1,1,361,0,0.414032," ","integrate((A+B*sin(x))/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{B {\left(a + b\right)} {\left(a - b\right)}^{2} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(\sqrt{a^{2} - b^{2}} A b {\left| a - b \right|} + \sqrt{a^{2} - b^{2}} A {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(A b - A {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}} - \frac{{\left(B a - B b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{b^{2} - a {\left| b \right|}}"," ",0,"-B*(a + b)*(a - b)^2*log(tan(1/2*x)^2 + 1/2*(2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (sqrt(a^2 - b^2)*A*b*abs(a - b) + sqrt(a^2 - b^2)*A*abs(a - b)*abs(b))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (A*b - A*abs(b))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)) - (B*a - B*b)*log(tan(1/2*x)^2 + 1/2*(2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/(b^2 - a*abs(b))","B",0
2,1,18,0,0.851745," ","integrate((A+B*sin(x))/(1+cos(x)),x, algorithm=""giac"")","B \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + A \tan\left(\frac{1}{2} \, x\right)"," ",0,"B*log(tan(1/2*x)^2 + 1) + A*tan(1/2*x)","A",0
3,1,39,0,1.936357," ","integrate((A+B*sin(x))/(1-cos(x)),x, algorithm=""giac"")","-B \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 2 \, B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right) - \frac{2 \, B \tan\left(\frac{1}{2} \, x\right) + A}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-B*log(tan(1/2*x)^2 + 1) + 2*B*log(abs(tan(1/2*x))) - (2*B*tan(1/2*x) + A)/tan(1/2*x)","A",0
4,1,407,0,0.472708," ","integrate((b+c+sin(x))/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{{\left(a + b\right)} {\left(a - b\right)}^{2} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(\sqrt{a^{2} - b^{2}} b^{2} {\left| a - b \right|} + \sqrt{a^{2} - b^{2}} b c {\left| a - b \right|} + \sqrt{a^{2} - b^{2}} b {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} c {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(b^{2} + b c - b {\left| b \right|} - c {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}} - \frac{{\left(a - b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + \frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{b^{2} - a {\left| b \right|}}"," ",0,"-(a + b)*(a - b)^2*log(tan(1/2*x)^2 + 1/2*(2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (sqrt(a^2 - b^2)*b^2*abs(a - b) + sqrt(a^2 - b^2)*b*c*abs(a - b) + sqrt(a^2 - b^2)*b*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*c*abs(a - b)*abs(b))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (b^2 + b*c - b*abs(b) - c*abs(b))*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)) - (a - b)*log(tan(1/2*x)^2 + 1/2*(2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/(b^2 - a*abs(b))","B",0
5,1,103,0,0.365108," ","integrate((b+c+sin(x))/(a-b*cos(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a + 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(b + c\right)}}{\sqrt{a^{2} - b^{2}}} + \frac{\log\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} + a - b\right)}{b} - \frac{\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(2*a + 2*b) + arctan((a*tan(1/2*x) + b*tan(1/2*x))/sqrt(a^2 - b^2)))*(b + c)/sqrt(a^2 - b^2) + log(a*tan(1/2*x)^2 + b*tan(1/2*x)^2 + a - b)/b - log(tan(1/2*x)^2 + 1)/b","B",0
6,1,121,0,3.956422," ","integrate((A+B*tan(x))/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} A}{\sqrt{a^{2} - b^{2}}} + \frac{B \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b\right)}{a} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{a} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{a}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*A/sqrt(a^2 - b^2) + B*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - a - b)/a - B*log(abs(tan(1/2*x) + 1))/a - B*log(abs(tan(1/2*x) - 1))/a","B",0
7,1,116,0,0.382374," ","integrate((A+B*cot(x))/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{B a \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b\right)}{a^{2} - b^{2}} - \frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} A}{\sqrt{a^{2} - b^{2}}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a + b}"," ",0,"-B*a*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - a - b)/(a^2 - b^2) - 2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*A/sqrt(a^2 - b^2) + B*log(abs(tan(1/2*x)))/(a + b)","A",0
8,1,115,0,0.413154," ","integrate((A+B*csc(x))/(a+b*cos(x)),x, algorithm=""giac"")","\frac{B b \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b\right)}{a^{2} - b^{2}} - \frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - b \tan\left(\frac{1}{2} \, x\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} A}{\sqrt{a^{2} - b^{2}}} + \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{a + b}"," ",0,"B*b*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - a - b)/(a^2 - b^2) - 2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x))/sqrt(a^2 - b^2)))*A/sqrt(a^2 - b^2) + B*log(abs(tan(1/2*x)))/(a + b)","A",0
9,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^4/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((-2*c^4*a^4+8*c^3*b*a^3*d-12*c^2*b^2*a^2*d^2+8*c*b^3*a*d^3-2*b^4*d^4)*1/2/a^4/sqrt(a^2-b^2)*(atan((-a*tan((f*x+exp(1))/2)+b*tan((f*x+exp(1))/2))/sqrt(a^2-b^2))+pi*sign(2*b-2*a)*floor((f*x+exp(1))/2/pi+1/2))-(8*c^3*a^3*d-12*c^2*b*a^2*d^2+8*c*b^2*a*d^3+4*c*a^3*d^3-2*b^3*d^4-b*a^2*d^4)*1/4/a^4*ln(abs(tan((f*x+exp(1))/2)-1))+(8*c^3*a^3*d-12*c^2*b*a^2*d^2+8*c*b^2*a*d^3+4*c*a^3*d^3-2*b^3*d^4-b*a^2*d^4)*1/4/a^4*ln(abs(tan((f*x+exp(1))/2)+1))+(-36*tan((f*x+exp(1))/2)^5*c^2*a^2*d^2+24*tan((f*x+exp(1))/2)^5*c*b*a*d^3+12*tan((f*x+exp(1))/2)^5*c*a^2*d^3-6*tan((f*x+exp(1))/2)^5*b^2*d^4-3*tan((f*x+exp(1))/2)^5*b*a*d^4-6*tan((f*x+exp(1))/2)^5*a^2*d^4+72*tan((f*x+exp(1))/2)^3*c^2*a^2*d^2-48*tan((f*x+exp(1))/2)^3*c*b*a*d^3+12*tan((f*x+exp(1))/2)^3*b^2*d^4+4*tan((f*x+exp(1))/2)^3*a^2*d^4-36*tan((f*x+exp(1))/2)*c^2*a^2*d^2+24*tan((f*x+exp(1))/2)*c*b*a*d^3-12*tan((f*x+exp(1))/2)*c*a^2*d^3-6*tan((f*x+exp(1))/2)*b^2*d^4+3*tan((f*x+exp(1))/2)*b*a*d^4-6*tan((f*x+exp(1))/2)*a^2*d^4)*1/6/a^3/(tan((f*x+exp(1))/2)^2-1)^3)","F(-2)",0
10,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^3/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((-2*c^3*a^3+6*c^2*b*a^2*d-6*c*b^2*a*d^2+2*b^3*d^3)*1/2/a^3/sqrt(a^2-b^2)*(atan((-a*tan((f*x+exp(1))/2)+b*tan((f*x+exp(1))/2))/sqrt(a^2-b^2))+pi*sign(2*b-2*a)*floor((f*x+exp(1))/2/pi+1/2))+(-6*c^2*a^2*d+6*c*b*a*d^2-2*b^2*d^3-a^2*d^3)*1/4/a^3*ln(abs(tan((f*x+exp(1))/2)-1))-(-6*c^2*a^2*d+6*c*b*a*d^2-2*b^2*d^3-a^2*d^3)*1/4/a^3*ln(abs(tan((f*x+exp(1))/2)+1))-(6*tan((f*x+exp(1))/2)^3*c*a*d^2-2*tan((f*x+exp(1))/2)^3*b*d^3-tan((f*x+exp(1))/2)^3*a*d^3-6*tan((f*x+exp(1))/2)*c*a*d^2+2*tan((f*x+exp(1))/2)*b*d^3-tan((f*x+exp(1))/2)*a*d^3)*1/2/a^2/(tan((f*x+exp(1))/2)^2-1)^2)","F(-2)",0
11,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^2/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*((-2*c^2*a^2+4*c*b*a*d-2*b^2*d^2)*1/2/a^2/sqrt(a^2-b^2)*(atan((-a*tan((f*x+exp(1))/2)+b*tan((f*x+exp(1))/2))/sqrt(a^2-b^2))+pi*sign(2*b-2*a)*floor((f*x+exp(1))/2/pi+1/2))-(2*c*a*d-b*d^2)*1/2/a^2*ln(abs(tan((f*x+exp(1))/2)-1))+(2*c*a*d-b*d^2)*1/2/a^2*ln(abs(tan((f*x+exp(1))/2)+1))-tan((f*x+exp(1))/2)*d^2/a/(tan((f*x+exp(1))/2)^2-1))","F(-2)",0
12,-2,0,0,0.000000," ","integrate((c+d*sec(f*x+e))/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)2/f*(-d*1/2/a*ln(abs(tan((f*x+exp(1))/2)-1))+d*1/2/a*ln(abs(tan((f*x+exp(1))/2)+1))+(-2*c*a+2*b*d)/a*1/2/sqrt(a^2-b^2)*(atan((-a*tan((f*x+exp(1))/2)+b*tan((f*x+exp(1))/2))/sqrt(a^2-b^2))+pi*sign(2*b-2*a)*floor((f*x+exp(1))/2/pi+1/2)))","F(-2)",0
13,1,511,0,0.765984," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e)),x, algorithm=""giac"")","\frac{\frac{{\left(\sqrt{a^{2} - b^{2}} a c {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} {\left(2 \, a - b\right)} d {\left| a - b \right|} + \sqrt{a^{2} - b^{2}} {\left| a c - b d \right|} {\left| a - b \right|}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{\frac{b c - a d + \sqrt{{\left(a c + b c + a d + b d\right)} {\left(a c - b c - a d + b d\right)} + {\left(b c - a d\right)}^{2}}}{a c - b c - a d + b d}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} {\left(a c - b d\right)}^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} c {\left| a c - b d \right|} - {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d {\left| a c - b d \right|}} + \frac{{\left(\sqrt{-c^{2} + d^{2}} a {\left(c - 2 \, d\right)} {\left| -c + d \right|} + \sqrt{-c^{2} + d^{2}} b d {\left| -c + d \right|} - \sqrt{-c^{2} + d^{2}} {\left| a c - b d \right|} {\left| -c + d \right|}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{\frac{b c - a d - \sqrt{{\left(a c + b c + a d + b d\right)} {\left(a c - b c - a d + b d\right)} + {\left(b c - a d\right)}^{2}}}{a c - b c - a d + b d}}}\right)\right)}}{{\left(a c - b d\right)}^{2} {\left(c^{2} - 2 \, c d + d^{2}\right)} + {\left(c^{2} d - 2 \, c d^{2} + d^{3}\right)} a {\left| a c - b d \right|} - {\left(c^{3} - 2 \, c^{2} d + c d^{2}\right)} b {\left| a c - b d \right|}}}{f}"," ",0,"((sqrt(a^2 - b^2)*a*c*abs(a - b) - sqrt(a^2 - b^2)*(2*a - b)*d*abs(a - b) + sqrt(a^2 - b^2)*abs(a*c - b*d)*abs(a - b))*(pi*floor(1/2*(f*x + e)/pi + 1/2) + arctan(tan(1/2*f*x + 1/2*e)/sqrt((b*c - a*d + sqrt((a*c + b*c + a*d + b*d)*(a*c - b*c - a*d + b*d) + (b*c - a*d)^2))/(a*c - b*c - a*d + b*d))))/((a^2 - 2*a*b + b^2)*(a*c - b*d)^2 + (a^2*b - 2*a*b^2 + b^3)*c*abs(a*c - b*d) - (a^3 - 2*a^2*b + a*b^2)*d*abs(a*c - b*d)) + (sqrt(-c^2 + d^2)*a*(c - 2*d)*abs(-c + d) + sqrt(-c^2 + d^2)*b*d*abs(-c + d) - sqrt(-c^2 + d^2)*abs(a*c - b*d)*abs(-c + d))*(pi*floor(1/2*(f*x + e)/pi + 1/2) + arctan(tan(1/2*f*x + 1/2*e)/sqrt((b*c - a*d - sqrt((a*c + b*c + a*d + b*d)*(a*c - b*c - a*d + b*d) + (b*c - a*d)^2))/(a*c - b*c - a*d + b*d))))/((a*c - b*d)^2*(c^2 - 2*c*d + d^2) + (c^2*d - 2*c*d^2 + d^3)*a*abs(a*c - b*d) - (c^3 - 2*c^2*d + c*d^2)*b*abs(a*c - b*d)))/f","B",0
14,1,342,0,1.653492," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{2}}{{\left(a^{2} c^{2} - 2 \, a b c d + b^{2} d^{2}\right)} \sqrt{a^{2} - b^{2}}} - \frac{d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{{\left(a c^{3} - b c^{2} d - a c d^{2} + b d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c - d\right)}} - \frac{{\left(2 \, a c^{2} d - b c d^{2} - a d^{3}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, c + 2 \, d\right) + \arctan\left(-\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{-c^{2} + d^{2}}}\right)\right)}}{{\left(a^{2} c^{4} - 2 \, a b c^{3} d - a^{2} c^{2} d^{2} + b^{2} c^{2} d^{2} + 2 \, a b c d^{3} - b^{2} d^{4}\right)} \sqrt{-c^{2} + d^{2}}}\right)}}{f}"," ",0,"2*((pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*f*x + 1/2*e) - b*tan(1/2*f*x + 1/2*e))/sqrt(a^2 - b^2)))*a^2/((a^2*c^2 - 2*a*b*c*d + b^2*d^2)*sqrt(a^2 - b^2)) - d^2*tan(1/2*f*x + 1/2*e)/((a*c^3 - b*c^2*d - a*c*d^2 + b*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 - d*tan(1/2*f*x + 1/2*e)^2 - c - d)) - (2*a*c^2*d - b*c*d^2 - a*d^3)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(-2*c + 2*d) + arctan(-(c*tan(1/2*f*x + 1/2*e) - d*tan(1/2*f*x + 1/2*e))/sqrt(-c^2 + d^2)))/((a^2*c^4 - 2*a*b*c^3*d - a^2*c^2*d^2 + b^2*c^2*d^2 + 2*a*b*c*d^3 - b^2*d^4)*sqrt(-c^2 + d^2)))/f","B",0
15,1,770,0,3.846221," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - b \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} a^{3}}{{\left(a^{3} c^{3} - 3 \, a^{2} b c^{2} d + 3 \, a b^{2} c d^{2} - b^{3} d^{3}\right)} \sqrt{a^{2} - b^{2}}} + \frac{{\left(6 \, a^{2} c^{4} d - 6 \, a b c^{3} d^{2} - 5 \, a^{2} c^{2} d^{3} + 2 \, b^{2} c^{2} d^{3} + 2 \, a^{2} d^{5} + b^{2} d^{5}\right)} {\left(\pi \left \lfloor \frac{f x + e}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, c - 2 \, d\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{\sqrt{-c^{2} + d^{2}}}\right)\right)}}{{\left(a^{3} c^{7} - 3 \, a^{2} b c^{6} d - 2 \, a^{3} c^{5} d^{2} + 3 \, a b^{2} c^{5} d^{2} + 6 \, a^{2} b c^{4} d^{3} - b^{3} c^{4} d^{3} + a^{3} c^{3} d^{4} - 6 \, a b^{2} c^{3} d^{4} - 3 \, a^{2} b c^{2} d^{5} + 2 \, b^{3} c^{2} d^{5} + 3 \, a b^{2} c d^{6} - b^{3} d^{7}\right)} \sqrt{-c^{2} + d^{2}}} - \frac{6 \, a c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 5 \, a c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, b c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 \, a c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2 \, a d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a c^{3} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 5 \, a c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, b c^{2} d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, b c d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - b d^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{{\left(a^{2} c^{6} - 2 \, a b c^{5} d - 2 \, a^{2} c^{4} d^{2} + b^{2} c^{4} d^{2} + 4 \, a b c^{3} d^{3} + a^{2} c^{2} d^{4} - 2 \, b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + b^{2} d^{6}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c - d\right)}^{2}}}{f}"," ",0,"(2*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*f*x + 1/2*e) - b*tan(1/2*f*x + 1/2*e))/sqrt(a^2 - b^2)))*a^3/((a^3*c^3 - 3*a^2*b*c^2*d + 3*a*b^2*c*d^2 - b^3*d^3)*sqrt(a^2 - b^2)) + (6*a^2*c^4*d - 6*a*b*c^3*d^2 - 5*a^2*c^2*d^3 + 2*b^2*c^2*d^3 + 2*a^2*d^5 + b^2*d^5)*(pi*floor(1/2*(f*x + e)/pi + 1/2)*sgn(2*c - 2*d) + arctan((c*tan(1/2*f*x + 1/2*e) - d*tan(1/2*f*x + 1/2*e))/sqrt(-c^2 + d^2)))/((a^3*c^7 - 3*a^2*b*c^6*d - 2*a^3*c^5*d^2 + 3*a*b^2*c^5*d^2 + 6*a^2*b*c^4*d^3 - b^3*c^4*d^3 + a^3*c^3*d^4 - 6*a*b^2*c^3*d^4 - 3*a^2*b*c^2*d^5 + 2*b^3*c^2*d^5 + 3*a*b^2*c*d^6 - b^3*d^7)*sqrt(-c^2 + d^2)) - (6*a*c^3*d^2*tan(1/2*f*x + 1/2*e)^3 - 5*a*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 4*b*c^2*d^3*tan(1/2*f*x + 1/2*e)^3 - 3*a*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 3*b*c*d^4*tan(1/2*f*x + 1/2*e)^3 + 2*a*d^5*tan(1/2*f*x + 1/2*e)^3 + b*d^5*tan(1/2*f*x + 1/2*e)^3 - 6*a*c^3*d^2*tan(1/2*f*x + 1/2*e) - 5*a*c^2*d^3*tan(1/2*f*x + 1/2*e) + 4*b*c^2*d^3*tan(1/2*f*x + 1/2*e) + 3*a*c*d^4*tan(1/2*f*x + 1/2*e) + 3*b*c*d^4*tan(1/2*f*x + 1/2*e) + 2*a*d^5*tan(1/2*f*x + 1/2*e) - b*d^5*tan(1/2*f*x + 1/2*e))/((a^2*c^6 - 2*a*b*c^5*d - 2*a^2*c^4*d^2 + b^2*c^4*d^2 + 4*a*b*c^3*d^3 + a^2*c^2*d^4 - 2*b^2*c^2*d^4 - 2*a*b*c*d^5 + b^2*d^6)*(c*tan(1/2*f*x + 1/2*e)^2 - d*tan(1/2*f*x + 1/2*e)^2 - c - d)^2))/f","A",0
16,0,0,0,0.000000," ","integrate((c+d*sec(f*x+e))^(1/2)/(a+b*cos(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{d \sec\left(f x + e\right) + c}}{b \cos\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sec(f*x + e) + c)/(b*cos(f*x + e) + a), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(a+b*cos(f*x+e))/(c+d*sec(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(f x + e\right) + a\right)} \sqrt{d \sec\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*cos(f*x + e) + a)*sqrt(d*sec(f*x + e) + c)), x)","F",0
18,1,459,0,0.446979," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d)),x, algorithm=""giac"")","-{\left(\frac{C {\left(a + b\right)} {\left(a - b\right)}^{2} \log\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + \frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(\sqrt{a^{2} - b^{2}} B {\left(2 \, a - b\right)} {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} A b {\left| a - b \right|} - \sqrt{a^{2} - b^{2}} A {\left| a - b \right|} {\left| b \right|} + \sqrt{a^{2} - b^{2}} B {\left| a - b \right|} {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{\frac{2 \, a + \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{{\left(a^{2} - 2 \, a b + b^{2}\right)} b^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} {\left| b \right|}} + \frac{{\left(2 \, B a - A b - B b + A {\left| b \right|} - B {\left| b \right|}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{\frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{a - b}}}\right)\right)}}{b^{2} - a {\left| b \right|}} + \frac{{\left(C a - C b\right)} \log\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + \frac{2 \, a - \sqrt{-4 \, {\left(a + b\right)} {\left(a - b\right)} + 4 \, a^{2}}}{2 \, {\left(a - b\right)}}\right)}{b^{2} - a {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"-(C*(a + b)*(a - b)^2*log(tan(1/2*x*e + 1/2*d)^2 + 1/2*(2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (sqrt(a^2 - b^2)*B*(2*a - b)*abs(a - b) - sqrt(a^2 - b^2)*A*b*abs(a - b) - sqrt(a^2 - b^2)*A*abs(a - b)*abs(b) + sqrt(a^2 - b^2)*B*abs(a - b)*abs(b))*(pi*floor(1/2*(x*e + d)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x*e + 1/2*d)/sqrt((2*a + sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/((a^2 - 2*a*b + b^2)*b^2 + (a^3 - 2*a^2*b + a*b^2)*abs(b)) + (2*B*a - A*b - B*b + A*abs(b) - B*abs(b))*(pi*floor(1/2*(x*e + d)/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x*e + 1/2*d)/sqrt((2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))))/(b^2 - a*abs(b)) + (C*a - C*b)*log(tan(1/2*x*e + 1/2*d)^2 + 1/2*(2*a - sqrt(-4*(a + b)*(a - b) + 4*a^2))/(a - b))/(b^2 - a*abs(b)))*e^(-1)","B",0
19,1,173,0,0.922907," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^2,x, algorithm=""giac"")","-2 \, {\left(\frac{{\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)} {\left(A a - B b\right)}}{{\left(a^{2} - b^{2}\right)}^{\frac{3}{2}}} - \frac{B a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - A b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - C a - C b}{{\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + a + b\right)} {\left(a^{2} - b^{2}\right)}}\right)} e^{\left(-1\right)}"," ",0,"-2*((pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x*e + 1/2*d) - b*tan(1/2*x*e + 1/2*d))/sqrt(a^2 - b^2)))*(A*a - B*b)/(a^2 - b^2)^(3/2) - (B*a*tan(1/2*x*e + 1/2*d) - A*b*tan(1/2*x*e + 1/2*d) - C*a - C*b)/((a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + a + b)*(a^2 - b^2)))*e^(-1)","A",0
20,1,502,0,0.753442," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^3,x, algorithm=""giac"")","{\left(\frac{{\left(2 \, A a^{2} - 3 \, B a b + A b^{2}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a - 2 \, b\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, B a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - B a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 3 \, A a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + B a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + A b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, C a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, C a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, C a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, C b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, B a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, A a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + B a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, A a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + B a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + A b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 2 \, C a^{3} - 4 \, C a^{2} b - 2 \, C a b^{2}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + a + b\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"((2*A*a^2 - 3*B*a*b + A*b^2)*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(2*a - 2*b) + arctan((a*tan(1/2*x*e + 1/2*d) - b*tan(1/2*x*e + 1/2*d))/sqrt(a^2 - b^2)))/((a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)) + (2*B*a^3*tan(1/2*x*e + 1/2*d)^3 - 4*A*a^2*b*tan(1/2*x*e + 1/2*d)^3 - B*a^2*b*tan(1/2*x*e + 1/2*d)^3 + 3*A*a*b^2*tan(1/2*x*e + 1/2*d)^3 + B*a*b^2*tan(1/2*x*e + 1/2*d)^3 + A*b^3*tan(1/2*x*e + 1/2*d)^3 - 2*B*b^3*tan(1/2*x*e + 1/2*d)^3 - 2*C*a^3*tan(1/2*x*e + 1/2*d)^2 - 2*C*a^2*b*tan(1/2*x*e + 1/2*d)^2 + 2*C*a*b^2*tan(1/2*x*e + 1/2*d)^2 + 2*C*b^3*tan(1/2*x*e + 1/2*d)^2 + 2*B*a^3*tan(1/2*x*e + 1/2*d) - 4*A*a^2*b*tan(1/2*x*e + 1/2*d) + B*a^2*b*tan(1/2*x*e + 1/2*d) - 3*A*a*b^2*tan(1/2*x*e + 1/2*d) + B*a*b^2*tan(1/2*x*e + 1/2*d) + A*b^3*tan(1/2*x*e + 1/2*d) + 2*B*b^3*tan(1/2*x*e + 1/2*d) - 2*C*a^3 - 4*C*a^2*b - 2*C*a*b^2)/((a^4 - 2*a^2*b^2 + b^4)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + a + b)^2))*e^(-1)","B",0
21,1,960,0,1.439164," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+b*cos(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{3 \, {\left(2 \, A a^{3} - 4 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, a + 2 \, b\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} - \frac{6 \, B a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, B a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 3 \, A a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, A b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 3 \, B b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, C a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 6 \, C a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 6 \, C a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 6 \, C b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, B a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 36 \, A a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 16 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 32 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 28 \, B a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, A b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 12 \, C a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 24 \, C a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 24 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, C a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, B a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, A a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 6 \, B a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 27 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 12 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 27 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, A a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 12 \, B a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, A b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, B b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, C a^{5} - 18 \, C a^{4} b - 20 \, C a^{3} b^{2} - 12 \, C a^{2} b^{3} - 6 \, C a b^{4} - 2 \, C b^{5}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + a + b\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"-1/3*(3*(2*A*a^3 - 4*B*a^2*b + 3*A*a*b^2 - B*b^3)*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x*e + 1/2*d) - b*tan(1/2*x*e + 1/2*d))/sqrt(a^2 - b^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sqrt(a^2 - b^2)) - (6*B*a^5*tan(1/2*x*e + 1/2*d)^5 - 18*A*a^4*b*tan(1/2*x*e + 1/2*d)^5 - 6*B*a^4*b*tan(1/2*x*e + 1/2*d)^5 + 27*A*a^3*b^2*tan(1/2*x*e + 1/2*d)^5 + 12*B*a^3*b^2*tan(1/2*x*e + 1/2*d)^5 - 6*A*a^2*b^3*tan(1/2*x*e + 1/2*d)^5 - 27*B*a^2*b^3*tan(1/2*x*e + 1/2*d)^5 + 3*A*a*b^4*tan(1/2*x*e + 1/2*d)^5 + 12*B*a*b^4*tan(1/2*x*e + 1/2*d)^5 - 6*A*b^5*tan(1/2*x*e + 1/2*d)^5 + 3*B*b^5*tan(1/2*x*e + 1/2*d)^5 - 6*C*a^5*tan(1/2*x*e + 1/2*d)^4 - 6*C*a^4*b*tan(1/2*x*e + 1/2*d)^4 + 12*C*a^3*b^2*tan(1/2*x*e + 1/2*d)^4 + 12*C*a^2*b^3*tan(1/2*x*e + 1/2*d)^4 - 6*C*a*b^4*tan(1/2*x*e + 1/2*d)^4 - 6*C*b^5*tan(1/2*x*e + 1/2*d)^4 + 12*B*a^5*tan(1/2*x*e + 1/2*d)^3 - 36*A*a^4*b*tan(1/2*x*e + 1/2*d)^3 + 16*B*a^3*b^2*tan(1/2*x*e + 1/2*d)^3 + 32*A*a^2*b^3*tan(1/2*x*e + 1/2*d)^3 - 28*B*a*b^4*tan(1/2*x*e + 1/2*d)^3 + 4*A*b^5*tan(1/2*x*e + 1/2*d)^3 - 12*C*a^5*tan(1/2*x*e + 1/2*d)^2 - 24*C*a^4*b*tan(1/2*x*e + 1/2*d)^2 + 24*C*a^2*b^3*tan(1/2*x*e + 1/2*d)^2 + 12*C*a*b^4*tan(1/2*x*e + 1/2*d)^2 + 6*B*a^5*tan(1/2*x*e + 1/2*d) - 18*A*a^4*b*tan(1/2*x*e + 1/2*d) + 6*B*a^4*b*tan(1/2*x*e + 1/2*d) - 27*A*a^3*b^2*tan(1/2*x*e + 1/2*d) + 12*B*a^3*b^2*tan(1/2*x*e + 1/2*d) - 6*A*a^2*b^3*tan(1/2*x*e + 1/2*d) + 27*B*a^2*b^3*tan(1/2*x*e + 1/2*d) - 3*A*a*b^4*tan(1/2*x*e + 1/2*d) + 12*B*a*b^4*tan(1/2*x*e + 1/2*d) - 6*A*b^5*tan(1/2*x*e + 1/2*d) - 3*B*b^5*tan(1/2*x*e + 1/2*d) - 6*C*a^5 - 18*C*a^4*b - 20*C*a^3*b^2 - 12*C*a^2*b^3 - 6*C*a*b^4 - 2*C*b^5)/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + a + b)^3))*e^(-1)","B",0
