c^{2} d^{9}\right)} f x \cos\left(f x + e\right)^{2} + 36 \, {\left(a^{3} c^{9} d^{2} - 4 \, a^{3} c^{7} d^{4} + 6 \, a^{3} c^{5} d^{6} - 4 \, a^{3} c^{3} d^{8} + a^{3} c d^{10}\right)} f x \cos\left(f x + e\right) + 12 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{3} c^{6} d^{5} + 6 \, a^{3} c^{4} d^{7} - 4 \, a^{3} c^{2} d^{9} + a^{3} d^{11}\right)} f x + 3 \, {\left(7 \, a^{3} c^{2} d^{8} - 2 \, a^{3} d^{10} - {\left(6 \, a^{2} b + b^{3}\right)} c^{7} d^{3} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{6} d^{4} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{5} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{4} d^{6} + {\left(7 \, a^{3} c^{5} d^{5} - 2 \, a^{3} c^{3} d^{7} - {\left(6 \, a^{2} b + b^{3}\right)} c^{10} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{8} d^{2} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{7} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(7 \, a^{3} c^{4} d^{6} - 2 \, a^{3} c^{2} d^{8} - {\left(6 \, a^{2} b + b^{3}\right)} c^{9} d + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{8} d^{2} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{7} d^{3} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{6} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(7 \, a^{3} c^{3} d^{7} - 2 \, a^{3} c d^{9} - {\left(6 \, a^{2} b + b^{3}\right)} c^{8} d^{2} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{7} d^{3} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{4} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{5} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(b^{3} c^{10} d + 6 \, a b^{2} c^{9} d^{2} + 23 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c d^{10} - 11 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{8} d^{3} + {\left(26 \, a^{3} + 33 \, a b^{2}\right)} c^{7} d^{4} + {\left(21 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{5} - {\left(43 \, a^{3} + 39 \, a b^{2}\right)} c^{5} d^{6} + 6 \, {\left(2 \, a^{2} b + b^{3}\right)} c^{4} d^{7} + {\left(18 \, a b^{2} c^{11} + 6 \, a^{2} b c^{4} d^{7} - 11 \, a^{3} c^{3} d^{8} - {\left(54 \, a^{2} b + 13 \, b^{3}\right)} c^{10} d + 12 \, {\left(3 \, a^{3} + a b^{2}\right)} c^{9} d^{2} + {\left(69 \, a^{2} b + 11 \, b^{3}\right)} c^{8} d^{3} - {\left(68 \, a^{3} + 33 \, a b^{2}\right)} c^{7} d^{4} - {\left(21 \, a^{2} b - 2 \, b^{3}\right)} c^{6} d^{5} + {\left(43 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(b^{3} c^{11} + 6 \, a b^{2} c^{10} d - 5 \, a^{3} c^{2} d^{9} - {\left(27 \, a^{2} b + 10 \, b^{3}\right)} c^{9} d^{2} + {\left(20 \, a^{3} + 21 \, a b^{2}\right)} c^{8} d^{3} + {\left(24 \, a^{2} b + 7 \, b^{3}\right)} c^{7} d^{4} - 5 \, {\left(7 \, a^{3} + 6 \, a b^{2}\right)} c^{6} d^{5} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{6} + {\left(20 \, a^{3} + 3 \, a b^{2}\right)} c^{4} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(c^{15} - 4 \, c^{13} d^{2} + 6 \, c^{11} d^{4} - 4 \, c^{9} d^{6} + c^{7} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{14} d - 4 \, c^{12} d^{3} + 6 \, c^{10} d^{5} - 4 \, c^{8} d^{7} + c^{6} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{13} d^{2} - 4 \, c^{11} d^{4} + 6 \, c^{9} d^{6} - 4 \, c^{7} d^{8} + c^{5} d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{12} d^{3} - 4 \, c^{10} d^{5} + 6 \, c^{8} d^{7} - 4 \, c^{6} d^{9} + c^{4} d^{11}\right)} f\right)}}, \frac{6 \, {\left(a^{3} c^{11} - 4 \, a^{3} c^{9} d^{2} + 6 \, a^{3} c^{7} d^{4} - 4 \, a^{3} c^{5} d^{6} + a^{3} c^{3} d^{8}\right)} f x \cos\left(f x + e\right)^{3} + 18 \, {\left(a^{3} c^{10} d - 4 \, a^{3} c^{8} d^{3} + 6 \, a^{3} c^{6} d^{5} - 4 \, a^{3} c^{4} d^{7} + a^{3} c^{2} d^{9}\right)} f x \cos\left(f x + e\right)^{2} + 18 \, {\left(a^{3} c^{9} d^{2} - 4 \, a^{3} c^{7} d^{4} + 6 \, a^{3} c^{5} d^{6} - 4 \, a^{3} c^{3} d^{8} + a^{3} c d^{10}\right)} f x \cos\left(f x + e\right) + 6 \, {\left(a^{3} c^{8} d^{3} - 4 \, a^{3} c^{6} d^{5} + 6 \, a^{3} c^{4} d^{7} - 4 \, a^{3} c^{2} d^{9} + a^{3} d^{11}\right)} f x - 3 \, {\left(7 \, a^{3} c^{2} d^{8} - 2 \, a^{3} d^{10} - {\left(6 \, a^{2} b + b^{3}\right)} c^{7} d^{3} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{6} d^{4} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{5} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{4} d^{6} + {\left(7 \, a^{3} c^{5} d^{5} - 2 \, a^{3} c^{3} d^{7} - {\left(6 \, a^{2} b + b^{3}\right)} c^{10} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{8} d^{2} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{7} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(7 \, a^{3} c^{4} d^{6} - 2 \, a^{3} c^{2} d^{8} - {\left(6 \, a^{2} b + b^{3}\right)} c^{9} d + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{8} d^{2} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{7} d^{3} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{6} d^{4}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(7 \, a^{3} c^{3} d^{7} - 2 \, a^{3} c d^{9} - {\left(6 \, a^{2} b + b^{3}\right)} c^{8} d^{2} + 4 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{7} d^{3} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{4} - {\left(8 \, a^{3} - 3 \, a b^{2}\right)} c^{5} d^{5}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(b^{3} c^{10} d + 6 \, a b^{2} c^{9} d^{2} + 23 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c d^{10} - 11 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{8} d^{3} + {\left(26 \, a^{3} + 33 \, a b^{2}\right)} c^{7} d^{4} + {\left(21 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{5} - {\left(43 \, a^{3} + 39 \, a b^{2}\right)} c^{5} d^{6} + 6 \, {\left(2 \, a^{2} b + b^{3}\right)} c^{4} d^{7} + {\left(18 \, a b^{2} c^{11} + 6 \, a^{2} b c^{4} d^{7} - 11 \, a^{3} c^{3} d^{8} - {\left(54 \, a^{2} b + 13 \, b^{3}\right)} c^{10} d + 12 \, {\left(3 \, a^{3} + a b^{2}\right)} c^{9} d^{2} + {\left(69 \, a^{2} b + 11 \, b^{3}\right)} c^{8} d^{3} - {\left(68 \, a^{3} + 33 \, a b^{2}\right)} c^{7} d^{4} - {\left(21 \, a^{2} b - 2 \, b^{3}\right)} c^{6} d^{5} + {\left(43 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{6}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(b^{3} c^{11} + 6 \, a b^{2} c^{10} d - 5 \, a^{3} c^{2} d^{9} - {\left(27 \, a^{2} b + 10 \, b^{3}\right)} c^{9} d^{2} + {\left(20 \, a^{3} + 21 \, a b^{2}\right)} c^{8} d^{3} + {\left(24 \, a^{2} b + 7 \, b^{3}\right)} c^{7} d^{4} - 5 \, {\left(7 \, a^{3} + 6 \, a b^{2}\right)} c^{6} d^{5} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{6} + {\left(20 \, a^{3} + 3 \, a b^{2}\right)} c^{4} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(c^{15} - 4 \, c^{13} d^{2} + 6 \, c^{11} d^{4} - 4 \, c^{9} d^{6} + c^{7} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(c^{14} d - 4 \, c^{12} d^{3} + 6 \, c^{10} d^{5} - 4 \, c^{8} d^{7} + c^{6} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{13} d^{2} - 4 \, c^{11} d^{4} + 6 \, c^{9} d^{6} - 4 \, c^{7} d^{8} + c^{5} d^{10}\right)} f \cos\left(f x + e\right) + {\left(c^{12} d^{3} - 4 \, c^{10} d^{5} + 6 \, c^{8} d^{7} - 4 \, c^{6} d^{9} + c^{4} d^{11}\right)} f\right)}}\right]"," ",0,"[1/12*(12*(a^3*c^11 - 4*a^3*c^9*d^2 + 6*a^3*c^7*d^4 - 4*a^3*c^5*d^6 + a^3*c^3*d^8)*f*x*cos(f*x + e)^3 + 36*(a^3*c^10*d - 4*a^3*c^8*d^3 + 6*a^3*c^6*d^5 - 4*a^3*c^4*d^7 + a^3*c^2*d^9)*f*x*cos(f*x + e)^2 + 36*(a^3*c^9*d^2 - 4*a^3*c^7*d^4 + 6*a^3*c^5*d^6 - 4*a^3*c^3*d^8 + a^3*c*d^10)*f*x*cos(f*x + e) + 12*(a^3*c^8*d^3 - 4*a^3*c^6*d^5 + 6*a^3*c^4*d^7 - 4*a^3*c^2*d^9 + a^3*d^11)*f*x + 3*(7*a^3*c^2*d^8 - 2*a^3*d^10 - (6*a^2*b + b^3)*c^7*d^3 + 4*(2*a^3 + 3*a*b^2)*c^6*d^4 - (9*a^2*b + 4*b^3)*c^5*d^5 - (8*a^3 - 3*a*b^2)*c^4*d^6 + (7*a^3*c^5*d^5 - 2*a^3*c^3*d^7 - (6*a^2*b + b^3)*c^10 + 4*(2*a^3 + 3*a*b^2)*c^9*d - (9*a^2*b + 4*b^3)*c^8*d^2 - (8*a^3 - 3*a*b^2)*c^7*d^3)*cos(f*x + e)^3 + 3*(7*a^3*c^4*d^6 - 2*a^3*c^2*d^8 - (6*a^2*b + b^3)*c^9*d + 4*(2*a^3 + 3*a*b^2)*c^8*d^2 - (9*a^2*b + 4*b^3)*c^7*d^3 - (8*a^3 - 3*a*b^2)*c^6*d^4)*cos(f*x + e)^2 + 3*(7*a^3*c^3*d^7 - 2*a^3*c*d^9 - (6*a^2*b + b^3)*c^8*d^2 + 4*(2*a^3 + 3*a*b^2)*c^7*d^3 - (9*a^2*b + 4*b^3)*c^6*d^4 - (8*a^3 - 3*a*b^2)*c^5*d^5)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(b^3*c^10*d + 6*a*b^2*c^9*d^2 + 23*a^3*c^3*d^8 - 6*a^3*c*d^10 - 11*(3*a^2*b + b^3)*c^8*d^3 + (26*a^3 + 33*a*b^2)*c^7*d^4 + (21*a^2*b + 4*b^3)*c^6*d^5 - (43*a^3 + 39*a*b^2)*c^5*d^6 + 6*(2*a^2*b + b^3)*c^4*d^7 + (18*a*b^2*c^11 + 6*a^2*b*c^4*d^7 - 11*a^3*c^3*d^8 - (54*a^2*b + 13*b^3)*c^10*d + 12*(3*a^3 + a*b^2)*c^9*d^2 + (69*a^2*b + 11*b^3)*c^8*d^3 - (68*a^3 + 33*a*b^2)*c^7*d^4 - (21*a^2*b - 2*b^3)*c^6*d^5 + (43*a^3 + 3*a*b^2)*c^5*d^6)*cos(f*x + e)^2 + 3*(b^3*c^11 + 6*a*b^2*c^10*d - 5*a^3*c^2*d^9 - (27*a^2*b + 10*b^3)*c^9*d^2 + (20*a^3 + 21*a*b^2)*c^8*d^3 + (24*a^2*b + 7*b^3)*c^7*d^4 - 5*(7*a^3 + 6*a*b^2)*c^6*d^5 + (3*a^2*b + 2*b^3)*c^5*d^6 + (20*a^3 + 3*a*b^2)*c^4*d^7)*cos(f*x + e))*sin(f*x + e))/((c^15 - 4*c^13*d^2 + 6*c^11*d^4 - 4*c^9*d^6 + c^7*d^8)*f*cos(f*x + e)^3 + 3*(c^14*d - 4*c^12*d^3 + 6*c^10*d^5 - 4*c^8*d^7 + c^6*d^9)*f*cos(f*x + e)^2 + 3*(c^13*d^2 - 4*c^11*d^4 + 6*c^9*d^6 - 4*c^7*d^8 + c^5*d^10)*f*cos(f*x + e) + (c^12*d^3 - 4*c^10*d^5 + 6*c^8*d^7 - 4*c^6*d^9 + c^4*d^11)*f), 1/6*(6*(a^3*c^11 - 4*a^3*c^9*d^2 + 6*a^3*c^7*d^4 - 4*a^3*c^5*d^6 + a^3*c^3*d^8)*f*x*cos(f*x + e)^3 + 18*(a^3*c^10*d - 4*a^3*c^8*d^3 + 6*a^3*c^6*d^5 - 4*a^3*c^4*d^7 + a^3*c^2*d^9)*f*x*cos(f*x + e)^2 + 18*(a^3*c^9*d^2 - 4*a^3*c^7*d^4 + 6*a^3*c^5*d^6 - 4*a^3*c^3*d^8 + a^3*c*d^10)*f*x*cos(f*x + e) + 6*(a^3*c^8*d^3 - 4*a^3*c^6*d^5 + 6*a^3*c^4*d^7 - 4*a^3*c^2*d^9 + a^3*d^11)*f*x - 3*(7*a^3*c^2*d^8 - 2*a^3*d^10 - (6*a^2*b + b^3)*c^7*d^3 + 4*(2*a^3 + 3*a*b^2)*c^6*d^4 - (9*a^2*b + 4*b^3)*c^5*d^5 - (8*a^3 - 3*a*b^2)*c^4*d^6 + (7*a^3*c^5*d^5 - 2*a^3*c^3*d^7 - (6*a^2*b + b^3)*c^10 + 4*(2*a^3 + 3*a*b^2)*c^9*d - (9*a^2*b + 4*b^3)*c^8*d^2 - (8*a^3 - 3*a*b^2)*c^7*d^3)*cos(f*x + e)^3 + 3*(7*a^3*c^4*d^6 - 2*a^3*c^2*d^8 - (6*a^2*b + b^3)*c^9*d + 4*(2*a^3 + 3*a*b^2)*c^8*d^2 - (9*a^2*b + 4*b^3)*c^7*d^3 - (8*a^3 - 3*a*b^2)*c^6*d^4)*cos(f*x + e)^2 + 3*(7*a^3*c^3*d^7 - 2*a^3*c*d^9 - (6*a^2*b + b^3)*c^8*d^2 + 4*(2*a^3 + 3*a*b^2)*c^7*d^3 - (9*a^2*b + 4*b^3)*c^6*d^4 - (8*a^3 - 3*a*b^2)*c^5*d^5)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (b^3*c^10*d + 6*a*b^2*c^9*d^2 + 23*a^3*c^3*d^8 - 6*a^3*c*d^10 - 11*(3*a^2*b + b^3)*c^8*d^3 + (26*a^3 + 33*a*b^2)*c^7*d^4 + (21*a^2*b + 4*b^3)*c^6*d^5 - (43*a^3 + 39*a*b^2)*c^5*d^6 + 6*(2*a^2*b + b^3)*c^4*d^7 + (18*a*b^2*c^11 + 6*a^2*b*c^4*d^7 - 11*a^3*c^3*d^8 - (54*a^2*b + 13*b^3)*c^10*d + 12*(3*a^3 + a*b^2)*c^9*d^2 + (69*a^2*b + 11*b^3)*c^8*d^3 - (68*a^3 + 33*a*b^2)*c^7*d^4 - (21*a^2*b - 2*b^3)*c^6*d^5 + (43*a^3 + 3*a*b^2)*c^5*d^6)*cos(f*x + e)^2 + 3*(b^3*c^11 + 6*a*b^2*c^10*d - 5*a^3*c^2*d^9 - (27*a^2*b + 10*b^3)*c^9*d^2 + (20*a^3 + 21*a*b^2)*c^8*d^3 + (24*a^2*b + 7*b^3)*c^7*d^4 - 5*(7*a^3 + 6*a*b^2)*c^6*d^5 + (3*a^2*b + 2*b^3)*c^5*d^6 + (20*a^3 + 3*a*b^2)*c^4*d^7)*cos(f*x + e))*sin(f*x + e))/((c^15 - 4*c^13*d^2 + 6*c^11*d^4 - 4*c^9*d^6 + c^7*d^8)*f*cos(f*x + e)^3 + 3*(c^14*d - 4*c^12*d^3 + 6*c^10*d^5 - 4*c^8*d^7 + c^6*d^9)*f*cos(f*x + e)^2 + 3*(c^13*d^2 - 4*c^11*d^4 + 6*c^9*d^6 - 4*c^7*d^8 + c^5*d^10)*f*cos(f*x + e) + (c^12*d^3 - 4*c^10*d^5 + 6*c^8*d^7 - 4*c^6*d^9 + c^4*d^11)*f)]","B",0
197,1,4346,0,1.128796," ","integrate((a+b*sec(f*x+e))^3/(c+d*sec(f*x+e))^5,x, algorithm=""fricas"")","\left[\frac{48 \, {\left(a^{3} c^{14} - 5 \, a^{3} c^{12} d^{2} + 10 \, a^{3} c^{10} d^{4} - 10 \, a^{3} c^{8} d^{6} + 5 \, a^{3} c^{6} d^{8} - a^{3} c^{4} d^{10}\right)} f x \cos\left(f x + e\right)^{4} + 192 \, {\left(a^{3} c^{13} d - 5 \, a^{3} c^{11} d^{3} + 10 \, a^{3} c^{9} d^{5} - 10 \, a^{3} c^{7} d^{7} + 5 \, a^{3} c^{5} d^{9} - a^{3} c^{3} d^{11}\right)} f x \cos\left(f x + e\right)^{3} + 288 \, {\left(a^{3} c^{12} d^{2} - 5 \, a^{3} c^{10} d^{4} + 10 \, a^{3} c^{8} d^{6} - 10 \, a^{3} c^{6} d^{8} + 5 \, a^{3} c^{4} d^{10} - a^{3} c^{2} d^{12}\right)} f x \cos\left(f x + e\right)^{2} + 192 \, {\left(a^{3} c^{11} d^{3} - 5 \, a^{3} c^{9} d^{5} + 10 \, a^{3} c^{7} d^{7} - 10 \, a^{3} c^{5} d^{9} + 5 \, a^{3} c^{3} d^{11} - a^{3} c d^{13}\right)} f x \cos\left(f x + e\right) + 48 \, {\left(a^{3} c^{10} d^{4} - 5 \, a^{3} c^{8} d^{6} + 10 \, a^{3} c^{6} d^{8} - 10 \, a^{3} c^{4} d^{10} + 5 \, a^{3} c^{2} d^{12} - a^{3} d^{14}\right)} f x + 3 \, {\left(63 \, a^{3} c^{4} d^{9} - 36 \, a^{3} c^{2} d^{11} + 8 \, a^{3} d^{13} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{9} d^{4} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{8} d^{5} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{7} d^{6} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{6} d^{7} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{8} + {\left(63 \, a^{3} c^{8} d^{5} - 36 \, a^{3} c^{6} d^{7} + 8 \, a^{3} c^{4} d^{9} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{13} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{12} d - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{11} d^{2} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{10} d^{3} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{9} d^{4}\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(63 \, a^{3} c^{7} d^{6} - 36 \, a^{3} c^{5} d^{8} + 8 \, a^{3} c^{3} d^{10} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{12} d + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{11} d^{2} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{10} d^{3} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{9} d^{4} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{8} d^{5}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(63 \, a^{3} c^{6} d^{7} - 36 \, a^{3} c^{4} d^{9} + 8 \, a^{3} c^{2} d^{11} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{11} d^{2} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{10} d^{3} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{9} d^{4} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{8} d^{5} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{7} d^{6}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(63 \, a^{3} c^{5} d^{8} - 36 \, a^{3} c^{3} d^{10} + 8 \, a^{3} c d^{12} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{10} d^{3} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d^{4} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{8} d^{5} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{7} d^{6} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{7}\right)} \cos\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \log\left(\frac{2 \, c d \cos\left(f x + e\right) - {\left(c^{2} - 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, \sqrt{c^{2} - d^{2}} {\left(d \cos\left(f x + e\right) + c\right)} \sin\left(f x + e\right) + 2 \, c^{2} - d^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c d \cos\left(f x + e\right) + d^{2}}\right) + 2 \, {\left(2 \, b^{3} c^{12} d^{2} + 18 \, a b^{2} c^{11} d^{3} - 116 \, a^{3} c^{3} d^{11} + 24 \, a^{3} c d^{13} - {\left(150 \, a^{2} b + 41 \, b^{3}\right)} c^{10} d^{4} + 77 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d^{5} - {\left(15 \, a^{2} b + 29 \, b^{3}\right)} c^{8} d^{6} - {\left(271 \, a^{3} + 201 \, a b^{2}\right)} c^{7} d^{7} + {\left(165 \, a^{2} b + 68 \, b^{3}\right)} c^{6} d^{8} + {\left(209 \, a^{3} - 48 \, a b^{2}\right)} c^{5} d^{9} + {\left(72 \, a b^{2} c^{14} - 18 \, a^{2} b c^{5} d^{9} + 50 \, a^{3} c^{4} d^{10} - 4 \, {\left(72 \, a^{2} b + 17 \, b^{3}\right)} c^{13} d + 60 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} c^{12} d^{2} + {\left(312 \, a^{2} b + 29 \, b^{3}\right)} c^{11} d^{3} - {\left(520 \, a^{3} + 267 \, a b^{2}\right)} c^{10} d^{4} - {\left(93 \, a^{2} b - 41 \, b^{3}\right)} c^{9} d^{5} + {\left(475 \, a^{3} + 21 \, a b^{2}\right)} c^{8} d^{6} + {\left(87 \, a^{2} b - 2 \, b^{3}\right)} c^{7} d^{7} - {\left(245 \, a^{3} + 6 \, a b^{2}\right)} c^{6} d^{8}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, b^{3} c^{14} + 108 \, a b^{2} c^{13} d + 104 \, a^{3} c^{3} d^{11} - {\left(648 \, a^{2} b + 203 \, b^{3}\right)} c^{12} d^{2} + 15 \, {\left(40 \, a^{3} + 51 \, a b^{2}\right)} c^{11} d^{3} + {\left(339 \, a^{2} b + 47 \, b^{3}\right)} c^{10} d^{4} - {\left(1189 \, a^{3} + 933 \, a b^{2}\right)} c^{9} d^{5} + {\left(321 \, a^{2} b + 152 \, b^{3}\right)} c^{8} d^{6} + {\left(997 \, a^{3} + 84 \, a b^{2}\right)} c^{7} d^{7} - 4 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{6} d^{8} - 8 \, {\left(64 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{9}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, b^{3} c^{13} d + 72 \, a b^{2} c^{12} d^{2} - 407 \, a^{3} c^{4} d^{10} + 84 \, a^{3} c^{2} d^{12} - 8 \, {\left(66 \, a^{2} b + 19 \, b^{3}\right)} c^{11} d^{3} + 8 \, {\left(65 \, a^{3} + 93 \, a b^{2}\right)} c^{10} d^{4} + {\left(84 \, a^{2} b - 47 \, b^{3}\right)} c^{9} d^{5} - {\left(964 \, a^{3} + 759 \, a b^{2}\right)} c^{8} d^{6} + {\left(471 \, a^{2} b + 203 \, b^{3}\right)} c^{7} d^{7} + {\left(767 \, a^{3} - 57 \, a b^{2}\right)} c^{6} d^{8} - 3 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{9}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{48 \, {\left({\left(c^{19} - 5 \, c^{17} d^{2} + 10 \, c^{15} d^{4} - 10 \, c^{13} d^{6} + 5 \, c^{11} d^{8} - c^{9} d^{10}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{18} d - 5 \, c^{16} d^{3} + 10 \, c^{14} d^{5} - 10 \, c^{12} d^{7} + 5 \, c^{10} d^{9} - c^{8} d^{11}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{17} d^{2} - 5 \, c^{15} d^{4} + 10 \, c^{13} d^{6} - 10 \, c^{11} d^{8} + 5 \, c^{9} d^{10} - c^{7} d^{12}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{16} d^{3} - 5 \, c^{14} d^{5} + 10 \, c^{12} d^{7} - 10 \, c^{10} d^{9} + 5 \, c^{8} d^{11} - c^{6} d^{13}\right)} f \cos\left(f x + e\right) + {\left(c^{15} d^{4} - 5 \, c^{13} d^{6} + 10 \, c^{11} d^{8} - 10 \, c^{9} d^{10} + 5 \, c^{7} d^{12} - c^{5} d^{14}\right)} f\right)}}, \frac{24 \, {\left(a^{3} c^{14} - 5 \, a^{3} c^{12} d^{2} + 10 \, a^{3} c^{10} d^{4} - 10 \, a^{3} c^{8} d^{6} + 5 \, a^{3} c^{6} d^{8} - a^{3} c^{4} d^{10}\right)} f x \cos\left(f x + e\right)^{4} + 96 \, {\left(a^{3} c^{13} d - 5 \, a^{3} c^{11} d^{3} + 10 \, a^{3} c^{9} d^{5} - 10 \, a^{3} c^{7} d^{7} + 5 \, a^{3} c^{5} d^{9} - a^{3} c^{3} d^{11}\right)} f x \cos\left(f x + e\right)^{3} + 144 \, {\left(a^{3} c^{12} d^{2} - 5 \, a^{3} c^{10} d^{4} + 10 \, a^{3} c^{8} d^{6} - 10 \, a^{3} c^{6} d^{8} + 5 \, a^{3} c^{4} d^{10} - a^{3} c^{2} d^{12}\right)} f x \cos\left(f x + e\right)^{2} + 96 \, {\left(a^{3} c^{11} d^{3} - 5 \, a^{3} c^{9} d^{5} + 10 \, a^{3} c^{7} d^{7} - 10 \, a^{3} c^{5} d^{9} + 5 \, a^{3} c^{3} d^{11} - a^{3} c d^{13}\right)} f x \cos\left(f x + e\right) + 24 \, {\left(a^{3} c^{10} d^{4} - 5 \, a^{3} c^{8} d^{6} + 10 \, a^{3} c^{6} d^{8} - 10 \, a^{3} c^{4} d^{10} + 5 \, a^{3} c^{2} d^{12} - a^{3} d^{14}\right)} f x - 3 \, {\left(63 \, a^{3} c^{4} d^{9} - 36 \, a^{3} c^{2} d^{11} + 8 \, a^{3} d^{13} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{9} d^{4} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{8} d^{5} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{7} d^{6} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{6} d^{7} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{8} + {\left(63 \, a^{3} c^{8} d^{5} - 36 \, a^{3} c^{6} d^{7} + 8 \, a^{3} c^{4} d^{9} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{13} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{12} d - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{11} d^{2} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{10} d^{3} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{9} d^{4}\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(63 \, a^{3} c^{7} d^{6} - 36 \, a^{3} c^{5} d^{8} + 8 \, a^{3} c^{3} d^{10} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{12} d + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{11} d^{2} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{10} d^{3} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{9} d^{4} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{8} d^{5}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(63 \, a^{3} c^{6} d^{7} - 36 \, a^{3} c^{4} d^{9} + 8 \, a^{3} c^{2} d^{11} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{11} d^{2} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{10} d^{3} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{9} d^{4} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{8} d^{5} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{7} d^{6}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(63 \, a^{3} c^{5} d^{8} - 36 \, a^{3} c^{3} d^{10} + 8 \, a^{3} c d^{12} - 4 \, {\left(6 \, a^{2} b + b^{3}\right)} c^{10} d^{3} + 20 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d^{4} - 9 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} c^{8} d^{5} - 5 \, {\left(8 \, a^{3} - 9 \, a b^{2}\right)} c^{7} d^{6} - {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{6} d^{7}\right)} \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \arctan\left(-\frac{\sqrt{-c^{2} + d^{2}} {\left(d \cos\left(f x + e\right) + c\right)}}{{\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)}\right) + {\left(2 \, b^{3} c^{12} d^{2} + 18 \, a b^{2} c^{11} d^{3} - 116 \, a^{3} c^{3} d^{11} + 24 \, a^{3} c d^{13} - {\left(150 \, a^{2} b + 41 \, b^{3}\right)} c^{10} d^{4} + 77 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{9} d^{5} - {\left(15 \, a^{2} b + 29 \, b^{3}\right)} c^{8} d^{6} - {\left(271 \, a^{3} + 201 \, a b^{2}\right)} c^{7} d^{7} + {\left(165 \, a^{2} b + 68 \, b^{3}\right)} c^{6} d^{8} + {\left(209 \, a^{3} - 48 \, a b^{2}\right)} c^{5} d^{9} + {\left(72 \, a b^{2} c^{14} - 18 \, a^{2} b c^{5} d^{9} + 50 \, a^{3} c^{4} d^{10} - 4 \, {\left(72 \, a^{2} b + 17 \, b^{3}\right)} c^{13} d + 60 \, {\left(4 \, a^{3} + 3 \, a b^{2}\right)} c^{12} d^{2} + {\left(312 \, a^{2} b + 29 \, b^{3}\right)} c^{11} d^{3} - {\left(520 \, a^{3} + 267 \, a b^{2}\right)} c^{10} d^{4} - {\left(93 \, a^{2} b - 41 \, b^{3}\right)} c^{9} d^{5} + {\left(475 \, a^{3} + 21 \, a b^{2}\right)} c^{8} d^{6} + {\left(87 \, a^{2} b - 2 \, b^{3}\right)} c^{7} d^{7} - {\left(245 \, a^{3} + 6 \, a b^{2}\right)} c^{6} d^{8}\right)} \cos\left(f x + e\right)^{3} + {\left(12 \, b^{3} c^{14} + 108 \, a b^{2} c^{13} d + 104 \, a^{3} c^{3} d^{11} - {\left(648 \, a^{2} b + 203 \, b^{3}\right)} c^{12} d^{2} + 15 \, {\left(40 \, a^{3} + 51 \, a b^{2}\right)} c^{11} d^{3} + {\left(339 \, a^{2} b + 47 \, b^{3}\right)} c^{10} d^{4} - {\left(1189 \, a^{3} + 933 \, a b^{2}\right)} c^{9} d^{5} + {\left(321 \, a^{2} b + 152 \, b^{3}\right)} c^{8} d^{6} + {\left(997 \, a^{3} + 84 \, a b^{2}\right)} c^{7} d^{7} - 4 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{6} d^{8} - 8 \, {\left(64 \, a^{3} + 3 \, a b^{2}\right)} c^{5} d^{9}\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, b^{3} c^{13} d + 72 \, a b^{2} c^{12} d^{2} - 407 \, a^{3} c^{4} d^{10} + 84 \, a^{3} c^{2} d^{12} - 8 \, {\left(66 \, a^{2} b + 19 \, b^{3}\right)} c^{11} d^{3} + 8 \, {\left(65 \, a^{3} + 93 \, a b^{2}\right)} c^{10} d^{4} + {\left(84 \, a^{2} b - 47 \, b^{3}\right)} c^{9} d^{5} - {\left(964 \, a^{3} + 759 \, a b^{2}\right)} c^{8} d^{6} + {\left(471 \, a^{2} b + 203 \, b^{3}\right)} c^{7} d^{7} + {\left(767 \, a^{3} - 57 \, a b^{2}\right)} c^{6} d^{8} - 3 \, {\left(9 \, a^{2} b + 4 \, b^{3}\right)} c^{5} d^{9}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, {\left({\left(c^{19} - 5 \, c^{17} d^{2} + 10 \, c^{15} d^{4} - 10 \, c^{13} d^{6} + 5 \, c^{11} d^{8} - c^{9} d^{10}\right)} f \cos\left(f x + e\right)^{4} + 4 \, {\left(c^{18} d - 5 \, c^{16} d^{3} + 10 \, c^{14} d^{5} - 10 \, c^{12} d^{7} + 5 \, c^{10} d^{9} - c^{8} d^{11}\right)} f \cos\left(f x + e\right)^{3} + 6 \, {\left(c^{17} d^{2} - 5 \, c^{15} d^{4} + 10 \, c^{13} d^{6} - 10 \, c^{11} d^{8} + 5 \, c^{9} d^{10} - c^{7} d^{12}\right)} f \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{16} d^{3} - 5 \, c^{14} d^{5} + 10 \, c^{12} d^{7} - 10 \, c^{10} d^{9} + 5 \, c^{8} d^{11} - c^{6} d^{13}\right)} f \cos\left(f x + e\right) + {\left(c^{15} d^{4} - 5 \, c^{13} d^{6} + 10 \, c^{11} d^{8} - 10 \, c^{9} d^{10} + 5 \, c^{7} d^{12} - c^{5} d^{14}\right)} f\right)}}\right]"," ",0,"[1/48*(48*(a^3*c^14 - 5*a^3*c^12*d^2 + 10*a^3*c^10*d^4 - 10*a^3*c^8*d^6 + 5*a^3*c^6*d^8 - a^3*c^4*d^10)*f*x*cos(f*x + e)^4 + 192*(a^3*c^13*d - 5*a^3*c^11*d^3 + 10*a^3*c^9*d^5 - 10*a^3*c^7*d^7 + 5*a^3*c^5*d^9 - a^3*c^3*d^11)*f*x*cos(f*x + e)^3 + 288*(a^3*c^12*d^2 - 5*a^3*c^10*d^4 + 10*a^3*c^8*d^6 - 10*a^3*c^6*d^8 + 5*a^3*c^4*d^10 - a^3*c^2*d^12)*f*x*cos(f*x + e)^2 + 192*(a^3*c^11*d^3 - 5*a^3*c^9*d^5 + 10*a^3*c^7*d^7 - 10*a^3*c^5*d^9 + 5*a^3*c^3*d^11 - a^3*c*d^13)*f*x*cos(f*x + e) + 48*(a^3*c^10*d^4 - 5*a^3*c^8*d^6 + 10*a^3*c^6*d^8 - 10*a^3*c^4*d^10 + 5*a^3*c^2*d^12 - a^3*d^14)*f*x + 3*(63*a^3*c^4*d^9 - 36*a^3*c^2*d^11 + 8*a^3*d^13 - 4*(6*a^2*b + b^3)*c^9*d^4 + 20*(2*a^3 + 3*a*b^2)*c^8*d^5 - 9*(8*a^2*b + 3*b^3)*c^7*d^6 - 5*(8*a^3 - 9*a*b^2)*c^6*d^7 - (9*a^2*b + 4*b^3)*c^5*d^8 + (63*a^3*c^8*d^5 - 36*a^3*c^6*d^7 + 8*a^3*c^4*d^9 - 4*(6*a^2*b + b^3)*c^13 + 20*(2*a^3 + 3*a*b^2)*c^12*d - 9*(8*a^2*b + 3*b^3)*c^11*d^2 - 5*(8*a^3 - 9*a*b^2)*c^10*d^3 - (9*a^2*b + 4*b^3)*c^9*d^4)*cos(f*x + e)^4 + 4*(63*a^3*c^7*d^6 - 36*a^3*c^5*d^8 + 8*a^3*c^3*d^10 - 4*(6*a^2*b + b^3)*c^12*d + 20*(2*a^3 + 3*a*b^2)*c^11*d^2 - 9*(8*a^2*b + 3*b^3)*c^10*d^3 - 5*(8*a^3 - 9*a*b^2)*c^9*d^4 - (9*a^2*b + 4*b^3)*c^8*d^5)*cos(f*x + e)^3 + 6*(63*a^3*c^6*d^7 - 36*a^3*c^4*d^9 + 8*a^3*c^2*d^11 - 4*(6*a^2*b + b^3)*c^11*d^2 + 20*(2*a^3 + 3*a*b^2)*c^10*d^3 - 9*(8*a^2*b + 3*b^3)*c^9*d^4 - 5*(8*a^3 - 9*a*b^2)*c^8*d^5 - (9*a^2*b + 4*b^3)*c^7*d^6)*cos(f*x + e)^2 + 4*(63*a^3*c^5*d^8 - 36*a^3*c^3*d^10 + 8*a^3*c*d^12 - 4*(6*a^2*b + b^3)*c^10*d^3 + 20*(2*a^3 + 3*a*b^2)*c^9*d^4 - 9*(8*a^2*b + 3*b^3)*c^8*d^5 - 5*(8*a^3 - 9*a*b^2)*c^7*d^6 - (9*a^2*b + 4*b^3)*c^6*d^7)*cos(f*x + e))*sqrt(c^2 - d^2)*log((2*c*d*cos(f*x + e) - (c^2 - 2*d^2)*cos(f*x + e)^2 - 2*sqrt(c^2 - d^2)*(d*cos(f*x + e) + c)*sin(f*x + e) + 2*c^2 - d^2)/(c^2*cos(f*x + e)^2 + 2*c*d*cos(f*x + e) + d^2)) + 2*(2*b^3*c^12*d^2 + 18*a*b^2*c^11*d^3 - 116*a^3*c^3*d^11 + 24*a^3*c*d^13 - (150*a^2*b + 41*b^3)*c^10*d^4 + 77*(2*a^3 + 3*a*b^2)*c^9*d^5 - (15*a^2*b + 29*b^3)*c^8*d^6 - (271*a^3 + 201*a*b^2)*c^7*d^7 + (165*a^2*b + 68*b^3)*c^6*d^8 + (209*a^3 - 48*a*b^2)*c^5*d^9 + (72*a*b^2*c^14 - 18*a^2*b*c^5*d^9 + 50*a^3*c^4*d^10 - 4*(72*a^2*b + 17*b^3)*c^13*d + 60*(4*a^3 + 3*a*b^2)*c^12*d^2 + (312*a^2*b + 29*b^3)*c^11*d^3 - (520*a^3 + 267*a*b^2)*c^10*d^4 - (93*a^2*b - 41*b^3)*c^9*d^5 + (475*a^3 + 21*a*b^2)*c^8*d^6 + (87*a^2*b - 2*b^3)*c^7*d^7 - (245*a^3 + 6*a*b^2)*c^6*d^8)*cos(f*x + e)^3 + (12*b^3*c^14 + 108*a*b^2*c^13*d + 104*a^3*c^3*d^11 - (648*a^2*b + 203*b^3)*c^12*d^2 + 15*(40*a^3 + 51*a*b^2)*c^11*d^3 + (339*a^2*b + 47*b^3)*c^10*d^4 - (1189*a^3 + 933*a*b^2)*c^9*d^5 + (321*a^2*b + 152*b^3)*c^8*d^6 + (997*a^3 + 84*a*b^2)*c^7*d^7 - 4*(3*a^2*b + 2*b^3)*c^6*d^8 - 8*(64*a^3 + 3*a*b^2)*c^5*d^9)*cos(f*x + e)^2 + (8*b^3*c^13*d + 72*a*b^2*c^12*d^2 - 407*a^3*c^4*d^10 + 84*a^3*c^2*d^12 - 8*(66*a^2*b + 19*b^3)*c^11*d^3 + 8*(65*a^3 + 93*a*b^2)*c^10*d^4 + (84*a^2*b - 47*b^3)*c^9*d^5 - (964*a^3 + 759*a*b^2)*c^8*d^6 + (471*a^2*b + 203*b^3)*c^7*d^7 + (767*a^3 - 57*a*b^2)*c^6*d^8 - 3*(9*a^2*b + 4*b^3)*c^5*d^9)*cos(f*x + e))*sin(f*x + e))/((c^19 - 5*c^17*d^2 + 10*c^15*d^4 - 10*c^13*d^6 + 5*c^11*d^8 - c^9*d^10)*f*cos(f*x + e)^4 + 4*(c^18*d - 5*c^16*d^3 + 10*c^14*d^5 - 10*c^12*d^7 + 5*c^10*d^9 - c^8*d^11)*f*cos(f*x + e)^3 + 6*(c^17*d^2 - 5*c^15*d^4 + 10*c^13*d^6 - 10*c^11*d^8 + 5*c^9*d^10 - c^7*d^12)*f*cos(f*x + e)^2 + 4*(c^16*d^3 - 5*c^14*d^5 + 10*c^12*d^7 - 10*c^10*d^9 + 5*c^8*d^11 - c^6*d^13)*f*cos(f*x + e) + (c^15*d^4 - 5*c^13*d^6 + 10*c^11*d^8 - 10*c^9*d^10 + 5*c^7*d^12 - c^5*d^14)*f), 1/24*(24*(a^3*c^14 - 5*a^3*c^12*d^2 + 10*a^3*c^10*d^4 - 10*a^3*c^8*d^6 + 5*a^3*c^6*d^8 - a^3*c^4*d^10)*f*x*cos(f*x + e)^4 + 96*(a^3*c^13*d - 5*a^3*c^11*d^3 + 10*a^3*c^9*d^5 - 10*a^3*c^7*d^7 + 5*a^3*c^5*d^9 - a^3*c^3*d^11)*f*x*cos(f*x + e)^3 + 144*(a^3*c^12*d^2 - 5*a^3*c^10*d^4 + 10*a^3*c^8*d^6 - 10*a^3*c^6*d^8 + 5*a^3*c^4*d^10 - a^3*c^2*d^12)*f*x*cos(f*x + e)^2 + 96*(a^3*c^11*d^3 - 5*a^3*c^9*d^5 + 10*a^3*c^7*d^7 - 10*a^3*c^5*d^9 + 5*a^3*c^3*d^11 - a^3*c*d^13)*f*x*cos(f*x + e) + 24*(a^3*c^10*d^4 - 5*a^3*c^8*d^6 + 10*a^3*c^6*d^8 - 10*a^3*c^4*d^10 + 5*a^3*c^2*d^12 - a^3*d^14)*f*x - 3*(63*a^3*c^4*d^9 - 36*a^3*c^2*d^11 + 8*a^3*d^13 - 4*(6*a^2*b + b^3)*c^9*d^4 + 20*(2*a^3 + 3*a*b^2)*c^8*d^5 - 9*(8*a^2*b + 3*b^3)*c^7*d^6 - 5*(8*a^3 - 9*a*b^2)*c^6*d^7 - (9*a^2*b + 4*b^3)*c^5*d^8 + (63*a^3*c^8*d^5 - 36*a^3*c^6*d^7 + 8*a^3*c^4*d^9 - 4*(6*a^2*b + b^3)*c^13 + 20*(2*a^3 + 3*a*b^2)*c^12*d - 9*(8*a^2*b + 3*b^3)*c^11*d^2 - 5*(8*a^3 - 9*a*b^2)*c^10*d^3 - (9*a^2*b + 4*b^3)*c^9*d^4)*cos(f*x + e)^4 + 4*(63*a^3*c^7*d^6 - 36*a^3*c^5*d^8 + 8*a^3*c^3*d^10 - 4*(6*a^2*b + b^3)*c^12*d + 20*(2*a^3 + 3*a*b^2)*c^11*d^2 - 9*(8*a^2*b + 3*b^3)*c^10*d^3 - 5*(8*a^3 - 9*a*b^2)*c^9*d^4 - (9*a^2*b + 4*b^3)*c^8*d^5)*cos(f*x + e)^3 + 6*(63*a^3*c^6*d^7 - 36*a^3*c^4*d^9 + 8*a^3*c^2*d^11 - 4*(6*a^2*b + b^3)*c^11*d^2 + 20*(2*a^3 + 3*a*b^2)*c^10*d^3 - 9*(8*a^2*b + 3*b^3)*c^9*d^4 - 5*(8*a^3 - 9*a*b^2)*c^8*d^5 - (9*a^2*b + 4*b^3)*c^7*d^6)*cos(f*x + e)^2 + 4*(63*a^3*c^5*d^8 - 36*a^3*c^3*d^10 + 8*a^3*c*d^12 - 4*(6*a^2*b + b^3)*c^10*d^3 + 20*(2*a^3 + 3*a*b^2)*c^9*d^4 - 9*(8*a^2*b + 3*b^3)*c^8*d^5 - 5*(8*a^3 - 9*a*b^2)*c^7*d^6 - (9*a^2*b + 4*b^3)*c^6*d^7)*cos(f*x + e))*sqrt(-c^2 + d^2)*arctan(-sqrt(-c^2 + d^2)*(d*cos(f*x + e) + c)/((c^2 - d^2)*sin(f*x + e))) + (2*b^3*c^12*d^2 + 18*a*b^2*c^11*d^3 - 116*a^3*c^3*d^11 + 24*a^3*c*d^13 - (150*a^2*b + 41*b^3)*c^10*d^4 + 77*(2*a^3 + 3*a*b^2)*c^9*d^5 - (15*a^2*b + 29*b^3)*c^8*d^6 - (271*a^3 + 201*a*b^2)*c^7*d^7 + (165*a^2*b + 68*b^3)*c^6*d^8 + (209*a^3 - 48*a*b^2)*c^5*d^9 + (72*a*b^2*c^14 - 18*a^2*b*c^5*d^9 + 50*a^3*c^4*d^10 - 4*(72*a^2*b + 17*b^3)*c^13*d + 60*(4*a^3 + 3*a*b^2)*c^12*d^2 + (312*a^2*b + 29*b^3)*c^11*d^3 - (520*a^3 + 267*a*b^2)*c^10*d^4 - (93*a^2*b - 41*b^3)*c^9*d^5 + (475*a^3 + 21*a*b^2)*c^8*d^6 + (87*a^2*b - 2*b^3)*c^7*d^7 - (245*a^3 + 6*a*b^2)*c^6*d^8)*cos(f*x + e)^3 + (12*b^3*c^14 + 108*a*b^2*c^13*d + 104*a^3*c^3*d^11 - (648*a^2*b + 203*b^3)*c^12*d^2 + 15*(40*a^3 + 51*a*b^2)*c^11*d^3 + (339*a^2*b + 47*b^3)*c^10*d^4 - (1189*a^3 + 933*a*b^2)*c^9*d^5 + (321*a^2*b + 152*b^3)*c^8*d^6 + (997*a^3 + 84*a*b^2)*c^7*d^7 - 4*(3*a^2*b + 2*b^3)*c^6*d^8 - 8*(64*a^3 + 3*a*b^2)*c^5*d^9)*cos(f*x + e)^2 + (8*b^3*c^13*d + 72*a*b^2*c^12*d^2 - 407*a^3*c^4*d^10 + 84*a^3*c^2*d^12 - 8*(66*a^2*b + 19*b^3)*c^11*d^3 + 8*(65*a^3 + 93*a*b^2)*c^10*d^4 + (84*a^2*b - 47*b^3)*c^9*d^5 - (964*a^3 + 759*a*b^2)*c^8*d^6 + (471*a^2*b + 203*b^3)*c^7*d^7 + (767*a^3 - 57*a*b^2)*c^6*d^8 - 3*(9*a^2*b + 4*b^3)*c^5*d^9)*cos(f*x + e))*sin(f*x + e))/((c^19 - 5*c^17*d^2 + 10*c^15*d^4 - 10*c^13*d^6 + 5*c^11*d^8 - c^9*d^10)*f*cos(f*x + e)^4 + 4*(c^18*d - 5*c^16*d^3 + 10*c^14*d^5 - 10*c^12*d^7 + 5*c^10*d^9 - c^8*d^11)*f*cos(f*x + e)^3 + 6*(c^17*d^2 - 5*c^15*d^4 + 10*c^13*d^6 - 10*c^11*d^8 + 5*c^9*d^10 - c^7*d^12)*f*cos(f*x + e)^2 + 4*(c^16*d^3 - 5*c^14*d^5 + 10*c^12*d^7 - 10*c^10*d^9 + 5*c^8*d^11 - c^6*d^13)*f*cos(f*x + e) + (c^15*d^4 - 5*c^13*d^6 + 10*c^11*d^8 - 10*c^9*d^10 + 5*c^7*d^12 - c^5*d^14)*f)]","B",0
198,0,0,0,0.793536," ","integrate((c+d*sec(f*x+e))*(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c), x)","F",0
199,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,1.279948," ","integrate((a+b*sec(f*x+e))^(3/2)*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b d \sec\left(f x + e\right)^{2} + a c + {\left(b c + a d\right)} \sec\left(f x + e\right)\right)} \sqrt{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((b*d*sec(f*x + e)^2 + a*c + (b*c + a*d)*sec(f*x + e))*sqrt(b*sec(f*x + e) + a), x)","F",0
201,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,0,0,0,1.465862," ","integrate((a+b*sec(f*x+e))^(5/2)*(c+d*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} d \sec\left(f x + e\right)^{3} + a^{2} c + {\left(b^{2} c + 2 \, a b d\right)} \sec\left(f x + e\right)^{2} + {\left(2 \, a b c + a^{2} d\right)} \sec\left(f x + e\right)\right)} \sqrt{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral((b^2*d*sec(f*x + e)^3 + a^2*c + (b^2*c + 2*a*b*d)*sec(f*x + e)^2 + (2*a*b*c + a^2*d)*sec(f*x + e))*sqrt(b*sec(f*x + e) + a), x)","F",0
203,0,0,0,1.380896," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{d \sec\left(f x + e\right) + c}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral((d*sec(f*x + e) + c)/sqrt(b*sec(f*x + e) + a), x)","F",0
204,-1,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,0,0,0,1.591804," ","integrate((c+d*sec(f*x+e))/(a+b*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} {\left(d \sec\left(f x + e\right) + c\right)}}{b^{3} \sec\left(f x + e\right)^{3} + 3 \, a b^{2} \sec\left(f x + e\right)^{2} + 3 \, a^{2} b \sec\left(f x + e\right) + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*(d*sec(f*x + e) + c)/(b^3*sec(f*x + e)^3 + 3*a*b^2*sec(f*x + e)^2 + 3*a^2*b*sec(f*x + e) + a^3), x)","F",0
207,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)*(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,0,0,0,9.290598," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sec\left(f x + e\right) + c}}{d^{3} \sec\left(f x + e\right)^{3} + 3 \, c d^{2} \sec\left(f x + e\right)^{2} + 3 \, c^{2} d \sec\left(f x + e\right) + c^{3}}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^(3/2)*sqrt(d*sec(f*x + e) + c)/(d^3*sec(f*x + e)^3 + 3*c*d^2*sec(f*x + e)^2 + 3*c^2*d*sec(f*x + e) + c^3), x)","F",0
213,0,0,0,8.698743," ","integrate((a+b*sec(f*x+e))^(3/2)/(c+d*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sec\left(f x + e\right) + c}}{d^{4} \sec\left(f x + e\right)^{4} + 4 \, c d^{3} \sec\left(f x + e\right)^{3} + 6 \, c^{2} d^{2} \sec\left(f x + e\right)^{2} + 4 \, c^{3} d \sec\left(f x + e\right) + c^{4}}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)^(3/2)*sqrt(d*sec(f*x + e) + c)/(d^4*sec(f*x + e)^4 + 4*c*d^3*sec(f*x + e)^3 + 6*c^2*d^2*sec(f*x + e)^2 + 4*c^3*d*sec(f*x + e) + c^4), x)","F",0
214,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(7/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(5/2)/(c+d*sec(f*x+e))^(9/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,0,0,0,4.521491," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d \sec\left(f x + e\right) + c}}{\sqrt{b \sec\left(f x + e\right) + a}}, x\right)"," ",0,"integral(sqrt(d*sec(f*x + e) + c)/sqrt(b*sec(f*x + e) + a), x)","F",0
219,0,0,0,5.836422," ","integrate(1/(c+d*sec(f*x+e))^(1/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sec\left(f x + e\right) + a} \sqrt{d \sec\left(f x + e\right) + c}}{b d \sec\left(f x + e\right)^{2} + a c + {\left(b c + a d\right)} \sec\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sec(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)/(b*d*sec(f*x + e)^2 + a*c + (b*c + a*d)*sec(f*x + e)), x)","F",0
220,-1,0,0,0.000000," ","integrate(1/(c+d*sec(f*x+e))^(3/2)/(a+b*sec(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(1/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(1/3)/(c+d*sec(f*x+e))^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(2/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(5/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(2/3)/(c+d*sec(f*x+e))^(8/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(4/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(7/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((a+b*sec(f*x+e))^(4/3)/(c+d*sec(f*x+e))^(10/3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,0,0,0,1.009643," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n} {\left(a \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n*(a*sec(f*x + e) + a)^m, x)","F",0
231,0,0,0,0.784018," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} \sec\left(f x + e\right)^{3} + 3 \, a^{3} \sec\left(f x + e\right)^{2} + 3 \, a^{3} \sec\left(f x + e\right) + a^{3}\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((a^3*sec(f*x + e)^3 + 3*a^3*sec(f*x + e)^2 + 3*a^3*sec(f*x + e) + a^3)*((d*sec(f*x + e))^p*c)^n, x)","F",0
232,0,0,0,0.916749," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2)*((d*sec(f*x + e))^p*c)^n, x)","F",0
233,0,0,0,0.956278," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sec\left(f x + e\right) + a\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((a*sec(f*x + e) + a)*((d*sec(f*x + e))^p*c)^n, x)","F",0
234,0,0,0,0.676946," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{a \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n/(a*sec(f*x + e) + a), x)","F",0
235,0,0,0,0.471461," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+a*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{a^{2} \sec\left(f x + e\right)^{2} + 2 \, a^{2} \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n/(a^2*sec(f*x + e)^2 + 2*a^2*sec(f*x + e) + a^2), x)","F",0
236,0,0,0,0.520568," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \sec\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n*(b*sec(f*x + e) + a)^m, x)","F",0
237,0,0,0,0.438185," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{3} \sec\left(f x + e\right)^{3} + 3 \, a b^{2} \sec\left(f x + e\right)^{2} + 3 \, a^{2} b \sec\left(f x + e\right) + a^{3}\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b^3*sec(f*x + e)^3 + 3*a*b^2*sec(f*x + e)^2 + 3*a^2*b*sec(f*x + e) + a^3)*((d*sec(f*x + e))^p*c)^n, x)","F",0
238,0,0,0,0.467323," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2)*((d*sec(f*x + e))^p*c)^n, x)","F",0
239,0,0,0,0.452322," ","integrate((c*(d*sec(f*x+e))^p)^n*(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(f x + e\right) + a\right)} \left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}, x\right)"," ",0,"integral((b*sec(f*x + e) + a)*((d*sec(f*x + e))^p*c)^n, x)","F",0
240,0,0,0,0.441116," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{b \sec\left(f x + e\right) + a}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n/(b*sec(f*x + e) + a), x)","F",0
241,0,0,0,0.488151," ","integrate((c*(d*sec(f*x+e))^p)^n/(a+b*sec(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(\left(d \sec\left(f x + e\right)\right)^{p} c\right)^{n}}{b^{2} \sec\left(f x + e\right)^{2} + 2 \, a b \sec\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral(((d*sec(f*x + e))^p*c)^n/(b^2*sec(f*x + e)^2 + 2*a*b*sec(f*x + e) + a^2), x)","F",0
