1,1,57,0,0.150104," ","integrate(2/(3-cos(4+6*x)),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
2,1,57,0,0.220206," ","integrate(2*csc(4+6*x)/(-cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
3,1,57,0,0.127935," ","integrate(1/(1+sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
4,1,57,0,0.145657," ","integrate(1/(2-cos(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
5,1,57,0,0.156995," ","integrate(1/(cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
6,1,16,0,1.542447," ","integrate(sec(2+3*x)^2/(1+2*tan(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(sqrt(2)*tan(3*x + 2))","A",0
7,1,57,0,0.282838," ","integrate(csc(2+3*x)^2/(2+cot(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - 2 \, \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - 2 \, \cos\left(6 \, x + 4\right) + 2}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - 2*sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - 2*cos(6*x + 4) + 2)) + 2)","A",0
8,1,39,0,0.167141," ","integrate(2/(1-3*cos(4+6*x)),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
9,1,39,0,0.237877," ","integrate(2*csc(4+6*x)/(-3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
10,1,39,0,0.162280," ","integrate(1/(-1+3*sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
11,1,39,0,0.165876," ","integrate(1/(2-3*cos(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
12,1,39,0,0.202080," ","integrate(1/(-cos(2+3*x)^2+2*sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
13,1,39,0,1.483666," ","integrate(sec(2+3*x)^2/(-1+2*tan(2+3*x)^2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{2} \log\left({\left| \frac{1}{2} \, \sqrt{2} + \tan\left(3 \, x + 2\right) \right|}\right) + \frac{1}{12} \, \sqrt{2} \log\left({\left| -\frac{1}{2} \, \sqrt{2} + \tan\left(3 \, x + 2\right) \right|}\right)"," ",0,"-1/12*sqrt(2)*log(abs(1/2*sqrt(2) + tan(3*x + 2))) + 1/12*sqrt(2)*log(abs(-1/2*sqrt(2) + tan(3*x + 2)))","A",0
14,1,39,0,0.357398," ","integrate(csc(2+3*x)^2/(2-cot(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*tan(3*x + 2))/abs(2*sqrt(2) + 4*tan(3*x + 2)))","A",0
15,1,57,0,0.144924," ","integrate(2/(3+cos(4+6*x)),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
16,1,57,0,0.225378," ","integrate(2*csc(4+6*x)/(cot(4+6*x)+3*csc(4+6*x)),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
17,1,57,0,0.145731," ","integrate(1/(2-sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
18,1,57,0,0.145039," ","integrate(1/(1+cos(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
19,1,57,0,0.157590," ","integrate(1/(2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
20,1,17,0,1.231937," ","integrate(sec(2+3*x)^2/(2+tan(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} \tan\left(3 \, x + 2\right)\right)"," ",0,"1/6*sqrt(2)*arctan(1/2*sqrt(2)*tan(3*x + 2))","A",0
21,1,57,0,0.326817," ","integrate(csc(2+3*x)^2/(1+2*cot(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{2} {\left(3 \, x + \arctan\left(-\frac{\sqrt{2} \sin\left(6 \, x + 4\right) - \sin\left(6 \, x + 4\right)}{\sqrt{2} \cos\left(6 \, x + 4\right) + \sqrt{2} - \cos\left(6 \, x + 4\right) + 1}\right) + 2\right)}"," ",0,"1/6*sqrt(2)*(3*x + arctan(-(sqrt(2)*sin(6*x + 4) - sin(6*x + 4))/(sqrt(2)*cos(6*x + 4) + sqrt(2) - cos(6*x + 4) + 1)) + 2)","A",0
22,1,39,0,0.163610," ","integrate(-2/(1+3*cos(4+6*x)),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
23,1,39,0,0.239676," ","integrate(-2*csc(4+6*x)/(3*cot(4+6*x)+csc(4+6*x)),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
24,1,39,0,0.186730," ","integrate(1/(-2+3*sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
25,1,39,0,0.170981," ","integrate(1/(1-3*cos(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
26,1,39,0,0.205687," ","integrate(1/(-2*cos(2+3*x)^2+sin(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
27,1,37,0,1.293828," ","integrate(sec(2+3*x)^2/(-2+tan(2+3*x)^2),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{2} \log\left({\left| \sqrt{2} + \tan\left(3 \, x + 2\right) \right|}\right) + \frac{1}{12} \, \sqrt{2} \log\left({\left| -\sqrt{2} + \tan\left(3 \, x + 2\right) \right|}\right)"," ",0,"-1/12*sqrt(2)*log(abs(sqrt(2) + tan(3*x + 2))) + 1/12*sqrt(2)*log(abs(-sqrt(2) + tan(3*x + 2)))","A",0
28,1,39,0,0.417811," ","integrate(csc(2+3*x)^2/(1-2*cot(2+3*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(3 \, x + 2\right) \right|}}\right)"," ",0,"1/12*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(3*x + 2))/abs(2*sqrt(2) + 2*tan(3*x + 2)))","A",0
29,1,24,0,0.137165," ","integrate((x+sin(x))^2,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} - 2 \, x \cos\left(x\right) + \frac{1}{2} \, x - \frac{1}{4} \, \sin\left(2 \, x\right) + 2 \, \sin\left(x\right)"," ",0,"1/3*x^3 - 2*x*cos(x) + 1/2*x - 1/4*sin(2*x) + 2*sin(x)","A",0
30,1,46,0,0.136954," ","integrate((x+sin(x))^3,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{3}{4} \, x^{2} - \frac{3}{4} \, {\left(4 \, x^{2} - 7\right)} \cos\left(x\right) - \frac{3}{4} \, x \sin\left(2 \, x\right) + 6 \, x \sin\left(x\right) + \frac{1}{12} \, \cos\left(3 \, x\right) - \frac{3}{8} \, \cos\left(2 \, x\right)"," ",0,"1/4*x^4 + 3/4*x^2 - 3/4*(4*x^2 - 7)*cos(x) - 3/4*x*sin(2*x) + 6*x*sin(x) + 1/12*cos(3*x) - 3/8*cos(2*x)","A",0
31,0,0,0,0.000000," ","integrate(sin(b*x+a)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{\sin\left(b x + a\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(sin(b*x + a)/(d*x^2 + c), x)","F",0
32,0,0,0,0.000000," ","integrate(sin(b*x+a)/(e*x^2+d*x+c),x, algorithm=""giac"")","\int \frac{\sin\left(b x + a\right)}{e x^{2} + d x + c}\,{d x}"," ",0,"integrate(sin(b*x + a)/(e*x^2 + d*x + c), x)","F",0
33,1,8,0,0.124973," ","integrate(sin((-7+x)^(1/2))/(-7+x)^(1/2),x, algorithm=""giac"")","-2 \, \cos\left(\sqrt{x - 7}\right)"," ",0,"-2*cos(sqrt(x - 7))","A",0
34,0,0,0,0.000000," ","integrate(sin(x)*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b - \frac{a}{x^{2}}} \sin\left(x\right)}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(b - a/x^2)*sin(x)/sqrt(-b*x^2 + a), x)","F",0
35,1,11,0,0.136563," ","integrate(1/x/(1+sin(log(x))),x, algorithm=""giac"")","-\frac{2}{\tan\left(\frac{1}{2} \, \log\left(x\right)\right) + 1}"," ",0,"-2/(tan(1/2*log(x)) + 1)","A",0
36,1,630,0,9.106932," ","integrate(sin((b*x+a)/(d*x+c)),x, algorithm=""giac"")","\frac{{\left(b^{3} c^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - 2 \, a b^{2} c d \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - \frac{{\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + a^{2} b d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + \frac{2 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - \frac{{\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + b^{3} c^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - 2 \, a b^{2} c d \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - \frac{{\left(b x + a\right)} b^{2} c^{2} d \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + a^{2} b d^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + \frac{2 \, {\left(b x + a\right)} a b c d^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - \frac{{\left(b x + a\right)} a^{2} d^{3} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + b^{2} c^{2} d \sin\left(\frac{b x + a}{d x + c}\right) - 2 \, a b c d^{2} \sin\left(\frac{b x + a}{d x + c}\right) + a^{2} d^{3} \sin\left(\frac{b x + a}{d x + c}\right)\right)} {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)}}{b d^{2} - \frac{{\left(b x + a\right)} d^{3}}{d x + c}}"," ",0,"(b^3*c^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) - 2*a*b^2*c*d*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) - (b*x + a)*b^2*c^2*d*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + a^2*b*d^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) + 2*(b*x + a)*a*b*c*d^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - (b*x + a)*a^2*d^3*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + b^3*c^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) - 2*a*b^2*c*d*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) - (b*x + a)*b^2*c^2*d*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + a^2*b*d^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) + 2*(b*x + a)*a*b*c*d^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - (b*x + a)*a^2*d^3*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + b^2*c^2*d*sin((b*x + a)/(d*x + c)) - 2*a*b*c*d^2*sin((b*x + a)/(d*x + c)) + a^2*d^3*sin((b*x + a)/(d*x + c)))*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)/(b*d^2 - (b*x + a)*d^3/(d*x + c))","B",0
37,1,681,0,62.661393," ","integrate(sin((b*x+a)/(d*x+c))^2,x, algorithm=""giac"")","\frac{{\left(2 \, b^{3} c^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) - 4 \, a b^{2} c d \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) - \frac{2 \, {\left(b x + a\right)} b^{2} c^{2} d \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} + 2 \, a^{2} b d^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) + \frac{4 \, {\left(b x + a\right)} a b c d^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} - \frac{2 \, {\left(b x + a\right)} a^{2} d^{3} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} - 2 \, b^{3} c^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + 4 \, a b^{2} c d \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + \frac{2 \, {\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - 2 \, a^{2} b d^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) - \frac{4 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} + \frac{2 \, {\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - b^{2} c^{2} d \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) + 2 \, a b c d^{2} \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) - a^{2} d^{3} \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) + b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)}}{2 \, {\left(b d^{2} - \frac{{\left(b x + a\right)} d^{3}}{d x + c}\right)}}"," ",0,"1/2*(2*b^3*c^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) - 4*a*b^2*c*d*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) - 2*(b*x + a)*b^2*c^2*d*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) + 2*a^2*b*d^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) + 4*(b*x + a)*a*b*c*d^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) - 2*(b*x + a)*a^2*d^3*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) - 2*b^3*c^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) + 4*a*b^2*c*d*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) + 2*(b*x + a)*b^2*c^2*d*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 2*a^2*b*d^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) - 4*(b*x + a)*a*b*c*d^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 2*(b*x + a)*a^2*d^3*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - b^2*c^2*d*cos(2*(b*x + a)/(d*x + c)) + 2*a*b*c*d^2*cos(2*(b*x + a)/(d*x + c)) - a^2*d^3*cos(2*(b*x + a)/(d*x + c)) + b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)/(b*d^2 - (b*x + a)*d^3/(d*x + c))","B",0
38,1,1239,0,177.526083," ","integrate(sin((b*x+a)/(d*x+c))^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{3} c^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - 6 \, a b^{2} c d \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - \frac{3 \, {\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + 3 \, a^{2} b d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + \frac{6 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - \frac{3 \, {\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{b}{d}\right) \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - 3 \, b^{3} c^{2} \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + 6 \, a b^{2} c d \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + \frac{3 \, {\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - 3 \, a^{2} b d^{2} \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) - \frac{6 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} + \frac{3 \, {\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{3 \, b}{d}\right) \operatorname{Ci}\left(-\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - 3 \, b^{3} c^{2} \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + 6 \, a b^{2} c d \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + \frac{3 \, {\left(b x + a\right)} b^{2} c^{2} d \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - 3 \, a^{2} b d^{2} \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) - \frac{6 \, {\left(b x + a\right)} a b c d^{2} \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} + \frac{3 \, {\left(b x + a\right)} a^{2} d^{3} \sin\left(\frac{3 \, b}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} + 3 \, b^{3} c^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - 6 \, a b^{2} c d \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - \frac{3 \, {\left(b x + a\right)} b^{2} c^{2} d \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + 3 \, a^{2} b d^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + \frac{6 \, {\left(b x + a\right)} a b c d^{2} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - \frac{3 \, {\left(b x + a\right)} a^{2} d^{3} \sin\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - b^{2} c^{2} d \sin\left(\frac{3 \, {\left(b x + a\right)}}{d x + c}\right) + 2 \, a b c d^{2} \sin\left(\frac{3 \, {\left(b x + a\right)}}{d x + c}\right) - a^{2} d^{3} \sin\left(\frac{3 \, {\left(b x + a\right)}}{d x + c}\right) + 3 \, b^{2} c^{2} d \sin\left(\frac{b x + a}{d x + c}\right) - 6 \, a b c d^{2} \sin\left(\frac{b x + a}{d x + c}\right) + 3 \, a^{2} d^{3} \sin\left(\frac{b x + a}{d x + c}\right)\right)} {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)}}{4 \, {\left(b d^{2} - \frac{{\left(b x + a\right)} d^{3}}{d x + c}\right)}}"," ",0,"1/4*(3*b^3*c^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) - 6*a*b^2*c*d*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) - 3*(b*x + a)*b^2*c^2*d*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 3*a^2*b*d^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d) + 6*(b*x + a)*a*b*c*d^2*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*(b*x + a)*a^2*d^3*cos(b/d)*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*b^3*c^2*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d) + 6*a*b^2*c*d*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d) + 3*(b*x + a)*b^2*c^2*d*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*a^2*b*d^2*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d) - 6*(b*x + a)*a*b*c*d^2*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 3*(b*x + a)*a^2*d^3*cos(3*b/d)*cos_integral(-3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*b^3*c^2*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d) + 6*a*b^2*c*d*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d) + 3*(b*x + a)*b^2*c^2*d*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*a^2*b*d^2*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d) - 6*(b*x + a)*a*b*c*d^2*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 3*(b*x + a)*a^2*d^3*sin(3*b/d)*sin_integral(3*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 3*b^3*c^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) - 6*a*b^2*c*d*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) - 3*(b*x + a)*b^2*c^2*d*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 3*a^2*b*d^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) + 6*(b*x + a)*a*b*c*d^2*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 3*(b*x + a)*a^2*d^3*sin(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - b^2*c^2*d*sin(3*(b*x + a)/(d*x + c)) + 2*a*b*c*d^2*sin(3*(b*x + a)/(d*x + c)) - a^2*d^3*sin(3*(b*x + a)/(d*x + c)) + 3*b^2*c^2*d*sin((b*x + a)/(d*x + c)) - 6*a*b*c*d^2*sin((b*x + a)/(d*x + c)) + 3*a^2*d^3*sin((b*x + a)/(d*x + c)))*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)/(b*d^2 - (b*x + a)*d^3/(d*x + c))","B",0
39,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-sin(sqrt(-a*x + 1)/sqrt(a*x + 1))^3/(a^2*x^2 - 1), x)","F",0
40,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-sin(sqrt(-a*x + 1)/sqrt(a*x + 1))^2/(a^2*x^2 - 1), x)","F",0
41,0,0,0,0.000000," ","integrate(sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-sin(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/sin((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} \sin\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*sin(sqrt(-a*x + 1)/sqrt(a*x + 1))^2), x)","F",0
44,1,24,0,0.137335," ","integrate((x+cos(x))^2,x, algorithm=""giac"")","\frac{1}{3} \, x^{3} + 2 \, x \sin\left(x\right) + \frac{1}{2} \, x + 2 \, \cos\left(x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/3*x^3 + 2*x*sin(x) + 1/2*x + 2*cos(x) + 1/4*sin(2*x)","A",0
45,1,46,0,0.145164," ","integrate((x+cos(x))^3,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{3}{4} \, x^{2} + 6 \, x \cos\left(x\right) + \frac{3}{4} \, x \sin\left(2 \, x\right) + \frac{3}{4} \, {\left(4 \, x^{2} - 7\right)} \sin\left(x\right) + \frac{3}{8} \, \cos\left(2 \, x\right) + \frac{1}{12} \, \sin\left(3 \, x\right)"," ",0,"1/4*x^4 + 3/4*x^2 + 6*x*cos(x) + 3/4*x*sin(2*x) + 3/4*(4*x^2 - 7)*sin(x) + 3/8*cos(2*x) + 1/12*sin(3*x)","A",0
46,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{d x^{2} + c}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x^2 + c), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(b*x+a)/(e*x^2+d*x+c),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{e x^{2} + d x + c}\,{d x}"," ",0,"integrate(cos(b*x + a)/(e*x^2 + d*x + c), x)","F",0
48,1,8,0,0.141173," ","integrate(x*cos((x^2+1)^(1/2))/(x^2+1)^(1/2),x, algorithm=""giac"")","\sin\left(\sqrt{x^{2} + 1}\right)"," ",0,"sin(sqrt(x^2 + 1))","A",0
49,1,17,0,0.118603," ","integrate(x*cos(3^(1/2)*(x^2+2)^(1/2))/(x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \sin\left(\sqrt{3} \sqrt{x^{2} + 2}\right)"," ",0,"1/3*sqrt(3)*sin(sqrt(3)*sqrt(x^2 + 2))","A",0
50,1,19,0,0.148686," ","integrate((-1+2*x)*cos((6+3*(-1+2*x)^2)^(1/2))/(6+3*(-1+2*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{6} \, \sin\left(\sqrt{3} \sqrt{4 \, x^{2} - 4 \, x + 3}\right)"," ",0,"1/6*sin(sqrt(3)*sqrt(4*x^2 - 4*x + 3))","A",0
51,1,633,0,12.268735," ","integrate(cos((b*x+a)/(d*x+c)),x, algorithm=""giac"")","-\frac{{\left(b^{3} c^{2} \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right) - 2 \, a b^{2} c d \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right) - \frac{{\left(b x + a\right)} b^{2} c^{2} d \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right)}{d x + c} + a^{2} b d^{2} \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right) + \frac{2 \, {\left(b x + a\right)} a b c d^{2} \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right)}{d x + c} - \frac{{\left(b x + a\right)} a^{2} d^{3} \operatorname{Ci}\left(-\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) \sin\left(\frac{b}{d}\right)}{d x + c} - b^{3} c^{2} \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + 2 \, a b^{2} c d \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) + \frac{{\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - a^{2} b d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right) - \frac{2 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} + \frac{{\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{b}{d}\right) \operatorname{Si}\left(\frac{b - \frac{{\left(b x + a\right)} d}{d x + c}}{d}\right)}{d x + c} - b^{2} c^{2} d \cos\left(\frac{b x + a}{d x + c}\right) + 2 \, a b c d^{2} \cos\left(\frac{b x + a}{d x + c}\right) - a^{2} d^{3} \cos\left(\frac{b x + a}{d x + c}\right)\right)} {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)}}{b d^{2} - \frac{{\left(b x + a\right)} d^{3}}{d x + c}}"," ",0,"-(b^3*c^2*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d) - 2*a*b^2*c*d*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d) - (b*x + a)*b^2*c^2*d*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d)/(d*x + c) + a^2*b*d^2*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d) + 2*(b*x + a)*a*b*c*d^2*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d)/(d*x + c) - (b*x + a)*a^2*d^3*cos_integral(-(b - (b*x + a)*d/(d*x + c))/d)*sin(b/d)/(d*x + c) - b^3*c^2*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) + 2*a*b^2*c*d*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) + (b*x + a)*b^2*c^2*d*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - a^2*b*d^2*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d) - 2*(b*x + a)*a*b*c*d^2*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + (b*x + a)*a^2*d^3*cos(b/d)*sin_integral((b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - b^2*c^2*d*cos((b*x + a)/(d*x + c)) + 2*a*b*c*d^2*cos((b*x + a)/(d*x + c)) - a^2*d^3*cos((b*x + a)/(d*x + c)))*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)/(b*d^2 - (b*x + a)*d^3/(d*x + c))","B",0
52,1,683,0,68.629069," ","integrate(cos((b*x+a)/(d*x+c))^2,x, algorithm=""giac"")","-\frac{{\left(2 \, b^{3} c^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) - 4 \, a b^{2} c d \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) - \frac{2 \, {\left(b x + a\right)} b^{2} c^{2} d \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} + 2 \, a^{2} b d^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right) + \frac{4 \, {\left(b x + a\right)} a b c d^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} - \frac{2 \, {\left(b x + a\right)} a^{2} d^{3} \operatorname{Ci}\left(-\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) \sin\left(\frac{2 \, b}{d}\right)}{d x + c} - 2 \, b^{3} c^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + 4 \, a b^{2} c d \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) + \frac{2 \, {\left(b x + a\right)} b^{2} c^{2} d \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - 2 \, a^{2} b d^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right) - \frac{4 \, {\left(b x + a\right)} a b c d^{2} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} + \frac{2 \, {\left(b x + a\right)} a^{2} d^{3} \cos\left(\frac{2 \, b}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b - \frac{{\left(b x + a\right)} d}{d x + c}\right)}}{d}\right)}{d x + c} - b^{2} c^{2} d \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) + 2 \, a b c d^{2} \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) - a^{2} d^{3} \cos\left(\frac{2 \, {\left(b x + a\right)}}{d x + c}\right) - b^{2} c^{2} d + 2 \, a b c d^{2} - a^{2} d^{3}\right)} {\left(\frac{b c}{{\left(b c - a d\right)}^{2}} - \frac{a d}{{\left(b c - a d\right)}^{2}}\right)}}{2 \, {\left(b d^{2} - \frac{{\left(b x + a\right)} d^{3}}{d x + c}\right)}}"," ",0,"-1/2*(2*b^3*c^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) - 4*a*b^2*c*d*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) - 2*(b*x + a)*b^2*c^2*d*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) + 2*a^2*b*d^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d) + 4*(b*x + a)*a*b*c*d^2*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) - 2*(b*x + a)*a^2*d^3*cos_integral(-2*(b - (b*x + a)*d/(d*x + c))/d)*sin(2*b/d)/(d*x + c) - 2*b^3*c^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) + 4*a*b^2*c*d*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) + 2*(b*x + a)*b^2*c^2*d*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - 2*a^2*b*d^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d) - 4*(b*x + a)*a*b*c*d^2*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) + 2*(b*x + a)*a^2*d^3*cos(2*b/d)*sin_integral(2*(b - (b*x + a)*d/(d*x + c))/d)/(d*x + c) - b^2*c^2*d*cos(2*(b*x + a)/(d*x + c)) + 2*a*b*c*d^2*cos(2*(b*x + a)/(d*x + c)) - a^2*d^3*cos(2*(b*x + a)/(d*x + c)) - b^2*c^2*d + 2*a*b*c*d^2 - a^2*d^3)*(b*c/(b*c - a*d)^2 - a*d/(b*c - a*d)^2)/(b*d^2 - (b*x + a)*d^3/(d*x + c))","B",0
53,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^3/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{3}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^3/(a^2*x^2 - 1), x)","F",0
54,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2/(a^2*x^2 - 1), x)","F",0
55,0,0,0,0.000000," ","integrate(cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))/(-a^2*x^2+1),x, algorithm=""giac"")","\int -\frac{\cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}{a^{2} x^{2} - 1}\,{d x}"," ",0,"integrate(-cos(sqrt(-a*x + 1)/sqrt(a*x + 1))/(a^2*x^2 - 1), x)","F",0
56,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2)),x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))), x)","F",0
57,0,0,0,0.000000," ","integrate(1/(-a^2*x^2+1)/cos((-a*x+1)^(1/2)/(a*x+1)^(1/2))^2,x, algorithm=""giac"")","\int -\frac{1}{{\left(a^{2} x^{2} - 1\right)} \cos\left(\frac{\sqrt{-a x + 1}}{\sqrt{a x + 1}}\right)^{2}}\,{d x}"," ",0,"integrate(-1/((a^2*x^2 - 1)*cos(sqrt(-a*x + 1)/sqrt(a*x + 1))^2), x)","F",0
58,1,8,0,0.142965," ","integrate(tan(x^(1/2))/x^(1/2),x, algorithm=""giac"")","-2 \, \log\left({\left| \cos\left(\sqrt{x}\right) \right|}\right)"," ",0,"-2*log(abs(cos(sqrt(x))))","A",0
59,1,12,0,0.122286," ","integrate(tan(x^(1/2))^2/x^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{x} + 2 \, \tan\left(\sqrt{x}\right)"," ",0,"-2*sqrt(x) + 2*tan(sqrt(x))","A",0
60,0,0,0,0.000000," ","integrate(x^(1/2)*tan(x^(1/2)),x, algorithm=""giac"")","\int \sqrt{x} \tan\left(\sqrt{x}\right)\,{d x}"," ",0,"integrate(sqrt(x)*tan(sqrt(x)), x)","F",0
61,1,18,0,8.595465," ","integrate(1/2*b*tan(c*x^2+b*x+a)/c+x*tan(c*x^2+b*x+a),x, algorithm=""giac"")","-\frac{\log\left({\left| \cos\left(c x^{2} + b x + a\right) \right|}\right)}{2 \, c}"," ",0,"-1/2*log(abs(cos(c*x^2 + b*x + a)))/c","A",0
62,1,22,0,0.129336," ","integrate(cot(x^(1/2))^2/x^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{x} - \frac{1}{\tan\left(\frac{1}{2} \, \sqrt{x}\right)} + \tan\left(\frac{1}{2} \, \sqrt{x}\right)"," ",0,"-2*sqrt(x) - 1/tan(1/2*sqrt(x)) + tan(1/2*sqrt(x))","A",0
63,0,0,0,0.000000," ","integrate((a+b*sec(d*x+c))^(1/2)/(1+cos(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(d x + c\right) + a}}{\cos\left(d x + c\right) + 1}\,{d x}"," ",0,"integrate(sqrt(b*sec(d*x + c) + a)/(cos(d*x + c) + 1), x)","F",0
64,1,948,0,1.153244," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) + 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) + 2 \right|}}\right) + \sqrt{2} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) - 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) - 2 \right|}}\right) - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{2 \, b}"," ",0,"1/2*(sqrt(2)*log(abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 30*tan(1/2*a)^2 - 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) + 2)/abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 30*tan(1/2*a)^2 + 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) + 2)) + sqrt(2)*log(abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 + 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a) + 30*tan(1/2*a)^2 - 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) - 2)/abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 + 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a) + 30*tan(1/2*a)^2 + 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) - 2)) - 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
65,1,948,0,1.194306," ","integrate(sec(b*x+a)*sec(2*b*x+2*a),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) + 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} - 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} - 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} + 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) - 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) + 2 \right|}}\right) + \sqrt{2} \log\left(\frac{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) - 2 \right|}}{{\left| 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{6} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{5} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{6} - 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{4} + 12 \, \tan\left(\frac{1}{2} \, a\right)^{5} + 40 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 30 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 30 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 40 \, \tan\left(\frac{1}{2} \, a\right)^{3} - 12 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 30 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \sqrt{2} {\left(\tan\left(\frac{1}{2} \, a\right)^{6} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{4} + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)} - 2 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 12 \, \tan\left(\frac{1}{2} \, a\right) - 2 \right|}}\right) - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} + 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} - \tan\left(\frac{1}{2} \, b x + 2 \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{3} - 3 \, \tan\left(\frac{1}{2} \, b x + 2 \, a\right) \tan\left(\frac{1}{2} \, a\right) + 3 \, \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, b x + 2 \, a\right) - 3 \, \tan\left(\frac{1}{2} \, a\right) - 1 \right|}\right)}{2 \, b}"," ",0,"1/2*(sqrt(2)*log(abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 30*tan(1/2*a)^2 - 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) + 2)/abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 - 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 - 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 + 12*tan(1/2*b*x + 2*a)*tan(1/2*a) - 30*tan(1/2*a)^2 + 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) + 2)) + sqrt(2)*log(abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 + 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a) + 30*tan(1/2*a)^2 - 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) - 2)/abs(2*tan(1/2*b*x + 2*a)*tan(1/2*a)^6 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a)^5 + 2*tan(1/2*a)^6 - 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^4 + 12*tan(1/2*a)^5 + 40*tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 30*tan(1/2*a)^4 + 30*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - 40*tan(1/2*a)^3 - 12*tan(1/2*b*x + 2*a)*tan(1/2*a) + 30*tan(1/2*a)^2 + 2*sqrt(2)*(tan(1/2*a)^6 + 3*tan(1/2*a)^4 + 3*tan(1/2*a)^2 + 1) - 2*tan(1/2*b*x + 2*a) + 12*tan(1/2*a) - 2)) - 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 + 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 - tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 - tan(1/2*b*x + 2*a) + 3*tan(1/2*a) - 1)) + 2*log(abs(tan(1/2*b*x + 2*a)*tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a)^2 + tan(1/2*a)^3 - 3*tan(1/2*b*x + 2*a)*tan(1/2*a) + 3*tan(1/2*a)^2 + tan(1/2*b*x + 2*a) - 3*tan(1/2*a) - 1)))/b","B",0
66,1,6,0,0.121799," ","integrate(sin(x)*sin(2*x),x, algorithm=""giac"")","\frac{2}{3} \, \sin\left(x\right)^{3}"," ",0,"2/3*sin(x)^3","A",0
67,1,13,0,0.135466," ","integrate(sin(x)*sin(3*x),x, algorithm=""giac"")","-\frac{1}{8} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/8*sin(4*x) + 1/4*sin(2*x)","A",0
68,1,13,0,0.138473," ","integrate(sin(x)*sin(4*x),x, algorithm=""giac"")","-\frac{8}{5} \, \sin\left(x\right)^{5} + \frac{4}{3} \, \sin\left(x\right)^{3}"," ",0,"-8/5*sin(x)^5 + 4/3*sin(x)^3","A",0
69,1,29,0,0.135605," ","integrate(sin(x)*sin(m*x),x, algorithm=""giac"")","-\frac{\sin\left(m x + x\right)}{2 \, {\left(m + 1\right)}} + \frac{\sin\left(m x - x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*sin(m*x + x)/(m + 1) + 1/2*sin(m*x - x)/(m - 1)","A",0
70,1,11,0,0.127420," ","integrate(cos(2*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{6} \, \cos\left(3 \, x\right) + \frac{1}{2} \, \cos\left(x\right)"," ",0,"-1/6*cos(3*x) + 1/2*cos(x)","A",0
71,1,13,0,0.121876," ","integrate(cos(3*x)*sin(x),x, algorithm=""giac"")","-\sin\left(x\right)^{4} + \frac{1}{2} \, \sin\left(x\right)^{2}"," ",0,"-sin(x)^4 + 1/2*sin(x)^2","A",0
72,1,13,0,0.122758," ","integrate(cos(4*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{10} \, \cos\left(5 \, x\right) + \frac{1}{6} \, \cos\left(3 \, x\right)"," ",0,"-1/10*cos(5*x) + 1/6*cos(3*x)","A",0
73,1,29,0,0.132771," ","integrate(cos(m*x)*sin(x),x, algorithm=""giac"")","-\frac{\cos\left(m x + x\right)}{2 \, {\left(m + 1\right)}} + \frac{\cos\left(m x - x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*cos(m*x + x)/(m + 1) + 1/2*cos(m*x - x)/(m - 1)","A",0
74,0,0,0,0.000000," ","integrate(sin(x)*tan(2*x),x, algorithm=""giac"")","\int \sin\left(x\right) \tan\left(2 \, x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(2*x), x)","F",0
75,1,364,0,0.265997," ","integrate(sin(x)*tan(3*x),x, algorithm=""giac"")","\frac{\log\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, x\right) + 1}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - \log\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, x\right) + 1}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \log\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, x\right) + 1}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) - \log\left(\frac{\tan\left(\frac{1}{2} \, x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 18 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, x\right) + 1}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 2 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) - 2 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) - 24 \, \tan\left(\frac{1}{2} \, x\right)}{12 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"1/12*(log((tan(1/2*x)^4 + 8*tan(1/2*x)^3 + 18*tan(1/2*x)^2 + 8*tan(1/2*x) + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - log((tan(1/2*x)^4 - 8*tan(1/2*x)^3 + 18*tan(1/2*x)^2 - 8*tan(1/2*x) + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 2*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - 2*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + log((tan(1/2*x)^4 + 8*tan(1/2*x)^3 + 18*tan(1/2*x)^2 + 8*tan(1/2*x) + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)) - log((tan(1/2*x)^4 - 8*tan(1/2*x)^3 + 18*tan(1/2*x)^2 - 8*tan(1/2*x) + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)) + 2*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) - 2*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) - 24*tan(1/2*x))/(tan(1/2*x)^2 + 1)","B",0
76,0,0,0,0.000000," ","integrate(sin(x)*tan(4*x),x, algorithm=""giac"")","\int \sin\left(x\right) \tan\left(4 \, x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(4*x), x)","F",0
77,0,0,0,0.000000," ","integrate(sin(x)*tan(5*x),x, algorithm=""giac"")","\int \sin\left(x\right) \tan\left(5 \, x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(5*x), x)","F",0
78,0,0,0,0.000000," ","integrate(sin(x)*tan(6*x),x, algorithm=""giac"")","\int \sin\left(x\right) \tan\left(6 \, x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(6*x), x)","F",0
79,0,0,0,0.000000," ","integrate(sin(x)*tan(n*x),x, algorithm=""giac"")","\int \sin\left(x\right) \tan\left(n x\right)\,{d x}"," ",0,"integrate(sin(x)*tan(n*x), x)","F",0
80,1,19,0,0.138200," ","integrate(cot(2*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(-\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"-1/4*log(sin(x) + 1) + 1/4*log(-sin(x) + 1) + sin(x)","B",0
81,1,34,0,0.149549," ","integrate(cot(3*x)*sin(x),x, algorithm=""giac"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}{{\left| 4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}\right) + \sin\left(x\right)"," ",0,"1/6*sqrt(3)*log(abs(-4*sqrt(3) + 8*sin(x))/abs(4*sqrt(3) + 8*sin(x))) + sin(x)","B",0
82,1,50,0,0.137996," ","integrate(cot(4*x)*sin(x),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right) + \sin\left(x\right)"," ",0,"1/8*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x))) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1) + sin(x)","B",0
83,1,111,0,0.325597," ","integrate(cot(5*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} + 5} + \sin\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| -\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\sqrt{5} + 5} + \sin\left(x\right) \right|}\right) - \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| \sqrt{-\frac{1}{8} \, \sqrt{5} + \frac{5}{8}} + \sin\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{-\frac{1}{8} \, \sqrt{5} + \frac{5}{8}} + \sin\left(x\right) \right|}\right) + \sin\left(x\right)"," ",0,"-1/20*sqrt(2*sqrt(5) + 10)*log(abs(1/2*sqrt(1/2)*sqrt(sqrt(5) + 5) + sin(x))) + 1/20*sqrt(2*sqrt(5) + 10)*log(abs(-1/2*sqrt(1/2)*sqrt(sqrt(5) + 5) + sin(x))) - 1/20*sqrt(-2*sqrt(5) + 10)*log(abs(sqrt(-1/8*sqrt(5) + 5/8) + sin(x))) + 1/20*sqrt(-2*sqrt(5) + 10)*log(abs(-sqrt(-1/8*sqrt(5) + 5/8) + sin(x))) + sin(x)","B",0
84,1,70,0,0.167567," ","integrate(cot(6*x)*sin(x),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}{{\left| 4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}\right) - \frac{1}{12} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-\sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left({\left| 2 \, \sin\left(x\right) + 1 \right|}\right) + \frac{1}{12} \, \log\left({\left| 2 \, \sin\left(x\right) - 1 \right|}\right) + \sin\left(x\right)"," ",0,"1/12*sqrt(3)*log(abs(-4*sqrt(3) + 8*sin(x))/abs(4*sqrt(3) + 8*sin(x))) - 1/12*log(sin(x) + 1) + 1/12*log(-sin(x) + 1) - 1/12*log(abs(2*sin(x) + 1)) + 1/12*log(abs(2*sin(x) - 1)) + sin(x)","B",0
85,1,49,0,0.170724," ","integrate(sec(2*x)*sin(x),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}\right)"," ",0,"1/4*sqrt(2)*log(abs(-4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6)/abs(4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6))","B",0
86,1,24,0,0.141756," ","integrate(sec(3*x)*sin(x),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(-\sin\left(x\right)^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| 4 \, \sin\left(x\right)^{2} - 1 \right|}\right)"," ",0,"1/6*log(-sin(x)^2 + 1) - 1/6*log(abs(4*sin(x)^2 - 1))","A",0
87,1,133,0,0.142325," ","integrate(sec(4*x)*sin(x),x, algorithm=""giac"")","-\frac{2.16139547686000 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 0.0395661298966000\right)}{\frac{140 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 28.1312524456150} - \frac{4.18450863968000 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 0.446462692172000\right)}{\frac{140 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 44.3876588494000} - \frac{20.9929814212000 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 2.23982880884000\right)}{\frac{140 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 404.466590643000} - \frac{1380.66111446200 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 25.2741423691000\right)}{\frac{140 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 10892.9855019000}"," ",0,"-2.16139547686000*log(-(cos(x) - 1)/(cos(x) + 1) - 0.0395661298966000)/(140*(cos(x) - 1)/(cos(x) + 1) + 28.1312524456150) - 4.18450863968000*log(-(cos(x) - 1)/(cos(x) + 1) - 0.446462692172000)/(140*(cos(x) - 1)/(cos(x) + 1) + 44.3876588494000) - 20.9929814212000*log(-(cos(x) - 1)/(cos(x) + 1) - 2.23982880884000)/(140*(cos(x) - 1)/(cos(x) + 1) + 404.466590643000) - 1380.66111446200*log(-(cos(x) - 1)/(cos(x) + 1) - 25.2741423691000)/(140*(cos(x) - 1)/(cos(x) + 1) - 10892.9855019000)","B",0
88,1,67,0,0.160328," ","integrate(sec(5*x)*sin(x),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{{\left| 32 \, \sin\left(x\right)^{2} - 4 \, \sqrt{5} - 12 \right|}}{{\left| 32 \, \sin\left(x\right)^{2} + 4 \, \sqrt{5} - 12 \right|}}\right) - \frac{1}{10} \, \log\left(-\sin\left(x\right)^{2} + 1\right) + \frac{1}{20} \, \log\left({\left| 16 \, \sin\left(x\right)^{4} - 12 \, \sin\left(x\right)^{2} + 1 \right|}\right)"," ",0,"1/20*sqrt(5)*log(abs(32*sin(x)^2 - 4*sqrt(5) - 12)/abs(32*sin(x)^2 + 4*sqrt(5) - 12)) - 1/10*log(-sin(x)^2 + 1) + 1/20*log(abs(16*sin(x)^4 - 12*sin(x)^2 + 1))","A",0
89,1,182,0,0.164071," ","integrate(sec(6*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}{{\left| 4 \, \sqrt{2} - \frac{2 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 6 \right|}}\right) - \frac{2.39014968180000 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 0.0173323801210000\right)}{\frac{268 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 60.0540532247402} + \frac{5.82951931426000 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 0.588790706481000\right)}{\frac{268 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 121.584934401100} + \frac{16.8155413244667 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1.69839637242000\right)}{\frac{268 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 559.622604171000} - \frac{7956.25491093333 \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 57.6954805410000\right)}{\frac{268 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - 168981.261592000}"," ",0,"-1/12*sqrt(2)*log(abs(-4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6)/abs(4*sqrt(2) - 2*(cos(x) - 1)/(cos(x) + 1) - 6)) - 2.39014968180000*log(-(cos(x) - 1)/(cos(x) + 1) - 0.0173323801210000)/(268*(cos(x) - 1)/(cos(x) + 1) + 60.0540532247402) + 5.82951931426000*log(-(cos(x) - 1)/(cos(x) + 1) - 0.588790706481000)/(268*(cos(x) - 1)/(cos(x) + 1) + 121.584934401100) + 16.8155413244667*log(-(cos(x) - 1)/(cos(x) + 1) - 1.69839637242000)/(268*(cos(x) - 1)/(cos(x) + 1) + 559.622604171000) - 7956.25491093333*log(-(cos(x) - 1)/(cos(x) + 1) - 57.6954805410000)/(268*(cos(x) - 1)/(cos(x) + 1) - 168981.261592000)","B",0
90,1,17,0,0.138926," ","integrate(csc(2*x)*sin(x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"1/4*log(sin(x) + 1) - 1/4*log(-sin(x) + 1)","B",0
91,1,31,0,0.180106," ","integrate(csc(3*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 2 \, \tan\left(x\right) \right|}}{{\left| 2 \, \sqrt{3} + 2 \, \tan\left(x\right) \right|}}\right)"," ",0,"-1/6*sqrt(3)*log(abs(-2*sqrt(3) + 2*tan(x))/abs(2*sqrt(3) + 2*tan(x)))","A",0
92,1,48,0,0.135566," ","integrate(csc(4*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right) - \frac{1}{8} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1/8*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x))) - 1/8*log(sin(x) + 1) + 1/8*log(-sin(x) + 1)","B",0
93,1,105,0,0.281583," ","integrate(csc(5*x)*sin(x),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| \sqrt{2 \, \sqrt{5} + 5} + \tan\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{2 \, \sqrt{5} + 5} + \tan\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| \sqrt{-2 \, \sqrt{5} + 5} + \tan\left(x\right) \right|}\right) - \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{-2 \, \sqrt{5} + 5} + \tan\left(x\right) \right|}\right)"," ",0,"-1/20*sqrt(2*sqrt(5) + 10)*log(abs(sqrt(2*sqrt(5) + 5) + tan(x))) + 1/20*sqrt(2*sqrt(5) + 10)*log(abs(-sqrt(2*sqrt(5) + 5) + tan(x))) + 1/20*sqrt(-2*sqrt(5) + 10)*log(abs(sqrt(-2*sqrt(5) + 5) + tan(x))) - 1/20*sqrt(-2*sqrt(5) + 10)*log(abs(-sqrt(-2*sqrt(5) + 5) + tan(x)))","A",0
94,1,68,0,0.150529," ","integrate(csc(6*x)*sin(x),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}{{\left| 4 \, \sqrt{3} + 8 \, \sin\left(x\right) \right|}}\right) + \frac{1}{12} \, \log\left(\sin\left(x\right) + 1\right) - \frac{1}{12} \, \log\left(-\sin\left(x\right) + 1\right) + \frac{1}{12} \, \log\left({\left| 2 \, \sin\left(x\right) + 1 \right|}\right) - \frac{1}{12} \, \log\left({\left| 2 \, \sin\left(x\right) - 1 \right|}\right)"," ",0,"1/12*sqrt(3)*log(abs(-4*sqrt(3) + 8*sin(x))/abs(4*sqrt(3) + 8*sin(x))) + 1/12*log(sin(x) + 1) - 1/12*log(-sin(x) + 1) + 1/12*log(abs(2*sin(x) + 1)) - 1/12*log(abs(2*sin(x) - 1))","B",0
95,1,6,0,0.133076," ","integrate(csc(x)*sin(3*x),x, algorithm=""giac"")","x + \sin\left(2 \, x\right)"," ",0,"x + sin(2*x)","A",0
96,1,6,0,0.131173," ","integrate(csc(3*x)*sin(6*x),x, algorithm=""giac"")","\frac{2}{3} \, \sin\left(3 \, x\right)"," ",0,"2/3*sin(3*x)","A",0
97,1,6,0,0.131090," ","integrate(cos(x)*sin(2*x),x, algorithm=""giac"")","-\frac{2}{3} \, \cos\left(x\right)^{3}"," ",0,"-2/3*cos(x)^3","A",0
98,1,13,0,0.136896," ","integrate(cos(x)*sin(3*x),x, algorithm=""giac"")","-\cos\left(x\right)^{4} + \frac{1}{2} \, \cos\left(x\right)^{2}"," ",0,"-cos(x)^4 + 1/2*cos(x)^2","A",0
99,1,13,0,0.123292," ","integrate(cos(x)*sin(4*x),x, algorithm=""giac"")","-\frac{8}{5} \, \cos\left(x\right)^{5} + \frac{4}{3} \, \cos\left(x\right)^{3}"," ",0,"-8/5*cos(x)^5 + 4/3*cos(x)^3","A",0
100,1,29,0,0.138679," ","integrate(cos(x)*sin(m*x),x, algorithm=""giac"")","-\frac{\cos\left(m x + x\right)}{2 \, {\left(m + 1\right)}} - \frac{\cos\left(m x - x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"-1/2*cos(m*x + x)/(m + 1) - 1/2*cos(m*x - x)/(m - 1)","A",0
101,1,11,0,0.134953," ","integrate(cos(x)*cos(2*x),x, algorithm=""giac"")","\frac{1}{6} \, \sin\left(3 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"1/6*sin(3*x) + 1/2*sin(x)","A",0
102,1,13,0,0.133630," ","integrate(cos(x)*cos(3*x),x, algorithm=""giac"")","\frac{1}{8} \, \sin\left(4 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/8*sin(4*x) + 1/4*sin(2*x)","A",0
103,1,13,0,0.135820," ","integrate(cos(x)*cos(4*x),x, algorithm=""giac"")","\frac{1}{10} \, \sin\left(5 \, x\right) + \frac{1}{6} \, \sin\left(3 \, x\right)"," ",0,"1/10*sin(5*x) + 1/6*sin(3*x)","A",0
104,1,29,0,0.136197," ","integrate(cos(x)*cos(m*x),x, algorithm=""giac"")","\frac{\sin\left(m x + x\right)}{2 \, {\left(m + 1\right)}} + \frac{\sin\left(m x - x\right)}{2 \, {\left(m - 1\right)}}"," ",0,"1/2*sin(m*x + x)/(m + 1) + 1/2*sin(m*x - x)/(m - 1)","A",0
105,0,0,0,0.000000," ","integrate(cos(x)*tan(2*x),x, algorithm=""giac"")","\int \cos\left(x\right) \tan\left(2 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*tan(2*x), x)","F",0
106,0,0,0,0.000000," ","integrate(cos(x)*tan(3*x),x, algorithm=""giac"")","\int \cos\left(x\right) \tan\left(3 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*tan(3*x), x)","F",0
107,0,0,0,0.000000," ","integrate(cos(x)*tan(4*x),x, algorithm=""giac"")","\int \cos\left(x\right) \tan\left(4 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*tan(4*x), x)","F",0
108,0,0,0,0.000000," ","integrate(cos(x)*tan(5*x),x, algorithm=""giac"")","\int \cos\left(x\right) \tan\left(5 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*tan(5*x), x)","F",0
109,0,0,0,0.000000," ","integrate(cos(x)*tan(6*x),x, algorithm=""giac"")","\int \cos\left(x\right) \tan\left(6 \, x\right)\,{d x}"," ",0,"integrate(cos(x)*tan(6*x), x)","F",0
110,1,19,0,0.141086," ","integrate(cos(x)*cot(2*x),x, algorithm=""giac"")","\cos\left(x\right) - \frac{1}{4} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"cos(x) - 1/4*log(cos(x) + 1) + 1/4*log(-cos(x) + 1)","B",0
111,1,39,0,0.132250," ","integrate(cos(x)*cot(3*x),x, algorithm=""giac"")","\cos\left(x\right) - \frac{1}{6} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{6} \, \log\left(-\cos\left(x\right) + 1\right) - \frac{1}{6} \, \log\left({\left| 2 \, \cos\left(x\right) + 1 \right|}\right) + \frac{1}{6} \, \log\left({\left| 2 \, \cos\left(x\right) - 1 \right|}\right)"," ",0,"cos(x) - 1/6*log(cos(x) + 1) + 1/6*log(-cos(x) + 1) - 1/6*log(abs(2*cos(x) + 1)) + 1/6*log(abs(2*cos(x) - 1))","A",0
112,1,50,0,0.140014," ","integrate(cos(x)*cot(4*x),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \cos\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \cos\left(x\right) \right|}}\right) + \cos\left(x\right) - \frac{1}{8} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"1/8*sqrt(2)*log(abs(-2*sqrt(2) + 4*cos(x))/abs(2*sqrt(2) + 4*cos(x))) + cos(x) - 1/8*log(cos(x) + 1) + 1/8*log(-cos(x) + 1)","B",0
113,1,117,0,0.159857," ","integrate(cos(x)*cot(5*x),x, algorithm=""giac"")","\frac{1}{20} \, \sqrt{5} \log\left(\frac{{\left| -2 \, \sqrt{5} + 8 \, \cos\left(x\right) + 2 \right|}}{{\left| 2 \, \sqrt{5} + 8 \, \cos\left(x\right) + 2 \right|}}\right) + \frac{1}{20} \, \sqrt{5} \log\left(\frac{{\left| -2 \, \sqrt{5} + 8 \, \cos\left(x\right) - 2 \right|}}{{\left| 2 \, \sqrt{5} + 8 \, \cos\left(x\right) - 2 \right|}}\right) + \cos\left(x\right) - \frac{1}{10} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{10} \, \log\left(-\cos\left(x\right) + 1\right) - \frac{1}{20} \, \log\left({\left| 4 \, \cos\left(x\right)^{2} + 2 \, \cos\left(x\right) - 1 \right|}\right) + \frac{1}{20} \, \log\left({\left| 4 \, \cos\left(x\right)^{2} - 2 \, \cos\left(x\right) - 1 \right|}\right)"," ",0,"1/20*sqrt(5)*log(abs(-2*sqrt(5) + 8*cos(x) + 2)/abs(2*sqrt(5) + 8*cos(x) + 2)) + 1/20*sqrt(5)*log(abs(-2*sqrt(5) + 8*cos(x) - 2)/abs(2*sqrt(5) + 8*cos(x) - 2)) + cos(x) - 1/10*log(cos(x) + 1) + 1/10*log(-cos(x) + 1) - 1/20*log(abs(4*cos(x)^2 + 2*cos(x) - 1)) + 1/20*log(abs(4*cos(x)^2 - 2*cos(x) - 1))","A",0
114,1,70,0,0.174709," ","integrate(cos(x)*cot(6*x),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{3} + 8 \, \cos\left(x\right) \right|}}{{\left| 4 \, \sqrt{3} + 8 \, \cos\left(x\right) \right|}}\right) + \cos\left(x\right) - \frac{1}{12} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-\cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left({\left| 2 \, \cos\left(x\right) + 1 \right|}\right) + \frac{1}{12} \, \log\left({\left| 2 \, \cos\left(x\right) - 1 \right|}\right)"," ",0,"1/12*sqrt(3)*log(abs(-4*sqrt(3) + 8*cos(x))/abs(4*sqrt(3) + 8*cos(x))) + cos(x) - 1/12*log(cos(x) + 1) + 1/12*log(-cos(x) + 1) - 1/12*log(abs(2*cos(x) + 1)) + 1/12*log(abs(2*cos(x) - 1))","B",0
115,0,0,0,0.000000," ","integrate(cos(x)*cot(n*x),x, algorithm=""giac"")","\int \cos\left(x\right) \cot\left(n x\right)\,{d x}"," ",0,"integrate(cos(x)*cot(n*x), x)","F",0
116,1,31,0,0.134183," ","integrate(cos(x)*sec(2*x),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left({\left| \frac{1}{2} \, \sqrt{2} + \sin\left(x\right) \right|}\right) - \frac{1}{4} \, \sqrt{2} \log\left({\left| -\frac{1}{2} \, \sqrt{2} + \sin\left(x\right) \right|}\right)"," ",0,"1/4*sqrt(2)*log(abs(1/2*sqrt(2) + sin(x))) - 1/4*sqrt(2)*log(abs(-1/2*sqrt(2) + sin(x)))","B",0
117,1,31,0,0.169166," ","integrate(cos(x)*sec(3*x),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{3} \log\left(\frac{{\left| -2 \, \sqrt{3} + 6 \, \tan\left(x\right) \right|}}{{\left| 2 \, \sqrt{3} + 6 \, \tan\left(x\right) \right|}}\right)"," ",0,"-1/6*sqrt(3)*log(abs(-2*sqrt(3) + 6*tan(x))/abs(2*sqrt(3) + 6*tan(x)))","A",0
118,1,99,0,0.275687," ","integrate(cos(x)*sec(4*x),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left| \frac{1}{2} \, \sqrt{\sqrt{2} + 2} + \sin\left(x\right) \right|}\right) + \frac{1}{8} \, \sqrt{-\sqrt{2} + 2} \log\left({\left| -\frac{1}{2} \, \sqrt{\sqrt{2} + 2} + \sin\left(x\right) \right|}\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left({\left| \sqrt{-\frac{1}{4} \, \sqrt{2} + \frac{1}{2}} + \sin\left(x\right) \right|}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 2} \log\left({\left| -\sqrt{-\frac{1}{4} \, \sqrt{2} + \frac{1}{2}} + \sin\left(x\right) \right|}\right)"," ",0,"-1/8*sqrt(-sqrt(2) + 2)*log(abs(1/2*sqrt(sqrt(2) + 2) + sin(x))) + 1/8*sqrt(-sqrt(2) + 2)*log(abs(-1/2*sqrt(sqrt(2) + 2) + sin(x))) + 1/8*sqrt(sqrt(2) + 2)*log(abs(sqrt(-1/4*sqrt(2) + 1/2) + sin(x))) - 1/8*sqrt(sqrt(2) + 2)*log(abs(-sqrt(-1/4*sqrt(2) + 1/2) + sin(x)))","B",0
119,1,105,0,0.283725," ","integrate(cos(x)*sec(5*x),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| \sqrt{\frac{2}{5} \, \sqrt{5} + 1} + \tan\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{-2 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{\frac{2}{5} \, \sqrt{5} + 1} + \tan\left(x\right) \right|}\right) + \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| \sqrt{-\frac{2}{5} \, \sqrt{5} + 1} + \tan\left(x\right) \right|}\right) - \frac{1}{20} \, \sqrt{2 \, \sqrt{5} + 10} \log\left({\left| -\sqrt{-\frac{2}{5} \, \sqrt{5} + 1} + \tan\left(x\right) \right|}\right)"," ",0,"-1/20*sqrt(-2*sqrt(5) + 10)*log(abs(sqrt(2/5*sqrt(5) + 1) + tan(x))) + 1/20*sqrt(-2*sqrt(5) + 10)*log(abs(-sqrt(2/5*sqrt(5) + 1) + tan(x))) + 1/20*sqrt(2*sqrt(5) + 10)*log(abs(sqrt(-2/5*sqrt(5) + 1) + tan(x))) - 1/20*sqrt(2*sqrt(5) + 10)*log(abs(-sqrt(-2/5*sqrt(5) + 1) + tan(x)))","A",0
120,1,132,0,0.245471," ","integrate(cos(x)*sec(6*x),x, algorithm=""giac"")","\frac{1}{24} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left({\left| \frac{1}{4} \, \sqrt{6} + \frac{1}{4} \, \sqrt{2} + \sin\left(x\right) \right|}\right) + \frac{1}{24} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left({\left| \frac{1}{4} \, \sqrt{6} - \frac{1}{4} \, \sqrt{2} + \sin\left(x\right) \right|}\right) - \frac{1}{24} \, {\left(\sqrt{6} + \sqrt{2}\right)} \log\left({\left| -\frac{1}{4} \, \sqrt{6} + \frac{1}{4} \, \sqrt{2} + \sin\left(x\right) \right|}\right) - \frac{1}{24} \, {\left(\sqrt{6} - \sqrt{2}\right)} \log\left({\left| -\frac{1}{4} \, \sqrt{6} - \frac{1}{4} \, \sqrt{2} + \sin\left(x\right) \right|}\right) + \frac{1}{12} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(x\right) \right|}}\right)"," ",0,"1/24*(sqrt(6) - sqrt(2))*log(abs(1/4*sqrt(6) + 1/4*sqrt(2) + sin(x))) + 1/24*(sqrt(6) + sqrt(2))*log(abs(1/4*sqrt(6) - 1/4*sqrt(2) + sin(x))) - 1/24*(sqrt(6) + sqrt(2))*log(abs(-1/4*sqrt(6) + 1/4*sqrt(2) + sin(x))) - 1/24*(sqrt(6) - sqrt(2))*log(abs(-1/4*sqrt(6) - 1/4*sqrt(2) + sin(x))) + 1/12*sqrt(2)*log(abs(-2*sqrt(2) + 4*sin(x))/abs(2*sqrt(2) + 4*sin(x)))","A",0
121,1,21,0,0.140670," ","integrate(cos(2*x)*sec(x),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\sin\left(x\right) + 1\right) + \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right) + 2 \, \sin\left(x\right)"," ",0,"-1/2*log(sin(x) + 1) + 1/2*log(-sin(x) + 1) + 2*sin(x)","B",0
122,1,25,0,0.125849," ","integrate(cos(4*x)*sec(2*x),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(\sin\left(2 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(-\sin\left(2 \, x\right) + 1\right) + \sin\left(2 \, x\right)"," ",0,"-1/4*log(sin(2*x) + 1) + 1/4*log(-sin(2*x) + 1) + sin(2*x)","B",0
123,1,17,0,0.122595," ","integrate(cos(x)*csc(2*x),x, algorithm=""giac"")","-\frac{1}{4} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"-1/4*log(cos(x) + 1) + 1/4*log(-cos(x) + 1)","B",0
124,1,24,0,0.139868," ","integrate(cos(x)*csc(3*x),x, algorithm=""giac"")","\frac{1}{6} \, \log\left(-\cos\left(x\right)^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| 4 \, \cos\left(x\right)^{2} - 1 \right|}\right)"," ",0,"1/6*log(-cos(x)^2 + 1) - 1/6*log(abs(4*cos(x)^2 - 1))","A",0
125,1,48,0,0.134946," ","integrate(cos(x)*csc(4*x),x, algorithm=""giac"")","-\frac{1}{8} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \cos\left(x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \cos\left(x\right) \right|}}\right) - \frac{1}{8} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{8} \, \log\left(-\cos\left(x\right) + 1\right)"," ",0,"-1/8*sqrt(2)*log(abs(-2*sqrt(2) + 4*cos(x))/abs(2*sqrt(2) + 4*cos(x))) - 1/8*log(cos(x) + 1) + 1/8*log(-cos(x) + 1)","B",0
126,1,67,0,0.140126," ","integrate(cos(x)*csc(5*x),x, algorithm=""giac"")","-\frac{1}{20} \, \sqrt{5} \log\left(\frac{{\left| 32 \, \cos\left(x\right)^{2} - 4 \, \sqrt{5} - 12 \right|}}{{\left| 32 \, \cos\left(x\right)^{2} + 4 \, \sqrt{5} - 12 \right|}}\right) + \frac{1}{10} \, \log\left(-\cos\left(x\right)^{2} + 1\right) - \frac{1}{20} \, \log\left({\left| 16 \, \cos\left(x\right)^{4} - 12 \, \cos\left(x\right)^{2} + 1 \right|}\right)"," ",0,"-1/20*sqrt(5)*log(abs(32*cos(x)^2 - 4*sqrt(5) - 12)/abs(32*cos(x)^2 + 4*sqrt(5) - 12)) + 1/10*log(-cos(x)^2 + 1) - 1/20*log(abs(16*cos(x)^4 - 12*cos(x)^2 + 1))","A",0
127,1,68,0,0.150699," ","integrate(cos(x)*csc(6*x),x, algorithm=""giac"")","-\frac{1}{12} \, \sqrt{3} \log\left(\frac{{\left| -4 \, \sqrt{3} + 8 \, \cos\left(x\right) \right|}}{{\left| 4 \, \sqrt{3} + 8 \, \cos\left(x\right) \right|}}\right) - \frac{1}{12} \, \log\left(\cos\left(x\right) + 1\right) + \frac{1}{12} \, \log\left(-\cos\left(x\right) + 1\right) - \frac{1}{12} \, \log\left({\left| 2 \, \cos\left(x\right) + 1 \right|}\right) + \frac{1}{12} \, \log\left({\left| 2 \, \cos\left(x\right) - 1 \right|}\right)"," ",0,"-1/12*sqrt(3)*log(abs(-4*sqrt(3) + 8*cos(x))/abs(4*sqrt(3) + 8*cos(x))) - 1/12*log(cos(x) + 1) + 1/12*log(-cos(x) + 1) - 1/12*log(abs(2*cos(x) + 1)) + 1/12*log(abs(2*cos(x) - 1))","B",0
128,1,25,0,0.126449," ","integrate(cos(6*x)^3*sin(x),x, algorithm=""giac"")","-\frac{1}{152} \, \cos\left(19 \, x\right) + \frac{1}{136} \, \cos\left(17 \, x\right) - \frac{3}{56} \, \cos\left(7 \, x\right) + \frac{3}{40} \, \cos\left(5 \, x\right)"," ",0,"-1/152*cos(19*x) + 1/136*cos(17*x) - 3/56*cos(7*x) + 3/40*cos(5*x)","A",0
129,1,25,0,0.140969," ","integrate(cos(6*x)^3*sin(9*x),x, algorithm=""giac"")","-\frac{1}{216} \, \cos\left(27 \, x\right) - \frac{1}{40} \, \cos\left(15 \, x\right) + \frac{1}{72} \, \cos\left(9 \, x\right) - \frac{1}{8} \, \cos\left(3 \, x\right)"," ",0,"-1/216*cos(27*x) - 1/40*cos(15*x) + 1/72*cos(9*x) - 1/8*cos(3*x)","A",0
130,1,19,0,0.124219," ","integrate(cos(2*x)*sin(6*x)^2,x, algorithm=""giac"")","-\frac{1}{56} \, \sin\left(14 \, x\right) - \frac{1}{40} \, \sin\left(10 \, x\right) + \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"-1/56*sin(14*x) - 1/40*sin(10*x) + 1/4*sin(2*x)","A",0
131,1,17,0,0.125031," ","integrate(cos(x)*sin(6*x)^2,x, algorithm=""giac"")","-\frac{1}{52} \, \sin\left(13 \, x\right) - \frac{1}{44} \, \sin\left(11 \, x\right) + \frac{1}{2} \, \sin\left(x\right)"," ",0,"-1/52*sin(13*x) - 1/44*sin(11*x) + 1/2*sin(x)","A",0
132,1,49,0,0.139946," ","integrate(cos(x)*sin(6*x)^3,x, algorithm=""giac"")","\frac{32768}{19} \, \cos\left(x\right)^{19} - \frac{131072}{17} \, \cos\left(x\right)^{17} + 14336 \, \cos\left(x\right)^{15} - 14336 \, \cos\left(x\right)^{13} + 8320 \, \cos\left(x\right)^{11} - 2816 \, \cos\left(x\right)^{9} + \frac{3672}{7} \, \cos\left(x\right)^{7} - \frac{216}{5} \, \cos\left(x\right)^{5}"," ",0,"32768/19*cos(x)^19 - 131072/17*cos(x)^17 + 14336*cos(x)^15 - 14336*cos(x)^13 + 8320*cos(x)^11 - 2816*cos(x)^9 + 3672/7*cos(x)^7 - 216/5*cos(x)^5","A",0
133,1,23,0,0.140413," ","integrate(cos(7*x)*sin(6*x)^3,x, algorithm=""giac"")","\frac{1}{200} \, \cos\left(25 \, x\right) - \frac{3}{104} \, \cos\left(13 \, x\right) + \frac{1}{88} \, \cos\left(11 \, x\right) + \frac{3}{8} \, \cos\left(x\right)"," ",0,"1/200*cos(25*x) - 3/104*cos(13*x) + 1/88*cos(11*x) + 3/8*cos(x)","A",0
134,1,31,0,0.124763," ","integrate(cos(3*x)^2*sin(2*x)^3,x, algorithm=""giac"")","\frac{1}{192} \, \cos\left(12 \, x\right) - \frac{3}{128} \, \cos\left(8 \, x\right) + \frac{1}{48} \, \cos\left(6 \, x\right) + \frac{3}{64} \, \cos\left(4 \, x\right) - \frac{3}{16} \, \cos\left(2 \, x\right)"," ",0,"1/192*cos(12*x) - 3/128*cos(8*x) + 1/48*cos(6*x) + 3/64*cos(4*x) - 3/16*cos(2*x)","A",0
135,1,23,0,0.123729," ","integrate(sin(b*x+a)*sin(b*x+c),x, algorithm=""giac"")","\frac{1}{2} \, x \cos\left(a - c\right) - \frac{\sin\left(2 \, b x + a + c\right)}{4 \, b}"," ",0,"1/2*x*cos(a - c) - 1/4*sin(2*b*x + a + c)/b","A",0
136,1,23,0,0.137441," ","integrate(-sin(b*x-c)*sin(b*x+a),x, algorithm=""giac"")","-\frac{1}{2} \, x \cos\left(a + c\right) + \frac{\sin\left(2 \, b x + a - c\right)}{4 \, b}"," ",0,"-1/2*x*cos(a + c) + 1/4*sin(2*b*x + a - c)/b","A",0
137,1,23,0,0.123640," ","integrate(cos(b*x+a)*cos(b*x+c),x, algorithm=""giac"")","\frac{1}{2} \, x \cos\left(a - c\right) + \frac{\sin\left(2 \, b x + a + c\right)}{4 \, b}"," ",0,"1/2*x*cos(a - c) + 1/4*sin(2*b*x + a + c)/b","A",0
138,1,23,0,0.148536," ","integrate(cos(b*x-c)*cos(b*x+a),x, algorithm=""giac"")","\frac{1}{2} \, x \cos\left(a + c\right) + \frac{\sin\left(2 \, b x + a - c\right)}{4 \, b}"," ",0,"1/2*x*cos(a + c) + 1/4*sin(2*b*x + a - c)/b","A",0
139,-2,0,0,0.000000," ","integrate(tan(b*x+a)*tan(b*x+c),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)2/b*(-1/2*b*x+(2*tan(a/2)^2*tan(c/2)^3-2*tan(a/2)^2*tan(c/2)+8*tan(a/2)*tan(c/2)^2-2*tan(c/2)^3+2*tan(c/2))/(8*tan(a/2)^2*tan(c/2)^2-8*tan(a/2)*tan(c/2)^3+8*tan(a/2)*tan(c/2)-8*tan(c/2)^2)*ln(abs(2*tan(b*x)*tan(c/2)+tan(c/2)^2-1))+(2*tan(a/2)^3*tan(c/2)^2-2*tan(a/2)^3+8*tan(a/2)^2*tan(c/2)-2*tan(a/2)*tan(c/2)^2+2*tan(a/2))/(-8*tan(a/2)^3*tan(c/2)+8*tan(a/2)^2*tan(c/2)^2-8*tan(a/2)^2+8*tan(a/2)*tan(c/2))*ln(abs(2*tan(b*x)*tan(a/2)+tan(a/2)^2-1)))","F(-2)",0
140,-2,0,0,0.000000," ","integrate(-tan(b*x-c)*tan(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)-2/b*(-1/2*b*x+(-2*tan(a/2)^2*tan(c/2)^3+2*tan(a/2)^2*tan(c/2)+8*tan(a/2)*tan(c/2)^2+2*tan(c/2)^3-2*tan(c/2))/(8*tan(a/2)^2*tan(c/2)^2+8*tan(a/2)*tan(c/2)^3-8*tan(a/2)*tan(c/2)-8*tan(c/2)^2)*ln(abs(2*tan(b*x)*tan(c/2)-tan(c/2)^2+1))+(-2*tan(a/2)^3*tan(c/2)^2+2*tan(a/2)^3+8*tan(a/2)^2*tan(c/2)+2*tan(a/2)*tan(c/2)^2-2*tan(a/2))/(-8*tan(a/2)^3*tan(c/2)-8*tan(a/2)^2*tan(c/2)^2+8*tan(a/2)^2+8*tan(a/2)*tan(c/2))*ln(abs(2*tan(b*x)*tan(a/2)+tan(a/2)^2-1)))","F(-2)",0
141,-2,0,0,0.000000," ","integrate(cot(b*x+a)*cot(b*x+c),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)2/b*(-1/2*b*x+(tan(a/2)^2*tan(c/2)^4-2*tan(a/2)^2*tan(c/2)^2+tan(a/2)^2+4*tan(a/2)*tan(c/2)^3-4*tan(a/2)*tan(c/2)-tan(c/2)^4+2*tan(c/2)^2-1)/(4*tan(a/2)^2*tan(c/2)^3-4*tan(a/2)^2*tan(c/2)-4*tan(a/2)*tan(c/2)^4+8*tan(a/2)*tan(c/2)^2-4*tan(a/2)-4*tan(c/2)^3+4*tan(c/2))*ln(abs(tan(b*x)*tan(c/2)^2-tan(b*x)-2*tan(c/2)))+(tan(a/2)^4*tan(c/2)^2-tan(a/2)^4+4*tan(a/2)^3*tan(c/2)-2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2-4*tan(a/2)*tan(c/2)+tan(c/2)^2-1)/(-4*tan(a/2)^4*tan(c/2)+4*tan(a/2)^3*tan(c/2)^2-4*tan(a/2)^3+8*tan(a/2)^2*tan(c/2)-4*tan(a/2)*tan(c/2)^2+4*tan(a/2)-4*tan(c/2))*ln(abs(tan(b*x)*tan(a/2)^2-tan(b*x)-2*tan(a/2))))","F(-2)",0
142,-2,0,0,0.000000," ","integrate(-cot(b*x-c)*cot(b*x+a),x, algorithm=""giac"")","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError >> Unable to parse Giac output: Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)-2/b*(-1/2*b*x+(tan(a/2)^2*tan(c/2)^4-2*tan(a/2)^2*tan(c/2)^2+tan(a/2)^2-4*tan(a/2)*tan(c/2)^3+4*tan(a/2)*tan(c/2)-tan(c/2)^4+2*tan(c/2)^2-1)/(-4*tan(a/2)^2*tan(c/2)^3+4*tan(a/2)^2*tan(c/2)-4*tan(a/2)*tan(c/2)^4+8*tan(a/2)*tan(c/2)^2-4*tan(a/2)+4*tan(c/2)^3-4*tan(c/2))*ln(abs(tan(b*x)*tan(c/2)^2-tan(b*x)+2*tan(c/2)))+(tan(a/2)^4*tan(c/2)^2-tan(a/2)^4-4*tan(a/2)^3*tan(c/2)-2*tan(a/2)^2*tan(c/2)^2+2*tan(a/2)^2+4*tan(a/2)*tan(c/2)+tan(c/2)^2-1)/(4*tan(a/2)^4*tan(c/2)+4*tan(a/2)^3*tan(c/2)^2-4*tan(a/2)^3-8*tan(a/2)^2*tan(c/2)-4*tan(a/2)*tan(c/2)^2+4*tan(a/2)+4*tan(c/2))*ln(abs(tan(b*x)*tan(a/2)^2-tan(b*x)-2*tan(a/2))))","F(-2)",0
143,1,171,0,0.232948," ","integrate(sec(b*x+a)*sec(b*x+c),x, algorithm=""giac"")","\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left({\left| 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, c\right)^{2} + 1 \right|}\right)}{2 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} b}"," ",0,"1/2*(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*log(abs(2*tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c) - 2*tan(b*x + a)*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a)^2*tan(1/2*c)^2 + 2*tan(b*x + a)*tan(1/2*a) - tan(1/2*a)^2 - 2*tan(b*x + a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) - tan(1/2*c)^2 + 1))/((tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c))*b)","B",0
144,1,169,0,0.217383," ","integrate(sec(b*x-c)*sec(b*x+a),x, algorithm=""giac"")","-\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left({\left| 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) + \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, c\right)^{2} - 1 \right|}\right)}{2 \, {\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)\right)} b}"," ",0,"-1/2*(tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*log(abs(2*tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c) + 2*tan(b*x + a)*tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*a)^2*tan(1/2*c)^2 - 2*tan(b*x + a)*tan(1/2*a) + tan(1/2*a)^2 - 2*tan(b*x + a)*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c) + tan(1/2*c)^2 - 1))/((tan(1/2*a)^2*tan(1/2*c) + tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*a) - tan(1/2*c))*b)","B",0
145,1,396,0,0.238323," ","integrate(csc(b*x+a)*csc(b*x+c),x, algorithm=""giac"")","\frac{\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, c\right)^{4} + 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 1\right)} \log\left({\left| \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right) + 2 \, \tan\left(\frac{1}{2} \, c\right) \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} - \tan\left(\frac{1}{2} \, a\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)} - \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left({\left| \tan\left(b x + a\right) \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)}}{2 \, b}"," ",0,"1/2*((tan(1/2*a)^4*tan(1/2*c)^4 + 4*tan(1/2*a)^3*tan(1/2*c)^3 - tan(1/2*a)^4 + 4*tan(1/2*a)^3*tan(1/2*c) + 4*tan(1/2*a)*tan(1/2*c)^3 - tan(1/2*c)^4 + 4*tan(1/2*a)*tan(1/2*c) + 1)*log(abs(tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + a)*tan(1/2*a)^2 + 4*tan(b*x + a)*tan(1/2*a)*tan(1/2*c) - 2*tan(1/2*a)^2*tan(1/2*c) - tan(b*x + a)*tan(1/2*c)^2 + 2*tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + a) - 2*tan(1/2*a) + 2*tan(1/2*c)))/(tan(1/2*a)^4*tan(1/2*c)^3 - tan(1/2*a)^3*tan(1/2*c)^4 - tan(1/2*a)^4*tan(1/2*c) + 6*tan(1/2*a)^3*tan(1/2*c)^2 - 6*tan(1/2*a)^2*tan(1/2*c)^3 + tan(1/2*a)*tan(1/2*c)^4 - tan(1/2*a)^3 + 6*tan(1/2*a)^2*tan(1/2*c) - 6*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*c)^3 + tan(1/2*a) - tan(1/2*c)) - (tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*log(abs(tan(b*x + a)))/(tan(1/2*a)^2*tan(1/2*c) - tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*a) - tan(1/2*c)))/b","B",0
146,1,397,0,0.227150," ","integrate(-csc(b*x-c)*csc(b*x+a),x, algorithm=""giac"")","\frac{\frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right)^{4} - 4 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right) - 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, c\right)^{4} - 4 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 1\right)} \log\left({\left| \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) - \tan\left(b x + a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(b x + a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, c\right) \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{4} - \tan\left(\frac{1}{2} \, a\right)^{4} \tan\left(\frac{1}{2} \, c\right) - 6 \, \tan\left(\frac{1}{2} \, a\right)^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{4} + \tan\left(\frac{1}{2} \, a\right)^{3} + 6 \, \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 6 \, \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)} - \frac{{\left(\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + \tan\left(\frac{1}{2} \, a\right)^{2} + \tan\left(\frac{1}{2} \, c\right)^{2} + 1\right)} \log\left({\left| \tan\left(b x + a\right) \right|}\right)}{\tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, c\right) + \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{1}{2} \, c\right)^{2} - \tan\left(\frac{1}{2} \, a\right) - \tan\left(\frac{1}{2} \, c\right)}}{2 \, b}"," ",0,"1/2*((tan(1/2*a)^4*tan(1/2*c)^4 - 4*tan(1/2*a)^3*tan(1/2*c)^3 - tan(1/2*a)^4 - 4*tan(1/2*a)^3*tan(1/2*c) - 4*tan(1/2*a)*tan(1/2*c)^3 - tan(1/2*c)^4 - 4*tan(1/2*a)*tan(1/2*c) + 1)*log(abs(tan(b*x + a)*tan(1/2*a)^2*tan(1/2*c)^2 - tan(b*x + a)*tan(1/2*a)^2 - 4*tan(b*x + a)*tan(1/2*a)*tan(1/2*c) + 2*tan(1/2*a)^2*tan(1/2*c) - tan(b*x + a)*tan(1/2*c)^2 + 2*tan(1/2*a)*tan(1/2*c)^2 + tan(b*x + a) - 2*tan(1/2*a) - 2*tan(1/2*c)))/(tan(1/2*a)^4*tan(1/2*c)^3 + tan(1/2*a)^3*tan(1/2*c)^4 - tan(1/2*a)^4*tan(1/2*c) - 6*tan(1/2*a)^3*tan(1/2*c)^2 - 6*tan(1/2*a)^2*tan(1/2*c)^3 - tan(1/2*a)*tan(1/2*c)^4 + tan(1/2*a)^3 + 6*tan(1/2*a)^2*tan(1/2*c) + 6*tan(1/2*a)*tan(1/2*c)^2 + tan(1/2*c)^3 - tan(1/2*a) - tan(1/2*c)) - (tan(1/2*a)^2*tan(1/2*c)^2 + tan(1/2*a)^2 + tan(1/2*c)^2 + 1)*log(abs(tan(b*x + a)))/(tan(1/2*a)^2*tan(1/2*c) + tan(1/2*a)*tan(1/2*c)^2 - tan(1/2*a) - tan(1/2*c)))/b","B",0
147,0,0,0,0.000000," ","integrate((sin(x)*tan(x))^(1/2),x, algorithm=""giac"")","\int \sqrt{\sin\left(x\right) \tan\left(x\right)}\,{d x}"," ",0,"integrate(sqrt(sin(x)*tan(x)), x)","F",0
148,0,0,0,0.000000," ","integrate((sin(x)*tan(x))^(3/2),x, algorithm=""giac"")","\int \left(\sin\left(x\right) \tan\left(x\right)\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((sin(x)*tan(x))^(3/2), x)","F",0
149,0,0,0,0.000000," ","integrate((sin(x)*tan(x))^(5/2),x, algorithm=""giac"")","\int \left(\sin\left(x\right) \tan\left(x\right)\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((sin(x)*tan(x))^(5/2), x)","F",0
150,1,12,0,0.156406," ","integrate((cos(x)*cot(x))^(1/2),x, algorithm=""giac"")","2 \, \mathrm{sgn}\left(\cos\left(x\right)\right) \mathrm{sgn}\left(\sin\left(x\right)\right) \sqrt{\sin\left(x\right)}"," ",0,"2*sgn(cos(x))*sgn(sin(x))*sqrt(sin(x))","A",0
151,1,19,0,0.148375," ","integrate((cos(x)*cot(x))^(3/2),x, algorithm=""giac"")","-\frac{2}{3} \, {\left(\sin\left(x\right)^{\frac{3}{2}} + \frac{3}{\sqrt{\sin\left(x\right)}}\right)} \mathrm{sgn}\left(\cos\left(x\right)\right) \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-2/3*(sin(x)^(3/2) + 3/sqrt(sin(x)))*sgn(cos(x))*sgn(sin(x))","A",0
152,1,27,0,0.142714," ","integrate((cos(x)*cot(x))^(5/2),x, algorithm=""giac"")","\frac{2}{15} \, {\left(3 \, \sin\left(x\right)^{\frac{5}{2}} - 30 \, \sqrt{\sin\left(x\right)} - \frac{5}{\sin\left(x\right)^{\frac{3}{2}}}\right)} \mathrm{sgn}\left(\cos\left(x\right)\right) \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"2/15*(3*sin(x)^(5/2) - 30*sqrt(sin(x)) - 5/sin(x)^(3/2))*sgn(cos(x))*sgn(sin(x))","A",0
153,0,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))^2,x, algorithm=""giac"")","\int \frac{x \cos\left(x\right)}{{\left(b \sin\left(x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(x*cos(x)/(b*sin(x) + a)^2, x)","F",0
154,0,0,0,0.000000," ","integrate(x*cos(x)/(a+b*sin(x))^3,x, algorithm=""giac"")","\int \frac{x \cos\left(x\right)}{{\left(b \sin\left(x\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(x*cos(x)/(b*sin(x) + a)^3, x)","F",0
155,0,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))^2,x, algorithm=""giac"")","\int \frac{x \sin\left(x\right)}{{\left(b \cos\left(x\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(x*sin(x)/(b*cos(x) + a)^2, x)","F",0
156,0,0,0,0.000000," ","integrate(x*sin(x)/(a+b*cos(x))^3,x, algorithm=""giac"")","\int \frac{x \sin\left(x\right)}{{\left(b \cos\left(x\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(x*sin(x)/(b*cos(x) + a)^3, x)","F",0
157,1,322,0,0.357303," ","integrate(x*sec(x)^2/(a+b*tan(x))^2,x, algorithm=""giac"")","-\frac{2 \, b x \tan\left(\frac{1}{2} \, x\right)^{2} - a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a x \tan\left(\frac{1}{2} \, x\right) + 2 \, b \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right) - 2 \, b x + a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + a b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, a^{2} b \tan\left(\frac{1}{2} \, x\right) - 2 \, b^{3} \tan\left(\frac{1}{2} \, x\right) - a^{3} - a b^{2}\right)}}"," ",0,"-1/2*(2*b*x*tan(1/2*x)^2 - a*log(4*(a^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 - 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 4*a*x*tan(1/2*x) + 2*b*log(4*(a^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 - 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x) - 2*b*x + a*log(4*(a^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 - 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)))/(a^3*tan(1/2*x)^2 + a*b^2*tan(1/2*x)^2 - 2*a^2*b*tan(1/2*x) - 2*b^3*tan(1/2*x) - a^3 - a*b^2)","B",0
158,1,322,0,0.344592," ","integrate(x*csc(x)^2/(a+b*cot(x))^2,x, algorithm=""giac"")","-\frac{2 \, a x \tan\left(\frac{1}{2} \, x\right)^{2} - b \log\left(\frac{4 \, {\left(b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b x \tan\left(\frac{1}{2} \, x\right) + 2 \, a \log\left(\frac{4 \, {\left(b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right) - 2 \, a x + b \log\left(\frac{4 \, {\left(b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{2 \, {\left(a^{2} b \tan\left(\frac{1}{2} \, x\right)^{2} + b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, a^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, x\right) - a^{2} b - b^{3}\right)}}"," ",0,"-1/2*(2*a*x*tan(1/2*x)^2 - b*log(4*(b^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 + 4*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 4*b*x*tan(1/2*x) + 2*a*log(4*(b^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 + 4*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x) - 2*a*x + b*log(4*(b^2*tan(1/2*x)^4 - 4*a*b*tan(1/2*x)^3 + 4*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)))/(a^2*b*tan(1/2*x)^2 + b^3*tan(1/2*x)^2 - 2*a^3*tan(1/2*x) - 2*a*b^2*tan(1/2*x) - a^2*b - b^3)","B",0
159,1,40,0,0.616132," ","integrate(sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(d x + c\right)}{\sqrt{a b}}\right)}{\sqrt{a b} d}"," ",0,"(pi*floor((d*x + c)/pi + 1/2)*sgn(b) + arctan(b*tan(d*x + c)/sqrt(a*b)))/(sqrt(a*b)*d)","A",0
160,0,0,0,0.000000," ","integrate(x*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""giac"")","\int \frac{x \sec\left(d x + c\right)^{2}}{b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x*sec(d*x + c)^2/(b*tan(d*x + c)^2 + a), x)","F",0
161,0,0,0,0.000000," ","integrate(x^2*sec(d*x+c)^2/(a+b*tan(d*x+c)^2),x, algorithm=""giac"")","\int \frac{x^{2} \sec\left(d x + c\right)^{2}}{b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2*sec(d*x + c)^2/(b*tan(d*x + c)^2 + a), x)","F",0
162,1,76,0,0.971551," ","integrate(sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, b + 2 \, c\right) + \arctan\left(\frac{b \tan\left(d x + c\right) + c \tan\left(d x + c\right)}{\sqrt{a b + a c + b c + c^{2}}}\right)}{\sqrt{a b + a c + b c + c^{2}} d}"," ",0,"(pi*floor((d*x + c)/pi + 1/2)*sgn(2*b + 2*c) + arctan((b*tan(d*x + c) + c*tan(d*x + c))/sqrt(a*b + a*c + b*c + c^2)))/(sqrt(a*b + a*c + b*c + c^2)*d)","B",0
163,0,0,0,0.000000," ","integrate(x*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""giac"")","\int \frac{x \sec\left(d x + c\right)^{2}}{c \sec\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x*sec(d*x + c)^2/(c*sec(d*x + c)^2 + b*tan(d*x + c)^2 + a), x)","F",0
164,0,0,0,0.000000," ","integrate(x^2*sec(d*x+c)^2/(a+c*sec(d*x+c)^2+b*tan(d*x+c)^2),x, algorithm=""giac"")","\int \frac{x^{2} \sec\left(d x + c\right)^{2}}{c \sec\left(d x + c\right)^{2} + b \tan\left(d x + c\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2*sec(d*x + c)^2/(c*sec(d*x + c)^2 + b*tan(d*x + c)^2 + a), x)","F",0
165,-2,0,0,0.000000," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(1/2*(6*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-3*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(f*x+exp(1))/f^4-1/2*(-6*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+f^3*x^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(f*x+exp(1))/f^4)","F(-2)",0
166,-2,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-2*f^3*(-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(f*x+exp(1))/(-2*f^3)^2-4*f^4*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(f*x+exp(1))/(-2*f^3)^2)","F(-2)",0
167,-2,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-1/2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(f*x+exp(1))/f^2-1/2*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/f)","F(-2)",0
168,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))-sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))+4*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))+2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))+sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2+sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2)/(4*tan(1/2*exp(1))^2+4)","F(-2)",0
169,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^2,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2+2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-8*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)+2*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))-f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))-2*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2+2*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2-f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2+f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*f*x)^2+f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2-f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*f*x)^2+2*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))+2*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))-2*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+2*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2)/(4*x*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+4*x*tan(1/2*exp(1))^2+4*x*tan(1/2*f*x)^2+4*x)","F(-2)",0
170,-2,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)*(c+c*sin(f*x+e))^(1/2)/x^3,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2-2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2+2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-8*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)-4*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))-4*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)+f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))+f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))+4*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)+4*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2-4*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))-2*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))+2*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))-f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2+f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*f*x)^2-f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2+f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*f*x)^2-4*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2-2*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2-f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2)/(8*x^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+8*x^2*tan(1/2*exp(1))^2+8*x^2*tan(1/2*f*x)^2+8*x^2)","F(-2)",0
171,-2,0,0,0.000000," ","integrate(x^3*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(1/2*(6*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-3*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(f*x+exp(1))/f^4+1/64*(6*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-12*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(2*f*x+2*exp(1))/f^4-1/2*(-6*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+c*f^3*x^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(f*x+exp(1))/f^4+1/64*(-12*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+8*c*f^3*x^3*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(2*f*x+2*exp(1))/f^4)","F(-2)",0
172,-2,0,0,0.000000," ","integrate(x^2*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-2*f^3*(-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*sin(f*x+exp(1))/(-2*f^3)^2+32*f^3*(-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi)))*cos(2*f*x+2*exp(1))/(-32*f^3)^2-128*c*f^4*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(2*f*x+2*exp(1))/(-32*f^3)^2-4*c*f^4*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(f*x+exp(1))/(-2*f^3)^2)","F(-2)",0
173,-2,0,0,0.000000," ","integrate(x*(c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2),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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-1/16*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(2*f*x+2*exp(1))/f^2-1/2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(f*x+exp(1))/f^2-1/2*c*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*sin(f*x+exp(1))/f+1/8*c*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*cos(2*f*x+2*exp(1))/f)","F(-2)",0
174,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(-2*c*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))+c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))+8*c*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))-2*c*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2+2*c*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2+4*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))-c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2+c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(exp(1))^2-4*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))+c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2-c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(exp(1))+8*c*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(exp(1))^2+2*c*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2+4*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))*tan(exp(1))^2+c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2-4*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))*tan(exp(1))^2-c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1)))/(8*tan(1/2*exp(1))^2*tan(exp(1))^2+8*tan(1/2*exp(1))^2+8*tan(exp(1))^2+8)","F(-2)",0
175,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^2,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(exp(1))^2-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*f*x)^2*tan(exp(1))^2-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)*tan(exp(1))^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*f*x)^2*tan(exp(1))+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(exp(1))-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2+c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2)/(4*x*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*x*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+4*x*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+4*x*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*x*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*x*tan(f*x)^2*tan(1/2*exp(1))^2+4*x*tan(f*x)^2*tan(1/2*f*x)^2+4*x*tan(f*x)^2*tan(exp(1))^2+4*x*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+4*x*tan(1/2*exp(1))^2*tan(exp(1))^2+4*x*tan(1/2*f*x)^2*tan(exp(1))^2+4*x*tan(f*x)^2+4*x*tan(1/2*exp(1))^2+4*x*tan(1/2*f*x)^2+4*x*tan(exp(1))^2+4*x)","F(-2)",0
176,-2,0,0,0.000000," ","integrate((c+c*sin(f*x+e))^(3/2)*(a-a*sin(f*x+e))^(1/2)/x^3,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)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)Unable to check sign: (4*pi/x/2)>(-4*pi/x/2)sqrt(2*a)*sqrt(2*c)*(2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(exp(1))^2-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*f*x)^2*tan(exp(1))^2-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))^2-8*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(exp(1))+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(exp(1))^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)*tan(exp(1))^2-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*f*x)^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(exp(1))+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*f*x)^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(exp(1))+2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-8*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)*tan(exp(1))^2-2*c*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2-4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)*tan(exp(1))^2-2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)*tan(exp(1))^2-8*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(exp(1))-8*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*f*x)^2*tan(exp(1))+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(exp(1))^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(exp(1))^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*f*x)^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*f*x)^2*tan(exp(1))-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*f*x)^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*f*x)^2*tan(exp(1))+2*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)*tan(exp(1))^2+4*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-8*c*f*x*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-4*c*f^2*x^2*Si(f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-4*c*f^2*x^2*Si(2*f*x)*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2-2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))*tan(1/2*f*x)^2*tan(exp(1))^2+2*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*im(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))-c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+4*c*f^2*x^2*sign(sin(1/2*(f*x+exp(1))-1/4*pi))*sign(cos(1/2*(f*x+exp(1))-1/4*pi))*re(Ci(-2*f*x))*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1)))/(8*x^2*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+8*x^2*tan(f*x)^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+8*x^2*tan(f*x)^2*tan(1/2*exp(1))^2*tan(exp(1))^2+8*x^2*tan(f*x)^2*tan(1/2*f*x)^2*tan(exp(1))^2+8*x^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2*tan(exp(1))^2+8*x^2*tan(f*x)^2*tan(1/2*exp(1))^2+8*x^2*tan(f*x)^2*tan(1/2*f*x)^2+8*x^2*tan(f*x)^2*tan(exp(1))^2+8*x^2*tan(1/2*exp(1))^2*tan(1/2*f*x)^2+8*x^2*tan(1/2*exp(1))^2*tan(exp(1))^2+8*x^2*tan(1/2*f*x)^2*tan(exp(1))^2+8*x^2*tan(f*x)^2+8*x^2*tan(1/2*exp(1))^2+8*x^2*tan(1/2*f*x)^2+8*x^2*tan(exp(1))^2+8*x^2)","F(-2)",0
177,0,0,0,0.000000," ","integrate((h*x+g)^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(h x + g\right)}^{3} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)^3*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
178,0,0,0,0.000000," ","integrate((h*x+g)^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(h x + g\right)}^{2} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)^2*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
179,0,0,0,0.000000," ","integrate((h*x+g)*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(h x + g\right)} \sqrt{-a \sin\left(f x + e\right) + a}}{\sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((h*x + g)*sqrt(-a*sin(f*x + e) + a)/sqrt(c*sin(f*x + e) + c), x)","F",0
180,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e))^(1/2)/(h*x+g)/(c+c*sin(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a}}{{\left(h x + g\right)} \sqrt{c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)/((h*x + g)*sqrt(c*sin(f*x + e) + c)), x)","F",0
181,0,0,0,0.000000," ","integrate(x^3*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x^{3}}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x^3/(c*sin(f*x + e) + c)^(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate(x^2*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x^{2}}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x^2/(c*sin(f*x + e) + c)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(x*(a-a*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-a \sin\left(f x + e\right) + a} x}{{\left(c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-a*sin(f*x + e) + a)*x/(c*sin(f*x + e) + c)^(3/2), x)","F",0
184,0,0,0,0.000000," ","integrate(z^2*(1+cos(z))^(1/2)/(1-cos(z))^(1/2),z, algorithm=""giac"")","\int \frac{z^{2} \sqrt{\cos\left(z\right) + 1}}{\sqrt{-\cos\left(z\right) + 1}}\,{d z}"," ",0,"integrate(z^2*sqrt(cos(z) + 1)/sqrt(-cos(z) + 1), z)","F",0
185,1,51,0,0.175476," ","integrate((a+a*cos(x))*(A+B*sec(x)),x, algorithm=""giac"")","B a \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - B a \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right) + {\left(A a + B a\right)} x + \frac{2 \, A a \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"B*a*log(abs(tan(1/2*x) + 1)) - B*a*log(abs(tan(1/2*x) - 1)) + (A*a + B*a)*x + 2*A*a*tan(1/2*x)/(tan(1/2*x)^2 + 1)","B",0
186,1,100,0,0.161714," ","integrate((a+a*cos(x))^2*(A+B*sec(x)),x, algorithm=""giac"")","B a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - B a^{2} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right) + \frac{1}{2} \, {\left(3 \, A a^{2} + 4 \, B a^{2}\right)} x + \frac{3 \, A a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, B a^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, A a^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, B a^{2} \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{2}}"," ",0,"B*a^2*log(abs(tan(1/2*x) + 1)) - B*a^2*log(abs(tan(1/2*x) - 1)) + 1/2*(3*A*a^2 + 4*B*a^2)*x + (3*A*a^2*tan(1/2*x)^3 + 2*B*a^2*tan(1/2*x)^3 + 5*A*a^2*tan(1/2*x) + 2*B*a^2*tan(1/2*x))/(tan(1/2*x)^2 + 1)^2","A",0
187,1,125,0,0.175816," ","integrate((a+a*cos(x))^3*(A+B*sec(x)),x, algorithm=""giac"")","B a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - B a^{3} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right) + \frac{1}{2} \, {\left(5 \, A a^{3} + 7 \, B a^{3}\right)} x + \frac{15 \, A a^{3} \tan\left(\frac{1}{2} \, x\right)^{5} + 15 \, B a^{3} \tan\left(\frac{1}{2} \, x\right)^{5} + 40 \, A a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 36 \, B a^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 33 \, A a^{3} \tan\left(\frac{1}{2} \, x\right) + 21 \, B a^{3} \tan\left(\frac{1}{2} \, x\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{3}}"," ",0,"B*a^3*log(abs(tan(1/2*x) + 1)) - B*a^3*log(abs(tan(1/2*x) - 1)) + 1/2*(5*A*a^3 + 7*B*a^3)*x + 1/3*(15*A*a^3*tan(1/2*x)^5 + 15*B*a^3*tan(1/2*x)^5 + 40*A*a^3*tan(1/2*x)^3 + 36*B*a^3*tan(1/2*x)^3 + 33*A*a^3*tan(1/2*x) + 21*B*a^3*tan(1/2*x))/(tan(1/2*x)^2 + 1)^3","A",0
188,1,149,0,0.159820," ","integrate((a+a*cos(x))^4*(A+B*sec(x)),x, algorithm=""giac"")","B a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - B a^{4} \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right) + \frac{1}{8} \, {\left(35 \, A a^{4} + 48 \, B a^{4}\right)} x + \frac{105 \, A a^{4} \tan\left(\frac{1}{2} \, x\right)^{7} + 120 \, B a^{4} \tan\left(\frac{1}{2} \, x\right)^{7} + 385 \, A a^{4} \tan\left(\frac{1}{2} \, x\right)^{5} + 424 \, B a^{4} \tan\left(\frac{1}{2} \, x\right)^{5} + 511 \, A a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 520 \, B a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 279 \, A a^{4} \tan\left(\frac{1}{2} \, x\right) + 216 \, B a^{4} \tan\left(\frac{1}{2} \, x\right)}{12 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}^{4}}"," ",0,"B*a^4*log(abs(tan(1/2*x) + 1)) - B*a^4*log(abs(tan(1/2*x) - 1)) + 1/8*(35*A*a^4 + 48*B*a^4)*x + 1/12*(105*A*a^4*tan(1/2*x)^7 + 120*B*a^4*tan(1/2*x)^7 + 385*A*a^4*tan(1/2*x)^5 + 424*B*a^4*tan(1/2*x)^5 + 511*A*a^4*tan(1/2*x)^3 + 520*B*a^4*tan(1/2*x)^3 + 279*A*a^4*tan(1/2*x) + 216*B*a^4*tan(1/2*x))/(tan(1/2*x)^2 + 1)^4","A",0
189,1,46,0,0.152063," ","integrate((A+B*sec(x))/(a+a*cos(x)),x, algorithm=""giac"")","\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} + \frac{A \tan\left(\frac{1}{2} \, x\right) - B \tan\left(\frac{1}{2} \, x\right)}{a}"," ",0,"B*log(abs(tan(1/2*x) + 1))/a - B*log(abs(tan(1/2*x) - 1))/a + (A*tan(1/2*x) - B*tan(1/2*x))/a","A",0
190,1,77,0,0.161550," ","integrate((A+B*sec(x))/(a+a*cos(x))^2,x, algorithm=""giac"")","\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{a^{2}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{a^{2}} + \frac{A a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - B a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, A a^{4} \tan\left(\frac{1}{2} \, x\right) - 9 \, B a^{4} \tan\left(\frac{1}{2} \, x\right)}{6 \, a^{6}}"," ",0,"B*log(abs(tan(1/2*x) + 1))/a^2 - B*log(abs(tan(1/2*x) - 1))/a^2 + 1/6*(A*a^4*tan(1/2*x)^3 - B*a^4*tan(1/2*x)^3 + 3*A*a^4*tan(1/2*x) - 9*B*a^4*tan(1/2*x))/a^6","A",0
191,1,102,0,0.161817," ","integrate((A+B*sec(x))/(a+a*cos(x))^3,x, algorithm=""giac"")","\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{a^{3}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{a^{3}} + \frac{3 \, A a^{12} \tan\left(\frac{1}{2} \, x\right)^{5} - 3 \, B a^{12} \tan\left(\frac{1}{2} \, x\right)^{5} + 10 \, A a^{12} \tan\left(\frac{1}{2} \, x\right)^{3} - 20 \, B a^{12} \tan\left(\frac{1}{2} \, x\right)^{3} + 15 \, A a^{12} \tan\left(\frac{1}{2} \, x\right) - 105 \, B a^{12} \tan\left(\frac{1}{2} \, x\right)}{60 \, a^{15}}"," ",0,"B*log(abs(tan(1/2*x) + 1))/a^3 - B*log(abs(tan(1/2*x) - 1))/a^3 + 1/60*(3*A*a^12*tan(1/2*x)^5 - 3*B*a^12*tan(1/2*x)^5 + 10*A*a^12*tan(1/2*x)^3 - 20*B*a^12*tan(1/2*x)^3 + 15*A*a^12*tan(1/2*x) - 105*B*a^12*tan(1/2*x))/a^15","A",0
192,1,126,0,0.154888," ","integrate((A+B*sec(x))/(a+a*cos(x))^4,x, algorithm=""giac"")","\frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{a^{4}} - \frac{B \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{a^{4}} + \frac{15 \, A a^{24} \tan\left(\frac{1}{2} \, x\right)^{7} - 15 \, B a^{24} \tan\left(\frac{1}{2} \, x\right)^{7} + 63 \, A a^{24} \tan\left(\frac{1}{2} \, x\right)^{5} - 105 \, B a^{24} \tan\left(\frac{1}{2} \, x\right)^{5} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, x\right)^{3} - 385 \, B a^{24} \tan\left(\frac{1}{2} \, x\right)^{3} + 105 \, A a^{24} \tan\left(\frac{1}{2} \, x\right) - 1575 \, B a^{24} \tan\left(\frac{1}{2} \, x\right)}{840 \, a^{28}}"," ",0,"B*log(abs(tan(1/2*x) + 1))/a^4 - B*log(abs(tan(1/2*x) - 1))/a^4 + 1/840*(15*A*a^24*tan(1/2*x)^7 - 15*B*a^24*tan(1/2*x)^7 + 63*A*a^24*tan(1/2*x)^5 - 105*B*a^24*tan(1/2*x)^5 + 105*A*a^24*tan(1/2*x)^3 - 385*B*a^24*tan(1/2*x)^3 + 105*A*a^24*tan(1/2*x) - 1575*B*a^24*tan(1/2*x))/a^28","A",0
193,1,134,0,0.209588," ","integrate((a+a*cos(x))^(5/2)*(A+B*sec(x)),x, algorithm=""giac"")","\frac{1}{30} \, \sqrt{2} {\left(48 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)^{5} - 160 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)^{3} - 40 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)^{3} - 15 \, \sqrt{2} B a^{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 240 \, A a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) + 180 \, B a^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/30*sqrt(2)*(48*A*a^2*sgn(cos(1/2*x))*sin(1/2*x)^5 - 160*A*a^2*sgn(cos(1/2*x))*sin(1/2*x)^3 - 40*B*a^2*sgn(cos(1/2*x))*sin(1/2*x)^3 - 15*sqrt(2)*B*a^2*log(abs(-2*sqrt(2) + 4*sin(1/2*x))/abs(2*sqrt(2) + 4*sin(1/2*x)))*sgn(cos(1/2*x)) + 240*A*a^2*sgn(cos(1/2*x))*sin(1/2*x) + 180*B*a^2*sgn(cos(1/2*x))*sin(1/2*x))*sqrt(a)","A",0
194,1,92,0,0.188918," ","integrate((a+a*cos(x))^(3/2)*(A+B*sec(x)),x, algorithm=""giac"")","-\frac{1}{6} \, \sqrt{2} {\left(8 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)^{3} + 3 \, \sqrt{2} B a \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 24 \, A a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) - 12 \, B a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"-1/6*sqrt(2)*(8*A*a*sgn(cos(1/2*x))*sin(1/2*x)^3 + 3*sqrt(2)*B*a*log(abs(-2*sqrt(2) + 4*sin(1/2*x))/abs(2*sqrt(2) + 4*sin(1/2*x)))*sgn(cos(1/2*x)) - 24*A*a*sgn(cos(1/2*x))*sin(1/2*x) - 12*B*a*sgn(cos(1/2*x))*sin(1/2*x))*sqrt(a)","A",0
195,1,61,0,0.179811," ","integrate((a+a*cos(x))^(1/2)*(A+B*sec(x)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} B \log\left(\frac{{\left| -2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}{{\left| 2 \, \sqrt{2} + 4 \, \sin\left(\frac{1}{2} \, x\right) \right|}}\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 4 \, A \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"-1/2*sqrt(2)*(sqrt(2)*B*log(abs(-2*sqrt(2) + 4*sin(1/2*x))/abs(2*sqrt(2) + 4*sin(1/2*x)))*sgn(cos(1/2*x)) - 4*A*sgn(cos(1/2*x))*sin(1/2*x))*sqrt(a)","A",0
196,1,133,0,0.702288," ","integrate((A+B*sec(x))/(a+a*cos(x))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(A \sqrt{a} - B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2}\right)}{2 \, a} + \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{\sqrt{a}} - \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{\sqrt{a}}"," ",0,"-1/2*sqrt(2)*(A*sqrt(a) - B*sqrt(a))*log((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2)/a + B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 - a*(2*sqrt(2) + 3)))/sqrt(a) - B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 + a*(2*sqrt(2) - 3)))/sqrt(a)","B",0
197,1,168,0,0.763567," ","integrate((A+B*sec(x))/(a+a*cos(x))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(A \sqrt{a} - 5 \, B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2}\right)}{8 \, a^{2}} + \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{3}{2}}} - \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{3}{2}}} + \frac{\sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a} {\left(\sqrt{2} A a - \sqrt{2} B a\right)} \tan\left(\frac{1}{2} \, x\right)}{4 \, a^{3}}"," ",0,"-1/8*sqrt(2)*(A*sqrt(a) - 5*B*sqrt(a))*log((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2)/a^2 + B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(3/2) - B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(3/2) + 1/4*sqrt(a*tan(1/2*x)^2 + a)*(sqrt(2)*A*a - sqrt(2)*B*a)*tan(1/2*x)/a^3","B",0
198,1,199,0,0.945133," ","integrate((A+B*sec(x))/(a+a*cos(x))^(5/2),x, algorithm=""giac"")","\frac{1}{32} \, \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a} {\left(\frac{2 \, \sqrt{2} {\left(A a^{5} - B a^{5}\right)} \tan\left(\frac{1}{2} \, x\right)^{2}}{a^{8}} + \frac{\sqrt{2} {\left(5 \, A a^{5} - 13 \, B a^{5}\right)}}{a^{8}}\right)} \tan\left(\frac{1}{2} \, x\right) - \frac{\sqrt{2} {\left(3 \, A \sqrt{a} - 43 \, B \sqrt{a}\right)} \log\left({\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2}\right)}{64 \, a^{3}} + \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} - a {\left(2 \, \sqrt{2} + 3\right)} \right|}\right)}{a^{\frac{5}{2}}} - \frac{B \log\left({\left| {\left(\sqrt{a} \tan\left(\frac{1}{2} \, x\right) - \sqrt{a \tan\left(\frac{1}{2} \, x\right)^{2} + a}\right)}^{2} + a {\left(2 \, \sqrt{2} - 3\right)} \right|}\right)}{a^{\frac{5}{2}}}"," ",0,"1/32*sqrt(a*tan(1/2*x)^2 + a)*(2*sqrt(2)*(A*a^5 - B*a^5)*tan(1/2*x)^2/a^8 + sqrt(2)*(5*A*a^5 - 13*B*a^5)/a^8)*tan(1/2*x) - 1/64*sqrt(2)*(3*A*sqrt(a) - 43*B*sqrt(a))*log((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2)/a^3 + B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 - a*(2*sqrt(2) + 3)))/a^(5/2) - B*log(abs((sqrt(a)*tan(1/2*x) - sqrt(a*tan(1/2*x)^2 + a))^2 + a*(2*sqrt(2) - 3)))/a^(5/2)","B",0
199,1,283,0,0.324422," ","integrate(x*(b+a*sin(x))/(a+b*sin(x))^2,x, algorithm=""giac"")","\frac{4 \, b x \tan\left(\frac{1}{2} \, x\right)^{2} + a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right) - 4 \, b x + a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, a b \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, a b \tan\left(\frac{1}{2} \, x\right) + a^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{2 \, {\left(a b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right) + a b\right)}}"," ",0,"1/2*(4*b*x*tan(1/2*x)^2 + a*log(4*(a^2*tan(1/2*x)^4 + 4*a*b*tan(1/2*x)^3 + 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 2*b*log(4*(a^2*tan(1/2*x)^4 + 4*a*b*tan(1/2*x)^3 + 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x) - 4*b*x + a*log(4*(a^2*tan(1/2*x)^4 + 4*a*b*tan(1/2*x)^3 + 2*a^2*tan(1/2*x)^2 + 4*b^2*tan(1/2*x)^2 + 4*a*b*tan(1/2*x) + a^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)))/(a*b*tan(1/2*x)^2 + 2*b^2*tan(1/2*x) + a*b)","B",0
200,1,397,0,0.323290," ","integrate(x*(b+a*cos(x))/(a+b*cos(x))^2,x, algorithm=""giac"")","\frac{a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a b \tan\left(\frac{1}{2} \, x\right)^{4} + b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - b \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a b \tan\left(\frac{1}{2} \, x\right)^{4} + b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 8 \, b x \tan\left(\frac{1}{2} \, x\right) + a \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a b \tan\left(\frac{1}{2} \, x\right)^{4} + b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + b \log\left(\frac{4 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a b \tan\left(\frac{1}{2} \, x\right)^{4} + b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, a^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{2 \, {\left(a b \tan\left(\frac{1}{2} \, x\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + a b + b^{2}\right)}}"," ",0,"1/2*(a*log(4*(a^2*tan(1/2*x)^4 - 2*a*b*tan(1/2*x)^4 + b^2*tan(1/2*x)^4 + 2*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + a^2 + 2*a*b + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - b*log(4*(a^2*tan(1/2*x)^4 - 2*a*b*tan(1/2*x)^4 + b^2*tan(1/2*x)^4 + 2*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + a^2 + 2*a*b + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 8*b*x*tan(1/2*x) + a*log(4*(a^2*tan(1/2*x)^4 - 2*a*b*tan(1/2*x)^4 + b^2*tan(1/2*x)^4 + 2*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + a^2 + 2*a*b + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)) + b*log(4*(a^2*tan(1/2*x)^4 - 2*a*b*tan(1/2*x)^4 + b^2*tan(1/2*x)^4 + 2*a^2*tan(1/2*x)^2 - 2*b^2*tan(1/2*x)^2 + a^2 + 2*a*b + b^2)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)))/(a*b*tan(1/2*x)^2 - b^2*tan(1/2*x)^2 + a*b + b^2)","B",0
201,1,8,0,0.125795," ","integrate((1+sin(x)^2)/(1-sin(x)^2),x, algorithm=""giac"")","-x + 2 \, \tan\left(x\right)"," ",0,"-x + 2*tan(x)","A",0
202,1,49,0,0.129260," ","integrate((1-sin(x)^2)/(1+sin(x)^2),x, algorithm=""giac"")","\sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - 2 \, \cos\left(2 \, x\right) + 2}\right)\right)} - x"," ",0,"sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - 2*sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - 2*cos(2*x) + 2))) - x","A",0
203,1,16,0,0.150239," ","integrate((1+cos(x)^2)/(1-cos(x)^2),x, algorithm=""giac"")","-x - \frac{1}{\tan\left(\frac{1}{2} \, x\right)} + \tan\left(\frac{1}{2} \, x\right)"," ",0,"-x - 1/tan(1/2*x) + tan(1/2*x)","A",0
204,1,49,0,0.129732," ","integrate((1-cos(x)^2)/(1+cos(x)^2),x, algorithm=""giac"")","\sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - x"," ",0,"sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - x","A",0
205,1,26,0,0.147077," ","integrate((-1+c^2/d^2+sin(x)^2)/(c+d*cos(x)),x, algorithm=""giac"")","\frac{c x}{d^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} d}"," ",0,"c*x/d^2 - 2*tan(1/2*x)/((tan(1/2*x)^2 + 1)*d)","A",0
206,1,110,0,0.137564," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)),x, algorithm=""giac"")","\frac{b c x}{d^{2}} - \frac{2 \, b \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} d} + \frac{2 \, {\left(b c^{2} - a d^{2} - b d^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, c + 2 \, d\right) + \arctan\left(-\frac{c \tan\left(\frac{1}{2} \, x\right) - d \tan\left(\frac{1}{2} \, x\right)}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{2}}"," ",0,"b*c*x/d^2 - 2*b*tan(1/2*x)/((tan(1/2*x)^2 + 1)*d) + 2*(b*c^2 - a*d^2 - b*d^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*c + 2*d) + arctan(-(c*tan(1/2*x) - d*tan(1/2*x))/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^2)","A",0
207,1,62,0,0.138946," ","integrate((a+b*sin(x)^2)/(c+c*cos(x)^2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a + 2 \, b\right)} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)}}{2 \, c} - \frac{b x}{c}"," ",0,"1/2*sqrt(2)*(a + 2*b)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1)))/c - b*x/c","A",0
208,1,29,0,0.145264," ","integrate((a+b*sin(x)^2)/(c-c*cos(x)^2),x, algorithm=""giac"")","\frac{b x}{c} + \frac{a \tan\left(\frac{1}{2} \, x\right)}{2 \, c} - \frac{a}{2 \, c \tan\left(\frac{1}{2} \, x\right)}"," ",0,"b*x/c + 1/2*a*tan(1/2*x)/c - 1/2*a/(c*tan(1/2*x))","A",0
209,1,58,0,0.154575," ","integrate((a+b*sin(x)^2)/(c+d*cos(x)^2),x, algorithm=""giac"")","-\frac{b x}{d} + \frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(x\right)}{\sqrt{c^{2} + c d}}\right)\right)} {\left(b c + a d + b d\right)}}{\sqrt{c^{2} + c d} d}"," ",0,"-b*x/d + (pi*floor(x/pi + 1/2)*sgn(c) + arctan(c*tan(x)/sqrt(c^2 + c*d)))*(b*c + a*d + b*d)/(sqrt(c^2 + c*d)*d)","A",0
210,1,22,0,0.145240," ","integrate((-1+c^2/d^2+cos(x)^2)/(c+d*sin(x)),x, algorithm=""giac"")","\frac{c x}{d^{2}} + \frac{2}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} d}"," ",0,"c*x/d^2 + 2/((tan(1/2*x)^2 + 1)*d)","A",0
211,1,93,0,0.154577," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)),x, algorithm=""giac"")","\frac{b c x}{d^{2}} - \frac{2 \, {\left(b c^{2} - a d^{2} - b d^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, x\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} d^{2}} + \frac{2 \, b}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)} d}"," ",0,"b*c*x/d^2 - 2*(b*c^2 - a*d^2 - b*d^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*x) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*d^2) + 2*b/((tan(1/2*x)^2 + 1)*d)","A",0
212,1,62,0,0.151173," ","integrate((a+b*cos(x)^2)/(c+c*sin(x)^2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a + 2 \, b\right)} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - 2 \, \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - 2 \, \cos\left(2 \, x\right) + 2}\right)\right)}}{2 \, c} - \frac{b x}{c}"," ",0,"1/2*sqrt(2)*(a + 2*b)*(x + arctan(-(sqrt(2)*sin(2*x) - 2*sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - 2*cos(2*x) + 2)))/c - b*x/c","A",0
213,1,23,0,0.149469," ","integrate((a+b*cos(x)^2)/(c-c*sin(x)^2),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{{\left| c \right|} \tan\left(x\right)}{c}\right)}{{\left| c \right|}} + \frac{a \tan\left(x\right)}{c}"," ",0,"b*arctan(abs(c)*tan(x)/c)/abs(c) + a*tan(x)/c","A",0
214,1,70,0,0.143011," ","integrate((a+b*cos(x)^2)/(c+d*sin(x)^2),x, algorithm=""giac"")","-\frac{b x}{d} + \frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, c + 2 \, d\right) + \arctan\left(\frac{c \tan\left(x\right) + d \tan\left(x\right)}{\sqrt{c^{2} + c d}}\right)\right)} {\left(b c + a d + b d\right)}}{\sqrt{c^{2} + c d} d}"," ",0,"-b*x/d + (pi*floor(x/pi + 1/2)*sgn(2*c + 2*d) + arctan((c*tan(x) + d*tan(x))/sqrt(c^2 + c*d)))*(b*c + a*d + b*d)/(sqrt(c^2 + c*d)*d)","A",0
215,1,125,0,0.165038," ","integrate((a+b*sec(x)^2)/(c+d*cos(x)),x, algorithm=""giac"")","-\frac{b d \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{c^{2}} + \frac{b d \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{c^{2}} - \frac{2 \, b \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)} c} - \frac{2 \, {\left(a c^{2} + b d^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, c + 2 \, d\right) + \arctan\left(-\frac{c \tan\left(\frac{1}{2} \, x\right) - d \tan\left(\frac{1}{2} \, x\right)}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} c^{2}}"," ",0,"-b*d*log(abs(tan(1/2*x) + 1))/c^2 + b*d*log(abs(tan(1/2*x) - 1))/c^2 - 2*b*tan(1/2*x)/((tan(1/2*x)^2 - 1)*c) - 2*(a*c^2 + b*d^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*c + 2*d) + arctan(-(c*tan(1/2*x) - d*tan(1/2*x))/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*c^2)","A",0
216,1,110,0,0.170365," ","integrate((a+b*csc(x)^2)/(c+d*sin(x)),x, algorithm=""giac"")","-\frac{b d \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{c^{2}} + \frac{b \tan\left(\frac{1}{2} \, x\right)}{2 \, c} + \frac{2 \, {\left(a c^{2} + b d^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(c\right) + \arctan\left(\frac{c \tan\left(\frac{1}{2} \, x\right) + d}{\sqrt{c^{2} - d^{2}}}\right)\right)}}{\sqrt{c^{2} - d^{2}} c^{2}} + \frac{2 \, b d \tan\left(\frac{1}{2} \, x\right) - b c}{2 \, c^{2} \tan\left(\frac{1}{2} \, x\right)}"," ",0,"-b*d*log(abs(tan(1/2*x)))/c^2 + 1/2*b*tan(1/2*x)/c + 2*(a*c^2 + b*d^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(c) + arctan((c*tan(1/2*x) + d)/sqrt(c^2 - d^2)))/(sqrt(c^2 - d^2)*c^2) + 1/2*(2*b*d*tan(1/2*x) - b*c)/(c^2*tan(1/2*x))","A",0
217,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{n}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^n, x)","F",0
218,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^n,x, algorithm=""giac"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{n}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^n, x)","F",0
219,1,316,0,0.663885," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^7,x, algorithm=""giac"")","-\frac{{\left(7 \, a^{6} b - 35 \, a^{4} b^{3} + 21 \, a^{2} b^{5} - b^{7}\right)} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{7 \, {\left(5 \, a^{6} b - 5 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + b^{7}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} - \frac{7 \, {\left(3 \, a^{6} b + 5 \, a^{4} b^{3} + a^{2} b^{5} - b^{7}\right)} \cos\left(3 \, d x + 3 \, c\right)}{64 \, d} - \frac{35 \, {\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(a^{7} - 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 7 \, a b^{6}\right)} \sin\left(7 \, d x + 7 \, c\right)}{448 \, d} + \frac{7 \, {\left(a^{7} - 9 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 5 \, a b^{6}\right)} \sin\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{7 \, {\left(a^{7} - a^{5} b^{2} - 5 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \sin\left(3 \, d x + 3 \, c\right)}{64 \, d} + \frac{35 \, {\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sin\left(d x + c\right)}{64 \, d}"," ",0,"-1/448*(7*a^6*b - 35*a^4*b^3 + 21*a^2*b^5 - b^7)*cos(7*d*x + 7*c)/d - 7/320*(5*a^6*b - 5*a^4*b^3 - 9*a^2*b^5 + b^7)*cos(5*d*x + 5*c)/d - 7/64*(3*a^6*b + 5*a^4*b^3 + a^2*b^5 - b^7)*cos(3*d*x + 3*c)/d - 35/64*(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*cos(d*x + c)/d + 1/448*(a^7 - 21*a^5*b^2 + 35*a^3*b^4 - 7*a*b^6)*sin(7*d*x + 7*c)/d + 7/320*(a^7 - 9*a^5*b^2 - 5*a^3*b^4 + 5*a*b^6)*sin(5*d*x + 5*c)/d + 7/64*(a^7 - a^5*b^2 - 5*a^3*b^4 - 3*a*b^6)*sin(3*d*x + 3*c)/d + 35/64*(a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sin(d*x + c)/d","B",0
220,1,235,0,0.315407," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""giac"")","\frac{5}{16} \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} x - \frac{{\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{3 \, {\left(a^{5} b - a b^{5}\right)} \cos\left(4 \, d x + 4 \, c\right)}{16 \, d} - \frac{15 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(2 \, d x + 2 \, c\right)}{32 \, d} + \frac{{\left(a^{6} - 15 \, a^{4} b^{2} + 15 \, a^{2} b^{4} - b^{6}\right)} \sin\left(6 \, d x + 6 \, c\right)}{192 \, d} + \frac{3 \, {\left(a^{6} - 5 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} \sin\left(4 \, d x + 4 \, c\right)}{64 \, d} + \frac{15 \, {\left(a^{6} + a^{4} b^{2} - a^{2} b^{4} - b^{6}\right)} \sin\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"5/16*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*x - 1/96*(3*a^5*b - 10*a^3*b^3 + 3*a*b^5)*cos(6*d*x + 6*c)/d - 3/16*(a^5*b - a*b^5)*cos(4*d*x + 4*c)/d - 15/32*(a^5*b + 2*a^3*b^3 + a*b^5)*cos(2*d*x + 2*c)/d + 1/192*(a^6 - 15*a^4*b^2 + 15*a^2*b^4 - b^6)*sin(6*d*x + 6*c)/d + 3/64*(a^6 - 5*a^4*b^2 - 5*a^2*b^4 + b^6)*sin(4*d*x + 4*c)/d + 15/64*(a^6 + a^4*b^2 - a^2*b^4 - b^6)*sin(2*d*x + 2*c)/d","A",0
221,1,187,0,0.292321," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","-\frac{{\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \cos\left(5 \, d x + 5 \, c\right)}{80 \, d} - \frac{5 \, {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(3 \, d x + 3 \, c\right)}{48 \, d} - \frac{5 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)}{8 \, d} + \frac{{\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sin\left(5 \, d x + 5 \, c\right)}{80 \, d} + \frac{5 \, {\left(a^{5} - 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \sin\left(3 \, d x + 3 \, c\right)}{48 \, d} + \frac{5 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/80*(5*a^4*b - 10*a^2*b^3 + b^5)*cos(5*d*x + 5*c)/d - 5/48*(3*a^4*b + 2*a^2*b^3 - b^5)*cos(3*d*x + 3*c)/d - 5/8*(a^4*b + 2*a^2*b^3 + b^5)*cos(d*x + c)/d + 1/80*(a^5 - 10*a^3*b^2 + 5*a*b^4)*sin(5*d*x + 5*c)/d + 5/48*(a^5 - 2*a^3*b^2 - 3*a*b^4)*sin(3*d*x + 3*c)/d + 5/8*(a^5 + 2*a^3*b^2 + a*b^4)*sin(d*x + c)/d","B",0
222,1,122,0,0.188095," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","\frac{3}{8} \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} x - \frac{{\left(a^{3} b - a b^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)}{8 \, d} - \frac{{\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{{\left(a^{4} - b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*(a^4 + 2*a^2*b^2 + b^4)*x - 1/8*(a^3*b - a*b^3)*cos(4*d*x + 4*c)/d - 1/2*(a^3*b + a*b^3)*cos(2*d*x + 2*c)/d + 1/32*(a^4 - 6*a^2*b^2 + b^4)*sin(4*d*x + 4*c)/d + 1/4*(a^4 - b^4)*sin(2*d*x + 2*c)/d","A",0
223,1,91,0,0.154235," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - b^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{3 \, {\left(a^{2} b + b^{3}\right)} \cos\left(d x + c\right)}{4 \, d} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)}{12 \, d} + \frac{3 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)}{4 \, d}"," ",0,"-1/12*(3*a^2*b - b^3)*cos(3*d*x + 3*c)/d - 3/4*(a^2*b + b^3)*cos(d*x + c)/d + 1/12*(a^3 - 3*a*b^2)*sin(3*d*x + 3*c)/d + 3/4*(a^3 + a*b^2)*sin(d*x + c)/d","A",0
224,1,50,0,0.154062," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{2} \, {\left(a^{2} + b^{2}\right)} x - \frac{a b \cos\left(2 \, d x + 2 \, c\right)}{2 \, d} + \frac{{\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/2*(a^2 + b^2)*x - 1/2*a*b*cos(2*d*x + 2*c)/d + 1/4*(a^2 - b^2)*sin(2*d*x + 2*c)/d","A",0
225,1,24,0,0.140727," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x, algorithm=""giac"")","-\frac{b \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-b*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
226,1,74,0,0.220636," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x, algorithm=""giac"")","-\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{\sqrt{a^{2} + b^{2}} d}"," ",0,"-log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(sqrt(a^2 + b^2)*d)","A",0
227,1,20,0,0.154246," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} b d}"," ",0,"-1/((b*tan(d*x + c) + a)*b*d)","A",0
228,1,221,0,0.230036," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{\log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \sqrt{a^{2} + b^{2}} \right|}}\right)}{{\left(a^{2} + b^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2} b\right)}}{{\left(a^{4} + a^{2} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/(a^2 + b^2)^(3/2) - 2*(a^3*tan(1/2*d*x + 1/2*c)^3 + 2*a*b^2*tan(1/2*d*x + 1/2*c)^3 + a^2*b*tan(1/2*d*x + 1/2*c)^2 - 2*b^3*tan(1/2*d*x + 1/2*c)^2 + a^3*tan(1/2*d*x + 1/2*c) - 2*a*b^2*tan(1/2*d*x + 1/2*c) - a^2*b)/((a^4 + a^2*b^2)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^2))/d","B",0
229,1,50,0,0.152520," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, b^{2} \tan\left(d x + c\right)^{2} + 3 \, a b \tan\left(d x + c\right) + a^{2} + b^{2}}{3 \, {\left(b \tan\left(d x + c\right) + a\right)}^{3} b^{3} d}"," ",0,"-1/3*(3*b^2*tan(d*x + c)^2 + 3*a*b*tan(d*x + c) + a^2 + b^2)/((b*tan(d*x + c) + a)^3*b^3*d)","A",0
230,1,588,0,0.309238," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^5,x, algorithm=""giac"")","-\frac{\frac{3 \, \log\left(\frac{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b - 2 \, \sqrt{a^{2} + b^{2}} \right|}}{{\left| 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, b + 2 \, \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 \, {\left(5 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 16 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} + 8 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{7} - 3 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 24 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 3 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 36 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 56 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 32 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 114 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 8 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, b^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 3 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 84 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 56 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 32 \, a b^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 23 \, a^{6} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 64 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 24 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 5 \, a^{7} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{6} b - 2 \, a^{4} b^{3}\right)}}{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a\right)}^{4}}}{8 \, d}"," ",0,"-1/8*(3*log(abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b - 2*sqrt(a^2 + b^2))/abs(2*a*tan(1/2*d*x + 1/2*c) - 2*b + 2*sqrt(a^2 + b^2)))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a^2 + b^2)) - 2*(5*a^7*tan(1/2*d*x + 1/2*c)^7 + 16*a^5*b^2*tan(1/2*d*x + 1/2*c)^7 + 8*a^3*b^4*tan(1/2*d*x + 1/2*c)^7 - 3*a^6*b*tan(1/2*d*x + 1/2*c)^6 - 48*a^4*b^3*tan(1/2*d*x + 1/2*c)^6 - 24*a^2*b^5*tan(1/2*d*x + 1/2*c)^6 + 3*a^7*tan(1/2*d*x + 1/2*c)^5 - 36*a^5*b^2*tan(1/2*d*x + 1/2*c)^5 + 56*a^3*b^4*tan(1/2*d*x + 1/2*c)^5 + 32*a*b^6*tan(1/2*d*x + 1/2*c)^5 - 15*a^6*b*tan(1/2*d*x + 1/2*c)^4 + 114*a^4*b^3*tan(1/2*d*x + 1/2*c)^4 + 8*a^2*b^5*tan(1/2*d*x + 1/2*c)^4 - 16*b^7*tan(1/2*d*x + 1/2*c)^4 + 3*a^7*tan(1/2*d*x + 1/2*c)^3 + 84*a^5*b^2*tan(1/2*d*x + 1/2*c)^3 - 56*a^3*b^4*tan(1/2*d*x + 1/2*c)^3 - 32*a*b^6*tan(1/2*d*x + 1/2*c)^3 + 23*a^6*b*tan(1/2*d*x + 1/2*c)^2 - 64*a^4*b^3*tan(1/2*d*x + 1/2*c)^2 - 24*a^2*b^5*tan(1/2*d*x + 1/2*c)^2 + 5*a^7*tan(1/2*d*x + 1/2*c) - 24*a^5*b^2*tan(1/2*d*x + 1/2*c) - 8*a^3*b^4*tan(1/2*d*x + 1/2*c) - 5*a^6*b - 2*a^4*b^3)/((a^8 + 2*a^6*b^2 + a^4*b^4)*(a*tan(1/2*d*x + 1/2*c)^2 - 2*b*tan(1/2*d*x + 1/2*c) - a)^4))/d","B",0
231,1,118,0,0.221346," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^6,x, algorithm=""giac"")","-\frac{15 \, b^{4} \tan\left(d x + c\right)^{4} + 30 \, a b^{3} \tan\left(d x + c\right)^{3} + 30 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 10 \, b^{4} \tan\left(d x + c\right)^{2} + 15 \, a^{3} b \tan\left(d x + c\right) + 5 \, a b^{3} \tan\left(d x + c\right) + 3 \, a^{4} + a^{2} b^{2} + 3 \, b^{4}}{15 \, {\left(b \tan\left(d x + c\right) + a\right)}^{5} b^{5} d}"," ",0,"-1/15*(15*b^4*tan(d*x + c)^4 + 30*a*b^3*tan(d*x + c)^3 + 30*a^2*b^2*tan(d*x + c)^2 + 10*b^4*tan(d*x + c)^2 + 15*a^3*b*tan(d*x + c) + 5*a*b^3*tan(d*x + c) + 3*a^4 + a^2*b^2 + 3*b^4)/((b*tan(d*x + c) + a)^5*b^5*d)","A",0
232,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(7/2), x)","F",0
233,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(5/2), x)","F",0
234,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(3/2), x)","F",0
235,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \cos\left(d x + c\right) + b \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(a*cos(d*x + c) + b*sin(d*x + c)), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-3/2), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-5/2), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(d x + c\right) + b \sin\left(d x + c\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + b*sin(d*x + c))^(-7/2), x)","F",0
240,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(7/2), x)","F",0
241,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(5/2), x)","F",0
242,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int {\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(3/2), x)","F",0
243,0,0,0,0.000000," ","integrate((2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/sqrt(2*cos(d*x + c) + 3*sin(d*x + c)), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-3/2), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-5/2), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(2*cos(d*x+c)+3*sin(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(2 \, \cos\left(d x + c\right) + 3 \, \sin\left(d x + c\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((2*cos(d*x + c) + 3*sin(d*x + c))^(-7/2), x)","F",0
248,1,23,0,0.446825," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^n,x, algorithm=""giac"")","-\frac{i \, e^{\left(i \, d n x + i \, c n + n \log\left(a\right)\right)}}{d n}"," ",0,"-I*e^(I*d*n*x + I*c*n + n*log(a))/(d*n)","A",0
249,1,52,0,0.190238," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)}}{8 \, d} - \frac{i \, a^{4} e^{\left(-4 i \, d x - 4 i \, c\right)}}{8 \, d} + \frac{a^{4} \sin\left(4 \, d x + 4 \, c\right)}{4 \, d}"," ",0,"-1/8*I*a^4*e^(4*I*d*x + 4*I*c)/d - 1/8*I*a^4*e^(-4*I*d*x - 4*I*c)/d + 1/4*a^4*sin(4*d*x + 4*c)/d","B",0
250,1,52,0,0.183232," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","-\frac{i \, a^{3} e^{\left(3 i \, d x + 3 i \, c\right)}}{6 \, d} - \frac{i \, a^{3} e^{\left(-3 i \, d x - 3 i \, c\right)}}{6 \, d} + \frac{a^{3} \sin\left(3 \, d x + 3 \, c\right)}{3 \, d}"," ",0,"-1/6*I*a^3*e^(3*I*d*x + 3*I*c)/d - 1/6*I*a^3*e^(-3*I*d*x - 3*I*c)/d + 1/3*a^3*sin(3*d*x + 3*c)/d","B",0
251,1,52,0,0.150789," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)}}{4 \, d} - \frac{i \, a^{2} e^{\left(-2 i \, d x - 2 i \, c\right)}}{4 \, d} + \frac{a^{2} \sin\left(2 \, d x + 2 \, c\right)}{2 \, d}"," ",0,"-1/4*I*a^2*e^(2*I*d*x + 2*I*c)/d - 1/4*I*a^2*e^(-2*I*d*x - 2*I*c)/d + 1/2*a^2*sin(2*d*x + 2*c)/d","B",0
252,1,24,0,0.149836," ","integrate(a*cos(d*x+c)+I*a*sin(d*x+c),x, algorithm=""giac"")","-\frac{i \, a \cos\left(d x + c\right)}{d} + \frac{a \sin\left(d x + c\right)}{d}"," ",0,"-I*a*cos(d*x + c)/d + a*sin(d*x + c)/d","A",0
253,1,21,0,0.134862," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x, algorithm=""giac"")","\frac{2}{a d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}}"," ",0,"2/(a*d*(tan(1/2*d*x + 1/2*c) - I))","A",0
254,1,30,0,0.153178," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{a^{2} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{2}}"," ",0,"-2*tan(1/2*d*x + 1/2*c)/(a^2*d*(tan(1/2*d*x + 1/2*c) - I)^2)","A",0
255,1,36,0,0.146112," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}}{3 \, a^{3} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{3}}"," ",0,"2/3*(3*tan(1/2*d*x + 1/2*c)^2 - 1)/(a^3*d*(tan(1/2*d*x + 1/2*c) - I)^3)","A",0
256,1,44,0,0.164806," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{a^{4} d {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i\right)}^{4}}"," ",0,"-2*(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c))/(a^4*d*(tan(1/2*d*x + 1/2*c) - I)^4)","A",0
257,1,17,0,0.567186," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","-\frac{2 i \, a^{\frac{5}{2}} e^{\left(\frac{5}{2} i \, d x + \frac{5}{2} i \, c\right)}}{5 \, d}"," ",0,"-2/5*I*a^(5/2)*e^(5/2*I*d*x + 5/2*I*c)/d","A",0
258,1,17,0,0.457263," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2 i \, a^{\frac{3}{2}} e^{\left(\frac{3}{2} i \, d x + \frac{3}{2} i \, c\right)}}{3 \, d}"," ",0,"-2/3*I*a^(3/2)*e^(3/2*I*d*x + 3/2*I*c)/d","A",0
259,1,25,0,0.138461," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","-\frac{2 i \, \sqrt{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right)}}{d}"," ",0,"-2*I*sqrt(a*cos(d*x + c) + I*a*sin(d*x + c))/d","A",0
260,1,37,0,0.334606," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 i}{d \sqrt{-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i}}}"," ",0,"2*I/(d*sqrt(-(a*tan(1/2*d*x + 1/2*c) - I*a)/(tan(1/2*d*x + 1/2*c) + I)))","A",0
261,1,65,0,1.227926," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(3/2),x, algorithm=""giac"")","-\frac{2 i \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}}{3 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i \, a\right)} d \sqrt{-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i}}}"," ",0,"-2/3*I*(tan(1/2*d*x + 1/2*c) + I)/((a*tan(1/2*d*x + 1/2*c) - I*a)*d*sqrt(-(a*tan(1/2*d*x + 1/2*c) - I*a)/(tan(1/2*d*x + 1/2*c) + I)))","B",0
262,1,67,0,3.298864," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\frac{2 i \, {\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right)}^{2}}{5 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i \, a\right)}^{2} d \sqrt{-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - i \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i}}}"," ",0,"2/5*I*(tan(1/2*d*x + 1/2*c) + I)^2/((a*tan(1/2*d*x + 1/2*c) - I*a)^2*d*sqrt(-(a*tan(1/2*d*x + 1/2*c) - I*a)/(tan(1/2*d*x + 1/2*c) + I)))","B",0
263,1,178,0,0.154044," ","integrate((a*sec(x)+b*tan(x))^5,x, algorithm=""giac"")","\frac{1}{16} \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} - 8 \, b^{5}\right)} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{16} \, {\left(3 \, a^{5} - 10 \, a^{3} b^{2} + 15 \, a b^{4} + 8 \, b^{5}\right)} \log\left(-\sin\left(x\right) + 1\right) + \frac{6 \, b^{5} \sin\left(x\right)^{4} - 3 \, a^{5} \sin\left(x\right)^{3} + 10 \, a^{3} b^{2} \sin\left(x\right)^{3} + 25 \, a b^{4} \sin\left(x\right)^{3} + 40 \, a^{2} b^{3} \sin\left(x\right)^{2} - 4 \, b^{5} \sin\left(x\right)^{2} + 5 \, a^{5} \sin\left(x\right) + 10 \, a^{3} b^{2} \sin\left(x\right) - 15 \, a b^{4} \sin\left(x\right) + 10 \, a^{4} b - 20 \, a^{2} b^{3}}{8 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}}"," ",0,"1/16*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 - 8*b^5)*log(sin(x) + 1) - 1/16*(3*a^5 - 10*a^3*b^2 + 15*a*b^4 + 8*b^5)*log(-sin(x) + 1) + 1/8*(6*b^5*sin(x)^4 - 3*a^5*sin(x)^3 + 10*a^3*b^2*sin(x)^3 + 25*a*b^4*sin(x)^3 + 40*a^2*b^3*sin(x)^2 - 4*b^5*sin(x)^2 + 5*a^5*sin(x) + 10*a^3*b^2*sin(x) - 15*a*b^4*sin(x) + 10*a^4*b - 20*a^2*b^3)/(sin(x)^2 - 1)^2","A",0
264,1,131,0,0.160158," ","integrate((a*sec(x)+b*tan(x))^4,x, algorithm=""giac"")","b^{4} x - \frac{2 \, {\left(3 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{5} - 3 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{5} + 12 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 24 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 10 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 24 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 3 \, a^{4} \tan\left(\frac{1}{2} \, x\right) - 3 \, b^{4} \tan\left(\frac{1}{2} \, x\right) + 4 \, a^{3} b - 8 \, a b^{3}\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}^{3}}"," ",0,"b^4*x - 2/3*(3*a^4*tan(1/2*x)^5 - 3*b^4*tan(1/2*x)^5 + 12*a^3*b*tan(1/2*x)^4 - 2*a^4*tan(1/2*x)^3 + 24*a^2*b^2*tan(1/2*x)^3 + 10*b^4*tan(1/2*x)^3 + 24*a*b^3*tan(1/2*x)^2 + 3*a^4*tan(1/2*x) - 3*b^4*tan(1/2*x) + 4*a^3*b - 8*a*b^3)/(tan(1/2*x)^2 - 1)^3","A",0
265,1,86,0,0.141918," ","integrate((a*sec(x)+b*tan(x))^3,x, algorithm=""giac"")","\frac{1}{4} \, {\left(a^{3} - 3 \, a b^{2} + 2 \, b^{3}\right)} \log\left(\sin\left(x\right) + 1\right) - \frac{1}{4} \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \log\left(-\sin\left(x\right) + 1\right) - \frac{b^{3} \sin\left(x\right)^{2} + a^{3} \sin\left(x\right) + 3 \, a b^{2} \sin\left(x\right) + 3 \, a^{2} b}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}}"," ",0,"1/4*(a^3 - 3*a*b^2 + 2*b^3)*log(sin(x) + 1) - 1/4*(a^3 - 3*a*b^2 - 2*b^3)*log(-sin(x) + 1) - 1/2*(b^3*sin(x)^2 + a^3*sin(x) + 3*a*b^2*sin(x) + 3*a^2*b)/(sin(x)^2 - 1)","A",0
266,1,40,0,0.160877," ","integrate((a*sec(x)+b*tan(x))^2,x, algorithm=""giac"")","-b^{2} x - \frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, x\right) + b^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, a b\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}"," ",0,"-b^2*x - 2*(a^2*tan(1/2*x) + b^2*tan(1/2*x) + 2*a*b)/(tan(1/2*x)^2 - 1)","A",0
267,1,34,0,0.128655," ","integrate(a*sec(x)+b*tan(x),x, algorithm=""giac"")","\frac{1}{4} \, a {\left(\log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) + 2 \right|}\right) - \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) - 2 \right|}\right)\right)} - b \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"1/4*a*(log(abs(1/sin(x) + sin(x) + 2)) - log(abs(1/sin(x) + sin(x) - 2))) - b*log(abs(cos(x)))","B",0
268,1,12,0,0.129522," ","integrate(1/(a*sec(x)+b*tan(x)),x, algorithm=""giac"")","\frac{\log\left({\left| b \sin\left(x\right) + a \right|}\right)}{b}"," ",0,"log(abs(b*sin(x) + a))/b","A",0
269,1,94,0,0.167537," ","integrate(1/(a*sec(x)+b*tan(x))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)} a}{\sqrt{a^{2} - b^{2}} b^{2}} - \frac{x}{b^{2}} - \frac{2 \, {\left(b \tan\left(\frac{1}{2} \, x\right) + a\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)} a b}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))*a/(sqrt(a^2 - b^2)*b^2) - x/b^2 - 2*(b*tan(1/2*x) + a)/((a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)*a*b)","A",0
270,1,43,0,0.137589," ","integrate(1/(a*sec(x)+b*tan(x))^3,x, algorithm=""giac"")","-\frac{\log\left({\left| b \sin\left(x\right) + a \right|}\right)}{b^{3}} + \frac{3 \, b \sin\left(x\right)^{2} + 2 \, a \sin\left(x\right) - b}{2 \, {\left(b \sin\left(x\right) + a\right)}^{2} b^{2}}"," ",0,"-log(abs(b*sin(x) + a))/b^3 + 1/2*(3*b*sin(x)^2 + 2*a*sin(x) - b)/((b*sin(x) + a)^2*b^2)","A",0
271,1,369,0,0.168383," ","integrate(1/(a*sec(x)+b*tan(x))^4,x, algorithm=""giac"")","-\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)\right)}}{{\left(a^{2} b^{4} - b^{6}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, a^{6} b \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{5} + 6 \, a^{7} \tan\left(\frac{1}{2} \, x\right)^{4} + 9 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 12 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{4} + 12 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{4} + 36 \, a^{6} b \tan\left(\frac{1}{2} \, x\right)^{3} - 6 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 8 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} + 8 \, b^{7} \tan\left(\frac{1}{2} \, x\right)^{3} + 12 \, a^{7} \tan\left(\frac{1}{2} \, x\right)^{2} + 48 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 42 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 12 \, a b^{6} \tan\left(\frac{1}{2} \, x\right)^{2} + 33 \, a^{6} b \tan\left(\frac{1}{2} \, x\right) - 24 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x\right) + 6 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x\right) + 6 \, a^{7} - 5 \, a^{5} b^{2} + 2 \, a^{3} b^{4}}{3 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a\right)}^{3}} + \frac{x}{b^{4}}"," ",0,"-(2*a^3 - 3*a*b^2)*(pi*floor(1/2*x/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x) + b)/sqrt(a^2 - b^2)))/((a^2*b^4 - b^6)*sqrt(a^2 - b^2)) + 1/3*(3*a^6*b*tan(1/2*x)^5 - 6*a^4*b^3*tan(1/2*x)^5 + 6*a^2*b^5*tan(1/2*x)^5 + 6*a^7*tan(1/2*x)^4 + 9*a^5*b^2*tan(1/2*x)^4 - 12*a^3*b^4*tan(1/2*x)^4 + 12*a*b^6*tan(1/2*x)^4 + 36*a^6*b*tan(1/2*x)^3 - 6*a^4*b^3*tan(1/2*x)^3 - 8*a^2*b^5*tan(1/2*x)^3 + 8*b^7*tan(1/2*x)^3 + 12*a^7*tan(1/2*x)^2 + 48*a^5*b^2*tan(1/2*x)^2 - 42*a^3*b^4*tan(1/2*x)^2 + 12*a*b^6*tan(1/2*x)^2 + 33*a^6*b*tan(1/2*x) - 24*a^4*b^3*tan(1/2*x) + 6*a^2*b^5*tan(1/2*x) + 6*a^7 - 5*a^5*b^2 + 2*a^3*b^4)/((a^5*b^3 - a^3*b^5)*(a*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a)^3) + x/b^4","B",0
272,1,91,0,0.138686," ","integrate(1/(a*sec(x)+b*tan(x))^5,x, algorithm=""giac"")","\frac{\log\left({\left| b \sin\left(x\right) + a \right|}\right)}{b^{5}} - \frac{25 \, b^{3} \sin\left(x\right)^{4} + 52 \, a b^{2} \sin\left(x\right)^{3} + 42 \, a^{2} b \sin\left(x\right)^{2} - 12 \, b^{3} \sin\left(x\right)^{2} + 12 \, a^{3} \sin\left(x\right) - 8 \, a b^{2} \sin\left(x\right) - 2 \, a^{2} b + 3 \, b^{3}}{12 \, {\left(b \sin\left(x\right) + a\right)}^{4} b^{4}}"," ",0,"log(abs(b*sin(x) + a))/b^5 - 1/12*(25*b^3*sin(x)^4 + 52*a*b^2*sin(x)^3 + 42*a^2*b*sin(x)^2 - 12*b^3*sin(x)^2 + 12*a^3*sin(x) - 8*a*b^2*sin(x) - 2*a^2*b + 3*b^3)/((b*sin(x) + a)^4*b^4)","A",0
273,1,62,0,0.140791," ","integrate((sec(x)+tan(x))^5,x, algorithm=""giac"")","\frac{25 \, \tan\left(\frac{1}{2} \, x\right)^{4} - 100 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 198 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 100 \, \tan\left(\frac{1}{2} \, x\right) + 25}{6 \, {\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}^{4}} + \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"1/6*(25*tan(1/2*x)^4 - 100*tan(1/2*x)^3 + 198*tan(1/2*x)^2 - 100*tan(1/2*x) + 25)/(tan(1/2*x) - 1)^4 + log(tan(1/2*x)^2 + 1) - 2*log(abs(tan(1/2*x) - 1))","B",0
274,1,20,0,0.154756," ","integrate((sec(x)+tan(x))^4,x, algorithm=""giac"")","x - \frac{8 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right) - 1\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}^{3}}"," ",0,"x - 8/3*(3*tan(1/2*x) - 1)/(tan(1/2*x) - 1)^3","A",0
275,1,48,0,0.171929," ","integrate((sec(x)+tan(x))^3,x, algorithm=""giac"")","-\frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, x\right) + 3}{{\left(\tan\left(\frac{1}{2} \, x\right) - 1\right)}^{2}} - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"-(3*tan(1/2*x)^2 - 10*tan(1/2*x) + 3)/(tan(1/2*x) - 1)^2 - log(tan(1/2*x)^2 + 1) + 2*log(abs(tan(1/2*x) - 1))","B",0
276,1,14,0,0.130346," ","integrate((sec(x)+tan(x))^2,x, algorithm=""giac"")","-x - \frac{4}{\tan\left(\frac{1}{2} \, x\right) - 1}"," ",0,"-x - 4/(tan(1/2*x) - 1)","A",0
277,1,31,0,0.146983," ","integrate(sec(x)+tan(x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) - 2 \right|}\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"1/4*log(abs(1/sin(x) + sin(x) + 2)) - 1/4*log(abs(1/sin(x) + sin(x) - 2)) - log(abs(cos(x)))","B",0
278,1,22,0,0.138301," ","integrate(1/(sec(x)+tan(x)),x, algorithm=""giac"")","-\log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)"," ",0,"-log(tan(1/2*x)^2 + 1) + 2*log(abs(tan(1/2*x) + 1))","B",0
279,1,14,0,0.150372," ","integrate(1/(sec(x)+tan(x))^2,x, algorithm=""giac"")","-x - \frac{4}{\tan\left(\frac{1}{2} \, x\right) + 1}"," ",0,"-x - 4/(tan(1/2*x) + 1)","A",0
280,1,45,0,0.162351," ","integrate(1/(sec(x)+tan(x))^3,x, algorithm=""giac"")","\frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 10 \, \tan\left(\frac{1}{2} \, x\right) + 3}{{\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{2}} + \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)"," ",0,"(3*tan(1/2*x)^2 + 10*tan(1/2*x) + 3)/(tan(1/2*x) + 1)^2 + log(tan(1/2*x)^2 + 1) - 2*log(abs(tan(1/2*x) + 1))","B",0
281,1,20,0,0.155453," ","integrate(1/(sec(x)+tan(x))^4,x, algorithm=""giac"")","x + \frac{8 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{3}}"," ",0,"x + 8/3*(3*tan(1/2*x) + 1)/(tan(1/2*x) + 1)^3","A",0
282,1,64,0,0.150454," ","integrate(1/(sec(x)+tan(x))^5,x, algorithm=""giac"")","-\frac{25 \, \tan\left(\frac{1}{2} \, x\right)^{4} + 100 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 198 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 100 \, \tan\left(\frac{1}{2} \, x\right) + 25}{6 \, {\left(\tan\left(\frac{1}{2} \, x\right) + 1\right)}^{4}} - \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + 2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)"," ",0,"-1/6*(25*tan(1/2*x)^4 + 100*tan(1/2*x)^3 + 198*tan(1/2*x)^2 + 100*tan(1/2*x) + 25)/(tan(1/2*x) + 1)^4 - log(tan(1/2*x)^2 + 1) + 2*log(abs(tan(1/2*x) + 1))","B",0
283,1,169,0,0.128452," ","integrate((a*cot(x)+b*csc(x))^5,x, algorithm=""giac"")","\frac{1}{16} \, {\left(8 \, a^{5} - 15 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \log\left(\cos\left(x\right) + 1\right) + \frac{1}{16} \, {\left(8 \, a^{5} + 15 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(-\cos\left(x\right) + 1\right) + \frac{6 \, a^{5} + 20 \, a^{3} b^{2} - 10 \, a b^{4} - {\left(25 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(x\right)^{3} - 8 \, {\left(a^{5} + 5 \, a^{3} b^{2}\right)} \cos\left(x\right)^{2} + 5 \, {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5}\right)} \cos\left(x\right)}{8 \, {\left(\cos\left(x\right) + 1\right)}^{2} {\left(\cos\left(x\right) - 1\right)}^{2}}"," ",0,"1/16*(8*a^5 - 15*a^4*b + 10*a^2*b^3 - 3*b^5)*log(cos(x) + 1) + 1/16*(8*a^5 + 15*a^4*b - 10*a^2*b^3 + 3*b^5)*log(-cos(x) + 1) + 1/8*(6*a^5 + 20*a^3*b^2 - 10*a*b^4 - (25*a^4*b + 10*a^2*b^3 - 3*b^5)*cos(x)^3 - 8*(a^5 + 5*a^3*b^2)*cos(x)^2 + 5*(3*a^4*b - 2*a^2*b^3 - b^5)*cos(x))/((cos(x) + 1)^2*(cos(x) - 1)^2)","A",0
284,1,215,0,0.157692," ","integrate((a*cot(x)+b*csc(x))^4,x, algorithm=""giac"")","\frac{1}{24} \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - \frac{1}{6} \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{3} + \frac{1}{4} \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - \frac{1}{6} \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + \frac{1}{24} \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + a^{4} x - \frac{5}{8} \, a^{4} \tan\left(\frac{1}{2} \, x\right) + \frac{3}{2} \, a^{3} b \tan\left(\frac{1}{2} \, x\right) - \frac{3}{4} \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right) - \frac{1}{2} \, a b^{3} \tan\left(\frac{1}{2} \, x\right) + \frac{3}{8} \, b^{4} \tan\left(\frac{1}{2} \, x\right) + \frac{15 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 36 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{2} + 18 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - a^{4} - 4 \, a^{3} b - 6 \, a^{2} b^{2} - 4 \, a b^{3} - b^{4}}{24 \, \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"1/24*a^4*tan(1/2*x)^3 - 1/6*a^3*b*tan(1/2*x)^3 + 1/4*a^2*b^2*tan(1/2*x)^3 - 1/6*a*b^3*tan(1/2*x)^3 + 1/24*b^4*tan(1/2*x)^3 + a^4*x - 5/8*a^4*tan(1/2*x) + 3/2*a^3*b*tan(1/2*x) - 3/4*a^2*b^2*tan(1/2*x) - 1/2*a*b^3*tan(1/2*x) + 3/8*b^4*tan(1/2*x) + 1/24*(15*a^4*tan(1/2*x)^2 + 36*a^3*b*tan(1/2*x)^2 + 18*a^2*b^2*tan(1/2*x)^2 - 12*a*b^3*tan(1/2*x)^2 - 9*b^4*tan(1/2*x)^2 - a^4 - 4*a^3*b - 6*a^2*b^2 - 4*a*b^3 - b^4)/tan(1/2*x)^3","B",0
285,1,86,0,0.145444," ","integrate((a*cot(x)+b*csc(x))^3,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \log\left(\cos\left(x\right) + 1\right) - \frac{1}{4} \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \log\left(-\cos\left(x\right) + 1\right) + \frac{a^{3} + 3 \, a b^{2} + {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(x\right)}{2 \, {\left(\cos\left(x\right) + 1\right)} {\left(\cos\left(x\right) - 1\right)}}"," ",0,"-1/4*(2*a^3 - 3*a^2*b + b^3)*log(cos(x) + 1) - 1/4*(2*a^3 + 3*a^2*b - b^3)*log(-cos(x) + 1) + 1/2*(a^3 + 3*a*b^2 + (3*a^2*b + b^3)*cos(x))/((cos(x) + 1)*(cos(x) - 1))","A",0
286,1,52,0,0.149754," ","integrate((a*cot(x)+b*csc(x))^2,x, algorithm=""giac"")","-a^{2} x + \frac{1}{2} \, a^{2} \tan\left(\frac{1}{2} \, x\right) - a b \tan\left(\frac{1}{2} \, x\right) + \frac{1}{2} \, b^{2} \tan\left(\frac{1}{2} \, x\right) - \frac{a^{2} + 2 \, a b + b^{2}}{2 \, \tan\left(\frac{1}{2} \, x\right)}"," ",0,"-a^2*x + 1/2*a^2*tan(1/2*x) - a*b*tan(1/2*x) + 1/2*b^2*tan(1/2*x) - 1/2*(a^2 + 2*a*b + b^2)/tan(1/2*x)","A",0
287,1,15,0,0.140998," ","integrate(a*cot(x)+b*csc(x),x, algorithm=""giac"")","a \log\left({\left| \sin\left(x\right) \right|}\right) + b \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"a*log(abs(sin(x))) + b*log(abs(tan(1/2*x)))","A",0
288,1,13,0,0.121370," ","integrate(1/(a*cot(x)+b*csc(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| a \cos\left(x\right) + b \right|}\right)}{a}"," ",0,"-log(abs(a*cos(x) + b))/a","A",0
289,1,107,0,0.137171," ","integrate(1/(a*cot(x)+b*csc(x))^2,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)} b}{\sqrt{-a^{2} + b^{2}} a^{2}} - \frac{x}{a^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b\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)))*b/(sqrt(-a^2 + b^2)*a^2) - x/a^2 - 2*tan(1/2*x)/((a*tan(1/2*x)^2 - b*tan(1/2*x)^2 - a - b)*a)","A",0
290,1,45,0,0.126391," ","integrate(1/(a*cot(x)+b*csc(x))^3,x, algorithm=""giac"")","\frac{\log\left({\left| a \cos\left(x\right) + b \right|}\right)}{a^{3}} + \frac{4 \, b \cos\left(x\right) + \frac{a^{2} + 3 \, b^{2}}{a}}{2 \, {\left(a \cos\left(x\right) + b\right)}^{2} a^{2}}"," ",0,"log(abs(a*cos(x) + b))/a^3 + 1/2*(4*b*cos(x) + (a^2 + 3*b^2)/a)/((a*cos(x) + b)^2*a^2)","A",0
291,1,282,0,0.195111," ","integrate(1/(a*cot(x)+b*csc(x))^4,x, algorithm=""giac"")","-\frac{{\left(3 \, a^{2} b - 2 \, b^{3}\right)} {\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(a^{6} - a^{4} b^{2}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{6 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{5} - 9 \, a^{3} b \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{5} + 15 \, a b^{3} \tan\left(\frac{1}{2} \, x\right)^{5} - 6 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{5} - 20 \, a^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 32 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 12 \, b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 6 \, a^{4} \tan\left(\frac{1}{2} \, x\right) + 9 \, a^{3} b \tan\left(\frac{1}{2} \, x\right) - 6 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x\right) - 15 \, a b^{3} \tan\left(\frac{1}{2} \, x\right) - 6 \, b^{4} \tan\left(\frac{1}{2} \, x\right)}{3 \, {\left(a^{5} - a^{3} b^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b\right)}^{3}} + \frac{x}{a^{4}}"," ",0,"-(3*a^2*b - 2*b^3)*(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^6 - a^4*b^2)*sqrt(-a^2 + b^2)) + 1/3*(6*a^4*tan(1/2*x)^5 - 9*a^3*b*tan(1/2*x)^5 - 6*a^2*b^2*tan(1/2*x)^5 + 15*a*b^3*tan(1/2*x)^5 - 6*b^4*tan(1/2*x)^5 - 20*a^4*tan(1/2*x)^3 + 32*a^2*b^2*tan(1/2*x)^3 - 12*b^4*tan(1/2*x)^3 + 6*a^4*tan(1/2*x) + 9*a^3*b*tan(1/2*x) - 6*a^2*b^2*tan(1/2*x) - 15*a*b^3*tan(1/2*x) - 6*b^4*tan(1/2*x))/((a^5 - a^3*b^2)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 - a - b)^3) + x/a^4","A",0
292,1,93,0,0.128219," ","integrate(1/(a*cot(x)+b*csc(x))^5,x, algorithm=""giac"")","-\frac{\log\left({\left| a \cos\left(x\right) + b \right|}\right)}{a^{5}} - \frac{48 \, a^{2} b \cos\left(x\right)^{3} + 12 \, {\left(a^{3} + 9 \, a b^{2}\right)} \cos\left(x\right)^{2} + 8 \, {\left(a^{2} b + 11 \, b^{3}\right)} \cos\left(x\right) - \frac{3 \, a^{4} - 2 \, a^{2} b^{2} - 25 \, b^{4}}{a}}{12 \, {\left(a \cos\left(x\right) + b\right)}^{4} a^{4}}"," ",0,"-log(abs(a*cos(x) + b))/a^5 - 1/12*(48*a^2*b*cos(x)^3 + 12*(a^3 + 9*a*b^2)*cos(x)^2 + 8*(a^2*b + 11*b^3)*cos(x) - (3*a^4 - 2*a^2*b^2 - 25*b^4)/a)/((a*cos(x) + b)^4*a^4)","A",0
293,1,22,0,0.123649," ","integrate((cot(x)+csc(x))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, \cos\left(x\right) - 1\right)}}{{\left(\cos\left(x\right) - 1\right)}^{2}} + \log\left(-\cos\left(x\right) + 1\right)"," ",0,"-2*(2*cos(x) - 1)/(cos(x) - 1)^2 + log(-cos(x) + 1)","A",0
294,1,20,0,0.130619," ","integrate((cot(x)+csc(x))^4,x, algorithm=""giac"")","x + \frac{2 \, {\left(3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}}{3 \, \tan\left(\frac{1}{2} \, x\right)^{3}}"," ",0,"x + 2/3*(3*tan(1/2*x)^2 - 1)/tan(1/2*x)^3","A",0
295,1,18,0,0.145840," ","integrate((cot(x)+csc(x))^3,x, algorithm=""giac"")","\frac{2}{\cos\left(x\right) - 1} - \log\left(-\cos\left(x\right) + 1\right)"," ",0,"2/(cos(x) - 1) - log(-cos(x) + 1)","A",0
296,1,12,0,0.157750," ","integrate((cot(x)+csc(x))^2,x, algorithm=""giac"")","-x - \frac{2}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-x - 2/tan(1/2*x)","A",0
297,1,11,0,0.151232," ","integrate(cot(x)+csc(x),x, algorithm=""giac"")","\log\left({\left| \sin\left(x\right) \right|}\right) + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"log(abs(sin(x))) + log(abs(tan(1/2*x)))","A",0
298,1,7,0,0.131969," ","integrate(1/(cot(x)+csc(x)),x, algorithm=""giac"")","-\log\left(\cos\left(x\right) + 1\right)"," ",0,"-log(cos(x) + 1)","A",0
299,1,10,0,0.143965," ","integrate(1/(cot(x)+csc(x))^2,x, algorithm=""giac"")","-x + 2 \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"-x + 2*tan(1/2*x)","A",0
300,1,14,0,0.141466," ","integrate(1/(cot(x)+csc(x))^3,x, algorithm=""giac"")","\frac{2}{\cos\left(x\right) + 1} + \log\left(\cos\left(x\right) + 1\right)"," ",0,"2/(cos(x) + 1) + log(cos(x) + 1)","A",0
301,1,16,0,0.128817," ","integrate(1/(cot(x)+csc(x))^4,x, algorithm=""giac"")","\frac{2}{3} \, \tan\left(\frac{1}{2} \, x\right)^{3} + x - 2 \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"2/3*tan(1/2*x)^3 + x - 2*tan(1/2*x)","A",0
302,1,22,0,0.121221," ","integrate(1/(cot(x)+csc(x))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, \cos\left(x\right) + 1\right)}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \log\left(\cos\left(x\right) + 1\right)"," ",0,"-2*(2*cos(x) + 1)/(cos(x) + 1)^2 - log(cos(x) + 1)","A",0
303,1,39,0,0.125293," ","integrate((csc(x)-sin(x))^4,x, algorithm=""giac"")","\frac{35}{8} \, x + \frac{11 \, \tan\left(x\right)^{3} + 13 \, \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2}} + \frac{9 \, \tan\left(x\right)^{2} - 1}{3 \, \tan\left(x\right)^{3}}"," ",0,"35/8*x + 1/8*(11*tan(x)^3 + 13*tan(x))/(tan(x)^2 + 1)^2 + 1/3*(9*tan(x)^2 - 1)/tan(x)^3","A",0
304,1,99,0,0.161332," ","integrate((csc(x)-sin(x))^3,x, algorithm=""giac"")","\frac{{\left(\frac{10 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + 1\right)} {\left(\cos\left(x\right) + 1\right)}}{8 \, {\left(\cos\left(x\right) - 1\right)}} - \frac{\cos\left(x\right) - 1}{8 \, {\left(\cos\left(x\right) + 1\right)}} - \frac{2 \, {\left(\frac{12 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{9 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 7\right)}}{3 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} - 1\right)}^{3}} - \frac{5}{4} \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)"," ",0,"1/8*(10*(cos(x) - 1)/(cos(x) + 1) + 1)*(cos(x) + 1)/(cos(x) - 1) - 1/8*(cos(x) - 1)/(cos(x) + 1) - 2/3*(12*(cos(x) - 1)/(cos(x) + 1) - 9*(cos(x) - 1)^2/(cos(x) + 1)^2 - 7)/((cos(x) - 1)/(cos(x) + 1) - 1)^3 - 5/4*log(-(cos(x) - 1)/(cos(x) + 1))","B",0
305,1,23,0,0.149648," ","integrate((csc(x)-sin(x))^2,x, algorithm=""giac"")","-\frac{3}{2} \, x - \frac{3 \, \tan\left(x\right)^{2} + 2}{2 \, {\left(\tan\left(x\right)^{3} + \tan\left(x\right)\right)}}"," ",0,"-3/2*x - 1/2*(3*tan(x)^2 + 2)/(tan(x)^3 + tan(x))","A",0
306,1,9,0,0.147580," ","integrate(csc(x)-sin(x),x, algorithm=""giac"")","\cos\left(x\right) + \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"cos(x) + log(abs(tan(1/2*x)))","A",0
307,1,17,0,0.138009," ","integrate(1/(csc(x)-sin(x)),x, algorithm=""giac"")","\frac{2}{\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} + 1}"," ",0,"2/((cos(x) - 1)/(cos(x) + 1) + 1)","B",0
308,1,6,0,0.130223," ","integrate(1/(csc(x)-sin(x))^2,x, algorithm=""giac"")","\frac{1}{3} \, \tan\left(x\right)^{3}"," ",0,"1/3*tan(x)^3","A",0
309,1,59,0,0.132110," ","integrate(1/(csc(x)-sin(x))^3,x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{5 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} - \frac{5 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{15 \, {\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + 1\right)}}{15 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} + 1\right)}^{5}}"," ",0,"-4/15*(5*(cos(x) - 1)/(cos(x) + 1) - 5*(cos(x) - 1)^2/(cos(x) + 1)^2 + 15*(cos(x) - 1)^3/(cos(x) + 1)^3 + 1)/((cos(x) - 1)/(cos(x) + 1) + 1)^5","B",0
310,1,13,0,0.122013," ","integrate(1/(csc(x)-sin(x))^4,x, algorithm=""giac"")","\frac{1}{7} \, \tan\left(x\right)^{7} + \frac{1}{5} \, \tan\left(x\right)^{5}"," ",0,"1/7*tan(x)^7 + 1/5*tan(x)^5","A",0
311,1,101,0,0.151613," ","integrate(1/(csc(x)-sin(x))^5,x, algorithm=""giac"")","\frac{16 \, {\left(\frac{9 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + \frac{36 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{126 \, {\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{441 \, {\left(\cos\left(x\right) - 1\right)}^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{315 \, {\left(\cos\left(x\right) - 1\right)}^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{210 \, {\left(\cos\left(x\right) - 1\right)}^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 1\right)}}{315 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} + 1\right)}^{9}}"," ",0,"16/315*(9*(cos(x) - 1)/(cos(x) + 1) + 36*(cos(x) - 1)^2/(cos(x) + 1)^2 - 126*(cos(x) - 1)^3/(cos(x) + 1)^3 + 441*(cos(x) - 1)^4/(cos(x) + 1)^4 - 315*(cos(x) - 1)^5/(cos(x) + 1)^5 + 210*(cos(x) - 1)^6/(cos(x) + 1)^6 + 1)/((cos(x) - 1)/(cos(x) + 1) + 1)^9","B",0
312,1,19,0,0.127433," ","integrate(1/(csc(x)-sin(x))^6,x, algorithm=""giac"")","\frac{1}{11} \, \tan\left(x\right)^{11} + \frac{2}{9} \, \tan\left(x\right)^{9} + \frac{1}{7} \, \tan\left(x\right)^{7}"," ",0,"1/11*tan(x)^11 + 2/9*tan(x)^9 + 1/7*tan(x)^7","A",0
313,1,143,0,0.142571," ","integrate(1/(csc(x)-sin(x))^7,x, algorithm=""giac"")","-\frac{32 \, {\left(\frac{13 \, {\left(\cos\left(x\right) - 1\right)}}{\cos\left(x\right) + 1} + \frac{78 \, {\left(\cos\left(x\right) - 1\right)}^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{286 \, {\left(\cos\left(x\right) - 1\right)}^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{2288 \, {\left(\cos\left(x\right) - 1\right)}^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{10296 \, {\left(\cos\left(x\right) - 1\right)}^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{16302 \, {\left(\cos\left(x\right) - 1\right)}^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{18018 \, {\left(\cos\left(x\right) - 1\right)}^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} - \frac{9009 \, {\left(\cos\left(x\right) - 1\right)}^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{3003 \, {\left(\cos\left(x\right) - 1\right)}^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}} + 1\right)}}{3003 \, {\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} + 1\right)}^{13}}"," ",0,"-32/3003*(13*(cos(x) - 1)/(cos(x) + 1) + 78*(cos(x) - 1)^2/(cos(x) + 1)^2 + 286*(cos(x) - 1)^3/(cos(x) + 1)^3 - 2288*(cos(x) - 1)^4/(cos(x) + 1)^4 + 10296*(cos(x) - 1)^5/(cos(x) + 1)^5 - 16302*(cos(x) - 1)^6/(cos(x) + 1)^6 + 18018*(cos(x) - 1)^7/(cos(x) + 1)^7 - 9009*(cos(x) - 1)^8/(cos(x) + 1)^8 + 3003*(cos(x) - 1)^9/(cos(x) + 1)^9 + 1)/((cos(x) - 1)/(cos(x) + 1) + 1)^13","B",0
314,0,0,0,0.000000," ","integrate((csc(x)-sin(x))^(7/2),x, algorithm=""giac"")","\int {\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(7/2), x)","F",0
315,0,0,0,0.000000," ","integrate((csc(x)-sin(x))^(5/2),x, algorithm=""giac"")","\int {\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(5/2), x)","F",0
316,0,0,0,0.000000," ","integrate((csc(x)-sin(x))^(3/2),x, algorithm=""giac"")","\int {\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(3/2), x)","F",0
317,0,0,0,0.000000," ","integrate((csc(x)-sin(x))^(1/2),x, algorithm=""giac"")","\int \sqrt{\csc\left(x\right) - \sin\left(x\right)}\,{d x}"," ",0,"integrate(sqrt(csc(x) - sin(x)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\csc\left(x\right) - \sin\left(x\right)}}\,{d x}"," ",0,"integrate(1/sqrt(csc(x) - sin(x)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-3/2), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-5/2), x)","F",0
321,0,0,0,0.000000," ","integrate(1/(csc(x)-sin(x))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(\csc\left(x\right) - \sin\left(x\right)\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((csc(x) - sin(x))^(-7/2), x)","F",0
322,1,35,0,0.135184," ","integrate((-cos(x)+sec(x))^4,x, algorithm=""giac"")","\frac{1}{3} \, \tan\left(x\right)^{3} + \frac{35}{8} \, x - \frac{13 \, \tan\left(x\right)^{3} + 11 \, \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2}} - 3 \, \tan\left(x\right)"," ",0,"1/3*tan(x)^3 + 35/8*x - 1/8*(13*tan(x)^3 + 11*tan(x))/(tan(x)^2 + 1)^2 - 3*tan(x)","A",0
323,1,39,0,0.145565," ","integrate((-cos(x)+sec(x))^3,x, algorithm=""giac"")","\frac{1}{3} \, \sin\left(x\right)^{3} - \frac{\sin\left(x\right)}{2 \, {\left(\sin\left(x\right)^{2} - 1\right)}} - \frac{5}{4} \, \log\left(\sin\left(x\right) + 1\right) + \frac{5}{4} \, \log\left(-\sin\left(x\right) + 1\right) + 2 \, \sin\left(x\right)"," ",0,"1/3*sin(x)^3 - 1/2*sin(x)/(sin(x)^2 - 1) - 5/4*log(sin(x) + 1) + 5/4*log(-sin(x) + 1) + 2*sin(x)","A",0
324,1,18,0,0.143445," ","integrate((-cos(x)+sec(x))^2,x, algorithm=""giac"")","-\frac{3}{2} \, x + \frac{\tan\left(x\right)}{2 \, {\left(\tan\left(x\right)^{2} + 1\right)}} + \tan\left(x\right)"," ",0,"-3/2*x + 1/2*tan(x)/(tan(x)^2 + 1) + tan(x)","A",0
325,1,29,0,0.153969," ","integrate(-cos(x)+sec(x),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(x\right)} + \sin\left(x\right) - 2 \right|}\right) - \sin\left(x\right)"," ",0,"1/4*log(abs(1/sin(x) + sin(x) + 2)) - 1/4*log(abs(1/sin(x) + sin(x) - 2)) - sin(x)","B",0
326,1,6,0,0.148909," ","integrate(1/(-cos(x)+sec(x)),x, algorithm=""giac"")","-\frac{1}{\sin\left(x\right)}"," ",0,"-1/sin(x)","A",0
327,1,6,0,0.146424," ","integrate(1/(-cos(x)+sec(x))^2,x, algorithm=""giac"")","-\frac{1}{3 \, \tan\left(x\right)^{3}}"," ",0,"-1/3/tan(x)^3","A",0
328,1,14,0,0.131641," ","integrate(1/(-cos(x)+sec(x))^3,x, algorithm=""giac"")","\frac{5 \, \sin\left(x\right)^{2} - 3}{15 \, \sin\left(x\right)^{5}}"," ",0,"1/15*(5*sin(x)^2 - 3)/sin(x)^5","A",0
329,1,14,0,0.141025," ","integrate(1/(-cos(x)+sec(x))^4,x, algorithm=""giac"")","-\frac{7 \, \tan\left(x\right)^{2} + 5}{35 \, \tan\left(x\right)^{7}}"," ",0,"-1/35*(7*tan(x)^2 + 5)/tan(x)^7","A",0
330,1,20,0,0.143285," ","integrate(1/(-cos(x)+sec(x))^5,x, algorithm=""giac"")","-\frac{63 \, \sin\left(x\right)^{4} - 90 \, \sin\left(x\right)^{2} + 35}{315 \, \sin\left(x\right)^{9}}"," ",0,"-1/315*(63*sin(x)^4 - 90*sin(x)^2 + 35)/sin(x)^9","A",0
331,1,20,0,0.124270," ","integrate(1/(-cos(x)+sec(x))^6,x, algorithm=""giac"")","-\frac{99 \, \tan\left(x\right)^{4} + 154 \, \tan\left(x\right)^{2} + 63}{693 \, \tan\left(x\right)^{11}}"," ",0,"-1/693*(99*tan(x)^4 + 154*tan(x)^2 + 63)/tan(x)^11","A",0
332,1,26,0,0.149466," ","integrate(1/(-cos(x)+sec(x))^7,x, algorithm=""giac"")","\frac{429 \, \sin\left(x\right)^{6} - 1001 \, \sin\left(x\right)^{4} + 819 \, \sin\left(x\right)^{2} - 231}{3003 \, \sin\left(x\right)^{13}}"," ",0,"1/3003*(429*sin(x)^6 - 1001*sin(x)^4 + 819*sin(x)^2 - 231)/sin(x)^13","A",0
333,0,0,0,0.000000," ","integrate((-cos(x)+sec(x))^(7/2),x, algorithm=""giac"")","\int {\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(7/2), x)","F",0
334,0,0,0,0.000000," ","integrate((-cos(x)+sec(x))^(5/2),x, algorithm=""giac"")","\int {\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(5/2), x)","F",0
335,0,0,0,0.000000," ","integrate((-cos(x)+sec(x))^(3/2),x, algorithm=""giac"")","\int {\left(-\cos\left(x\right) + \sec\left(x\right)\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((-cos(x) + sec(x))^(3/2), x)","F",0
336,1,46,0,0.204721," ","integrate((-cos(x)+sec(x))^(1/2),x, algorithm=""giac"")","-\frac{4 \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)\right) \mathrm{sgn}\left(\cos\left(x\right)\right)}{\frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2}} - 1}"," ",0,"-4*sgn(-tan(1/2*x)^3 - tan(1/2*x))*sgn(cos(x))/((sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 - 1)","B",0
337,0,0,0,0.000000," ","integrate(1/(-cos(x)+sec(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-\cos\left(x\right) + \sec\left(x\right)}}\,{d x}"," ",0,"integrate(1/sqrt(-cos(x) + sec(x)), x)","F",0
338,1,114,0,0.366364," ","integrate(1/(-cos(x)+sec(x))^(3/2),x, algorithm=""giac"")","-\frac{\frac{\tan\left(\frac{1}{2} \, x\right)^{2}}{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1} - 2 \, \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - \frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2}} - 2 \, \arcsin\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right) - 2 \, \log\left(-\frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2}}\right)}{16 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"-1/16*(tan(1/2*x)^2/(sqrt(-tan(1/2*x)^4 + 1) - 1) - 2*sqrt(-tan(1/2*x)^4 + 1) - (sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 - 2*arcsin(tan(1/2*x)^2) - 2*log(-(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2))/(sgn(tan(1/2*x)^4 - 1)*sgn(tan(1/2*x)))","B",0
339,1,170,0,0.404781," ","integrate(1/(-cos(x)+sec(x))^(5/2),x, algorithm=""giac"")","\frac{\frac{{\left(\frac{4 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2}} + 1\right)} \tan\left(\frac{1}{2} \, x\right)^{4}}{{\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{2}} - 4 \, \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2\right)} - \frac{4 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2}} - \frac{{\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4}} - 12 \, \arcsin\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right) + 12 \, \log\left(-\frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2}}\right)}{256 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"1/256*((4*(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 + 1)*tan(1/2*x)^4/(sqrt(-tan(1/2*x)^4 + 1) - 1)^2 - 4*sqrt(-tan(1/2*x)^4 + 1)*(tan(1/2*x)^2 - 2) - 4*(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 - (sqrt(-tan(1/2*x)^4 + 1) - 1)^2/tan(1/2*x)^4 - 12*arcsin(tan(1/2*x)^2) + 12*log(-(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2))/(sgn(tan(1/2*x)^4 - 1)*sgn(tan(1/2*x)))","B",0
340,1,229,0,0.449095," ","integrate(1/(-cos(x)+sec(x))^(7/2),x, algorithm=""giac"")","-\frac{\frac{{\left(\frac{3 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2}} - \frac{27 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4}} + 1\right)} \tan\left(\frac{1}{2} \, x\right)^{6}}{{\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{3}} - 4 \, \sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} {\left({\left(2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 3\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - 14\right)} + \frac{27 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2}} - \frac{3 \, {\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4}} - \frac{{\left(\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1\right)}^{3}}{\tan\left(\frac{1}{2} \, x\right)^{6}} + 60 \, \arcsin\left(\tan\left(\frac{1}{2} \, x\right)^{2}\right) + 60 \, \log\left(-\frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{4} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)^{2}}\right)}{3072 \, \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 1\right) \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)\right)}"," ",0,"-1/3072*((3*(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 - 27*(sqrt(-tan(1/2*x)^4 + 1) - 1)^2/tan(1/2*x)^4 + 1)*tan(1/2*x)^6/(sqrt(-tan(1/2*x)^4 + 1) - 1)^3 - 4*sqrt(-tan(1/2*x)^4 + 1)*((2*tan(1/2*x)^2 - 3)*tan(1/2*x)^2 - 14) + 27*(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2 - 3*(sqrt(-tan(1/2*x)^4 + 1) - 1)^2/tan(1/2*x)^4 - (sqrt(-tan(1/2*x)^4 + 1) - 1)^3/tan(1/2*x)^6 + 60*arcsin(tan(1/2*x)^2) + 60*log(-(sqrt(-tan(1/2*x)^4 + 1) - 1)/tan(1/2*x)^2))/(sgn(tan(1/2*x)^4 - 1)*sgn(tan(1/2*x)))","B",0
341,1,1375,0,5.637794," ","integrate((sin(x)+tan(x))^4,x, algorithm=""giac"")","\frac{8 \, \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{5} - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{2} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{2} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{5} - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{10} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{10} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{10} + 180 \, \tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right) - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{2} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{2} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{2} + 96 \, \tan\left(\frac{1}{2} \, x\right)^{9} \tan\left(x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{3} - 16 \, \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{5} - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{8} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{8} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{8} + 96 \, \tan\left(\frac{1}{2} \, x\right)^{9} + 180 \, \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right) + 366 \, x \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{2} + 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{2} - 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{7} \tan\left(x\right)^{2} - 256 \, \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{3} - 16 \, \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{5} + 366 \, x \tan\left(\frac{1}{2} \, x\right)^{6} + 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} - 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{6} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{7} - 360 \, \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right) + 366 \, x \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} + 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} - 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} + 1088 \, \tan\left(\frac{1}{2} \, x\right)^{5} \tan\left(x\right)^{2} - 256 \, \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{3} + 8 \, \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{5} + 366 \, x \tan\left(\frac{1}{2} \, x\right)^{4} + 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} - 48 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 1088 \, \tan\left(\frac{1}{2} \, x\right)^{5} - 360 \, \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right) - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{2} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{2} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{3} \tan\left(x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{3} + 8 \, \tan\left(x\right)^{5} - 183 \, x \tan\left(\frac{1}{2} \, x\right)^{2} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 128 \, \tan\left(\frac{1}{2} \, x\right)^{3} + 180 \, \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right) - 183 \, x \tan\left(x\right)^{2} - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(x\right)^{2} + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(x\right)^{2} + 96 \, \tan\left(\frac{1}{2} \, x\right) \tan\left(x\right)^{2} + 128 \, \tan\left(x\right)^{3} - 183 \, x - 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 24 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 96 \, \tan\left(\frac{1}{2} \, x\right) + 180 \, \tan\left(x\right)}{24 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{10} \tan\left(x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{10} + \tan\left(\frac{1}{2} \, x\right)^{8} \tan\left(x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{8} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{6} \tan\left(x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{6} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{4} + \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(x\right)^{2} + 1\right)}} + \frac{1}{32} \, \sin\left(4 \, x\right)"," ",0,"1/24*(8*tan(1/2*x)^10*tan(x)^5 - 183*x*tan(1/2*x)^10*tan(x)^2 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^10*tan(x)^2 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^10*tan(x)^2 + 128*tan(1/2*x)^10*tan(x)^3 + 8*tan(1/2*x)^8*tan(x)^5 - 183*x*tan(1/2*x)^10 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^10 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^10 + 180*tan(1/2*x)^10*tan(x) - 183*x*tan(1/2*x)^8*tan(x)^2 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8*tan(x)^2 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8*tan(x)^2 + 96*tan(1/2*x)^9*tan(x)^2 + 128*tan(1/2*x)^8*tan(x)^3 - 16*tan(1/2*x)^6*tan(x)^5 - 183*x*tan(1/2*x)^8 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8 + 96*tan(1/2*x)^9 + 180*tan(1/2*x)^8*tan(x) + 366*x*tan(1/2*x)^6*tan(x)^2 + 48*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6*tan(x)^2 - 48*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6*tan(x)^2 + 128*tan(1/2*x)^7*tan(x)^2 - 256*tan(1/2*x)^6*tan(x)^3 - 16*tan(1/2*x)^4*tan(x)^5 + 366*x*tan(1/2*x)^6 + 48*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 - 48*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 + 128*tan(1/2*x)^7 - 360*tan(1/2*x)^6*tan(x) + 366*x*tan(1/2*x)^4*tan(x)^2 + 48*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4*tan(x)^2 - 48*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4*tan(x)^2 + 1088*tan(1/2*x)^5*tan(x)^2 - 256*tan(1/2*x)^4*tan(x)^3 + 8*tan(1/2*x)^2*tan(x)^5 + 366*x*tan(1/2*x)^4 + 48*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4 - 48*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4 + 1088*tan(1/2*x)^5 - 360*tan(1/2*x)^4*tan(x) - 183*x*tan(1/2*x)^2*tan(x)^2 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2*tan(x)^2 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2*tan(x)^2 + 128*tan(1/2*x)^3*tan(x)^2 + 128*tan(1/2*x)^2*tan(x)^3 + 8*tan(x)^5 - 183*x*tan(1/2*x)^2 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + 128*tan(1/2*x)^3 + 180*tan(1/2*x)^2*tan(x) - 183*x*tan(x)^2 - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(x)^2 + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(x)^2 + 96*tan(1/2*x)*tan(x)^2 + 128*tan(x)^3 - 183*x - 24*log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + 24*log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + 96*tan(1/2*x) + 180*tan(x))/(tan(1/2*x)^10*tan(x)^2 + tan(1/2*x)^10 + tan(1/2*x)^8*tan(x)^2 + tan(1/2*x)^8 - 2*tan(1/2*x)^6*tan(x)^2 - 2*tan(1/2*x)^6 - 2*tan(1/2*x)^4*tan(x)^2 - 2*tan(1/2*x)^4 + tan(1/2*x)^2*tan(x)^2 + tan(1/2*x)^2 + tan(x)^2 + 1) + 1/32*sin(4*x)","B",0
342,1,173,0,0.451320," ","integrate((sin(x)+tan(x))^3,x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{4} - 2 \, \log\left(\frac{4}{\tan\left(x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} - 10 \, \tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} - 2 \, \log\left(\frac{4}{\tan\left(x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, x\right)^{4} - 3 \, \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right)^{2} - \tan\left(x\right)^{4} + 2 \, \log\left(\frac{4}{\tan\left(x\right)^{2} + 1}\right) \tan\left(x\right)^{2} - 3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 11 \, \tan\left(x\right)^{2} + 2 \, \log\left(\frac{4}{\tan\left(x\right)^{2} + 1}\right) - 13}{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{4} \tan\left(x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - \tan\left(x\right)^{2} - 1\right)}} + \frac{1}{12} \, \cos\left(3 \, x\right)"," ",0,"1/2*(tan(1/2*x)^4*tan(x)^4 - 2*log(4/(tan(x)^2 + 1))*tan(1/2*x)^4*tan(x)^2 - 10*tan(1/2*x)^4*tan(x)^2 - 2*log(4/(tan(x)^2 + 1))*tan(1/2*x)^4 - 8*tan(1/2*x)^4 - 3*tan(1/2*x)^2*tan(x)^2 - tan(x)^4 + 2*log(4/(tan(x)^2 + 1))*tan(x)^2 - 3*tan(1/2*x)^2 - 11*tan(x)^2 + 2*log(4/(tan(x)^2 + 1)) - 13)/(tan(1/2*x)^4*tan(x)^2 + tan(1/2*x)^4 - tan(x)^2 - 1) + 1/12*cos(3*x)","B",0
343,1,177,0,0.202491," ","integrate((sin(x)+tan(x))^2,x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{x \tan\left(\frac{1}{2} \, x\right)^{2} - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2} \, x\right)^{2} \tan\left(x\right) + x - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) + 4 \, \tan\left(\frac{1}{2} \, x\right) - \tan\left(x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1} - \frac{1}{4} \, \sin\left(2 \, x\right)"," ",0,"1/2*x - (x*tan(1/2*x)^2 - log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - tan(1/2*x)^2*tan(x) + x - log(2*(tan(1/2*x)^2 + 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) + 4*tan(1/2*x) - tan(x))/(tan(1/2*x)^2 + 1) - 1/4*sin(2*x)","B",0
344,1,11,0,0.140608," ","integrate(sin(x)+tan(x),x, algorithm=""giac"")","-\cos\left(x\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"-cos(x) - log(abs(cos(x)))","A",0
345,1,28,0,0.143566," ","integrate(1/(sin(x)+tan(x)),x, algorithm=""giac"")","\frac{\cos\left(x\right) - 1}{4 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{1}{4} \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)"," ",0,"1/4*(cos(x) - 1)/(cos(x) + 1) + 1/4*log(-(cos(x) - 1)/(cos(x) + 1))","A",0
346,1,31,0,0.140478," ","integrate(1/(sin(x)+tan(x))^2,x, algorithm=""giac"")","\frac{1}{40} \, \tan\left(\frac{1}{2} \, x\right)^{5} - \frac{1}{24} \, \tan\left(\frac{1}{2} \, x\right)^{3} - \frac{1}{8 \, \tan\left(\frac{1}{2} \, x\right)} - \frac{1}{8} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"1/40*tan(1/2*x)^5 - 1/24*tan(1/2*x)^3 - 1/8/tan(1/2*x) - 1/8*tan(1/2*x)","A",0
347,1,95,0,0.155720," ","integrate(1/(sin(x)+tan(x))^3,x, algorithm=""giac"")","\frac{{\left(\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1} + 1\right)} {\left(\cos\left(x\right) + 1\right)}}{64 \, {\left(\cos\left(x\right) - 1\right)}} + \frac{\cos\left(x\right) - 1}{32 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{{\left(\cos\left(x\right) - 1\right)}^{2}}{64 \, {\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{{\left(\cos\left(x\right) - 1\right)}^{3}}{192 \, {\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{{\left(\cos\left(x\right) - 1\right)}^{4}}{256 \, {\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{1}{64} \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)"," ",0,"1/64*((cos(x) - 1)/(cos(x) + 1) + 1)*(cos(x) + 1)/(cos(x) - 1) + 1/32*(cos(x) - 1)/(cos(x) + 1) + 1/64*(cos(x) - 1)^2/(cos(x) + 1)^2 - 1/192*(cos(x) - 1)^3/(cos(x) + 1)^3 - 1/256*(cos(x) - 1)^4/(cos(x) + 1)^4 - 1/64*log(-(cos(x) - 1)/(cos(x) + 1))","B",0
348,1,65,0,0.151340," ","integrate(1/(sin(x)+tan(x))^4,x, algorithm=""giac"")","\frac{1}{1408} \, \tan\left(\frac{1}{2} \, x\right)^{11} - \frac{1}{1152} \, \tan\left(\frac{1}{2} \, x\right)^{9} - \frac{3}{896} \, \tan\left(\frac{1}{2} \, x\right)^{7} + \frac{3}{640} \, \tan\left(\frac{1}{2} \, x\right)^{5} + \frac{1}{128} \, \tan\left(\frac{1}{2} \, x\right)^{3} + \frac{3 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}{384 \, \tan\left(\frac{1}{2} \, x\right)^{3}} - \frac{3}{128} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"1/1408*tan(1/2*x)^11 - 1/1152*tan(1/2*x)^9 - 3/896*tan(1/2*x)^7 + 3/640*tan(1/2*x)^5 + 1/128*tan(1/2*x)^3 + 1/384*(3*tan(1/2*x)^2 - 1)/tan(1/2*x)^3 - 3/128*tan(1/2*x)","A",0
349,1,131,0,0.211006," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{C c x}{b^{2} + c^{2}} + \frac{C b \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} - \frac{C b \log\left({\left| b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b \right|}\right)}{b^{2} + c^{2}} - \frac{A \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{\sqrt{b^{2} + c^{2}}}"," ",0,"C*c*x/(b^2 + c^2) + C*b*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) - C*b*log(abs(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))/(b^2 + c^2) - A*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/sqrt(b^2 + c^2)","A",0
350,1,130,0,0.186882," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""giac"")","-\frac{C c \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(A b^{2} \tan\left(\frac{1}{2} \, x\right) + C b c \tan\left(\frac{1}{2} \, x\right) + A c^{2} \tan\left(\frac{1}{2} \, x\right) + C b^{2}\right)}}{{\left(b^{3} + b c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}}"," ",0,"-C*c*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(A*b^2*tan(1/2*x) + C*b*c*tan(1/2*x) + A*c^2*tan(1/2*x) + C*b^2)/((b^3 + b*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))","A",0
351,1,199,0,0.238102," ","integrate((A+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","\frac{A \log\left(\frac{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{2 \, {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{A b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, C b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, A c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right) - A b^{2} c}{{\left(b^{4} + b^{2} c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}^{2}}"," ",0,"1/2*A*log(abs(-2*b*tan(1/2*x) + 2*c - 2*sqrt(b^2 + c^2))/abs(-2*b*tan(1/2*x) + 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + (A*b^3*tan(1/2*x)^3 + 2*A*b*c^2*tan(1/2*x)^3 + 2*C*b^3*tan(1/2*x)^2 + A*b^2*c*tan(1/2*x)^2 + 2*C*b*c^2*tan(1/2*x)^2 - 2*A*c^3*tan(1/2*x)^2 + A*b^3*tan(1/2*x) - 2*A*b*c^2*tan(1/2*x) - A*b^2*c)/((b^4 + b^2*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b)^2)","A",0
352,1,131,0,0.225084," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{B b x}{b^{2} + c^{2}} - \frac{B c \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} + \frac{B c \log\left({\left| b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b \right|}\right)}{b^{2} + c^{2}} - \frac{A \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{\sqrt{b^{2} + c^{2}}}"," ",0,"B*b*x/(b^2 + c^2) - B*c*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) + B*c*log(abs(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))/(b^2 + c^2) - A*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/sqrt(b^2 + c^2)","A",0
353,1,132,0,0.186804," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""giac"")","-\frac{B b \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(A b^{2} \tan\left(\frac{1}{2} \, x\right) + A c^{2} \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) - B b c\right)}}{{\left(b^{3} + b c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}}"," ",0,"-B*b*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(A*b^2*tan(1/2*x) + A*c^2*tan(1/2*x) - B*c^2*tan(1/2*x) - B*b*c)/((b^3 + b*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))","A",0
354,1,245,0,0.245918," ","integrate((A+B*cos(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","\frac{A \log\left(\frac{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{2 \, {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{A b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + A b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, A c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b c^{2} \tan\left(\frac{1}{2} \, x\right) - A b^{2} c}{{\left(b^{4} + b^{2} c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}^{2}}"," ",0,"1/2*A*log(abs(-2*b*tan(1/2*x) + 2*c - 2*sqrt(b^2 + c^2))/abs(-2*b*tan(1/2*x) + 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + (A*b^3*tan(1/2*x)^3 - 2*B*b^3*tan(1/2*x)^3 + 2*A*b*c^2*tan(1/2*x)^3 - 2*B*b*c^2*tan(1/2*x)^3 + A*b^2*c*tan(1/2*x)^2 + 2*B*b^2*c*tan(1/2*x)^2 - 2*A*c^3*tan(1/2*x)^2 + 2*B*c^3*tan(1/2*x)^2 + A*b^3*tan(1/2*x) + 2*B*b^3*tan(1/2*x) - 2*A*b*c^2*tan(1/2*x) + 2*B*b*c^2*tan(1/2*x) - A*b^2*c)/((b^4 + b^2*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b)^2)","B",0
355,1,287,0,0.346771," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(b^{3} c - b c^{3}\right)} \cos\left(4 \, x e + 4 \, d\right) e^{\left(-1\right)} - \frac{1}{3} \, {\left(3 \, \sqrt{b^{2} + c^{2}} b^{2} c - \sqrt{b^{2} + c^{2}} c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{7}{2} \, {\left(b^{3} c + b c^{3}\right)} \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 7 \, {\left(\sqrt{b^{2} + c^{2}} b^{2} c + \sqrt{b^{2} + c^{2}} c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{1}{32} \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} e^{\left(-1\right)} \sin\left(4 \, x e + 4 \, d\right) + \frac{1}{3} \, {\left(\sqrt{b^{2} + c^{2}} b^{3} - 3 \, \sqrt{b^{2} + c^{2}} b c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + \frac{7}{4} \, {\left(b^{4} - c^{4}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 7 \, {\left(\sqrt{b^{2} + c^{2}} b^{3} + \sqrt{b^{2} + c^{2}} b c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + \frac{35}{8} \, {\left(b^{4} + 2 \, b^{2} c^{2} + c^{4}\right)} x"," ",0,"-1/8*(b^3*c - b*c^3)*cos(4*x*e + 4*d)*e^(-1) - 1/3*(3*sqrt(b^2 + c^2)*b^2*c - sqrt(b^2 + c^2)*c^3)*cos(3*x*e + 3*d)*e^(-1) - 7/2*(b^3*c + b*c^3)*cos(2*x*e + 2*d)*e^(-1) - 7*(sqrt(b^2 + c^2)*b^2*c + sqrt(b^2 + c^2)*c^3)*cos(x*e + d)*e^(-1) + 1/32*(b^4 - 6*b^2*c^2 + c^4)*e^(-1)*sin(4*x*e + 4*d) + 1/3*(sqrt(b^2 + c^2)*b^3 - 3*sqrt(b^2 + c^2)*b*c^2)*e^(-1)*sin(3*x*e + 3*d) + 7/4*(b^4 - c^4)*e^(-1)*sin(2*x*e + 2*d) + 7*(sqrt(b^2 + c^2)*b^3 + sqrt(b^2 + c^2)*b*c^2)*e^(-1)*sin(x*e + d) + 35/8*(b^4 + 2*b^2*c^2 + c^4)*x","A",0
356,1,199,0,0.235091," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""giac"")","-\frac{3}{2} \, \sqrt{b^{2} + c^{2}} b c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - \frac{1}{12} \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{15}{4} \, {\left(b^{2} c + c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{1}{12} \, {\left(b^{3} - 3 \, b c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + \frac{3}{4} \, {\left(\sqrt{b^{2} + c^{2}} b^{2} - \sqrt{b^{2} + c^{2}} c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{15}{4} \, {\left(b^{3} + b c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}} x + \frac{3}{2} \, {\left(\sqrt{b^{2} + c^{2}} b^{2} + \sqrt{b^{2} + c^{2}} c^{2}\right)} x"," ",0,"-3/2*sqrt(b^2 + c^2)*b*c*cos(2*x*e + 2*d)*e^(-1) - 1/12*(3*b^2*c - c^3)*cos(3*x*e + 3*d)*e^(-1) - 15/4*(b^2*c + c^3)*cos(x*e + d)*e^(-1) + 1/12*(b^3 - 3*b*c^2)*e^(-1)*sin(3*x*e + 3*d) + 3/4*(sqrt(b^2 + c^2)*b^2 - sqrt(b^2 + c^2)*c^2)*e^(-1)*sin(2*x*e + 2*d) + 15/4*(b^3 + b*c^2)*e^(-1)*sin(x*e + d) + (b^2 + c^2)^(3/2)*x + 3/2*(sqrt(b^2 + c^2)*b^2 + sqrt(b^2 + c^2)*c^2)*x","A",0
357,1,92,0,0.167770," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""giac"")","-\frac{1}{2} \, b c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 2 \, \sqrt{b^{2} + c^{2}} c \cos\left(x e + d\right) e^{\left(-1\right)} + 2 \, \sqrt{b^{2} + c^{2}} b e^{\left(-1\right)} \sin\left(x e + d\right) + \frac{1}{4} \, {\left(b^{2} - c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{3}{2} \, {\left(b^{2} + c^{2}\right)} x"," ",0,"-1/2*b*c*cos(2*x*e + 2*d)*e^(-1) - 2*sqrt(b^2 + c^2)*c*cos(x*e + d)*e^(-1) + 2*sqrt(b^2 + c^2)*b*e^(-1)*sin(x*e + d) + 1/4*(b^2 - c^2)*e^(-1)*sin(2*x*e + 2*d) + 3/2*(b^2 + c^2)*x","A",0
358,1,35,0,0.123489," ","integrate(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2),x, algorithm=""giac"")","-c \cos\left(x e + d\right) e^{\left(-1\right)} + b e^{\left(-1\right)} \sin\left(x e + d\right) + \sqrt{b^{2} + c^{2}} x"," ",0,"-c*cos(x*e + d)*e^(-1) + b*e^(-1)*sin(x*e + d) + sqrt(b^2 + c^2)*x","A",0
359,1,43,0,0.160144," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2)),x, algorithm=""giac"")","-\frac{2 \, {\left(b + \sqrt{b^{2} + c^{2}}\right)} e^{\left(-1\right)}}{{\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b + \sqrt{b^{2} + c^{2}}\right)} c}"," ",0,"-2*(b + sqrt(b^2 + c^2))*e^(-1)/((c*tan(1/2*x*e + 1/2*d) + b + sqrt(b^2 + c^2))*c)","A",0
360,1,160,0,0.202835," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(8 \, b^{4} + 10 \, b^{2} c^{2} + 2 \, c^{4} + 3 \, {\left(2 \, b^{2} c^{2} + c^{4} + 2 \, \sqrt{b^{2} + c^{2}} b c^{2}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 3 \, {\left(4 \, b^{3} c + 3 \, b c^{3} + {\left(4 \, b^{2} c + c^{3}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, {\left(4 \, b^{3} + 3 \, b c^{2}\right)} \sqrt{b^{2} + c^{2}}\right)} e^{\left(-1\right)}}{3 \, {\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b + \sqrt{b^{2} + c^{2}}\right)}^{3} c^{3}}"," ",0,"-2/3*(8*b^4 + 10*b^2*c^2 + 2*c^4 + 3*(2*b^2*c^2 + c^4 + 2*sqrt(b^2 + c^2)*b*c^2)*tan(1/2*x*e + 1/2*d)^2 + 3*(4*b^3*c + 3*b*c^3 + (4*b^2*c + c^3)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d) + 2*(4*b^3 + 3*b*c^2)*sqrt(b^2 + c^2))*e^(-1)/((c*tan(1/2*x*e + 1/2*d) + b + sqrt(b^2 + c^2))^3*c^3)","A",0
361,1,346,0,0.609750," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(192 \, b^{7} + 352 \, b^{5} c^{2} + 200 \, b^{3} c^{4} + 35 \, b c^{6} + 15 \, {\left(4 \, b^{3} c^{4} + 3 \, b c^{6} + {\left(4 \, b^{2} c^{4} + c^{6}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 30 \, {\left(8 \, b^{4} c^{3} + 8 \, b^{2} c^{5} + c^{7} + 4 \, {\left(2 \, b^{3} c^{3} + b c^{5}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 20 \, {\left(24 \, b^{5} c^{2} + 32 \, b^{3} c^{4} + 9 \, b c^{6} + 2 \, {\left(12 \, b^{4} c^{2} + 10 \, b^{2} c^{4} + c^{6}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 10 \, {\left(48 \, b^{6} c + 76 \, b^{4} c^{3} + 31 \, b^{2} c^{5} + 2 \, c^{7} + {\left(48 \, b^{5} c + 52 \, b^{3} c^{3} + 11 \, b c^{5}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + {\left(192 \, b^{6} + 256 \, b^{4} c^{2} + 96 \, b^{2} c^{4} + 7 \, c^{6}\right)} \sqrt{b^{2} + c^{2}}\right)} e^{\left(-1\right)}}{15 \, {\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b + \sqrt{b^{2} + c^{2}}\right)}^{5} c^{5}}"," ",0,"-2/15*(192*b^7 + 352*b^5*c^2 + 200*b^3*c^4 + 35*b*c^6 + 15*(4*b^3*c^4 + 3*b*c^6 + (4*b^2*c^4 + c^6)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^4 + 30*(8*b^4*c^3 + 8*b^2*c^5 + c^7 + 4*(2*b^3*c^3 + b*c^5)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^3 + 20*(24*b^5*c^2 + 32*b^3*c^4 + 9*b*c^6 + 2*(12*b^4*c^2 + 10*b^2*c^4 + c^6)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^2 + 10*(48*b^6*c + 76*b^4*c^3 + 31*b^2*c^5 + 2*c^7 + (48*b^5*c + 52*b^3*c^3 + 11*b*c^5)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d) + (192*b^6 + 256*b^4*c^2 + 96*b^2*c^4 + 7*c^6)*sqrt(b^2 + c^2))*e^(-1)/((c*tan(1/2*x*e + 1/2*d) + b + sqrt(b^2 + c^2))^5*c^5)","A",0
362,1,599,0,2.524953," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(2560 \, b^{10} + 6528 \, b^{8} c^{2} + 5888 \, b^{6} c^{4} + 2248 \, b^{4} c^{6} + 340 \, b^{2} c^{8} + 12 \, c^{10} + 35 \, {\left(8 \, b^{4} c^{6} + 8 \, b^{2} c^{8} + c^{10} + 4 \, {\left(2 \, b^{3} c^{6} + b c^{8}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{6} + 105 \, {\left(16 \, b^{5} c^{5} + 20 \, b^{3} c^{7} + 5 \, b c^{9} + {\left(16 \, b^{4} c^{5} + 12 \, b^{2} c^{7} + c^{9}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 70 \, {\left(80 \, b^{6} c^{4} + 124 \, b^{4} c^{6} + 49 \, b^{2} c^{8} + 3 \, c^{10} + {\left(80 \, b^{5} c^{4} + 84 \, b^{3} c^{6} + 17 \, b c^{8}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 70 \, {\left(160 \, b^{7} c^{3} + 288 \, b^{5} c^{5} + 150 \, b^{3} c^{7} + 20 \, b c^{9} + {\left(160 \, b^{6} c^{3} + 208 \, b^{4} c^{5} + 66 \, b^{2} c^{7} + 3 \, c^{9}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 21 \, {\left(640 \, b^{8} c^{2} + 1312 \, b^{6} c^{4} + 856 \, b^{4} c^{6} + 186 \, b^{2} c^{8} + 7 \, c^{10} + 2 \, {\left(320 \, b^{7} c^{2} + 496 \, b^{5} c^{4} + 220 \, b^{3} c^{6} + 25 \, b c^{8}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 7 \, {\left(1280 \, b^{9} c + 2944 \, b^{7} c^{3} + 2288 \, b^{5} c^{5} + 676 \, b^{3} c^{7} + 57 \, b c^{9} + {\left(1280 \, b^{8} c + 2304 \, b^{6} c^{3} + 1296 \, b^{4} c^{5} + 236 \, b^{2} c^{7} + 7 \, c^{9}\right)} \sqrt{b^{2} + c^{2}}\right)} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 4 \, {\left(640 \, b^{9} + 1312 \, b^{7} c^{2} + 896 \, b^{5} c^{4} + 238 \, b^{3} c^{6} + 21 \, b c^{8}\right)} \sqrt{b^{2} + c^{2}}\right)} e^{\left(-1\right)}}{35 \, {\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b + \sqrt{b^{2} + c^{2}}\right)}^{7} c^{7}}"," ",0,"-2/35*(2560*b^10 + 6528*b^8*c^2 + 5888*b^6*c^4 + 2248*b^4*c^6 + 340*b^2*c^8 + 12*c^10 + 35*(8*b^4*c^6 + 8*b^2*c^8 + c^10 + 4*(2*b^3*c^6 + b*c^8)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^6 + 105*(16*b^5*c^5 + 20*b^3*c^7 + 5*b*c^9 + (16*b^4*c^5 + 12*b^2*c^7 + c^9)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^5 + 70*(80*b^6*c^4 + 124*b^4*c^6 + 49*b^2*c^8 + 3*c^10 + (80*b^5*c^4 + 84*b^3*c^6 + 17*b*c^8)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^4 + 70*(160*b^7*c^3 + 288*b^5*c^5 + 150*b^3*c^7 + 20*b*c^9 + (160*b^6*c^3 + 208*b^4*c^5 + 66*b^2*c^7 + 3*c^9)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^3 + 21*(640*b^8*c^2 + 1312*b^6*c^4 + 856*b^4*c^6 + 186*b^2*c^8 + 7*c^10 + 2*(320*b^7*c^2 + 496*b^5*c^4 + 220*b^3*c^6 + 25*b*c^8)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d)^2 + 7*(1280*b^9*c + 2944*b^7*c^3 + 2288*b^5*c^5 + 676*b^3*c^7 + 57*b*c^9 + (1280*b^8*c + 2304*b^6*c^3 + 1296*b^4*c^5 + 236*b^2*c^7 + 7*c^9)*sqrt(b^2 + c^2))*tan(1/2*x*e + 1/2*d) + 4*(640*b^9 + 1312*b^7*c^2 + 896*b^5*c^4 + 238*b^3*c^6 + 21*b*c^8)*sqrt(b^2 + c^2))*e^(-1)/((c*tan(1/2*x*e + 1/2*d) + b + sqrt(b^2 + c^2))^7*c^7)","B",0
363,1,151,0,0.183283," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""giac"")","-12 \, a^{2} c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(3 \, a^{2} c - c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - 6 \, {\left(5 \, a^{2} c + c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{2}{3} \, {\left(a^{3} - 3 \, a c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + 6 \, {\left(a^{3} - a c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 6 \, {\left(5 \, a^{3} + a c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + 4 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} x"," ",0,"-12*a^2*c*cos(2*x*e + 2*d)*e^(-1) - 2/3*(3*a^2*c - c^3)*cos(3*x*e + 3*d)*e^(-1) - 6*(5*a^2*c + c^3)*cos(x*e + d)*e^(-1) + 2/3*(a^3 - 3*a*c^2)*e^(-1)*sin(3*x*e + 3*d) + 6*(a^3 - a*c^2)*e^(-1)*sin(2*x*e + 2*d) + 6*(5*a^3 + a*c^2)*e^(-1)*sin(x*e + d) + 4*(5*a^3 + 3*a*c^2)*x","A",0
364,1,78,0,0.162760," ","integrate((2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""giac"")","-2 \, a c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 8 \, a c \cos\left(x e + d\right) e^{\left(-1\right)} + 8 \, a^{2} e^{\left(-1\right)} \sin\left(x e + d\right) + {\left(a^{2} - c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 2 \, {\left(3 \, a^{2} + c^{2}\right)} x"," ",0,"-2*a*c*cos(2*x*e + 2*d)*e^(-1) - 8*a*c*cos(x*e + d)*e^(-1) + 8*a^2*e^(-1)*sin(x*e + d) + (a^2 - c^2)*e^(-1)*sin(2*x*e + 2*d) + 2*(3*a^2 + c^2)*x","A",0
365,1,29,0,0.138825," ","integrate(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""giac"")","-2 \, c \cos\left(x e + d\right) e^{\left(-1\right)} + 2 \, a e^{\left(-1\right)} \sin\left(x e + d\right) + 2 \, a x"," ",0,"-2*c*cos(x*e + d)*e^(-1) + 2*a*e^(-1)*sin(x*e + d) + 2*a*x","A",0
366,1,23,0,0.125846," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""giac"")","\frac{e^{\left(-1\right)} \log\left({\left| c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a \right|}\right)}{2 \, c}"," ",0,"1/2*e^(-1)*log(abs(c*tan(1/2*x*e + 1/2*d) + a))/c","A",0
367,1,86,0,0.136357," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(\frac{2 \, a \log\left({\left| c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a \right|}\right)}{c^{3}} - \frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{c^{2}} - \frac{2 \, a c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a^{2} - c^{2}}{{\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)} c^{3}}\right)} e^{\left(-1\right)}"," ",0,"-1/8*(2*a*log(abs(c*tan(1/2*x*e + 1/2*d) + a))/c^3 - tan(1/2*x*e + 1/2*d)/c^2 - (2*a*c*tan(1/2*x*e + 1/2*d) + a^2 - c^2)/((c*tan(1/2*x*e + 1/2*d) + a)*c^3))*e^(-1)","A",0
368,1,171,0,0.166332," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""giac"")","\frac{1}{64} \, {\left(\frac{4 \, {\left(3 \, a^{2} + c^{2}\right)} \log\left({\left| c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a \right|}\right)}{c^{5}} + \frac{c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 6 \, a c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{c^{6}} - \frac{18 \, a^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 28 \, a^{3} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 4 \, a c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 11 \, a^{4} + c^{4}}{{\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}^{2} c^{5}}\right)} e^{\left(-1\right)}"," ",0,"1/64*(4*(3*a^2 + c^2)*log(abs(c*tan(1/2*x*e + 1/2*d) + a))/c^5 + (c^3*tan(1/2*x*e + 1/2*d)^2 - 6*a*c^2*tan(1/2*x*e + 1/2*d))/c^6 - (18*a^2*c^2*tan(1/2*x*e + 1/2*d)^2 + 6*c^4*tan(1/2*x*e + 1/2*d)^2 + 28*a^3*c*tan(1/2*x*e + 1/2*d) + 4*a*c^3*tan(1/2*x*e + 1/2*d) + 11*a^4 + c^4)/((c*tan(1/2*x*e + 1/2*d) + a)^2*c^5))*e^(-1)","A",0
369,1,304,0,0.211986," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{384} \, {\left(\frac{12 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} \log\left({\left| c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a \right|}\right)}{c^{7}} - \frac{110 \, a^{3} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 66 \, a c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 285 \, a^{4} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 144 \, a^{2} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 9 \, c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 249 \, a^{5} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 108 \, a^{3} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 9 \, a c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 73 \, a^{6} + 27 \, a^{4} c^{2} - 3 \, a^{2} c^{4} - c^{6}}{{\left(c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}^{3} c^{7}} - \frac{c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 6 \, a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 30 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 9 \, c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{c^{12}}\right)} e^{\left(-1\right)}"," ",0,"-1/384*(12*(5*a^3 + 3*a*c^2)*log(abs(c*tan(1/2*x*e + 1/2*d) + a))/c^7 - (110*a^3*c^3*tan(1/2*x*e + 1/2*d)^3 + 66*a*c^5*tan(1/2*x*e + 1/2*d)^3 + 285*a^4*c^2*tan(1/2*x*e + 1/2*d)^2 + 144*a^2*c^4*tan(1/2*x*e + 1/2*d)^2 - 9*c^6*tan(1/2*x*e + 1/2*d)^2 + 249*a^5*c*tan(1/2*x*e + 1/2*d) + 108*a^3*c^3*tan(1/2*x*e + 1/2*d) - 9*a*c^5*tan(1/2*x*e + 1/2*d) + 73*a^6 + 27*a^4*c^2 - 3*a^2*c^4 - c^6)/((c*tan(1/2*x*e + 1/2*d) + a)^3*c^7) - (c^8*tan(1/2*x*e + 1/2*d)^3 - 6*a*c^7*tan(1/2*x*e + 1/2*d)^2 + 30*a^2*c^6*tan(1/2*x*e + 1/2*d) + 9*c^8*tan(1/2*x*e + 1/2*d))/c^12)*e^(-1)","A",0
370,1,21,0,0.156974," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""giac"")","\frac{e^{\left(-1\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right)}{2 \, a}"," ",0,"1/2*e^(-1)*log(abs(tan(1/2*x*e + 1/2*d) + 1))/a","A",0
371,1,68,0,0.166444," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(\frac{2 \, \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right)}{a^{2}} - \frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{a^{2}} - \frac{2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{a^{2} {\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)}}\right)} e^{\left(-1\right)}"," ",0,"-1/8*(2*log(abs(tan(1/2*x*e + 1/2*d) + 1))/a^2 - tan(1/2*x*e + 1/2*d)/a^2 - 2*tan(1/2*x*e + 1/2*d)/(a^2*(tan(1/2*x*e + 1/2*d) + 1)))*e^(-1)","A",0
372,1,107,0,0.164545," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""giac"")","\frac{1}{64} \, {\left(\frac{16 \, \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right)}{a^{3}} - \frac{4 \, {\left(6 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3\right)}}{a^{3} {\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)}^{2}} + \frac{a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 6 \, a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{a^{6}}\right)} e^{\left(-1\right)}"," ",0,"1/64*(16*log(abs(tan(1/2*x*e + 1/2*d) + 1))/a^3 - 4*(6*tan(1/2*x*e + 1/2*d)^2 + 8*tan(1/2*x*e + 1/2*d) + 3)/(a^3*(tan(1/2*x*e + 1/2*d) + 1)^2) + (a^3*tan(1/2*x*e + 1/2*d)^2 - 6*a^3*tan(1/2*x*e + 1/2*d))/a^6)*e^(-1)","A",0
373,1,139,0,0.201094," ","integrate(1/(2*a+2*a*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{384} \, {\left(\frac{96 \, \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right)}{a^{4}} - \frac{4 \, {\left(44 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 105 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 87 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 24\right)}}{a^{4} {\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)}^{3}} - \frac{a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 6 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 39 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{a^{12}}\right)} e^{\left(-1\right)}"," ",0,"-1/384*(96*log(abs(tan(1/2*x*e + 1/2*d) + 1))/a^4 - 4*(44*tan(1/2*x*e + 1/2*d)^3 + 105*tan(1/2*x*e + 1/2*d)^2 + 87*tan(1/2*x*e + 1/2*d) + 24)/(a^4*(tan(1/2*x*e + 1/2*d) + 1)^3) - (a^8*tan(1/2*x*e + 1/2*d)^3 - 6*a^8*tan(1/2*x*e + 1/2*d)^2 + 39*a^8*tan(1/2*x*e + 1/2*d))/a^12)*e^(-1)","A",0
374,1,151,0,0.186562," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""giac"")","12 \, a^{2} c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(3 \, a^{2} c - c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - 6 \, {\left(5 \, a^{2} c + c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(a^{3} - 3 \, a c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + 6 \, {\left(a^{3} - a c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) - 6 \, {\left(5 \, a^{3} + a c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + 4 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} x"," ",0,"12*a^2*c*cos(2*x*e + 2*d)*e^(-1) - 2/3*(3*a^2*c - c^3)*cos(3*x*e + 3*d)*e^(-1) - 6*(5*a^2*c + c^3)*cos(x*e + d)*e^(-1) - 2/3*(a^3 - 3*a*c^2)*e^(-1)*sin(3*x*e + 3*d) + 6*(a^3 - a*c^2)*e^(-1)*sin(2*x*e + 2*d) - 6*(5*a^3 + a*c^2)*e^(-1)*sin(x*e + d) + 4*(5*a^3 + 3*a*c^2)*x","A",0
375,1,78,0,0.161149," ","integrate((2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""giac"")","2 \, a c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 8 \, a c \cos\left(x e + d\right) e^{\left(-1\right)} - 8 \, a^{2} e^{\left(-1\right)} \sin\left(x e + d\right) + {\left(a^{2} - c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 2 \, {\left(3 \, a^{2} + c^{2}\right)} x"," ",0,"2*a*c*cos(2*x*e + 2*d)*e^(-1) - 8*a*c*cos(x*e + d)*e^(-1) - 8*a^2*e^(-1)*sin(x*e + d) + (a^2 - c^2)*e^(-1)*sin(2*x*e + 2*d) + 2*(3*a^2 + c^2)*x","A",0
376,1,29,0,0.148558," ","integrate(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d),x, algorithm=""giac"")","-2 \, c \cos\left(x e + d\right) e^{\left(-1\right)} - 2 \, a e^{\left(-1\right)} \sin\left(x e + d\right) + 2 \, a x"," ",0,"-2*c*cos(x*e + d)*e^(-1) - 2*a*e^(-1)*sin(x*e + d) + 2*a*x","A",0
377,1,42,0,0.157663," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d)),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{\log\left({\left| a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c \right|}\right)}{c} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) \right|}\right)}{c}\right)} e^{\left(-1\right)}"," ",0,"-1/2*(log(abs(a*tan(1/2*x*e + 1/2*d) + c))/c - log(abs(tan(1/2*x*e + 1/2*d)))/c)*e^(-1)","A",0
378,1,115,0,0.167572," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(\frac{2 \, a \log\left({\left| a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c \right|}\right)}{c^{3}} - \frac{2 \, a \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) \right|}\right)}{c^{3}} - \frac{2 \, a^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a c}{{\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} a c^{2}}\right)} e^{\left(-1\right)}"," ",0,"1/8*(2*a*log(abs(a*tan(1/2*x*e + 1/2*d) + c))/c^3 - 2*a*log(abs(tan(1/2*x*e + 1/2*d)))/c^3 - (2*a^2*tan(1/2*x*e + 1/2*d) + c^2*tan(1/2*x*e + 1/2*d) + a*c)/((a*tan(1/2*x*e + 1/2*d)^2 + c*tan(1/2*x*e + 1/2*d))*a*c^2))*e^(-1)","A",0
379,1,239,0,0.205723," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^3,x, algorithm=""giac"")","\frac{1}{64} \, {\left(\frac{4 \, {\left(3 \, a^{2} + c^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) \right|}\right)}{c^{5}} - \frac{4 \, {\left(3 \, a^{3} + a c^{2}\right)} \log\left({\left| a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c \right|}\right)}{a c^{5}} + \frac{12 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 18 \, a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, a^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 4 \, a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - a^{2} c^{3}}{{\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} a^{2} c^{4}}\right)} e^{\left(-1\right)}"," ",0,"1/64*(4*(3*a^2 + c^2)*log(abs(tan(1/2*x*e + 1/2*d)))/c^5 - 4*(3*a^3 + a*c^2)*log(abs(a*tan(1/2*x*e + 1/2*d) + c))/(a*c^5) + (12*a^5*tan(1/2*x*e + 1/2*d)^3 + 4*a^3*c^2*tan(1/2*x*e + 1/2*d)^3 - 2*a*c^4*tan(1/2*x*e + 1/2*d)^3 + 18*a^4*c*tan(1/2*x*e + 1/2*d)^2 + 6*a^2*c^3*tan(1/2*x*e + 1/2*d)^2 - c^5*tan(1/2*x*e + 1/2*d)^2 + 4*a^3*c^2*tan(1/2*x*e + 1/2*d) - a^2*c^3)/((a*tan(1/2*x*e + 1/2*d)^2 + c*tan(1/2*x*e + 1/2*d))^2*a^2*c^4))*e^(-1)","A",0
380,1,363,0,0.247418," ","integrate(1/(2*a-2*a*cos(e*x+d)+2*c*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{384} \, {\left(\frac{12 \, {\left(5 \, a^{3} + 3 \, a c^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) \right|}\right)}{c^{7}} - \frac{12 \, {\left(5 \, a^{4} + 3 \, a^{2} c^{2}\right)} \log\left({\left| a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c \right|}\right)}{a c^{7}} + \frac{60 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 36 \, a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 3 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 150 \, a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 90 \, a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 3 \, a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 110 \, a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 66 \, a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 3 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 15 \, a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 9 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 3 \, a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a^{3} c^{5}}{{\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{3} a^{3} c^{6}}\right)} e^{\left(-1\right)}"," ",0,"-1/384*(12*(5*a^3 + 3*a*c^2)*log(abs(tan(1/2*x*e + 1/2*d)))/c^7 - 12*(5*a^4 + 3*a^2*c^2)*log(abs(a*tan(1/2*x*e + 1/2*d) + c))/(a*c^7) + (60*a^8*tan(1/2*x*e + 1/2*d)^5 + 36*a^6*c^2*tan(1/2*x*e + 1/2*d)^5 + 3*a^2*c^6*tan(1/2*x*e + 1/2*d)^5 + 150*a^7*c*tan(1/2*x*e + 1/2*d)^4 + 90*a^5*c^3*tan(1/2*x*e + 1/2*d)^4 + 3*a*c^7*tan(1/2*x*e + 1/2*d)^4 + 110*a^6*c^2*tan(1/2*x*e + 1/2*d)^3 + 66*a^4*c^4*tan(1/2*x*e + 1/2*d)^3 + 3*a^2*c^6*tan(1/2*x*e + 1/2*d)^3 + c^8*tan(1/2*x*e + 1/2*d)^3 + 15*a^5*c^3*tan(1/2*x*e + 1/2*d)^2 + 9*a^3*c^5*tan(1/2*x*e + 1/2*d)^2 - 3*a^4*c^4*tan(1/2*x*e + 1/2*d) + a^3*c^5)/((a*tan(1/2*x*e + 1/2*d)^2 + c*tan(1/2*x*e + 1/2*d))^3*a^3*c^6))*e^(-1)","A",0
381,1,151,0,0.202283," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""giac"")","-12 \, a^{2} b \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} + \frac{2}{3} \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - 6 \, {\left(5 \, a^{3} + a b^{2}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(3 \, a^{2} b - b^{3}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) - 6 \, {\left(a^{3} - a b^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 6 \, {\left(5 \, a^{2} b + b^{3}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + 4 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} x"," ",0,"-12*a^2*b*cos(2*x*e + 2*d)*e^(-1) + 2/3*(a^3 - 3*a*b^2)*cos(3*x*e + 3*d)*e^(-1) - 6*(5*a^3 + a*b^2)*cos(x*e + d)*e^(-1) - 2/3*(3*a^2*b - b^3)*e^(-1)*sin(3*x*e + 3*d) - 6*(a^3 - a*b^2)*e^(-1)*sin(2*x*e + 2*d) + 6*(5*a^2*b + b^3)*e^(-1)*sin(x*e + d) + 4*(5*a^3 + 3*a*b^2)*x","A",0
382,1,79,0,0.164953," ","integrate((2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""giac"")","-2 \, a b \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 8 \, a^{2} \cos\left(x e + d\right) e^{\left(-1\right)} + 8 \, a b e^{\left(-1\right)} \sin\left(x e + d\right) - {\left(a^{2} - b^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 2 \, {\left(3 \, a^{2} + b^{2}\right)} x"," ",0,"-2*a*b*cos(2*x*e + 2*d)*e^(-1) - 8*a^2*cos(x*e + d)*e^(-1) + 8*a*b*e^(-1)*sin(x*e + d) - (a^2 - b^2)*e^(-1)*sin(2*x*e + 2*d) + 2*(3*a^2 + b^2)*x","A",0
383,1,29,0,0.139067," ","integrate(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d),x, algorithm=""giac"")","-2 \, a \cos\left(x e + d\right) e^{\left(-1\right)} + 2 \, b e^{\left(-1\right)} \sin\left(x e + d\right) + 2 \, a x"," ",0,"-2*a*cos(x*e + d)*e^(-1) + 2*b*e^(-1)*sin(x*e + d) + 2*a*x","A",0
384,1,82,0,0.201876," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d)),x, algorithm=""giac"")","\frac{e^{\left(-1\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{2 \, {\left| b \right|}}"," ",0,"1/2*e^(-1)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a + 2*abs(b)))/abs(b)","B",0
385,1,196,0,0.218317," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{2 \, {\left(a^{2} \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) + b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a^{2}\right)}}{{\left(a b^{2} - b^{3}\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} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}} + \frac{a \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{2} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"-1/4*(2*(a^2*tan(1/2*x*e + 1/2*d) - a*b*tan(1/2*x*e + 1/2*d) + b^2*tan(1/2*x*e + 1/2*d) + a^2)/((a*b^2 - b^3)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + a + b)) + a*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a + 2*abs(b)))/(b^2*abs(b)))*e^(-1)","B",0
386,1,481,0,0.241246," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^3,x, algorithm=""giac"")","\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 9 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 10 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 9 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 18 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 9 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 9 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 2 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 5 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4}\right)}}{{\left(a^{2} b^{4} - 2 \, a b^{5} + 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} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{2}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{4} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"1/16*(2*(3*a^5*tan(1/2*x*e + 1/2*d)^3 - 9*a^4*b*tan(1/2*x*e + 1/2*d)^3 + 10*a^3*b^2*tan(1/2*x*e + 1/2*d)^3 - 6*a^2*b^3*tan(1/2*x*e + 1/2*d)^3 + a*b^4*tan(1/2*x*e + 1/2*d)^3 + b^5*tan(1/2*x*e + 1/2*d)^3 + 9*a^5*tan(1/2*x*e + 1/2*d)^2 - 18*a^4*b*tan(1/2*x*e + 1/2*d)^2 + 12*a^3*b^2*tan(1/2*x*e + 1/2*d)^2 - 6*a^2*b^3*tan(1/2*x*e + 1/2*d)^2 + a*b^4*tan(1/2*x*e + 1/2*d)^2 + 9*a^5*tan(1/2*x*e + 1/2*d) - 9*a^4*b*tan(1/2*x*e + 1/2*d) - 2*a^3*b^2*tan(1/2*x*e + 1/2*d) + 2*a^2*b^3*tan(1/2*x*e + 1/2*d) - 5*a*b^4*tan(1/2*x*e + 1/2*d) + b^5*tan(1/2*x*e + 1/2*d) + 3*a^5 - 4*a^3*b^2 - a*b^4)/((a^2*b^4 - 2*a*b^5 + b^6)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + a + b)^2) + (3*a^2 + b^2)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a + 2*abs(b)))/(b^4*abs(b)))*e^(-1)","B",0
387,1,1006,0,0.305936," ","integrate(1/(2*a+2*b*cos(e*x+d)+2*a*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{96} \, {\left(\frac{2 \, {\left(15 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 75 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 159 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 195 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 165 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 105 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 51 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 21 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 75 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 300 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 495 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 480 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 345 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 180 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 57 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 150 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 450 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 500 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 300 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 126 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 22 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 48 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 4 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 150 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 300 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 120 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 60 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 102 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 144 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 60 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 75 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 75 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 75 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 75 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 39 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 39 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 33 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 15 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 15 \, a^{8} - 31 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + 15 \, a^{2} b^{6}\right)}}{{\left(a^{3} b^{6} - 3 \, a^{2} b^{7} + 3 \, a b^{8} - b^{9}\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} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{3}} + \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{6} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"-1/96*(2*(15*a^8*tan(1/2*x*e + 1/2*d)^5 - 75*a^7*b*tan(1/2*x*e + 1/2*d)^5 + 159*a^6*b^2*tan(1/2*x*e + 1/2*d)^5 - 195*a^5*b^3*tan(1/2*x*e + 1/2*d)^5 + 165*a^4*b^4*tan(1/2*x*e + 1/2*d)^5 - 105*a^3*b^5*tan(1/2*x*e + 1/2*d)^5 + 51*a^2*b^6*tan(1/2*x*e + 1/2*d)^5 - 21*a*b^7*tan(1/2*x*e + 1/2*d)^5 + 6*b^8*tan(1/2*x*e + 1/2*d)^5 + 75*a^8*tan(1/2*x*e + 1/2*d)^4 - 300*a^7*b*tan(1/2*x*e + 1/2*d)^4 + 495*a^6*b^2*tan(1/2*x*e + 1/2*d)^4 - 480*a^5*b^3*tan(1/2*x*e + 1/2*d)^4 + 345*a^4*b^4*tan(1/2*x*e + 1/2*d)^4 - 180*a^3*b^5*tan(1/2*x*e + 1/2*d)^4 + 57*a^2*b^6*tan(1/2*x*e + 1/2*d)^4 - 12*a*b^7*tan(1/2*x*e + 1/2*d)^4 + 150*a^8*tan(1/2*x*e + 1/2*d)^3 - 450*a^7*b*tan(1/2*x*e + 1/2*d)^3 + 500*a^6*b^2*tan(1/2*x*e + 1/2*d)^3 - 300*a^5*b^3*tan(1/2*x*e + 1/2*d)^3 + 126*a^4*b^4*tan(1/2*x*e + 1/2*d)^3 + 22*a^3*b^5*tan(1/2*x*e + 1/2*d)^3 - 48*a^2*b^6*tan(1/2*x*e + 1/2*d)^3 + 12*a*b^7*tan(1/2*x*e + 1/2*d)^3 - 4*b^8*tan(1/2*x*e + 1/2*d)^3 + 150*a^8*tan(1/2*x*e + 1/2*d)^2 - 300*a^7*b*tan(1/2*x*e + 1/2*d)^2 + 120*a^6*b^2*tan(1/2*x*e + 1/2*d)^2 + 60*a^5*b^3*tan(1/2*x*e + 1/2*d)^2 - 102*a^4*b^4*tan(1/2*x*e + 1/2*d)^2 + 144*a^3*b^5*tan(1/2*x*e + 1/2*d)^2 - 60*a^2*b^6*tan(1/2*x*e + 1/2*d)^2 + 12*a*b^7*tan(1/2*x*e + 1/2*d)^2 + 75*a^8*tan(1/2*x*e + 1/2*d) - 75*a^7*b*tan(1/2*x*e + 1/2*d) - 75*a^6*b^2*tan(1/2*x*e + 1/2*d) + 75*a^5*b^3*tan(1/2*x*e + 1/2*d) - 39*a^4*b^4*tan(1/2*x*e + 1/2*d) + 39*a^3*b^5*tan(1/2*x*e + 1/2*d) + 33*a^2*b^6*tan(1/2*x*e + 1/2*d) - 15*a*b^7*tan(1/2*x*e + 1/2*d) + 6*b^8*tan(1/2*x*e + 1/2*d) + 15*a^8 - 31*a^6*b^2 + 9*a^4*b^4 + 15*a^2*b^6)/((a^3*b^6 - 3*a^2*b^7 + 3*a*b^8 - b^9)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + a + b)^3) + 3*(5*a^3 + 3*a*b^2)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) + 2*a + 2*abs(b)))/(b^6*abs(b)))*e^(-1)","B",0
388,1,151,0,0.181578," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""giac"")","12 \, a^{2} b \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} + 6 \, {\left(5 \, a^{3} + a b^{2}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} - \frac{2}{3} \, {\left(3 \, a^{2} b - b^{3}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) - 6 \, {\left(a^{3} - a b^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 6 \, {\left(5 \, a^{2} b + b^{3}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + 4 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} x"," ",0,"12*a^2*b*cos(2*x*e + 2*d)*e^(-1) - 2/3*(a^3 - 3*a*b^2)*cos(3*x*e + 3*d)*e^(-1) + 6*(5*a^3 + a*b^2)*cos(x*e + d)*e^(-1) - 2/3*(3*a^2*b - b^3)*e^(-1)*sin(3*x*e + 3*d) - 6*(a^3 - a*b^2)*e^(-1)*sin(2*x*e + 2*d) + 6*(5*a^2*b + b^3)*e^(-1)*sin(x*e + d) + 4*(5*a^3 + 3*a*b^2)*x","A",0
389,1,79,0,0.141685," ","integrate((2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""giac"")","2 \, a b \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} + 8 \, a^{2} \cos\left(x e + d\right) e^{\left(-1\right)} + 8 \, a b e^{\left(-1\right)} \sin\left(x e + d\right) - {\left(a^{2} - b^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + 2 \, {\left(3 \, a^{2} + b^{2}\right)} x"," ",0,"2*a*b*cos(2*x*e + 2*d)*e^(-1) + 8*a^2*cos(x*e + d)*e^(-1) + 8*a*b*e^(-1)*sin(x*e + d) - (a^2 - b^2)*e^(-1)*sin(2*x*e + 2*d) + 2*(3*a^2 + b^2)*x","A",0
390,1,29,0,0.143940," ","integrate(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d),x, algorithm=""giac"")","2 \, a \cos\left(x e + d\right) e^{\left(-1\right)} + 2 \, b e^{\left(-1\right)} \sin\left(x e + d\right) + 2 \, a x"," ",0,"2*a*cos(x*e + d)*e^(-1) + 2*b*e^(-1)*sin(x*e + d) + 2*a*x","A",0
391,1,82,0,0.210994," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d)),x, algorithm=""giac"")","\frac{e^{\left(-1\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{2 \, {\left| b \right|}}"," ",0,"1/2*e^(-1)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a + 2*abs(b)))/abs(b)","B",0
392,1,198,0,0.215927," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^2,x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{2 \, {\left(a^{2} \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) + b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - a^{2}\right)}}{{\left(a b^{2} - b^{3}\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} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}} + \frac{a \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{2} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"-1/4*(2*(a^2*tan(1/2*x*e + 1/2*d) - a*b*tan(1/2*x*e + 1/2*d) + b^2*tan(1/2*x*e + 1/2*d) - a^2)/((a*b^2 - b^3)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) + a + b)) + a*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a + 2*abs(b)))/(b^2*abs(b)))*e^(-1)","B",0
393,1,481,0,0.240676," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^3,x, algorithm=""giac"")","\frac{1}{16} \, {\left(\frac{2 \, {\left(3 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 9 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 10 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 9 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 18 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 9 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 9 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 2 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 5 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, a^{5} + 4 \, a^{3} b^{2} + a b^{4}\right)}}{{\left(a^{2} b^{4} - 2 \, a b^{5} + 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} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{2}} + \frac{{\left(3 \, a^{2} + b^{2}\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{4} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"1/16*(2*(3*a^5*tan(1/2*x*e + 1/2*d)^3 - 9*a^4*b*tan(1/2*x*e + 1/2*d)^3 + 10*a^3*b^2*tan(1/2*x*e + 1/2*d)^3 - 6*a^2*b^3*tan(1/2*x*e + 1/2*d)^3 + a*b^4*tan(1/2*x*e + 1/2*d)^3 + b^5*tan(1/2*x*e + 1/2*d)^3 - 9*a^5*tan(1/2*x*e + 1/2*d)^2 + 18*a^4*b*tan(1/2*x*e + 1/2*d)^2 - 12*a^3*b^2*tan(1/2*x*e + 1/2*d)^2 + 6*a^2*b^3*tan(1/2*x*e + 1/2*d)^2 - a*b^4*tan(1/2*x*e + 1/2*d)^2 + 9*a^5*tan(1/2*x*e + 1/2*d) - 9*a^4*b*tan(1/2*x*e + 1/2*d) - 2*a^3*b^2*tan(1/2*x*e + 1/2*d) + 2*a^2*b^3*tan(1/2*x*e + 1/2*d) - 5*a*b^4*tan(1/2*x*e + 1/2*d) + b^5*tan(1/2*x*e + 1/2*d) - 3*a^5 + 4*a^3*b^2 + a*b^4)/((a^2*b^4 - 2*a*b^5 + b^6)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) + a + b)^2) + (3*a^2 + b^2)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a + 2*abs(b)))/(b^4*abs(b)))*e^(-1)","B",0
394,1,1006,0,0.282498," ","integrate(1/(2*a+2*b*cos(e*x+d)-2*a*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{96} \, {\left(\frac{2 \, {\left(15 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 75 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 159 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 195 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 165 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 105 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 51 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 21 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 75 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 300 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 495 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 480 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 345 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 180 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 57 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 150 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 450 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 500 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 300 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 126 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 22 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 48 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 4 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 150 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 300 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 120 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 60 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 102 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 144 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 60 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 75 \, a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 75 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 75 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 75 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 39 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 39 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 33 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 15 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 15 \, a^{8} + 31 \, a^{6} b^{2} - 9 \, a^{4} b^{4} - 15 \, a^{2} b^{6}\right)}}{{\left(a^{3} b^{6} - 3 \, a^{2} b^{7} + 3 \, a b^{8} - b^{9}\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} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{3}} + \frac{3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \log\left(\frac{{\left| 2 \, 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 - 2 \, {\left| b \right|} \right|}}{{\left| 2 \, 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 + 2 \, {\left| b \right|} \right|}}\right)}{b^{6} {\left| b \right|}}\right)} e^{\left(-1\right)}"," ",0,"-1/96*(2*(15*a^8*tan(1/2*x*e + 1/2*d)^5 - 75*a^7*b*tan(1/2*x*e + 1/2*d)^5 + 159*a^6*b^2*tan(1/2*x*e + 1/2*d)^5 - 195*a^5*b^3*tan(1/2*x*e + 1/2*d)^5 + 165*a^4*b^4*tan(1/2*x*e + 1/2*d)^5 - 105*a^3*b^5*tan(1/2*x*e + 1/2*d)^5 + 51*a^2*b^6*tan(1/2*x*e + 1/2*d)^5 - 21*a*b^7*tan(1/2*x*e + 1/2*d)^5 + 6*b^8*tan(1/2*x*e + 1/2*d)^5 - 75*a^8*tan(1/2*x*e + 1/2*d)^4 + 300*a^7*b*tan(1/2*x*e + 1/2*d)^4 - 495*a^6*b^2*tan(1/2*x*e + 1/2*d)^4 + 480*a^5*b^3*tan(1/2*x*e + 1/2*d)^4 - 345*a^4*b^4*tan(1/2*x*e + 1/2*d)^4 + 180*a^3*b^5*tan(1/2*x*e + 1/2*d)^4 - 57*a^2*b^6*tan(1/2*x*e + 1/2*d)^4 + 12*a*b^7*tan(1/2*x*e + 1/2*d)^4 + 150*a^8*tan(1/2*x*e + 1/2*d)^3 - 450*a^7*b*tan(1/2*x*e + 1/2*d)^3 + 500*a^6*b^2*tan(1/2*x*e + 1/2*d)^3 - 300*a^5*b^3*tan(1/2*x*e + 1/2*d)^3 + 126*a^4*b^4*tan(1/2*x*e + 1/2*d)^3 + 22*a^3*b^5*tan(1/2*x*e + 1/2*d)^3 - 48*a^2*b^6*tan(1/2*x*e + 1/2*d)^3 + 12*a*b^7*tan(1/2*x*e + 1/2*d)^3 - 4*b^8*tan(1/2*x*e + 1/2*d)^3 - 150*a^8*tan(1/2*x*e + 1/2*d)^2 + 300*a^7*b*tan(1/2*x*e + 1/2*d)^2 - 120*a^6*b^2*tan(1/2*x*e + 1/2*d)^2 - 60*a^5*b^3*tan(1/2*x*e + 1/2*d)^2 + 102*a^4*b^4*tan(1/2*x*e + 1/2*d)^2 - 144*a^3*b^5*tan(1/2*x*e + 1/2*d)^2 + 60*a^2*b^6*tan(1/2*x*e + 1/2*d)^2 - 12*a*b^7*tan(1/2*x*e + 1/2*d)^2 + 75*a^8*tan(1/2*x*e + 1/2*d) - 75*a^7*b*tan(1/2*x*e + 1/2*d) - 75*a^6*b^2*tan(1/2*x*e + 1/2*d) + 75*a^5*b^3*tan(1/2*x*e + 1/2*d) - 39*a^4*b^4*tan(1/2*x*e + 1/2*d) + 39*a^3*b^5*tan(1/2*x*e + 1/2*d) + 33*a^2*b^6*tan(1/2*x*e + 1/2*d) - 15*a*b^7*tan(1/2*x*e + 1/2*d) + 6*b^8*tan(1/2*x*e + 1/2*d) - 15*a^8 + 31*a^6*b^2 - 9*a^4*b^4 - 15*a^2*b^6)/((a^3*b^6 - 3*a^2*b^7 + 3*a*b^8 - b^9)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) + a + b)^3) + 3*(5*a^3 + 3*a*b^2)*log(abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a - 2*abs(b))/abs(2*a*tan(1/2*x*e + 1/2*d) - 2*b*tan(1/2*x*e + 1/2*d) - 2*a + 2*abs(b)))/(b^6*abs(b)))*e^(-1)","B",0
395,1,286,0,0.301120," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{8} \, {\left(b^{3} c - b c^{3}\right)} \cos\left(4 \, x e + 4 \, d\right) e^{\left(-1\right)} - \frac{1}{3} \, {\left(3 \, a b^{2} c - a c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{1}{2} \, {\left(6 \, a^{2} b c + b^{3} c + b c^{3}\right)} \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - {\left(4 \, a^{3} c + 3 \, a b^{2} c + 3 \, a c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{1}{32} \, {\left(b^{4} - 6 \, b^{2} c^{2} + c^{4}\right)} e^{\left(-1\right)} \sin\left(4 \, x e + 4 \, d\right) + \frac{1}{3} \, {\left(a b^{3} - 3 \, a b c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + \frac{1}{4} \, {\left(6 \, a^{2} b^{2} + b^{4} - 6 \, a^{2} c^{2} - c^{4}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + {\left(4 \, a^{3} b + 3 \, a b^{3} + 3 \, a b c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + \frac{1}{8} \, {\left(8 \, a^{4} + 24 \, a^{2} b^{2} + 3 \, b^{4} + 24 \, a^{2} c^{2} + 6 \, b^{2} c^{2} + 3 \, c^{4}\right)} x"," ",0,"-1/8*(b^3*c - b*c^3)*cos(4*x*e + 4*d)*e^(-1) - 1/3*(3*a*b^2*c - a*c^3)*cos(3*x*e + 3*d)*e^(-1) - 1/2*(6*a^2*b*c + b^3*c + b*c^3)*cos(2*x*e + 2*d)*e^(-1) - (4*a^3*c + 3*a*b^2*c + 3*a*c^3)*cos(x*e + d)*e^(-1) + 1/32*(b^4 - 6*b^2*c^2 + c^4)*e^(-1)*sin(4*x*e + 4*d) + 1/3*(a*b^3 - 3*a*b*c^2)*e^(-1)*sin(3*x*e + 3*d) + 1/4*(6*a^2*b^2 + b^4 - 6*a^2*c^2 - c^4)*e^(-1)*sin(2*x*e + 2*d) + (4*a^3*b + 3*a*b^3 + 3*a*b*c^2)*e^(-1)*sin(x*e + d) + 1/8*(8*a^4 + 24*a^2*b^2 + 3*b^4 + 24*a^2*c^2 + 6*b^2*c^2 + 3*c^4)*x","A",0
396,1,167,0,0.198628," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""giac"")","-\frac{3}{2} \, a b c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - \frac{1}{12} \, {\left(3 \, b^{2} c - c^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{3}{4} \, {\left(4 \, a^{2} c + b^{2} c + c^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{1}{12} \, {\left(b^{3} - 3 \, b c^{2}\right)} e^{\left(-1\right)} \sin\left(3 \, x e + 3 \, d\right) + \frac{3}{4} \, {\left(a b^{2} - a c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{3}{4} \, {\left(4 \, a^{2} b + b^{3} + b c^{2}\right)} e^{\left(-1\right)} \sin\left(x e + d\right) + \frac{1}{2} \, {\left(2 \, a^{3} + 3 \, a b^{2} + 3 \, a c^{2}\right)} x"," ",0,"-3/2*a*b*c*cos(2*x*e + 2*d)*e^(-1) - 1/12*(3*b^2*c - c^3)*cos(3*x*e + 3*d)*e^(-1) - 3/4*(4*a^2*c + b^2*c + c^3)*cos(x*e + d)*e^(-1) + 1/12*(b^3 - 3*b*c^2)*e^(-1)*sin(3*x*e + 3*d) + 3/4*(a*b^2 - a*c^2)*e^(-1)*sin(2*x*e + 2*d) + 3/4*(4*a^2*b + b^3 + b*c^2)*e^(-1)*sin(x*e + d) + 1/2*(2*a^3 + 3*a*b^2 + 3*a*c^2)*x","A",0
397,1,81,0,0.149745," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^2,x, algorithm=""giac"")","-\frac{1}{2} \, b c \cos\left(2 \, x e + 2 \, d\right) e^{\left(-1\right)} - 2 \, a c \cos\left(x e + d\right) e^{\left(-1\right)} + 2 \, a b e^{\left(-1\right)} \sin\left(x e + d\right) + \frac{1}{4} \, {\left(b^{2} - c^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{1}{2} \, {\left(2 \, a^{2} + b^{2} + c^{2}\right)} x"," ",0,"-1/2*b*c*cos(2*x*e + 2*d)*e^(-1) - 2*a*c*cos(x*e + d)*e^(-1) + 2*a*b*e^(-1)*sin(x*e + d) + 1/4*(b^2 - c^2)*e^(-1)*sin(2*x*e + 2*d) + 1/2*(2*a^2 + b^2 + c^2)*x","A",0
398,1,27,0,0.146935," ","integrate(a+b*cos(e*x+d)+c*sin(e*x+d),x, algorithm=""giac"")","-c \cos\left(x e + d\right) e^{\left(-1\right)} + b e^{\left(-1\right)} \sin\left(x e + d\right) + a x"," ",0,"-c*cos(x*e + d)*e^(-1) + b*e^(-1)*sin(x*e + d) + a*x","A",0
399,1,91,0,0.164835," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d)),x, algorithm=""giac"")","-\frac{2 \, {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} e^{\left(-1\right)}}{\sqrt{a^{2} - b^{2} - c^{2}}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*e^(-1)/sqrt(a^2 - b^2 - c^2)","A",0
400,1,222,0,0.164027," ","integrate(1/(a+b*cos(e*x+d)+c*sin(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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} a}{{\left(a^{2} - b^{2} - c^{2}\right)}^{\frac{3}{2}}} + \frac{a b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - a c}{{\left(a^{3} - a^{2} b - a b^{2} + b^{3} - a c^{2} + b c^{2}\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} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\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) + c)/sqrt(a^2 - b^2 - c^2)))*a/(a^2 - b^2 - c^2)^(3/2) + (a*b*tan(1/2*x*e + 1/2*d) - b^2*tan(1/2*x*e + 1/2*d) - c^2*tan(1/2*x*e + 1/2*d) - a*c)/((a^3 - a^2*b - a*b^2 + b^3 - a*c^2 + b*c^2)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a + b)))*e^(-1)","A",0
401,1,892,0,0.315218," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^3,x, algorithm=""giac"")","-{\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} {\left(2 \, a^{2} + b^{2} + c^{2}\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} + 2 \, b^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} + \frac{4 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 11 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 9 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 5 \, a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 7 \, a^{2} b c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + a b^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, b^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, b c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 4 \, a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, a^{3} b c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 13 \, a^{2} b^{2} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, a b^{3} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - b^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 7 \, a^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, a b c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + b^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 4 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 5 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 5 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 11 \, a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3 \, a^{2} b c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 7 \, a b^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, b c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, a^{4} c + 3 \, a^{2} b^{2} c + b^{4} c + a^{2} c^{3} + b^{2} c^{3}}{{\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - 2 \, a^{4} c^{2} + 4 \, a^{3} b c^{2} - 4 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + a^{2} c^{4} - 2 \, a b c^{4} + b^{2} c^{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} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"-((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) + c)/sqrt(a^2 - b^2 - c^2)))*(2*a^2 + b^2 + c^2)/((a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4)*sqrt(a^2 - b^2 - c^2)) + (4*a^4*b*tan(1/2*x*e + 1/2*d)^3 - 11*a^3*b^2*tan(1/2*x*e + 1/2*d)^3 + 9*a^2*b^3*tan(1/2*x*e + 1/2*d)^3 - a*b^4*tan(1/2*x*e + 1/2*d)^3 - b^5*tan(1/2*x*e + 1/2*d)^3 - 5*a^3*c^2*tan(1/2*x*e + 1/2*d)^3 + 7*a^2*b*c^2*tan(1/2*x*e + 1/2*d)^3 + a*b^2*c^2*tan(1/2*x*e + 1/2*d)^3 - 3*b^3*c^2*tan(1/2*x*e + 1/2*d)^3 + 2*a*c^4*tan(1/2*x*e + 1/2*d)^3 - 2*b*c^4*tan(1/2*x*e + 1/2*d)^3 - 4*a^4*c*tan(1/2*x*e + 1/2*d)^2 + 12*a^3*b*c*tan(1/2*x*e + 1/2*d)^2 - 13*a^2*b^2*c*tan(1/2*x*e + 1/2*d)^2 + 6*a*b^3*c*tan(1/2*x*e + 1/2*d)^2 - b^4*c*tan(1/2*x*e + 1/2*d)^2 - 7*a^2*c^3*tan(1/2*x*e + 1/2*d)^2 + 6*a*b*c^3*tan(1/2*x*e + 1/2*d)^2 + b^2*c^3*tan(1/2*x*e + 1/2*d)^2 + 2*c^5*tan(1/2*x*e + 1/2*d)^2 + 4*a^4*b*tan(1/2*x*e + 1/2*d) - 5*a^3*b^2*tan(1/2*x*e + 1/2*d) - 3*a^2*b^3*tan(1/2*x*e + 1/2*d) + 5*a*b^4*tan(1/2*x*e + 1/2*d) - b^5*tan(1/2*x*e + 1/2*d) - 11*a^3*c^2*tan(1/2*x*e + 1/2*d) + 3*a^2*b*c^2*tan(1/2*x*e + 1/2*d) + 7*a*b^2*c^2*tan(1/2*x*e + 1/2*d) + b^3*c^2*tan(1/2*x*e + 1/2*d) + 2*a*c^4*tan(1/2*x*e + 1/2*d) + 2*b*c^4*tan(1/2*x*e + 1/2*d) - 4*a^4*c + 3*a^2*b^2*c + b^4*c + a^2*c^3 + b^2*c^3)/((a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^4*c^2 + 4*a^3*b*c^2 - 4*a*b^3*c^2 + 2*b^4*c^2 + a^2*c^4 - 2*a*b*c^4 + b^2*c^4)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a + b)^2))*e^(-1)","B",0
402,1,2671,0,0.575531," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^4,x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\frac{3 \, {\left(2 \, a^{3} + 3 \, a b^{2} + 3 \, a c^{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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6} - 3 \, a^{4} c^{2} + 6 \, a^{2} b^{2} c^{2} - 3 \, b^{4} c^{2} + 3 \, a^{2} c^{4} - 3 \, b^{2} c^{4} - c^{6}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} + \frac{18 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 81 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 141 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 120 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 60 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 33 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 21 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 27 \, a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 81 \, a^{5} b c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 72 \, a^{4} b^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 18 \, a^{3} b^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 27 \, a^{2} b^{4} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 45 \, a b^{5} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, b^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 18 \, a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 36 \, a^{3} b c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 36 \, a b^{3} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, b^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 12 \, a b c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, b^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 108 \, a^{6} b c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 261 \, a^{5} b^{2} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 336 \, a^{4} b^{3} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 264 \, a^{3} b^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 144 \, a^{2} b^{5} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 57 \, a b^{6} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, b^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 81 \, a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 216 \, a^{4} b c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 198 \, a^{3} b^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 108 \, a^{2} b^{3} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 81 \, a b^{4} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 36 \, b^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 36 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 36 \, a^{2} b c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 36 \, a b^{2} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 36 \, b^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 12 \, a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, b c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 36 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 108 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 76 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 60 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 100 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 44 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 12 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 108 \, a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 240 \, a^{5} b c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 162 \, a^{4} b^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 122 \, a^{3} b^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 174 \, a^{2} b^{4} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 78 \, a b^{5} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, b^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 42 \, a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 162 \, a^{3} b c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 210 \, a^{2} b^{2} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 102 \, a b^{3} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 12 \, b^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 8 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 12 \, a b c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 20 \, b^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 8 \, c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 36 \, a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 108 \, a^{6} b c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 108 \, a^{5} b^{2} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, a^{4} b^{3} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 84 \, a^{3} b^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 108 \, a^{2} b^{5} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 60 \, a b^{6} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, b^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 120 \, a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 132 \, a^{4} b c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 42 \, a^{3} b^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 36 \, a^{2} b^{3} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 18 \, a b^{4} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 36 \, b^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 18 \, a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 72 \, a^{2} b c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 54 \, a b^{2} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 36 \, b^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, b c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 18 \, a^{7} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 27 \, a^{6} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 21 \, a^{5} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 48 \, a^{4} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 12 \, a^{3} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 15 \, a^{2} b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 15 \, a b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, b^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 81 \, a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 27 \, a^{5} b c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 90 \, a^{4} b^{2} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 9 \, a^{2} b^{4} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 27 \, a b^{5} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, b^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 12 \, a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 42 \, a^{3} b c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 18 \, a^{2} b^{2} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 54 \, a b^{3} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, b^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 12 \, a b c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, b^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, a^{7} c + 21 \, a^{5} b^{2} c + 12 \, a^{3} b^{4} c - 15 \, a b^{6} c + 5 \, a^{5} c^{3} + 16 \, a^{3} b^{2} c^{3} - 21 \, a b^{4} c^{3} - 2 \, a^{3} c^{5} - 6 \, a b^{2} c^{5}}{{\left(a^{9} - 3 \, a^{8} b + 8 \, a^{6} b^{3} - 6 \, a^{5} b^{4} - 6 \, a^{4} b^{5} + 8 \, a^{3} b^{6} - 3 \, a b^{8} + b^{9} - 3 \, a^{7} c^{2} + 9 \, a^{6} b c^{2} - 3 \, a^{5} b^{2} c^{2} - 15 \, a^{4} b^{3} c^{2} + 15 \, a^{3} b^{4} c^{2} + 3 \, a^{2} b^{5} c^{2} - 9 \, a b^{6} c^{2} + 3 \, b^{7} c^{2} + 3 \, a^{5} c^{4} - 9 \, a^{4} b c^{4} + 6 \, a^{3} b^{2} c^{4} + 6 \, a^{2} b^{3} c^{4} - 9 \, a b^{4} c^{4} + 3 \, b^{5} c^{4} - a^{3} c^{6} + 3 \, a^{2} b c^{6} - 3 \, a b^{2} c^{6} + b^{3} c^{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} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a + b\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"-1/3*(3*(2*a^3 + 3*a*b^2 + 3*a*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6 - 3*a^4*c^2 + 6*a^2*b^2*c^2 - 3*b^4*c^2 + 3*a^2*c^4 - 3*b^2*c^4 - c^6)*sqrt(a^2 - b^2 - c^2)) + (18*a^7*b*tan(1/2*x*e + 1/2*d)^5 - 81*a^6*b^2*tan(1/2*x*e + 1/2*d)^5 + 141*a^5*b^3*tan(1/2*x*e + 1/2*d)^5 - 120*a^4*b^4*tan(1/2*x*e + 1/2*d)^5 + 60*a^3*b^5*tan(1/2*x*e + 1/2*d)^5 - 33*a^2*b^6*tan(1/2*x*e + 1/2*d)^5 + 21*a*b^7*tan(1/2*x*e + 1/2*d)^5 - 6*b^8*tan(1/2*x*e + 1/2*d)^5 - 27*a^6*c^2*tan(1/2*x*e + 1/2*d)^5 + 81*a^5*b*c^2*tan(1/2*x*e + 1/2*d)^5 - 72*a^4*b^2*c^2*tan(1/2*x*e + 1/2*d)^5 + 18*a^3*b^3*c^2*tan(1/2*x*e + 1/2*d)^5 - 27*a^2*b^4*c^2*tan(1/2*x*e + 1/2*d)^5 + 45*a*b^5*c^2*tan(1/2*x*e + 1/2*d)^5 - 18*b^6*c^2*tan(1/2*x*e + 1/2*d)^5 + 18*a^4*c^4*tan(1/2*x*e + 1/2*d)^5 - 36*a^3*b*c^4*tan(1/2*x*e + 1/2*d)^5 + 36*a*b^3*c^4*tan(1/2*x*e + 1/2*d)^5 - 18*b^4*c^4*tan(1/2*x*e + 1/2*d)^5 - 6*a^2*c^6*tan(1/2*x*e + 1/2*d)^5 + 12*a*b*c^6*tan(1/2*x*e + 1/2*d)^5 - 6*b^2*c^6*tan(1/2*x*e + 1/2*d)^5 - 18*a^7*c*tan(1/2*x*e + 1/2*d)^4 + 108*a^6*b*c*tan(1/2*x*e + 1/2*d)^4 - 261*a^5*b^2*c*tan(1/2*x*e + 1/2*d)^4 + 336*a^4*b^3*c*tan(1/2*x*e + 1/2*d)^4 - 264*a^3*b^4*c*tan(1/2*x*e + 1/2*d)^4 + 144*a^2*b^5*c*tan(1/2*x*e + 1/2*d)^4 - 57*a*b^6*c*tan(1/2*x*e + 1/2*d)^4 + 12*b^7*c*tan(1/2*x*e + 1/2*d)^4 - 81*a^5*c^3*tan(1/2*x*e + 1/2*d)^4 + 216*a^4*b*c^3*tan(1/2*x*e + 1/2*d)^4 - 198*a^3*b^2*c^3*tan(1/2*x*e + 1/2*d)^4 + 108*a^2*b^3*c^3*tan(1/2*x*e + 1/2*d)^4 - 81*a*b^4*c^3*tan(1/2*x*e + 1/2*d)^4 + 36*b^5*c^3*tan(1/2*x*e + 1/2*d)^4 + 36*a^3*c^5*tan(1/2*x*e + 1/2*d)^4 - 36*a^2*b*c^5*tan(1/2*x*e + 1/2*d)^4 - 36*a*b^2*c^5*tan(1/2*x*e + 1/2*d)^4 + 36*b^3*c^5*tan(1/2*x*e + 1/2*d)^4 - 12*a*c^7*tan(1/2*x*e + 1/2*d)^4 + 12*b*c^7*tan(1/2*x*e + 1/2*d)^4 + 36*a^7*b*tan(1/2*x*e + 1/2*d)^3 - 108*a^6*b^2*tan(1/2*x*e + 1/2*d)^3 + 76*a^5*b^3*tan(1/2*x*e + 1/2*d)^3 + 60*a^4*b^4*tan(1/2*x*e + 1/2*d)^3 - 100*a^3*b^5*tan(1/2*x*e + 1/2*d)^3 + 44*a^2*b^6*tan(1/2*x*e + 1/2*d)^3 - 12*a*b^7*tan(1/2*x*e + 1/2*d)^3 + 4*b^8*tan(1/2*x*e + 1/2*d)^3 - 108*a^6*c^2*tan(1/2*x*e + 1/2*d)^3 + 240*a^5*b*c^2*tan(1/2*x*e + 1/2*d)^3 - 162*a^4*b^2*c^2*tan(1/2*x*e + 1/2*d)^3 + 122*a^3*b^3*c^2*tan(1/2*x*e + 1/2*d)^3 - 174*a^2*b^4*c^2*tan(1/2*x*e + 1/2*d)^3 + 78*a*b^5*c^2*tan(1/2*x*e + 1/2*d)^3 + 4*b^6*c^2*tan(1/2*x*e + 1/2*d)^3 - 42*a^4*c^4*tan(1/2*x*e + 1/2*d)^3 + 162*a^3*b*c^4*tan(1/2*x*e + 1/2*d)^3 - 210*a^2*b^2*c^4*tan(1/2*x*e + 1/2*d)^3 + 102*a*b^3*c^4*tan(1/2*x*e + 1/2*d)^3 - 12*b^4*c^4*tan(1/2*x*e + 1/2*d)^3 + 8*a^2*c^6*tan(1/2*x*e + 1/2*d)^3 + 12*a*b*c^6*tan(1/2*x*e + 1/2*d)^3 - 20*b^2*c^6*tan(1/2*x*e + 1/2*d)^3 - 8*c^8*tan(1/2*x*e + 1/2*d)^3 - 36*a^7*c*tan(1/2*x*e + 1/2*d)^2 + 108*a^6*b*c*tan(1/2*x*e + 1/2*d)^2 - 108*a^5*b^2*c*tan(1/2*x*e + 1/2*d)^2 + 12*a^4*b^3*c*tan(1/2*x*e + 1/2*d)^2 + 84*a^3*b^4*c*tan(1/2*x*e + 1/2*d)^2 - 108*a^2*b^5*c*tan(1/2*x*e + 1/2*d)^2 + 60*a*b^6*c*tan(1/2*x*e + 1/2*d)^2 - 12*b^7*c*tan(1/2*x*e + 1/2*d)^2 - 120*a^5*c^3*tan(1/2*x*e + 1/2*d)^2 + 132*a^4*b*c^3*tan(1/2*x*e + 1/2*d)^2 + 42*a^3*b^2*c^3*tan(1/2*x*e + 1/2*d)^2 - 36*a^2*b^3*c^3*tan(1/2*x*e + 1/2*d)^2 + 18*a*b^4*c^3*tan(1/2*x*e + 1/2*d)^2 - 36*b^5*c^3*tan(1/2*x*e + 1/2*d)^2 + 18*a^3*c^5*tan(1/2*x*e + 1/2*d)^2 + 72*a^2*b*c^5*tan(1/2*x*e + 1/2*d)^2 - 54*a*b^2*c^5*tan(1/2*x*e + 1/2*d)^2 - 36*b^3*c^5*tan(1/2*x*e + 1/2*d)^2 - 12*a*c^7*tan(1/2*x*e + 1/2*d)^2 - 12*b*c^7*tan(1/2*x*e + 1/2*d)^2 + 18*a^7*b*tan(1/2*x*e + 1/2*d) - 27*a^6*b^2*tan(1/2*x*e + 1/2*d) - 21*a^5*b^3*tan(1/2*x*e + 1/2*d) + 48*a^4*b^4*tan(1/2*x*e + 1/2*d) - 12*a^3*b^5*tan(1/2*x*e + 1/2*d) - 15*a^2*b^6*tan(1/2*x*e + 1/2*d) + 15*a*b^7*tan(1/2*x*e + 1/2*d) - 6*b^8*tan(1/2*x*e + 1/2*d) - 81*a^6*c^2*tan(1/2*x*e + 1/2*d) + 27*a^5*b*c^2*tan(1/2*x*e + 1/2*d) + 90*a^4*b^2*c^2*tan(1/2*x*e + 1/2*d) + 9*a^2*b^4*c^2*tan(1/2*x*e + 1/2*d) - 27*a*b^5*c^2*tan(1/2*x*e + 1/2*d) - 18*b^6*c^2*tan(1/2*x*e + 1/2*d) + 12*a^4*c^4*tan(1/2*x*e + 1/2*d) + 42*a^3*b*c^4*tan(1/2*x*e + 1/2*d) + 18*a^2*b^2*c^4*tan(1/2*x*e + 1/2*d) - 54*a*b^3*c^4*tan(1/2*x*e + 1/2*d) - 18*b^4*c^4*tan(1/2*x*e + 1/2*d) - 6*a^2*c^6*tan(1/2*x*e + 1/2*d) - 12*a*b*c^6*tan(1/2*x*e + 1/2*d) - 6*b^2*c^6*tan(1/2*x*e + 1/2*d) - 18*a^7*c + 21*a^5*b^2*c + 12*a^3*b^4*c - 15*a*b^6*c + 5*a^5*c^3 + 16*a^3*b^2*c^3 - 21*a*b^4*c^3 - 2*a^3*c^5 - 6*a*b^2*c^5)/((a^9 - 3*a^8*b + 8*a^6*b^3 - 6*a^5*b^4 - 6*a^4*b^5 + 8*a^3*b^6 - 3*a*b^8 + b^9 - 3*a^7*c^2 + 9*a^6*b*c^2 - 3*a^5*b^2*c^2 - 15*a^4*b^3*c^2 + 15*a^3*b^4*c^2 + 3*a^2*b^5*c^2 - 9*a*b^6*c^2 + 3*b^7*c^2 + 3*a^5*c^4 - 9*a^4*b*c^4 + 6*a^3*b^2*c^4 + 6*a^2*b^3*c^4 - 9*a*b^4*c^4 + 3*b^5*c^4 - a^3*c^6 + 3*a^2*b*c^6 - 3*a*b^2*c^6 + b^3*c^6)*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a + b)^3))*e^(-1)","B",0
403,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int {\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(5/2), x)","F",0
404,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int {\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(3/2), x)","F",0
405,0,0,0,0.000000," ","integrate((2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}\,{d x}"," ",0,"integrate(sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
406,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2}}\,{d x}"," ",0,"integrate(1/sqrt(3*cos(e*x + d) + 5*sin(e*x + d) + 2), x)","F",0
407,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-3/2), x)","F",0
408,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-5/2), x)","F",0
409,0,0,0,0.000000," ","integrate(1/(2+3*cos(e*x+d)+5*sin(e*x+d))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, \cos\left(e x + d\right) + 5 \, \sin\left(e x + d\right) + 2\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((3*cos(e*x + d) + 5*sin(e*x + d) + 2)^(-7/2), x)","F",0
410,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(5/2), x)","F",0
411,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int {\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(3/2), x)","F",0
412,0,0,0,0.000000," ","integrate((a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
413,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(e*x + d) + c*sin(e*x + d) + a), x)","F",0
414,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-3/2), x)","F",0
415,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-5/2), x)","F",0
416,0,0,0,0.000000," ","integrate(1/(a+b*cos(e*x+d)+c*sin(e*x+d))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(e x + d\right) + c \sin\left(e x + d\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*cos(e*x + d) + c*sin(e*x + d) + a)^(-7/2), x)","F",0
417,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(5/2), x)","F",0
418,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) + 5)^(3/2), x)","F",0
419,0,0,0,0.000000," ","integrate((5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}\,{d x}"," ",0,"integrate(sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) + 5}}\,{d x}"," ",0,"integrate(1/sqrt(4*cos(e*x + d) + 3*sin(e*x + d) + 5), x)","F",0
421,1,284,0,0.743685," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\frac{1}{100} \, {\left(\frac{\sqrt{10} \log\left(\frac{{\left| -2 \, \sqrt{10} + 2 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \right|}}{{\left| 2 \, \sqrt{10} + 2 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \right|}}\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3\right)} - \frac{20 \, {\left(19 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{3} - 51 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 17 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 17 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3\right)}}{{\left({\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 6 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 6 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1\right)}^{2} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3\right)}\right)} e^{\left(-1\right)}"," ",0,"1/100*(sqrt(10)*log(abs(-2*sqrt(10) + 2*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 2*tan(1/2*x*e + 1/2*d) - 6)/abs(2*sqrt(10) + 2*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 2*tan(1/2*x*e + 1/2*d) - 6))/sgn(tan(1/2*x*e + 1/2*d) + 3) - 20*(19*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^3 - 51*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 - 17*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 17*tan(1/2*x*e + 1/2*d) - 3)/(((sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 - 6*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 6*tan(1/2*x*e + 1/2*d) - 1)^2*sgn(tan(1/2*x*e + 1/2*d) + 3)))*e^(-1)","B",0
422,1,417,0,0.974133," ","integrate(1/(5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\frac{1}{4000} \, {\left(\frac{3 \, \sqrt{10} \log\left(\frac{{\left| -2 \, \sqrt{10} + 2 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \right|}}{{\left| 2 \, \sqrt{10} + 2 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \right|}}\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3\right)} - \frac{20 \, {\left(797 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{7} - 7137 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{6} + 27543 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{5} - 30015 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{4} - 27105 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{3} - 7491 \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 859 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 859 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 69\right)}}{{\left({\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 6 \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 6 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1\right)}^{4} \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3\right)}\right)} e^{\left(-1\right)}"," ",0,"1/4000*(3*sqrt(10)*log(abs(-2*sqrt(10) + 2*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 2*tan(1/2*x*e + 1/2*d) - 6)/abs(2*sqrt(10) + 2*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 2*tan(1/2*x*e + 1/2*d) - 6))/sgn(tan(1/2*x*e + 1/2*d) + 3) - 20*(797*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^7 - 7137*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^6 + 27543*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^5 - 30015*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^4 - 27105*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^3 - 7491*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 - 859*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 859*tan(1/2*x*e + 1/2*d) - 69)/(((sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 - 6*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 6*tan(1/2*x*e + 1/2*d) - 1)^4*sgn(tan(1/2*x*e + 1/2*d) + 3)))*e^(-1)","B",0
423,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(7/2),x, algorithm=""giac"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(7/2), x)","F",0
424,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""giac"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(5/2), x)","F",0
425,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""giac"")","\int {\left(4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((4*cos(e*x + d) + 3*sin(e*x + d) - 5)^(3/2), x)","F",0
426,0,0,0,0.000000," ","integrate((-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}\,{d x}"," ",0,"integrate(sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5), x)","F",0
427,0,0,0,0.000000," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, \cos\left(e x + d\right) + 3 \, \sin\left(e x + d\right) - 5}}\,{d x}"," ",0,"integrate(1/sqrt(4*cos(e*x + d) + 3*sin(e*x + d) - 5), x)","F",0
428,1,249,0,0.529049," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(3/2),x, algorithm=""giac"")","-\frac{1}{450} \, {\left(\frac{9 \, \sqrt{10} \arctan\left(\frac{1}{10} \, \sqrt{10} {\left(-3 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 3 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - i\right)}\right)}{\mathrm{sgn}\left(-3 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)} + \frac{10 \, {\left(33 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{3} - 7 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 21 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 21 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 9 i\right)}}{{\left(-3 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 2 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} + 2 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3 i\right)}^{2} \mathrm{sgn}\left(-3 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)}\right)} e^{\left(-1\right)}"," ",0,"-1/450*(9*sqrt(10)*arctan(1/10*sqrt(10)*(-3*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 3*I*tan(1/2*x*e + 1/2*d) - I))/sgn(-3*tan(1/2*x*e + 1/2*d) + 1) + 10*(33*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^3 - 7*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 + 21*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 21*I*tan(1/2*x*e + 1/2*d) + 9*I)/((-3*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 - 2*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) + 2*I*tan(1/2*x*e + 1/2*d) + 3*I)^2*sgn(-3*tan(1/2*x*e + 1/2*d) + 1)))*e^(-1)","C",0
429,1,381,0,0.804632," ","integrate(1/(-5+4*cos(e*x+d)+3*sin(e*x+d))^(5/2),x, algorithm=""giac"")","-\frac{1}{162000} \, {\left(\frac{243 \, \sqrt{10} \arctan\left(\frac{1}{10} \, \sqrt{10} {\left(3 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 3 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + i\right)}\right)}{\mathrm{sgn}\left(-3 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)} + \frac{10 \, {\left(15039 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{7} + 6291 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{6} - 579 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{5} + 1645 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{4} + 25365 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{3} - 11367 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 4887 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 4887 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3807 i\right)}}{{\left(3 i \, {\left(\sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 2 i \, \sqrt{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1} - 2 i \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 i\right)}^{4} \mathrm{sgn}\left(-3 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1\right)}\right)} e^{\left(-1\right)}"," ",0,"-1/162000*(243*sqrt(10)*arctan(1/10*sqrt(10)*(3*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 3*I*tan(1/2*x*e + 1/2*d) + I))/sgn(-3*tan(1/2*x*e + 1/2*d) + 1) + 10*(15039*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^7 + 6291*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^6 - 579*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^5 + 1645*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^4 + 25365*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^3 - 11367*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 + 4887*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 4887*I*tan(1/2*x*e + 1/2*d) + 3807*I)/((3*I*(sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - tan(1/2*x*e + 1/2*d))^2 + 2*I*sqrt(tan(1/2*x*e + 1/2*d)^2 + 1) - 2*I*tan(1/2*x*e + 1/2*d) - 3*I)^4*sgn(-3*tan(1/2*x*e + 1/2*d) + 1)))*e^(-1)","C",0
430,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(7/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0Evaluation time: 1.02sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
431,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0Evaluation time: 0.43sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
432,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
433,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
434,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
435,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
436,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)+(b^2+c^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0Evaluation time: 0.84sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
437,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0Evaluation time: 0.44sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
438,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
439,-2,0,0,0.000000," ","integrate((b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
440,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(1/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
441,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(3/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
442,-2,0,0,0.000000," ","integrate(1/(b*cos(e*x+d)+c*sin(e*x+d)-(b^2+c^2)^(1/2))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Simplification assuming b near 0Evaluation time: 0.87sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Value","F(-2)",0
443,1,160,0,0.162868," ","integrate(sin(x)/(a+b*cos(x)+c*sin(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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} a c}{\sqrt{a^{2} - b^{2} - c^{2}} {\left(b^{2} + c^{2}\right)}} + \frac{c x}{b^{2} + c^{2}} - \frac{b \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - a - b\right)}{b^{2} + c^{2}} + \frac{b \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*a*c/(sqrt(a^2 - b^2 - c^2)*(b^2 + c^2)) + c*x/(b^2 + c^2) - b*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - a - b)/(b^2 + c^2) + b*log(tan(1/2*x)^2 + 1)/(b^2 + c^2)","A",0
444,1,25,0,0.136045," ","integrate(sin(x)/(1+cos(x)+sin(x)),x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{2} \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) - \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)"," ",0,"1/2*x + 1/2*log(tan(1/2*x)^2 + 1) - log(abs(tan(1/2*x) + 1))","A",0
445,1,158,0,0.145273," ","integrate(1/(a+c*sec(x)+b*tan(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 \, c\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - b}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)} a c}{{\left(a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}} + \frac{a x}{a^{2} + b^{2}} + \frac{b \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a + c\right)}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{a^{2} + b^{2}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*c) + arctan(-(a*tan(1/2*x) - c*tan(1/2*x) - b)/sqrt(-a^2 - b^2 + c^2)))*a*c/((a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)) + a*x/(a^2 + b^2) + b*log(-a*tan(1/2*x)^2 + c*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a + c)/(a^2 + b^2) - b*log(tan(1/2*x)^2 + 1)/(a^2 + b^2)","A",0
446,1,73,0,0.174071," ","integrate(sec(x)/(a+c*sec(x)+b*tan(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 \, c\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - b}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)}}{\sqrt{-a^{2} - b^{2} + c^{2}}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(2*a - 2*c) + arctan((a*tan(1/2*x) - c*tan(1/2*x) - b)/sqrt(-a^2 - b^2 + c^2)))/sqrt(-a^2 - b^2 + c^2)","A",0
447,1,161,0,0.173871," ","integrate(sec(x)^2/(a+c*sec(x)+b*tan(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 \, c\right) + \arctan\left(-\frac{a \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - b}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)} a c}{\sqrt{-a^{2} - b^{2} + c^{2}} {\left(b^{2} - c^{2}\right)}} + \frac{b \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, x\right) + a + c\right)}{b^{2} - c^{2}} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right)}{b - c} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)}{b + c}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*c) + arctan(-(a*tan(1/2*x) - c*tan(1/2*x) - b)/sqrt(-a^2 - b^2 + c^2)))*a*c/(sqrt(-a^2 - b^2 + c^2)*(b^2 - c^2)) + b*log(-a*tan(1/2*x)^2 + c*tan(1/2*x)^2 + 2*b*tan(1/2*x) + a + c)/(b^2 - c^2) - log(abs(tan(1/2*x) + 1))/(b - c) - log(abs(tan(1/2*x) - 1))/(b + c)","A",0
448,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2)/sec(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\sec\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)/sec(e*x + d)^(3/2), x)","F",0
449,0,0,0,0.000000," ","integrate((a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2)/sec(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}{\sqrt{\sec\left(e x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)/sqrt(sec(e*x + d)), x)","F",0
450,0,0,0,0.000000," ","integrate(sec(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\sec\left(e x + d\right)}}{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a}}\,{d x}"," ",0,"integrate(sqrt(sec(e*x + d))/sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a), x)","F",0
451,0,0,0,0.000000," ","integrate(sec(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""giac"")","\int \frac{\sec\left(e x + d\right)^{\frac{3}{2}}}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sec(e*x + d)^(3/2)/(b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2), x)","F",0
452,0,0,0,0.000000," ","integrate(sec(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""giac"")","\int \frac{\sec\left(e x + d\right)^{\frac{5}{2}}}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sec(e*x + d)^(5/2)/(b*sec(e*x + d) + c*tan(e*x + d) + a)^(5/2), x)","F",0
453,0,0,0,0.000000," ","integrate(cos(e*x+d)^(3/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""giac"")","\int {\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}} \cos\left(e x + d\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)*cos(e*x + d)^(3/2), x)","F",0
454,0,0,0,0.000000," ","integrate(cos(e*x+d)^(1/2)*(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d)), x)","F",0
455,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(1/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a} \sqrt{\cos\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sec(e*x + d) + c*tan(e*x + d) + a)*sqrt(cos(e*x + d))), x)","F",0
456,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(3/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{3}{2}} \cos\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(e*x + d) + c*tan(e*x + d) + a)^(3/2)*cos(e*x + d)^(3/2)), x)","F",0
457,0,0,0,0.000000," ","integrate(1/cos(e*x+d)^(5/2)/(a+b*sec(e*x+d)+c*tan(e*x+d))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \sec\left(e x + d\right) + c \tan\left(e x + d\right) + a\right)}^{\frac{5}{2}} \cos\left(e x + d\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*sec(e*x + d) + c*tan(e*x + d) + a)^(5/2)*cos(e*x + d)^(5/2)), x)","F",0
458,1,158,0,0.144769," ","integrate(1/(a+b*cot(x)+c*csc(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + \arctan\left(-\frac{b \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - a}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)} a c}{{\left(a^{2} + b^{2}\right)} \sqrt{-a^{2} - b^{2} + c^{2}}} + \frac{a x}{a^{2} + b^{2}} - \frac{b \log\left(-b \tan\left(\frac{1}{2} \, x\right)^{2} + c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x\right) + b + c\right)}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{a^{2} + b^{2}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*b + 2*c) + arctan(-(b*tan(1/2*x) - c*tan(1/2*x) - a)/sqrt(-a^2 - b^2 + c^2)))*a*c/((a^2 + b^2)*sqrt(-a^2 - b^2 + c^2)) + a*x/(a^2 + b^2) - b*log(-b*tan(1/2*x)^2 + c*tan(1/2*x)^2 + 2*a*tan(1/2*x) + b + c)/(a^2 + b^2) + b*log(tan(1/2*x)^2 + 1)/(a^2 + b^2)","A",0
459,1,73,0,0.148462," ","integrate(csc(x)/(a+b*cot(x)+c*csc(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, b - 2 \, c\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - a}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)}}{\sqrt{-a^{2} - b^{2} + c^{2}}}"," ",0,"-2*(pi*floor(1/2*x/pi + 1/2)*sgn(2*b - 2*c) + arctan((b*tan(1/2*x) - c*tan(1/2*x) - a)/sqrt(-a^2 - b^2 + c^2)))/sqrt(-a^2 - b^2 + c^2)","A",0
460,1,142,0,0.169019," ","integrate(csc(x)^2/(a+b*cot(x)+c*csc(x)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(-2 \, b + 2 \, c\right) + \arctan\left(-\frac{b \tan\left(\frac{1}{2} \, x\right) - c \tan\left(\frac{1}{2} \, x\right) - a}{\sqrt{-a^{2} - b^{2} + c^{2}}}\right)\right)} a c}{\sqrt{-a^{2} - b^{2} + c^{2}} {\left(b^{2} - c^{2}\right)}} - \frac{b \log\left(-b \tan\left(\frac{1}{2} \, x\right)^{2} + c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x\right) + b + c\right)}{b^{2} - c^{2}} + \frac{\log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)}{b + c}"," ",0,"2*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*b + 2*c) + arctan(-(b*tan(1/2*x) - c*tan(1/2*x) - a)/sqrt(-a^2 - b^2 + c^2)))*a*c/(sqrt(-a^2 - b^2 + c^2)*(b^2 - c^2)) - b*log(-b*tan(1/2*x)^2 + c*tan(1/2*x)^2 + 2*a*tan(1/2*x) + b + c)/(b^2 - c^2) + log(abs(tan(1/2*x)))/(b + c)","A",0
461,1,22,0,0.140345," ","integrate(csc(x)/(2+2*cot(x)+3*csc(x)),x, algorithm=""giac"")","2 \, \pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor + 2 \, \arctan\left(\tan\left(\frac{1}{2} \, x\right) + 2\right)"," ",0,"2*pi*floor(1/2*x/pi + 1/2) + 2*arctan(tan(1/2*x) + 2)","A",0
462,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/csc(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}}}{\csc\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)/csc(e*x + d)^(3/2), x)","F",0
463,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/csc(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a}}{\sqrt{\csc\left(e x + d\right)}}\,{d x}"," ",0,"integrate(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)/sqrt(csc(e*x + d)), x)","F",0
464,-1,0,0,0.000000," ","integrate(csc(e*x+d)^(1/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
465,-1,0,0,0.000000," ","integrate(csc(e*x+d)^(3/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate(csc(e*x+d)^(5/2)/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)*sin(e*x+d)^(3/2),x, algorithm=""giac"")","\int {\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}} \sin\left(e x + d\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)*sin(e*x + d)^(3/2), x)","F",0
468,0,0,0,0.000000," ","integrate((a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)*sin(e*x+d)^(1/2),x, algorithm=""giac"")","\int \sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}\,{d x}"," ",0,"integrate(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d)), x)","F",0
469,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(1/2)/sin(e*x+d)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a} \sqrt{\sin\left(e x + d\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(c*cot(e*x + d) + b*csc(e*x + d) + a)*sqrt(sin(e*x + d))), x)","F",0
470,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(3/2)/sin(e*x+d)^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{3}{2}} \sin\left(e x + d\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((c*cot(e*x + d) + b*csc(e*x + d) + a)^(3/2)*sin(e*x + d)^(3/2)), x)","F",0
471,0,0,0,0.000000," ","integrate(1/(a+c*cot(e*x+d)+b*csc(e*x+d))^(5/2)/sin(e*x+d)^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(c \cot\left(e x + d\right) + b \csc\left(e x + d\right) + a\right)}^{\frac{5}{2}} \sin\left(e x + d\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((c*cot(e*x + d) + b*csc(e*x + d) + a)^(5/2)*sin(e*x + d)^(5/2)), x)","F",0
472,1,1,0,0.137536," ","integrate(1/(cos(x)^2+sin(x)^2),x, algorithm=""giac"")","x"," ",0,"x","A",0
473,1,1,0,0.120079," ","integrate(1/(cos(x)^2+sin(x)^2)^2,x, algorithm=""giac"")","x"," ",0,"x","A",0
474,1,1,0,0.126690," ","integrate(1/(cos(x)^2+sin(x)^2)^3,x, algorithm=""giac"")","x"," ",0,"x","A",0
475,1,33,0,0.130726," ","integrate(1/(cos(x)^2-sin(x)^2),x, algorithm=""giac"")","\frac{1}{8} \, \log\left({\left| \frac{1}{\sin\left(2 \, x\right)} + \sin\left(2 \, x\right) + 2 \right|}\right) - \frac{1}{8} \, \log\left({\left| \frac{1}{\sin\left(2 \, x\right)} + \sin\left(2 \, x\right) - 2 \right|}\right)"," ",0,"1/8*log(abs(1/sin(2*x) + sin(2*x) + 2)) - 1/8*log(abs(1/sin(2*x) + sin(2*x) - 2))","B",0
476,1,6,0,0.119237," ","integrate(1/(cos(x)^2-sin(x)^2)^2,x, algorithm=""giac"")","\frac{1}{2} \, \tan\left(2 \, x\right)"," ",0,"1/2*tan(2*x)","A",0
477,1,37,0,0.134430," ","integrate(1/(cos(x)^2-sin(x)^2)^3,x, algorithm=""giac"")","-\frac{\sin\left(2 \, x\right)}{4 \, {\left(\sin\left(2 \, x\right)^{2} - 1\right)}} + \frac{1}{8} \, \log\left(\sin\left(2 \, x\right) + 1\right) - \frac{1}{8} \, \log\left(-\sin\left(2 \, x\right) + 1\right)"," ",0,"-1/4*sin(2*x)/(sin(2*x)^2 - 1) + 1/8*log(sin(2*x) + 1) - 1/8*log(-sin(2*x) + 1)","A",0
478,1,20,0,0.145980," ","integrate(1/(cos(x)^2+a^2*sin(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(a \tan\left(x\right)\right)}{a}"," ",0,"(pi*floor(x/pi + 1/2) + arctan(a*tan(x)))/a","B",0
479,1,22,0,0.133130," ","integrate(1/(b^2*cos(x)^2+sin(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{\tan\left(x\right)}{b}\right)}{b}"," ",0,"(pi*floor(x/pi + 1/2) + arctan(tan(x)/b))/b","A",0
480,1,26,0,0.127395," ","integrate(1/(b^2*cos(x)^2+a^2*sin(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{a \tan\left(x\right)}{b}\right)}{a b}"," ",0,"(pi*floor(x/pi + 1/2) + arctan(a*tan(x)/b))/(a*b)","A",0
481,1,61,0,0.128739," ","integrate(1/(4*cos(1+2*x)^2+3*sin(1+2*x)^2),x, algorithm=""giac"")","\frac{1}{12} \, \sqrt{3} {\left(2 \, x + \arctan\left(-\frac{2 \, \sqrt{3} \sin\left(4 \, x + 2\right) - 3 \, \sin\left(4 \, x + 2\right)}{2 \, \sqrt{3} \cos\left(4 \, x + 2\right) + 2 \, \sqrt{3} - 3 \, \cos\left(4 \, x + 2\right) + 3}\right) + 1\right)}"," ",0,"1/12*sqrt(3)*(2*x + arctan(-(2*sqrt(3)*sin(4*x + 2) - 3*sin(4*x + 2))/(2*sqrt(3)*cos(4*x + 2) + 2*sqrt(3) - 3*cos(4*x + 2) + 3)) + 1)","A",0
482,1,48,0,0.132304," ","integrate(sin(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""giac"")","\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(x\right)}{\sqrt{a b}}\right)\right)} a}{\sqrt{a b} {\left(a - b\right)}} - \frac{x}{a - b}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(b) + arctan(b*tan(x)/sqrt(a*b)))*a/(sqrt(a*b)*(a - b)) - x/(a - b)","A",0
483,1,48,0,0.135231," ","integrate(cos(x)^2/(a*cos(x)^2+b*sin(x)^2),x, algorithm=""giac"")","-\frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(x\right)}{\sqrt{a b}}\right)\right)} b}{\sqrt{a b} {\left(a - b\right)}} + \frac{x}{a - b}"," ",0,"-(pi*floor(x/pi + 1/2)*sgn(b) + arctan(b*tan(x)/sqrt(a*b)))*b/(sqrt(a*b)*(a - b)) + x/(a - b)","A",0
484,1,15,0,0.124435," ","integrate(1/(sec(x)^2+tan(x)^2),x, algorithm=""giac"")","\sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) - x"," ",0,"sqrt(2)*arctan(sqrt(2)*tan(x)) - x","A",0
485,1,27,0,0.148345," ","integrate(1/(sec(x)^2+tan(x)^2)^2,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) + x + \frac{\tan\left(x\right)}{2 \, \tan\left(x\right)^{2} + 1}"," ",0,"-1/2*sqrt(2)*arctan(sqrt(2)*tan(x)) + x + tan(x)/(2*tan(x)^2 + 1)","A",0
486,1,39,0,0.148607," ","integrate(1/(sec(x)^2+tan(x)^2)^3,x, algorithm=""giac"")","\frac{7}{8} \, \sqrt{2} \arctan\left(\sqrt{2} \tan\left(x\right)\right) - x - \frac{2 \, \tan\left(x\right)^{3} - \tan\left(x\right)}{4 \, {\left(2 \, \tan\left(x\right)^{2} + 1\right)}^{2}}"," ",0,"7/8*sqrt(2)*arctan(sqrt(2)*tan(x)) - x - 1/4*(2*tan(x)^3 - tan(x))/(2*tan(x)^2 + 1)^2","A",0
487,1,1,0,0.139108," ","integrate(1/(sec(x)^2-tan(x)^2),x, algorithm=""giac"")","x"," ",0,"x","A",0
488,1,1,0,0.148695," ","integrate(1/(sec(x)^2-tan(x)^2)^2,x, algorithm=""giac"")","x"," ",0,"x","A",0
489,1,1,0,0.141752," ","integrate(1/(sec(x)^2-tan(x)^2)^3,x, algorithm=""giac"")","x"," ",0,"x","A",0
490,1,49,0,0.141269," ","integrate(1/(cot(x)^2+csc(x)^2),x, algorithm=""giac"")","\sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - x"," ",0,"sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - x","A",0
491,1,60,0,0.135501," ","integrate(1/(cot(x)^2+csc(x)^2)^2,x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} + x - \frac{\tan\left(x\right)}{\tan\left(x\right)^{2} + 2}"," ",0,"-1/2*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) + x - tan(x)/(tan(x)^2 + 2)","A",0
492,1,69,0,0.132490," ","integrate(1/(cot(x)^2+csc(x)^2)^3,x, algorithm=""giac"")","\frac{7}{8} \, \sqrt{2} {\left(x + \arctan\left(-\frac{\sqrt{2} \sin\left(2 \, x\right) - \sin\left(2 \, x\right)}{\sqrt{2} \cos\left(2 \, x\right) + \sqrt{2} - \cos\left(2 \, x\right) + 1}\right)\right)} - x - \frac{\tan\left(x\right)^{3} - 2 \, \tan\left(x\right)}{4 \, {\left(\tan\left(x\right)^{2} + 2\right)}^{2}}"," ",0,"7/8*sqrt(2)*(x + arctan(-(sqrt(2)*sin(2*x) - sin(2*x))/(sqrt(2)*cos(2*x) + sqrt(2) - cos(2*x) + 1))) - x - 1/4*(tan(x)^3 - 2*tan(x))/(tan(x)^2 + 2)^2","A",0
493,1,3,0,0.150173," ","integrate(1/(cot(x)^2-csc(x)^2),x, algorithm=""giac"")","-x"," ",0,"-x","A",0
494,1,1,0,0.149841," ","integrate(1/(cot(x)^2-csc(x)^2)^2,x, algorithm=""giac"")","x"," ",0,"x","A",0
495,1,3,0,0.137800," ","integrate(1/(cot(x)^2-csc(x)^2)^3,x, algorithm=""giac"")","-x"," ",0,"-x","A",0
496,1,61,0,0.141953," ","integrate(1/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(2 \, a + 2 \, c\right) + \arctan\left(\frac{a \tan\left(x\right) + c \tan\left(x\right)}{\sqrt{a^{2} + a b + a c + b c}}\right)}{\sqrt{a^{2} + a b + a c + b c}}"," ",0,"(pi*floor(x/pi + 1/2)*sgn(2*a + 2*c) + arctan((a*tan(x) + c*tan(x))/sqrt(a^2 + a*b + a*c + b*c)))/sqrt(a^2 + a*b + a*c + b*c)","B",0
497,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""giac"")","\int \frac{x}{b \cos\left(x\right)^{2} + c \sin\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(x/(b*cos(x)^2 + c*sin(x)^2 + a), x)","F",0
498,0,0,0,0.000000," ","integrate(x^2/(a+b*cos(x)^2+c*sin(x)^2),x, algorithm=""giac"")","\int \frac{x^{2}}{b \cos\left(x\right)^{2} + c \sin\left(x\right)^{2} + a}\,{d x}"," ",0,"integrate(x^2/(b*cos(x)^2 + c*sin(x)^2 + a), x)","F",0
499,1,158,0,0.183210," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""giac"")","-\frac{1}{80} \, a^{4} b \cos\left(5 \, x e + 5 \, d\right) e^{\left(-1\right)} + \frac{1}{16} \, {\left(7 \, a^{4} b + 8 \, a^{2} b^{3}\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{1}{8} \, {\left(29 \, a^{4} b + 68 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} + \frac{1}{32} \, {\left(a^{5} + 4 \, a^{3} b^{2}\right)} e^{\left(-1\right)} \sin\left(4 \, x e + 4 \, d\right) - \frac{1}{4} \, {\left(a^{5} + 10 \, a^{3} b^{2} + 4 \, a b^{4}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{3}{8} \, {\left(a^{5} + 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} x"," ",0,"-1/80*a^4*b*cos(5*x*e + 5*d)*e^(-1) + 1/16*(7*a^4*b + 8*a^2*b^3)*cos(3*x*e + 3*d)*e^(-1) - 1/8*(29*a^4*b + 68*a^2*b^3 + 8*b^5)*cos(x*e + d)*e^(-1) + 1/32*(a^5 + 4*a^3*b^2)*e^(-1)*sin(4*x*e + 4*d) - 1/4*(a^5 + 10*a^3*b^2 + 4*a*b^4)*e^(-1)*sin(2*x*e + 2*d) + 3/8*(a^5 + 12*a^3*b^2 + 8*a*b^4)*x","A",0
500,1,79,0,0.148464," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""giac"")","\frac{1}{12} \, a^{2} b \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{1}{4} \, {\left(11 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(x e + d\right) e^{\left(-1\right)} - \frac{1}{4} \, {\left(a^{3} + 2 \, a b^{2}\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{1}{2} \, {\left(a^{3} + 4 \, a b^{2}\right)} x"," ",0,"1/12*a^2*b*cos(3*x*e + 3*d)*e^(-1) - 1/4*(11*a^2*b + 4*b^3)*cos(x*e + d)*e^(-1) - 1/4*(a^3 + 2*a*b^2)*e^(-1)*sin(2*x*e + 2*d) + 1/2*(a^3 + 4*a*b^2)*x","A",0
501,1,52,0,0.178519," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2),x, algorithm=""giac"")","-\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)} e^{\left(-1\right)}}{{\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)} b}"," ",0,"-2*(a*tan(1/2*x*e + 1/2*d) + b)*e^(-1)/((b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b)*b)","B",0
502,1,454,0,0.252616," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^2,x, algorithm=""giac"")","-\frac{2}{3} \, {\left(\frac{3 \, {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(b\right) + \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)\right)} a b}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}}} + \frac{3 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 6 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 6 \, a^{6} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 9 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 15 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 3 \, b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 4 \, a^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 6 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 18 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 6 \, a^{6} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 18 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, b^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 3 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 12 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a^{4} b^{3} - a^{2} b^{5} + 3 \, b^{7}}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"-2/3*(3*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(b) + arctan((b*tan(1/2*x*e + 1/2*d) + a)/sqrt(-a^2 + b^2)))*a*b/((a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)) + (3*a^5*b^2*tan(1/2*x*e + 1/2*d)^5 - 6*a^3*b^4*tan(1/2*x*e + 1/2*d)^5 + 6*a*b^6*tan(1/2*x*e + 1/2*d)^5 + 6*a^6*b*tan(1/2*x*e + 1/2*d)^4 - 9*a^4*b^3*tan(1/2*x*e + 1/2*d)^4 + 15*a^2*b^5*tan(1/2*x*e + 1/2*d)^4 + 3*b^7*tan(1/2*x*e + 1/2*d)^4 + 4*a^7*tan(1/2*x*e + 1/2*d)^3 + 2*a^5*b^2*tan(1/2*x*e + 1/2*d)^3 + 6*a^3*b^4*tan(1/2*x*e + 1/2*d)^3 + 18*a*b^6*tan(1/2*x*e + 1/2*d)^3 + 6*a^6*b*tan(1/2*x*e + 1/2*d)^2 + 18*a^2*b^5*tan(1/2*x*e + 1/2*d)^2 + 6*b^7*tan(1/2*x*e + 1/2*d)^2 + 3*a^5*b^2*tan(1/2*x*e + 1/2*d) + 12*a*b^6*tan(1/2*x*e + 1/2*d) + a^4*b^3 - a^2*b^5 + 3*b^7)/((a^4*b^3 - 2*a^2*b^5 + b^7)*(b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b)^3))*e^(-1)","B",0
503,-1,0,0,0.000000," ","integrate((d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,1,239,0,5.029113," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{32} \, a^{3} b e^{\left(-1\right)} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) \sin\left(4 \, x e + 4 \, d\right) + \frac{1}{12} \, {\left(a^{4} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) + 3 \, a^{2} b^{2} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right)\right)} \cos\left(3 \, x e + 3 \, d\right) e^{\left(-1\right)} - \frac{1}{4} \, {\left(3 \, a^{4} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) + 21 \, a^{2} b^{2} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) + 4 \, b^{4} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right)\right)} \cos\left(x e + d\right) e^{\left(-1\right)} - \frac{1}{4} \, {\left(4 \, a^{3} b \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) + 3 \, a b^{3} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right)\right)} e^{\left(-1\right)} \sin\left(2 \, x e + 2 \, d\right) + \frac{5}{8} \, {\left(3 \, a^{3} b \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) + 4 \, a b^{3} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right)\right)} x"," ",0,"1/32*a^3*b*e^(-1)*sgn(a*sin(x*e + d) + b)*sin(4*x*e + 4*d) + 1/12*(a^4*sgn(a*sin(x*e + d) + b) + 3*a^2*b^2*sgn(a*sin(x*e + d) + b))*cos(3*x*e + 3*d)*e^(-1) - 1/4*(3*a^4*sgn(a*sin(x*e + d) + b) + 21*a^2*b^2*sgn(a*sin(x*e + d) + b) + 4*b^4*sgn(a*sin(x*e + d) + b))*cos(x*e + d)*e^(-1) - 1/4*(4*a^3*b*sgn(a*sin(x*e + d) + b) + 3*a*b^3*sgn(a*sin(x*e + d) + b))*e^(-1)*sin(2*x*e + 2*d) + 5/8*(3*a^3*b*sgn(a*sin(x*e + d) + b) + 4*a*b^3*sgn(a*sin(x*e + d) + b))*x","A",0
505,1,98,0,0.205523," ","integrate((a+b*sin(e*x+d))*(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x, algorithm=""giac"")","-a^{2} \cos\left(x e + d\right) e^{\left(-1\right)} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) - b^{2} \cos\left(x e + d\right) e^{\left(-1\right)} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) - \frac{1}{4} \, a b e^{\left(-1\right)} \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right) \sin\left(2 \, x e + 2 \, d\right) + \frac{3}{2} \, a b x \mathrm{sgn}\left(a \sin\left(x e + d\right) + b\right)"," ",0,"-a^2*cos(x*e + d)*e^(-1)*sgn(a*sin(x*e + d) + b) - b^2*cos(x*e + d)*e^(-1)*sgn(a*sin(x*e + d) + b) - 1/4*a*b*e^(-1)*sgn(a*sin(x*e + d) + b)*sin(2*x*e + 2*d) + 3/2*a*b*x*sgn(a*sin(x*e + d) + b)","A",0
506,1,208,0,0.383933," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{{\left(x e - 2 \, \pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor + d\right)} b}{a \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)} + \frac{2 \, {\left(a^{2} - b^{2}\right)} \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)}{\sqrt{-a^{2} + b^{2}} a \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)}\right)} e^{\left(-1\right)}"," ",0,"((x*e - 2*pi*floor(1/2*(x*e + d)/pi + 1/2) + d)*b/(a*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b)) + 2*(a^2 - b^2)*arctan((b*tan(1/2*x*e + 1/2*d) + a)/sqrt(-a^2 + b^2))/(sqrt(-a^2 + b^2)*a*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b)))*e^(-1)","A",0
507,1,479,0,0.749975," ","integrate((a+b*sin(e*x+d))/(b^2+2*a*b*sin(e*x+d)+a^2*sin(e*x+d)^2)^(3/2),x, algorithm=""giac"")","{\left(\frac{a \arctan\left(\frac{b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a}{\sqrt{-a^{2} + b^{2}}}\right)}{{\left(a^{2} \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right) - b^{2} \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)\right)} \sqrt{-a^{2} + b^{2}}} - \frac{2 \, a^{3} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, a b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a^{3} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 5 \, a b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a^{2} b^{2} - 2 \, b^{4}}{{\left(a^{2} b^{2} \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right) - b^{4} \mathrm{sgn}\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)\right)} {\left(b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + b\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"(a*arctan((b*tan(1/2*x*e + 1/2*d) + a)/sqrt(-a^2 + b^2))/((a^2*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b) - b^2*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b))*sqrt(-a^2 + b^2)) - (2*a^3*b*tan(1/2*x*e + 1/2*d)^3 - 3*a*b^3*tan(1/2*x*e + 1/2*d)^3 + 2*a^4*tan(1/2*x*e + 1/2*d)^2 - 3*a^2*b^2*tan(1/2*x*e + 1/2*d)^2 - 2*b^4*tan(1/2*x*e + 1/2*d)^2 + 2*a^3*b*tan(1/2*x*e + 1/2*d) - 5*a*b^3*tan(1/2*x*e + 1/2*d) + a^2*b^2 - 2*b^4)/((a^2*b^2*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b) - b^4*sgn(b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b))*(b*tan(1/2*x*e + 1/2*d)^2 + 2*a*tan(1/2*x*e + 1/2*d) + b)^2))*e^(-1)","B",0
508,1,32,0,0.169308," ","integrate((a+b*cos(x))/(b^2+2*a*b*cos(x)+a^2*cos(x)^2),x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} - a - b}"," ",0,"-2*tan(1/2*x)/(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 - a - b)","B",0
509,1,5302,0,8.396760," ","integrate((d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a^{3} b c - 12 \, a^{2} b^{2} c + 20 \, a b^{3} c + 4 \, b^{4} c + 48 \, a^{3} c^{2} - 48 \, a^{2} b c^{2} - 24 \, a b^{2} c^{2} - 6 \, b^{3} c^{2} + 32 \, a^{2} c^{3} + 24 \, a b c^{3} + 4 \, b^{2} c^{3} - 16 \, a c^{4} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c + 34 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} - 24 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c - 12 \, {\left(b^{2} - 4 \, a c\right)} a b c - 4 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 28 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{2} - 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} d {\left| a - b + c \right|} - {\left(4 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 4 \, a b^{4} + 6 \, b^{5} - 16 \, a^{4} c + 24 \, a^{3} b c + 40 \, a^{2} b^{2} c - 44 \, a b^{3} c - 8 \, b^{4} c - 96 \, a^{3} c^{2} + 80 \, a^{2} b c^{2} + 52 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 80 \, a^{2} c^{3} - 8 \, a b c^{3} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} + 2 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} + 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c - 8 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c - 34 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c - 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c + 56 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} + 24 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} - \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 12 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 28 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 26 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 10 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} + \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left| a - b + c \right|} e\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 - 2 \, c + \sqrt{-4 \, {\left(a + b + c\right)} {\left(a - b + c\right)} + 4 \, {\left(a - c\right)}^{2}}}{a - b + c}}}\right)\right)}}{3 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 6 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6} - 5 \, b^{7} - 12 \, a^{6} c + 20 \, a^{5} b c + 47 \, a^{4} b^{2} c - 60 \, a^{3} b^{3} c - 46 \, a^{2} b^{4} c + 40 \, a b^{5} c + 11 \, b^{6} c - 92 \, a^{5} c^{2} + 80 \, a^{4} b c^{2} + 182 \, a^{3} b^{2} c^{2} - 94 \, a^{2} b^{3} c^{2} - 78 \, a b^{4} c^{2} - 6 \, b^{5} c^{2} - 184 \, a^{4} c^{3} + 56 \, a^{3} b c^{3} + 166 \, a^{2} b^{2} c^{3} + 36 \, a b^{3} c^{3} - 6 \, b^{4} c^{3} - 120 \, a^{3} c^{4} - 48 \, a^{2} b c^{4} + 23 \, a b^{2} c^{4} + 11 \, b^{3} c^{4} + 4 \, a^{2} c^{5} - 44 \, a b c^{5} - 5 \, b^{2} c^{5} + 20 \, a c^{6}} - \frac{{\left({\left(2 \, a^{2} b^{3} - 2 \, b^{5} - 8 \, a^{3} b c - 12 \, a^{2} b^{2} c + 20 \, a b^{3} c + 4 \, b^{4} c + 48 \, a^{3} c^{2} - 48 \, a^{2} b c^{2} - 24 \, a b^{2} c^{2} - 6 \, b^{3} c^{2} + 32 \, a^{2} c^{3} + 24 \, a b c^{3} + 4 \, b^{2} c^{3} - 16 \, a c^{4} - 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} + 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} + 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c - 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c - 34 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c - 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c + 56 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} + 24 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} + 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} - 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b - 2 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} + 2 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c + 12 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c - 12 \, {\left(b^{2} - 4 \, a c\right)} a b c - 4 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c - 4 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c + 28 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} + 8 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} + 7 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} + 6 \, {\left(b^{2} - 4 \, a c\right)} b c^{2} - 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} c^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} c^{3}\right)} d {\left| a - b + c \right|} - {\left(4 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 4 \, a b^{4} + 6 \, b^{5} - 16 \, a^{4} c + 24 \, a^{3} b c + 40 \, a^{2} b^{2} c - 44 \, a b^{3} c - 8 \, b^{4} c - 96 \, a^{3} c^{2} + 80 \, a^{2} b c^{2} + 52 \, a b^{2} c^{2} + 2 \, b^{3} c^{2} - 80 \, a^{2} c^{3} - 8 \, a b c^{3} + 3 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b^{2} - 2 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{3} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{4} - 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{3} c + 8 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} b c + 34 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b^{2} c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{3} c - 56 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a^{2} c^{2} - 24 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a b c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} b^{2} c^{2} + 20 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} a c^{3} + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{3} - 4 \, {\left(b^{2} - 4 \, a c\right)} a^{3} - \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} b + 6 \, {\left(b^{2} - 4 \, a c\right)} a^{2} b - 12 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b^{2} + 4 \, {\left(b^{2} - 4 \, a c\right)} a b^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{3} - 6 \, {\left(b^{2} - 4 \, a c\right)} b^{3} + 28 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a^{2} c - 24 \, {\left(b^{2} - 4 \, a c\right)} a^{2} c + 26 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a b c + 20 \, {\left(b^{2} - 4 \, a c\right)} a b c + 6 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b^{2} c + 8 \, {\left(b^{2} - 4 \, a c\right)} b^{2} c - 10 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} a c^{2} - 20 \, {\left(b^{2} - 4 \, a c\right)} a c^{2} - 5 \, \sqrt{a^{2} - a b + b c - c^{2} - \sqrt{b^{2} - 4 \, a c} {\left(a - b + c\right)}} \sqrt{b^{2} - 4 \, a c} b c^{2} - 2 \, {\left(b^{2} - 4 \, a c\right)} b c^{2}\right)} {\left| a - b + c \right|} e\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 - 2 \, c - \sqrt{-4 \, {\left(a + b + c\right)} {\left(a - b + c\right)} + 4 \, {\left(a - c\right)}^{2}}}{a - b + c}}}\right)\right)}}{3 \, a^{5} b^{2} - 5 \, a^{4} b^{3} - 6 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6} - 5 \, b^{7} - 12 \, a^{6} c + 20 \, a^{5} b c + 47 \, a^{4} b^{2} c - 60 \, a^{3} b^{3} c - 46 \, a^{2} b^{4} c + 40 \, a b^{5} c + 11 \, b^{6} c - 92 \, a^{5} c^{2} + 80 \, a^{4} b c^{2} + 182 \, a^{3} b^{2} c^{2} - 94 \, a^{2} b^{3} c^{2} - 78 \, a b^{4} c^{2} - 6 \, b^{5} c^{2} - 184 \, a^{4} c^{3} + 56 \, a^{3} b c^{3} + 166 \, a^{2} b^{2} c^{3} + 36 \, a b^{3} c^{3} - 6 \, b^{4} c^{3} - 120 \, a^{3} c^{4} - 48 \, a^{2} b c^{4} + 23 \, a b^{2} c^{4} + 11 \, b^{3} c^{4} + 4 \, a^{2} c^{5} - 44 \, a b c^{5} - 5 \, b^{2} c^{5} + 20 \, a c^{6}}"," ",0,"((2*a^2*b^3 - 2*b^5 - 8*a^3*b*c - 12*a^2*b^2*c + 20*a*b^3*c + 4*b^4*c + 48*a^3*c^2 - 48*a^2*b*c^2 - 24*a*b^2*c^2 - 6*b^3*c^2 + 32*a^2*c^3 + 24*a*b*c^3 + 4*b^2*c^3 - 16*a*c^4 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c + 34*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c - 56*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 - 24*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b - 2*(b^2 - 4*a*c)*a^2*b - 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 + 2*(b^2 - 4*a*c)*b^3 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c + 12*(b^2 - 4*a*c)*a^2*c + 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c - 12*(b^2 - 4*a*c)*a*b*c - 4*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c - 4*(b^2 - 4*a*c)*b^2*c + 28*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 + 8*(b^2 - 4*a*c)*a*c^2 + 7*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 + 6*(b^2 - 4*a*c)*b*c^2 - 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^3 - 4*(b^2 - 4*a*c)*c^3)*d*abs(a - b + c) - (4*a^3*b^2 - 6*a^2*b^3 - 4*a*b^4 + 6*b^5 - 16*a^4*c + 24*a^3*b*c + 40*a^2*b^2*c - 44*a*b^3*c - 8*b^4*c - 96*a^3*c^2 + 80*a^2*b*c^2 + 52*a*b^2*c^2 + 2*b^3*c^2 - 80*a^2*c^3 - 8*a*b*c^3 - 3*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 + 2*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 + 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c - 8*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c - 34*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c - 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c + 56*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 + 24*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 - 20*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3 - 4*(b^2 - 4*a*c)*a^3 - sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b + 6*(b^2 - 4*a*c)*a^2*b - 12*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 + 4*(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 - 6*(b^2 - 4*a*c)*b^3 + 28*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c - 24*(b^2 - 4*a*c)*a^2*c + 26*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c + 20*(b^2 - 4*a*c)*a*b*c + 6*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*b^2*c - 10*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 - 20*(b^2 - 4*a*c)*a*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 + sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*abs(a - b + c)*e)*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - 2*c + sqrt(-4*(a + b + c)*(a - b + c) + 4*(a - c)^2))/(a - b + c))))/(3*a^5*b^2 - 5*a^4*b^3 - 6*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6 - 5*b^7 - 12*a^6*c + 20*a^5*b*c + 47*a^4*b^2*c - 60*a^3*b^3*c - 46*a^2*b^4*c + 40*a*b^5*c + 11*b^6*c - 92*a^5*c^2 + 80*a^4*b*c^2 + 182*a^3*b^2*c^2 - 94*a^2*b^3*c^2 - 78*a*b^4*c^2 - 6*b^5*c^2 - 184*a^4*c^3 + 56*a^3*b*c^3 + 166*a^2*b^2*c^3 + 36*a*b^3*c^3 - 6*b^4*c^3 - 120*a^3*c^4 - 48*a^2*b*c^4 + 23*a*b^2*c^4 + 11*b^3*c^4 + 4*a^2*c^5 - 44*a*b*c^5 - 5*b^2*c^5 + 20*a*c^6) - ((2*a^2*b^3 - 2*b^5 - 8*a^3*b*c - 12*a^2*b^2*c + 20*a*b^3*c + 4*b^4*c + 48*a^3*c^2 - 48*a^2*b*c^2 - 24*a*b^2*c^2 - 6*b^3*c^2 + 32*a^2*c^3 + 24*a*b*c^3 + 4*b^2*c^3 - 16*a*c^4 - 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 + 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 + 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c - 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c - 34*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c - 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c + 56*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 + 24*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 + 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 - 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b - 2*(b^2 - 4*a*c)*a^2*b - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 + 2*(b^2 - 4*a*c)*b^3 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c + 12*(b^2 - 4*a*c)*a^2*c + 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c - 12*(b^2 - 4*a*c)*a*b*c - 4*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c - 4*(b^2 - 4*a*c)*b^2*c + 28*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 + 8*(b^2 - 4*a*c)*a*c^2 + 7*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 + 6*(b^2 - 4*a*c)*b*c^2 - 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*c^3 - 4*(b^2 - 4*a*c)*c^3)*d*abs(a - b + c) - (4*a^3*b^2 - 6*a^2*b^3 - 4*a*b^4 + 6*b^5 - 16*a^4*c + 24*a^3*b*c + 40*a^2*b^2*c - 44*a*b^3*c - 8*b^4*c - 96*a^3*c^2 + 80*a^2*b*c^2 + 52*a*b^2*c^2 + 2*b^3*c^2 - 80*a^2*c^3 - 8*a*b*c^3 + 3*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b^2 - 2*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^3 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^4 - 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^3*c + 8*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*b*c + 34*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b^2*c + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^3*c - 56*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a^2*c^2 - 24*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*b*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*b^2*c^2 + 20*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*a*c^3 + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^3 - 4*(b^2 - 4*a*c)*a^3 - sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*b + 6*(b^2 - 4*a*c)*a^2*b - 12*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b^2 + 4*(b^2 - 4*a*c)*a*b^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^3 - 6*(b^2 - 4*a*c)*b^3 + 28*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a^2*c - 24*(b^2 - 4*a*c)*a^2*c + 26*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*b*c + 20*(b^2 - 4*a*c)*a*b*c + 6*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b^2*c + 8*(b^2 - 4*a*c)*b^2*c - 10*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*a*c^2 - 20*(b^2 - 4*a*c)*a*c^2 - 5*sqrt(a^2 - a*b + b*c - c^2 - sqrt(b^2 - 4*a*c)*(a - b + c))*sqrt(b^2 - 4*a*c)*b*c^2 - 2*(b^2 - 4*a*c)*b*c^2)*abs(a - b + c)*e)*(pi*floor(1/2*x/pi + 1/2) + arctan(2*sqrt(1/2)*tan(1/2*x)/sqrt((2*a - 2*c - sqrt(-4*(a + b + c)*(a - b + c) + 4*(a - c)^2))/(a - b + c))))/(3*a^5*b^2 - 5*a^4*b^3 - 6*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6 - 5*b^7 - 12*a^6*c + 20*a^5*b*c + 47*a^4*b^2*c - 60*a^3*b^3*c - 46*a^2*b^4*c + 40*a*b^5*c + 11*b^6*c - 92*a^5*c^2 + 80*a^4*b*c^2 + 182*a^3*b^2*c^2 - 94*a^2*b^3*c^2 - 78*a*b^4*c^2 - 6*b^5*c^2 - 184*a^4*c^3 + 56*a^3*b*c^3 + 166*a^2*b^2*c^3 + 36*a*b^3*c^3 - 6*b^4*c^3 - 120*a^3*c^4 - 48*a^2*b*c^4 + 23*a*b^2*c^4 + 11*b^3*c^4 + 4*a^2*c^5 - 44*a*b*c^5 - 5*b^2*c^5 + 20*a*c^6)","B",0
510,1,2326,0,5.119320," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""giac"")","\frac{12 \, a^{5} x e \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 24 \, a^{3} b^{2} x e \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 36 \, a b^{4} x e \tan\left(x e\right)^{4} \tan\left(d\right)^{4} + 18 \, a^{4} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{4} \tan\left(d\right)^{4} + 12 \, a^{2} b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 6 \, b^{5} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 48 \, a^{5} x e \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 96 \, a^{3} b^{2} x e \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 144 \, a b^{4} x e \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 15 \, a^{4} b \tan\left(x e\right)^{4} \tan\left(d\right)^{4} + 36 \, a^{2} b^{3} \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 72 \, a^{4} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 48 \, a^{2} b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 24 \, b^{5} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 12 \, a^{5} \tan\left(x e\right)^{4} \tan\left(d\right)^{3} - 24 \, a^{3} b^{2} \tan\left(x e\right)^{4} \tan\left(d\right)^{3} - 48 \, a b^{4} \tan\left(x e\right)^{4} \tan\left(d\right)^{3} + 12 \, a^{5} \tan\left(x e\right)^{3} \tan\left(d\right)^{4} - 24 \, a^{3} b^{2} \tan\left(x e\right)^{3} \tan\left(d\right)^{4} - 48 \, a b^{4} \tan\left(x e\right)^{3} \tan\left(d\right)^{4} + 72 \, a^{5} x e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 144 \, a^{3} b^{2} x e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 216 \, a b^{4} x e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 18 \, a^{4} b \tan\left(x e\right)^{4} \tan\left(d\right)^{2} + 36 \, a^{2} b^{3} \tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 24 \, a^{4} b \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 72 \, a^{2} b^{3} \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 18 \, a^{4} b \tan\left(x e\right)^{2} \tan\left(d\right)^{4} + 36 \, a^{2} b^{3} \tan\left(x e\right)^{2} \tan\left(d\right)^{4} - 4 \, a^{5} \tan\left(x e\right)^{4} \tan\left(d\right) - 16 \, a^{3} b^{2} \tan\left(x e\right)^{4} \tan\left(d\right) + 108 \, a^{4} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 72 \, a^{2} b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 36 \, b^{5} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 48 \, a^{5} \tan\left(x e\right)^{3} \tan\left(d\right)^{2} + 24 \, a^{3} b^{2} \tan\left(x e\right)^{3} \tan\left(d\right)^{2} + 144 \, a b^{4} \tan\left(x e\right)^{3} \tan\left(d\right)^{2} - 48 \, a^{5} \tan\left(x e\right)^{2} \tan\left(d\right)^{3} + 24 \, a^{3} b^{2} \tan\left(x e\right)^{2} \tan\left(d\right)^{3} + 144 \, a b^{4} \tan\left(x e\right)^{2} \tan\left(d\right)^{3} - 4 \, a^{5} \tan\left(x e\right) \tan\left(d\right)^{4} - 16 \, a^{3} b^{2} \tan\left(x e\right) \tan\left(d\right)^{4} + 3 \, a^{4} b \tan\left(x e\right)^{4} - 48 \, a^{5} x e \tan\left(x e\right) \tan\left(d\right) + 96 \, a^{3} b^{2} x e \tan\left(x e\right) \tan\left(d\right) + 144 \, a b^{4} x e \tan\left(x e\right) \tan\left(d\right) - 24 \, a^{4} b \tan\left(x e\right)^{3} \tan\left(d\right) - 72 \, a^{2} b^{3} \tan\left(x e\right)^{3} \tan\left(d\right) + 36 \, a^{4} b \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 72 \, a^{2} b^{3} \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 24 \, a^{4} b \tan\left(x e\right) \tan\left(d\right)^{3} - 72 \, a^{2} b^{3} \tan\left(x e\right) \tan\left(d\right)^{3} + 3 \, a^{4} b \tan\left(d\right)^{4} + 4 \, a^{5} \tan\left(x e\right)^{3} + 16 \, a^{3} b^{2} \tan\left(x e\right)^{3} - 72 \, a^{4} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right) \tan\left(d\right) - 48 \, a^{2} b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right) \tan\left(d\right) + 24 \, b^{5} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right) \tan\left(d\right) + 48 \, a^{5} \tan\left(x e\right)^{2} \tan\left(d\right) - 24 \, a^{3} b^{2} \tan\left(x e\right)^{2} \tan\left(d\right) - 144 \, a b^{4} \tan\left(x e\right)^{2} \tan\left(d\right) + 48 \, a^{5} \tan\left(x e\right) \tan\left(d\right)^{2} - 24 \, a^{3} b^{2} \tan\left(x e\right) \tan\left(d\right)^{2} - 144 \, a b^{4} \tan\left(x e\right) \tan\left(d\right)^{2} + 4 \, a^{5} \tan\left(d\right)^{3} + 16 \, a^{3} b^{2} \tan\left(d\right)^{3} + 12 \, a^{5} x e - 24 \, a^{3} b^{2} x e - 36 \, a b^{4} x e + 18 \, a^{4} b \tan\left(x e\right)^{2} + 36 \, a^{2} b^{3} \tan\left(x e\right)^{2} - 24 \, a^{4} b \tan\left(x e\right) \tan\left(d\right) - 72 \, a^{2} b^{3} \tan\left(x e\right) \tan\left(d\right) + 18 \, a^{4} b \tan\left(d\right)^{2} + 36 \, a^{2} b^{3} \tan\left(d\right)^{2} + 18 \, a^{4} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) + 12 \, a^{2} b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) - 6 \, b^{5} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) - 12 \, a^{5} \tan\left(x e\right) + 24 \, a^{3} b^{2} \tan\left(x e\right) + 48 \, a b^{4} \tan\left(x e\right) - 12 \, a^{5} \tan\left(d\right) + 24 \, a^{3} b^{2} \tan\left(d\right) + 48 \, a b^{4} \tan\left(d\right) + 15 \, a^{4} b + 36 \, a^{2} b^{3}}{12 \, {\left(e \tan\left(x e\right)^{4} \tan\left(d\right)^{4} - 4 \, e \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 6 \, e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 4 \, e \tan\left(x e\right) \tan\left(d\right) + e\right)}}"," ",0,"1/12*(12*a^5*x*e*tan(x*e)^4*tan(d)^4 - 24*a^3*b^2*x*e*tan(x*e)^4*tan(d)^4 - 36*a*b^4*x*e*tan(x*e)^4*tan(d)^4 + 18*a^4*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^4*tan(d)^4 + 12*a^2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^4*tan(d)^4 - 6*b^5*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^4*tan(d)^4 - 48*a^5*x*e*tan(x*e)^3*tan(d)^3 + 96*a^3*b^2*x*e*tan(x*e)^3*tan(d)^3 + 144*a*b^4*x*e*tan(x*e)^3*tan(d)^3 + 15*a^4*b*tan(x*e)^4*tan(d)^4 + 36*a^2*b^3*tan(x*e)^4*tan(d)^4 - 72*a^4*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^3*tan(d)^3 - 48*a^2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^3*tan(d)^3 + 24*b^5*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^3*tan(d)^3 + 12*a^5*tan(x*e)^4*tan(d)^3 - 24*a^3*b^2*tan(x*e)^4*tan(d)^3 - 48*a*b^4*tan(x*e)^4*tan(d)^3 + 12*a^5*tan(x*e)^3*tan(d)^4 - 24*a^3*b^2*tan(x*e)^3*tan(d)^4 - 48*a*b^4*tan(x*e)^3*tan(d)^4 + 72*a^5*x*e*tan(x*e)^2*tan(d)^2 - 144*a^3*b^2*x*e*tan(x*e)^2*tan(d)^2 - 216*a*b^4*x*e*tan(x*e)^2*tan(d)^2 + 18*a^4*b*tan(x*e)^4*tan(d)^2 + 36*a^2*b^3*tan(x*e)^4*tan(d)^2 - 24*a^4*b*tan(x*e)^3*tan(d)^3 - 72*a^2*b^3*tan(x*e)^3*tan(d)^3 + 18*a^4*b*tan(x*e)^2*tan(d)^4 + 36*a^2*b^3*tan(x*e)^2*tan(d)^4 - 4*a^5*tan(x*e)^4*tan(d) - 16*a^3*b^2*tan(x*e)^4*tan(d) + 108*a^4*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^2*tan(d)^2 + 72*a^2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^2*tan(d)^2 - 36*b^5*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^2*tan(d)^2 - 48*a^5*tan(x*e)^3*tan(d)^2 + 24*a^3*b^2*tan(x*e)^3*tan(d)^2 + 144*a*b^4*tan(x*e)^3*tan(d)^2 - 48*a^5*tan(x*e)^2*tan(d)^3 + 24*a^3*b^2*tan(x*e)^2*tan(d)^3 + 144*a*b^4*tan(x*e)^2*tan(d)^3 - 4*a^5*tan(x*e)*tan(d)^4 - 16*a^3*b^2*tan(x*e)*tan(d)^4 + 3*a^4*b*tan(x*e)^4 - 48*a^5*x*e*tan(x*e)*tan(d) + 96*a^3*b^2*x*e*tan(x*e)*tan(d) + 144*a*b^4*x*e*tan(x*e)*tan(d) - 24*a^4*b*tan(x*e)^3*tan(d) - 72*a^2*b^3*tan(x*e)^3*tan(d) + 36*a^4*b*tan(x*e)^2*tan(d)^2 + 72*a^2*b^3*tan(x*e)^2*tan(d)^2 - 24*a^4*b*tan(x*e)*tan(d)^3 - 72*a^2*b^3*tan(x*e)*tan(d)^3 + 3*a^4*b*tan(d)^4 + 4*a^5*tan(x*e)^3 + 16*a^3*b^2*tan(x*e)^3 - 72*a^4*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)*tan(d) - 48*a^2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)*tan(d) + 24*b^5*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)*tan(d) + 48*a^5*tan(x*e)^2*tan(d) - 24*a^3*b^2*tan(x*e)^2*tan(d) - 144*a*b^4*tan(x*e)^2*tan(d) + 48*a^5*tan(x*e)*tan(d)^2 - 24*a^3*b^2*tan(x*e)*tan(d)^2 - 144*a*b^4*tan(x*e)*tan(d)^2 + 4*a^5*tan(d)^3 + 16*a^3*b^2*tan(d)^3 + 12*a^5*x*e - 24*a^3*b^2*x*e - 36*a*b^4*x*e + 18*a^4*b*tan(x*e)^2 + 36*a^2*b^3*tan(x*e)^2 - 24*a^4*b*tan(x*e)*tan(d) - 72*a^2*b^3*tan(x*e)*tan(d) + 18*a^4*b*tan(d)^2 + 36*a^2*b^3*tan(d)^2 + 18*a^4*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1)) + 12*a^2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1)) - 6*b^5*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1)) - 12*a^5*tan(x*e) + 24*a^3*b^2*tan(x*e) + 48*a*b^4*tan(x*e) - 12*a^5*tan(d) + 24*a^3*b^2*tan(d) + 48*a*b^4*tan(d) + 15*a^4*b + 36*a^2*b^3)/(e*tan(x*e)^4*tan(d)^4 - 4*e*tan(x*e)^3*tan(d)^3 + 6*e*tan(x*e)^2*tan(d)^2 - 4*e*tan(x*e)*tan(d) + e)","B",0
511,1,709,0,1.018130," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""giac"")","-\frac{2 \, a^{3} x e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 2 \, a b^{2} x e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + a^{2} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 4 \, a^{3} x e \tan\left(x e\right) \tan\left(d\right) - 4 \, a b^{2} x e \tan\left(x e\right) \tan\left(d\right) - a^{2} b \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 2 \, a^{2} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right) \tan\left(d\right) - 2 \, b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \tan\left(x e\right) \tan\left(d\right) + 2 \, a^{3} \tan\left(x e\right)^{2} \tan\left(d\right) + 4 \, a b^{2} \tan\left(x e\right)^{2} \tan\left(d\right) + 2 \, a^{3} \tan\left(x e\right) \tan\left(d\right)^{2} + 4 \, a b^{2} \tan\left(x e\right) \tan\left(d\right)^{2} + 2 \, a^{3} x e + 2 \, a b^{2} x e - a^{2} b \tan\left(x e\right)^{2} - a^{2} b \tan\left(d\right)^{2} + a^{2} b \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) + b^{3} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) - 2 \, a^{3} \tan\left(x e\right) - 4 \, a b^{2} \tan\left(x e\right) - 2 \, a^{3} \tan\left(d\right) - 4 \, a b^{2} \tan\left(d\right) - a^{2} b}{2 \, {\left(e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 2 \, e \tan\left(x e\right) \tan\left(d\right) + e\right)}}"," ",0,"-1/2*(2*a^3*x*e*tan(x*e)^2*tan(d)^2 + 2*a*b^2*x*e*tan(x*e)^2*tan(d)^2 + a^2*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^2*tan(d)^2 + b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)^2*tan(d)^2 - 4*a^3*x*e*tan(x*e)*tan(d) - 4*a*b^2*x*e*tan(x*e)*tan(d) - a^2*b*tan(x*e)^2*tan(d)^2 - 2*a^2*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)*tan(d) - 2*b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*tan(x*e)*tan(d) + 2*a^3*tan(x*e)^2*tan(d) + 4*a*b^2*tan(x*e)^2*tan(d) + 2*a^3*tan(x*e)*tan(d)^2 + 4*a*b^2*tan(x*e)*tan(d)^2 + 2*a^3*x*e + 2*a*b^2*x*e - a^2*b*tan(x*e)^2 - a^2*b*tan(d)^2 + a^2*b*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1)) + b^3*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1)) - 2*a^3*tan(x*e) - 4*a*b^2*tan(x*e) - 2*a^3*tan(d) - 4*a*b^2*tan(d) - a^2*b)/(e*tan(x*e)^2*tan(d)^2 - 2*e*tan(x*e)*tan(d) + e)","B",0
512,1,204,0,0.894127," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(x e + d\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(x e + d\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(3 \, a^{3} b - a b^{3}\right)} \log\left({\left| a \tan\left(x e + d\right) + b \right|}\right)}{a^{5} + 2 \, a^{3} b^{2} + a b^{4}} + \frac{2 \, {\left(3 \, a^{3} b \tan\left(x e + d\right) - a b^{3} \tan\left(x e + d\right) + a^{4} + 3 \, a^{2} b^{2} - 2 \, b^{4}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(a \tan\left(x e + d\right) + b\right)}}\right)} e^{\left(-1\right)}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(x*e + d)/(a^4 + 2*a^2*b^2 + b^4) + (3*a^2*b - b^3)*log(tan(x*e + d)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(3*a^3*b - a*b^3)*log(abs(a*tan(x*e + d) + b))/(a^5 + 2*a^3*b^2 + a*b^4) + 2*(3*a^3*b*tan(x*e + d) - a*b^3*tan(x*e + d) + a^4 + 3*a^2*b^2 - 2*b^4)/((a^4 + 2*a^2*b^2 + b^4)*(a*tan(x*e + d) + b)))*e^(-1)","B",0
513,1,451,0,1.938235," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, {\left(\frac{6 \, {\left(a^{5} - 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} {\left(x e + d\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{3 \, {\left(5 \, a^{4} b - 10 \, a^{2} b^{3} + b^{5}\right)} \log\left(\tan\left(x e + d\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(5 \, a^{5} b - 10 \, a^{3} b^{3} + a b^{5}\right)} \log\left({\left| a \tan\left(x e + d\right) + b \right|}\right)}{a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 4 \, a^{3} b^{6} + a b^{8}} + \frac{55 \, a^{7} b \tan\left(x e + d\right)^{3} - 110 \, a^{5} b^{3} \tan\left(x e + d\right)^{3} + 11 \, a^{3} b^{5} \tan\left(x e + d\right)^{3} + 6 \, a^{8} \tan\left(x e + d\right)^{2} + 135 \, a^{6} b^{2} \tan\left(x e + d\right)^{2} - 360 \, a^{4} b^{4} \tan\left(x e + d\right)^{2} + 39 \, a^{2} b^{6} \tan\left(x e + d\right)^{2} + 3 \, a^{7} b \tan\left(x e + d\right) + 90 \, a^{5} b^{3} \tan\left(x e + d\right) - 393 \, a^{3} b^{5} \tan\left(x e + d\right) + 48 \, a b^{7} \tan\left(x e + d\right) - 2 \, a^{8} - 7 \, a^{6} b^{2} + 10 \, a^{4} b^{4} - 139 \, a^{2} b^{6} + 22 \, b^{8}}{{\left(a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} {\left(a \tan\left(x e + d\right) + b\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"1/6*(6*(a^5 - 10*a^3*b^2 + 5*a*b^4)*(x*e + d)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(5*a^4*b - 10*a^2*b^3 + b^5)*log(tan(x*e + d)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(5*a^5*b - 10*a^3*b^3 + a*b^5)*log(abs(a*tan(x*e + d) + b))/(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 4*a^3*b^6 + a*b^8) + (55*a^7*b*tan(x*e + d)^3 - 110*a^5*b^3*tan(x*e + d)^3 + 11*a^3*b^5*tan(x*e + d)^3 + 6*a^8*tan(x*e + d)^2 + 135*a^6*b^2*tan(x*e + d)^2 - 360*a^4*b^4*tan(x*e + d)^2 + 39*a^2*b^6*tan(x*e + d)^2 + 3*a^7*b*tan(x*e + d) + 90*a^5*b^3*tan(x*e + d) - 393*a^3*b^5*tan(x*e + d) + 48*a*b^7*tan(x*e + d) - 2*a^8 - 7*a^6*b^2 + 10*a^4*b^4 - 139*a^2*b^6 + 22*b^8)/((a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8)*(a*tan(x*e + d) + b)^3))*e^(-1)","B",0
514,1,1751,0,2.435229," ","integrate((a+b*tan(e*x+d))*(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x, algorithm=""giac"")","-\frac{12 \, a^{3} b x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 12 \, a b^{3} x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 3 \, a^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 3 \, b^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 36 \, a^{3} b x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 36 \, a b^{3} x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{3} + 9 \, a^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 9 \, b^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 12 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{2} + 18 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right)^{2} + 12 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{3} + 18 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{3} + 36 \, a^{3} b x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) + 36 \, a b^{3} x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) - 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right) - 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} \tan\left(d\right) + 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right)^{2} - 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right)^{3} - 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right)^{3} + 2 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{3} - 9 \, a^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) + 9 \, b^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) - 18 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right) - 36 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} \tan\left(d\right) - 18 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right)^{2} - 36 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right)^{2} + 2 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right)^{3} - 12 \, a^{3} b x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) - 12 \, a b^{3} x e \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) + 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} + 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right)^{2} - 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) - 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) + 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right)^{2} + 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right)^{2} + 3 \, a^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) - 3 \, b^{4} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) + 12 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) + 18 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) + 12 \, a^{3} b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right) + 18 \, a b^{3} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right) + 3 \, a^{4} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) + 9 \, a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right)}{6 \, {\left(e \tan\left(x e\right)^{3} \tan\left(d\right)^{3} - 3 \, e \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + 3 \, e \tan\left(x e\right) \tan\left(d\right) - e\right)}}"," ",0,"-1/6*(12*a^3*b*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 + 12*a*b^3*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 - 3*a^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 + 3*b^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 - 36*a^3*b*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 - 36*a*b^3*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 - 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 - 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^3 + 9*a^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 - 9*b^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 + 12*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^2 + 18*a*b^3*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d)^2 + 12*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^3 + 18*a*b^3*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^3 + 36*a^3*b*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) + 36*a*b^3*x*e*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) - 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d) - 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)^3*tan(d) + 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 + 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d)^2 - 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d)^3 - 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d)^3 + 2*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e)^3 - 9*a^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) + 9*b^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) - 18*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d) - 36*a*b^3*sgn(a*tan(x*e + d) + b)*tan(x*e)^2*tan(d) - 18*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d)^2 - 36*a*b^3*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d)^2 + 2*a^3*b*sgn(a*tan(x*e + d) + b)*tan(d)^3 - 12*a^3*b*x*e*sgn(a*tan(x*e + d) + b) - 12*a*b^3*x*e*sgn(a*tan(x*e + d) + b) + 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)^2 + 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)^2 - 3*a^4*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) - 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) + 3*a^4*sgn(a*tan(x*e + d) + b)*tan(d)^2 + 9*a^2*b^2*sgn(a*tan(x*e + d) + b)*tan(d)^2 + 3*a^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b) - 3*b^4*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b) + 12*a^3*b*sgn(a*tan(x*e + d) + b)*tan(x*e) + 18*a*b^3*sgn(a*tan(x*e + d) + b)*tan(x*e) + 12*a^3*b*sgn(a*tan(x*e + d) + b)*tan(d) + 18*a*b^3*sgn(a*tan(x*e + d) + b)*tan(d) + 3*a^4*sgn(a*tan(x*e + d) + b) + 9*a^2*b^2*sgn(a*tan(x*e + d) + b))/(e*tan(x*e)^3*tan(d)^3 - 3*e*tan(x*e)^2*tan(d)^2 + 3*e*tan(x*e)*tan(d) - e)","B",0
515,1,395,0,0.459592," ","integrate((b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2)*(a+b*tan(e*x+d)),x, algorithm=""giac"")","-\frac{a^{2} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) + b^{2} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) \tan\left(d\right) - a^{2} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) - b^{2} \log\left(\frac{4 \, {\left(\tan\left(x e\right)^{4} \tan\left(d\right)^{2} - 2 \, \tan\left(x e\right)^{3} \tan\left(d\right) + \tan\left(x e\right)^{2} \tan\left(d\right)^{2} + \tan\left(x e\right)^{2} - 2 \, \tan\left(x e\right) \tan\left(d\right) + 1\right)}}{\tan\left(d\right)^{2} + 1}\right) \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) + 2 \, a b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(x e\right) + 2 \, a b \mathrm{sgn}\left(a \tan\left(x e + d\right) + b\right) \tan\left(d\right)}{2 \, {\left(e \tan\left(x e\right) \tan\left(d\right) - e\right)}}"," ",0,"-1/2*(a^2*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) + b^2*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b)*tan(x*e)*tan(d) - a^2*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b) - b^2*log(4*(tan(x*e)^4*tan(d)^2 - 2*tan(x*e)^3*tan(d) + tan(x*e)^2*tan(d)^2 + tan(x*e)^2 - 2*tan(x*e)*tan(d) + 1)/(tan(d)^2 + 1))*sgn(a*tan(x*e + d) + b) + 2*a*b*sgn(a*tan(x*e + d) + b)*tan(x*e) + 2*a*b*sgn(a*tan(x*e + d) + b)*tan(d))/(e*tan(x*e)*tan(d) - e)","B",0
516,1,554,0,3.068386," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\frac{2 \, {\left(\pi \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right) + 2 \, \arctan\left(\frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1}{2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}\right)\right)} a b}{a^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)} - \frac{{\left(a^{2} - b^{2}\right)} \log\left({\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 4\right)}{a^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)} + \frac{2 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| -b {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} - 2 \, a \right|}\right)}{a^{2} b \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{3} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)}\right)} e^{\left(-1\right)}"," ",0,"-1/2*(2*(pi*sgn(tan(1/2*x*e + 1/2*d)) + 2*arctan(1/2*(tan(1/2*x*e + 1/2*d)^2 - 1)/tan(1/2*x*e + 1/2*d)))*a*b/(a^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)) - (a^2 - b^2)*log((1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d))^2 + 4)/(a^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)) + 2*(a^2*b - b^3)*log(abs(-b*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) - 2*a))/(a^2*b*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^3*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)))*e^(-1)","B",0
517,1,1571,0,10.072620," ","integrate((a+b*tan(e*x+d))/(b^2+2*a*b*tan(e*x+d)+a^2*tan(e*x+d)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(\frac{4 \, {\left(a^{3} b - a b^{3}\right)} {\left(\pi \mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right) + 2 \, \arctan\left(\frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1}{2 \, \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}\right)\right)}}{a^{6} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{4} b^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{2} b^{4} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{6} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)} - \frac{{\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 4\right)}{a^{6} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{4} b^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{2} b^{4} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{6} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)} + \frac{2 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| -b {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} - 2 \, a \right|}\right)}{a^{6} b \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{4} b^{3} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{2} b^{5} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{7} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)} - \frac{3 \, a^{4} b^{4} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} - 18 \, a^{2} b^{6} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 3 \, b^{8} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}^{2} + 4 \, a^{7} b {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} + 28 \, a^{5} b^{3} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} - 68 \, a^{3} b^{5} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} + 4 \, a b^{7} {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} + 4 \, a^{8} + 40 \, a^{6} b^{2} - 60 \, a^{4} b^{4}}{{\left(a^{6} b^{2} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{4} b^{4} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + 3 \, a^{2} b^{6} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right) + b^{8} \mathrm{sgn}\left(-b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - b\right)\right)} {\left(b {\left(\frac{1}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)} - \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)} + 2 \, a\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"1/2*(4*(a^3*b - a*b^3)*(pi*sgn(tan(1/2*x*e + 1/2*d)) + 2*arctan(1/2*(tan(1/2*x*e + 1/2*d)^2 - 1)/tan(1/2*x*e + 1/2*d)))/(a^6*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^4*b^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^2*b^4*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^6*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)) - (a^4 - 6*a^2*b^2 + b^4)*log((1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d))^2 + 4)/(a^6*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^4*b^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^2*b^4*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^6*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)) + 2*(a^4*b - 6*a^2*b^3 + b^5)*log(abs(-b*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) - 2*a))/(a^6*b*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^4*b^3*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^2*b^5*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^7*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b)) - (3*a^4*b^4*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d))^2 - 18*a^2*b^6*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d))^2 + 3*b^8*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d))^2 + 4*a^7*b*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) + 28*a^5*b^3*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) - 68*a^3*b^5*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) + 4*a*b^7*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) + 4*a^8 + 40*a^6*b^2 - 60*a^4*b^4)/((a^6*b^2*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^4*b^4*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + 3*a^2*b^6*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b) + b^8*sgn(-b*tan(1/2*x*e + 1/2*d)^4 + 2*a*tan(1/2*x*e + 1/2*d)^3 + 2*b*tan(1/2*x*e + 1/2*d)^2 - 2*a*tan(1/2*x*e + 1/2*d) - b))*(b*(1/tan(1/2*x*e + 1/2*d) - tan(1/2*x*e + 1/2*d)) + 2*a)^2))*e^(-1)","B",0
518,1,470,0,0.390811," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""giac"")","\frac{1}{24} \, {\left(24 \, {\left(x e + d\right)} a b^{4} + 3 \, {\left(19 \, a^{4} b + 56 \, a^{2} b^{3} + 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right) - 3 \, {\left(19 \, a^{4} b + 56 \, a^{2} b^{3} + 8 \, b^{5}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1 \right|}\right) - \frac{2 \, {\left(24 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{7} - 63 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{7} + 240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{7} - 72 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{7} + 96 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{7} - 40 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 39 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 592 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 72 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 288 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 40 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 39 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 592 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 72 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 288 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 24 \, a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 63 \, a^{4} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 240 \, a^{3} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 72 \, a^{2} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 96 \, a b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1\right)}^{4}}\right)} e^{\left(-1\right)}"," ",0,"1/24*(24*(x*e + d)*a*b^4 + 3*(19*a^4*b + 56*a^2*b^3 + 8*b^5)*log(abs(tan(1/2*x*e + 1/2*d) + 1)) - 3*(19*a^4*b + 56*a^2*b^3 + 8*b^5)*log(abs(tan(1/2*x*e + 1/2*d) - 1)) - 2*(24*a^5*tan(1/2*x*e + 1/2*d)^7 - 63*a^4*b*tan(1/2*x*e + 1/2*d)^7 + 240*a^3*b^2*tan(1/2*x*e + 1/2*d)^7 - 72*a^2*b^3*tan(1/2*x*e + 1/2*d)^7 + 96*a*b^4*tan(1/2*x*e + 1/2*d)^7 - 40*a^5*tan(1/2*x*e + 1/2*d)^5 + 39*a^4*b*tan(1/2*x*e + 1/2*d)^5 - 592*a^3*b^2*tan(1/2*x*e + 1/2*d)^5 + 72*a^2*b^3*tan(1/2*x*e + 1/2*d)^5 - 288*a*b^4*tan(1/2*x*e + 1/2*d)^5 + 40*a^5*tan(1/2*x*e + 1/2*d)^3 + 39*a^4*b*tan(1/2*x*e + 1/2*d)^3 + 592*a^3*b^2*tan(1/2*x*e + 1/2*d)^3 + 72*a^2*b^3*tan(1/2*x*e + 1/2*d)^3 + 288*a*b^4*tan(1/2*x*e + 1/2*d)^3 - 24*a^5*tan(1/2*x*e + 1/2*d) - 63*a^4*b*tan(1/2*x*e + 1/2*d) - 240*a^3*b^2*tan(1/2*x*e + 1/2*d) - 72*a^2*b^3*tan(1/2*x*e + 1/2*d) - 96*a*b^4*tan(1/2*x*e + 1/2*d))/(tan(1/2*x*e + 1/2*d)^2 - 1)^4)*e^(-1)","B",0
519,1,191,0,0.251658," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, {\left(x e + d\right)} a b^{2} + {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right) - {\left(5 \, a^{2} b + 2 \, b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1 \right|}\right) - \frac{2 \, {\left(2 \, a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, a^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - a^{2} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, a b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"1/2*(2*(x*e + d)*a*b^2 + (5*a^2*b + 2*b^3)*log(abs(tan(1/2*x*e + 1/2*d) + 1)) - (5*a^2*b + 2*b^3)*log(abs(tan(1/2*x*e + 1/2*d) - 1)) - 2*(2*a^3*tan(1/2*x*e + 1/2*d)^3 - a^2*b*tan(1/2*x*e + 1/2*d)^3 + 4*a*b^2*tan(1/2*x*e + 1/2*d)^3 - 2*a^3*tan(1/2*x*e + 1/2*d) - a^2*b*tan(1/2*x*e + 1/2*d) - 4*a*b^2*tan(1/2*x*e + 1/2*d))/(tan(1/2*x*e + 1/2*d)^2 - 1)^2)*e^(-1)","B",0
520,1,145,0,0.277587," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2),x, algorithm=""giac"")","{\left(\frac{{\left(x e + d\right)} a}{b^{2}} - \frac{2 \, a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\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)} b} - \frac{2 \, {\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)} \sqrt{a^{2} - b^{2}}}{b^{2}}\right)} e^{\left(-1\right)}"," ",0,"((x*e + d)*a/b^2 - 2*a*tan(1/2*x*e + 1/2*d)/((a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + a + b)*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)))*sqrt(a^2 - b^2)/b^2)*e^(-1)","A",0
521,1,490,0,0.486297," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^2,x, algorithm=""giac"")","\frac{1}{3} \, {\left(\frac{3 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - 2 \, b^{6}\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} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a^{2} - b^{2}}} + \frac{3 \, {\left(x e + d\right)} a}{b^{4}} - \frac{6 \, a^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 15 \, a^{6} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 30 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 12 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 27 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 18 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 12 \, a^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 44 \, a^{5} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 68 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 36 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 6 \, a^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 15 \, a^{6} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 30 \, a^{4} b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 12 \, a^{3} b^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 27 \, a^{2} b^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 18 \, a b^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{{\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\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^6 - 5*a^4*b^2 + 3*a^2*b^4 - 2*b^6)*(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*b^4 - 2*a^2*b^6 + b^8)*sqrt(a^2 - b^2)) + 3*(x*e + d)*a/b^4 - (6*a^7*tan(1/2*x*e + 1/2*d)^5 - 15*a^6*b*tan(1/2*x*e + 1/2*d)^5 + 30*a^4*b^3*tan(1/2*x*e + 1/2*d)^5 - 12*a^3*b^4*tan(1/2*x*e + 1/2*d)^5 - 27*a^2*b^5*tan(1/2*x*e + 1/2*d)^5 + 18*a*b^6*tan(1/2*x*e + 1/2*d)^5 + 12*a^7*tan(1/2*x*e + 1/2*d)^3 - 44*a^5*b^2*tan(1/2*x*e + 1/2*d)^3 + 68*a^3*b^4*tan(1/2*x*e + 1/2*d)^3 - 36*a*b^6*tan(1/2*x*e + 1/2*d)^3 + 6*a^7*tan(1/2*x*e + 1/2*d) + 15*a^6*b*tan(1/2*x*e + 1/2*d) - 30*a^4*b^3*tan(1/2*x*e + 1/2*d) - 12*a^3*b^4*tan(1/2*x*e + 1/2*d) + 27*a^2*b^5*tan(1/2*x*e + 1/2*d) + 18*a*b^6*tan(1/2*x*e + 1/2*d))/((a^4*b^3 - 2*a^2*b^5 + b^7)*(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
522,1,652,0,0.512259," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x, algorithm=""giac"")","\frac{1}{6} \, {\left(6 \, {\left(x e + d\right)} a b^{3} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + 3 \, {\left(a^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + 9 \, a^{2} b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + 2 \, b^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right)\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right) - 3 \, {\left(a^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + 9 \, a^{2} b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + 2 \, b^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right)\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1 \right|}\right) + \frac{2 \, {\left(3 \, a^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 24 \, a^{3} b \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 9 \, a^{2} b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, a b^{3} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 40 \, a^{3} b \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 36 \, a b^{3} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, a^{4} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 24 \, a^{3} b \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 9 \, a^{2} b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, a b^{3} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)\right)}}{{\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"1/6*(6*(x*e + d)*a*b^3*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + 3*(a^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + 9*a^2*b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + 2*b^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)))*log(abs(tan(1/2*x*e + 1/2*d) + 1)) - 3*(a^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + 9*a^2*b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + 2*b^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)))*log(abs(tan(1/2*x*e + 1/2*d) - 1)) + 2*(3*a^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^5 - 24*a^3*b*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^5 + 9*a^2*b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^5 - 18*a*b^3*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^5 + 40*a^3*b*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^3 + 36*a*b^3*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)^3 - 3*a^4*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d) - 24*a^3*b*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d) - 9*a^2*b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d) - 18*a*b^3*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d))/(tan(1/2*x*e + 1/2*d)^2 - 1)^3)*e^(-1)","A",0
523,1,224,0,0.305042," ","integrate((a+b*sec(e*x+d))*(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x, algorithm=""giac"")","{\left({\left(x e + d\right)} a b \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) - \frac{2 \, a b \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 1} + {\left(a^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right)\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 1 \right|}\right) - {\left(a^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right) + b^{2} \mathrm{sgn}\left(b \cos\left(x e + d\right)^{2} + a \cos\left(x e + d\right)\right)\right)} \log\left({\left| \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 1 \right|}\right)\right)} e^{\left(-1\right)}"," ",0,"((x*e + d)*a*b*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) - 2*a*b*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d))*tan(1/2*x*e + 1/2*d)/(tan(1/2*x*e + 1/2*d)^2 - 1) + (a^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)))*log(abs(tan(1/2*x*e + 1/2*d) + 1)) - (a^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)) + b^2*sgn(b*cos(x*e + d)^2 + a*cos(x*e + d)))*log(abs(tan(1/2*x*e + 1/2*d) - 1)))*e^(-1)","A",0
524,1,1504,0,4.827154," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(1/2),x, algorithm=""giac"")","{\left(\frac{{\left(\sqrt{a^{2} - b^{2}} {\left| a - b \right|} {\left| b \right|} {\left| \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) \right|} + \sqrt{a^{2} - b^{2}} {\left(2 \, a + b\right)} {\left| a - b \right|} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} \arctan\left(\frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{\frac{a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + \sqrt{-{\left(a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} {\left(a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} + a^{2}}}{a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)}}}\right)}{{\left(a^{2} - a b\right)} {\left| b \right|} {\left| \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) \right|} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + {\left(a - b\right)} b^{2}} + \frac{{\left(a {\left| b \right|} {\left| \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) \right|} - b {\left| b \right|} {\left| \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) \right|} - 2 \, a^{2} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + a b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + b^{2} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} \arctan\left(\frac{\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{\sqrt{\frac{a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - \sqrt{-{\left(a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) + b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} {\left(a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} + a^{2}}}{a \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)}}}\right)}{a {\left| b \right|} {\left| \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) \right|} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b^{2}}\right)} e^{\left(-1\right)}"," ",0,"((sqrt(a^2 - b^2)*abs(a - b)*abs(b)*abs(sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)) + sqrt(a^2 - b^2)*(2*a + b)*abs(a - b)*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*arctan(tan(1/2*x*e + 1/2*d)/sqrt((a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + sqrt(-(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)) + a^2))/(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))))/((a^2 - a*b)*abs(b)*abs(sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + (a - b)*b^2) + (a*abs(b)*abs(sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)) - b*abs(b)*abs(sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)) - 2*a^2*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + a*b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + b^2*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*arctan(tan(1/2*x*e + 1/2*d)/sqrt((a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - sqrt(-(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) + b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)) + a^2))/(a*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))))/(a*abs(b)*abs(sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b^2))*e^(-1)","B",0
525,1,569,0,5.124426," ","integrate((a+b*sec(e*x+d))/(b^2+2*a*b*sec(e*x+d)+a^2*sec(e*x+d)^2)^(3/2),x, algorithm=""giac"")","{\left(\frac{{\left(2 \, a^{4} - 3 \, a^{2} b^{2} + 2 \, b^{4}\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)}{{\left(a^{2} b^{3} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b^{5} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\right)} \sqrt{a^{2} - b^{2}}} + \frac{2 \, a^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, a^{3} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, a b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, a^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 3 \, a^{3} b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 3 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, a b^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)}{{\left(a^{2} b^{2} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right) - b^{4} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)\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}} - \frac{{\left(x e - 2 \, \pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor + d\right)} a}{b^{3} \mathrm{sgn}\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 2 \, b \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - a - b\right)}\right)} e^{\left(-1\right)}"," ",0,"((2*a^4 - 3*a^2*b^2 + 2*b^4)*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^2*b^3*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b^5*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*sqrt(a^2 - b^2)) + (2*a^4*tan(1/2*x*e + 1/2*d)^3 - 3*a^3*b*tan(1/2*x*e + 1/2*d)^3 - 3*a^2*b^2*tan(1/2*x*e + 1/2*d)^3 + 4*a*b^3*tan(1/2*x*e + 1/2*d)^3 + 2*a^4*tan(1/2*x*e + 1/2*d) + 3*a^3*b*tan(1/2*x*e + 1/2*d) - 3*a^2*b^2*tan(1/2*x*e + 1/2*d) - 4*a*b^3*tan(1/2*x*e + 1/2*d))/((a^2*b^2*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b) - b^4*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b))*(a*tan(1/2*x*e + 1/2*d)^2 - b*tan(1/2*x*e + 1/2*d)^2 + a + b)^2) - (x*e - 2*pi*floor(1/2*(x*e + d)/pi + 1/2) + d)*a/(b^3*sgn(a*tan(1/2*x*e + 1/2*d)^4 - b*tan(1/2*x*e + 1/2*d)^4 + 2*b*tan(1/2*x*e + 1/2*d)^2 - a - b)))*e^(-1)","A",0
526,1,14,0,0.140656," ","integrate((cos(x)-I*sin(x))/(cos(x)+I*sin(x)),x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}^{2}}"," ",0,"-2*tan(1/2*x)/(tan(1/2*x) - I)^2","A",0
527,1,14,0,0.140207," ","integrate((cos(x)+I*sin(x))/(cos(x)-I*sin(x)),x, algorithm=""giac"")","-\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{{\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}^{2}}"," ",0,"-2*tan(1/2*x)/(tan(1/2*x) + I)^2","A",0
528,1,16,0,0.176446," ","integrate((cos(x)-sin(x))/(cos(x)+sin(x)),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \log\left({\left| \tan\left(x\right) + 1 \right|}\right)"," ",0,"-1/2*log(tan(x)^2 + 1) + log(abs(tan(x) + 1))","B",0
529,1,77,0,0.167425," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{{\left(B b + C c\right)} x}{b^{2} + c^{2}} + \frac{{\left(C b - B c\right)} \log\left(\tan\left(x\right)^{2} + 1\right)}{2 \, {\left(b^{2} + c^{2}\right)}} - \frac{{\left(C b c - B c^{2}\right)} \log\left({\left| c \tan\left(x\right) + b \right|}\right)}{b^{2} c + c^{3}}"," ",0,"(B*b + C*c)*x/(b^2 + c^2) + 1/2*(C*b - B*c)*log(tan(x)^2 + 1)/(b^2 + c^2) - (C*b*c - B*c^2)*log(abs(c*tan(x) + b))/(b^2*c + c^3)","A",0
530,1,132,0,0.235980," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""giac"")","-\frac{{\left(B b + C c\right)} \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(C b c \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) + C b^{2} - B b c\right)}}{{\left(b^{3} + b c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}}"," ",0,"-(B*b + C*c)*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(C*b*c*tan(1/2*x) - B*c^2*tan(1/2*x) + C*b^2 - B*b*c)/((b^3 + b*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))","A",0
531,1,26,0,0.202433," ","integrate((B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","-\frac{2 \, C c \tan\left(x\right) + C b + B c}{2 \, {\left(c \tan\left(x\right) + b\right)}^{2} c^{2}}"," ",0,"-1/2*(2*C*c*tan(x) + C*b + B*c)/((c*tan(x) + b)^2*c^2)","A",0
532,1,148,0,0.247729," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x)),x, algorithm=""giac"")","-\frac{A \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{\sqrt{b^{2} + c^{2}}} + \frac{{\left(B b + C c\right)} x}{b^{2} + c^{2}} + \frac{{\left(C b - B c\right)} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} - \frac{{\left(C b - B c\right)} \log\left({\left| b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b \right|}\right)}{b^{2} + c^{2}}"," ",0,"-A*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/sqrt(b^2 + c^2) + (B*b + C*c)*x/(b^2 + c^2) + (C*b - B*c)*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) - (C*b - B*c)*log(abs(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))/(b^2 + c^2)","A",0
533,1,150,0,0.233549," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^2,x, algorithm=""giac"")","-\frac{{\left(B b + C c\right)} \log\left(\frac{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| 2 \, b \tan\left(\frac{1}{2} \, x\right) - 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{{\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(A b^{2} \tan\left(\frac{1}{2} \, x\right) + C b c \tan\left(\frac{1}{2} \, x\right) + A c^{2} \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) + C b^{2} - B b c\right)}}{{\left(b^{3} + b c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}}"," ",0,"-(B*b + C*c)*log(abs(2*b*tan(1/2*x) - 2*c - 2*sqrt(b^2 + c^2))/abs(2*b*tan(1/2*x) - 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) - 2*(A*b^2*tan(1/2*x) + C*b*c*tan(1/2*x) + A*c^2*tan(1/2*x) - B*c^2*tan(1/2*x) + C*b^2 - B*b*c)/((b^3 + b*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b))","A",0
534,1,270,0,0.257586," ","integrate((A+B*cos(x)+C*sin(x))/(b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","\frac{A \log\left(\frac{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c - 2 \, \sqrt{b^{2} + c^{2}} \right|}}{{\left| -2 \, b \tan\left(\frac{1}{2} \, x\right) + 2 \, c + 2 \, \sqrt{b^{2} + c^{2}} \right|}}\right)}{2 \, {\left(b^{2} + c^{2}\right)}^{\frac{3}{2}}} + \frac{A b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, C b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, A c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, A b c^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b c^{2} \tan\left(\frac{1}{2} \, x\right) - A b^{2} c}{{\left(b^{4} + b^{2} c^{2}\right)} {\left(b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - b\right)}^{2}}"," ",0,"1/2*A*log(abs(-2*b*tan(1/2*x) + 2*c - 2*sqrt(b^2 + c^2))/abs(-2*b*tan(1/2*x) + 2*c + 2*sqrt(b^2 + c^2)))/(b^2 + c^2)^(3/2) + (A*b^3*tan(1/2*x)^3 - 2*B*b^3*tan(1/2*x)^3 + 2*A*b*c^2*tan(1/2*x)^3 - 2*B*b*c^2*tan(1/2*x)^3 + 2*C*b^3*tan(1/2*x)^2 + A*b^2*c*tan(1/2*x)^2 + 2*B*b^2*c*tan(1/2*x)^2 + 2*C*b*c^2*tan(1/2*x)^2 - 2*A*c^3*tan(1/2*x)^2 + 2*B*c^3*tan(1/2*x)^2 + A*b^3*tan(1/2*x) + 2*B*b^3*tan(1/2*x) - 2*A*b*c^2*tan(1/2*x) + 2*B*b*c^2*tan(1/2*x) - A*b^2*c)/((b^4 + b^2*c^2)*(b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - b)^2)","B",0
535,1,178,0,0.180339," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{B b x}{b^{2} + c^{2}} + \frac{B c \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - a - b\right)}{b^{2} + c^{2}} - \frac{B c \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} + \frac{2 \, {\left(B a b - A b^{2} - A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2} - c^{2}} {\left(b^{2} + c^{2}\right)}}"," ",0,"B*b*x/(b^2 + c^2) + B*c*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - a - b)/(b^2 + c^2) - B*c*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) + 2*(B*a*b - A*b^2 - A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/(sqrt(a^2 - b^2 - c^2)*(b^2 + c^2))","A",0
536,1,209,0,0.189748," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2,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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} {\left(A a - B b\right)}}{{\left(a^{2} - b^{2} - c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, x\right) - A a b \tan\left(\frac{1}{2} \, x\right) - B a b \tan\left(\frac{1}{2} \, x\right) + A b^{2} \tan\left(\frac{1}{2} \, x\right) + A c^{2} \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) + A a c - B b c\right)}}{{\left(a^{3} - a^{2} b - a b^{2} + b^{3} - a c^{2} + b c^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*(A*a - B*b)/(a^2 - b^2 - c^2)^(3/2) + 2*(B*a^2*tan(1/2*x) - A*a*b*tan(1/2*x) - B*a*b*tan(1/2*x) + A*b^2*tan(1/2*x) + A*c^2*tan(1/2*x) - B*c^2*tan(1/2*x) + A*a*c - B*b*c)/((a^3 - a^2*b - a*b^2 + b^3 - a*c^2 + b*c^2)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b))","A",0
537,1,1162,0,0.546167," ","integrate((A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(2 \, A a^{2} - 3 \, B a b + A b^{2} + A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} + 2 \, b^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} + \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} + 11 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + A a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + A b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 7 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, A a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, A a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} + 13 \, A a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 14 \, B a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, A a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 7 \, A a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, B a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, A a b c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - A b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, B b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, A c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right) - 4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right) + 5 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) + B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) + 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) + B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) - 5 \, A a b^{4} \tan\left(\frac{1}{2} \, x\right) - 3 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right) + A b^{5} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right) + 11 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) - 8 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) - 7 \, A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) + 8 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) - A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) + 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right) - 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right) + 4 \, A a^{4} c - 5 \, B a^{3} b c - 3 \, A a^{2} b^{2} c + 5 \, B a b^{3} c - A b^{4} c - A a^{2} c^{3} + 2 \, B a b c^{3} - A b^{2} c^{3}}{{\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - 2 \, a^{4} c^{2} + 4 \, a^{3} b c^{2} - 4 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + a^{2} c^{4} - 2 \, a b c^{4} + b^{2} c^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}^{2}}"," ",0,"-(2*A*a^2 - 3*B*a*b + A*b^2 + A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/((a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4)*sqrt(a^2 - b^2 - c^2)) + (2*B*a^5*tan(1/2*x)^3 - 4*A*a^4*b*tan(1/2*x)^3 - 5*B*a^4*b*tan(1/2*x)^3 + 11*A*a^3*b^2*tan(1/2*x)^3 + 5*B*a^3*b^2*tan(1/2*x)^3 - 9*A*a^2*b^3*tan(1/2*x)^3 - 5*B*a^2*b^3*tan(1/2*x)^3 + A*a*b^4*tan(1/2*x)^3 + 5*B*a*b^4*tan(1/2*x)^3 + A*b^5*tan(1/2*x)^3 - 2*B*b^5*tan(1/2*x)^3 + 5*A*a^3*c^2*tan(1/2*x)^3 - 4*B*a^3*c^2*tan(1/2*x)^3 - 7*A*a^2*b*c^2*tan(1/2*x)^3 + 4*B*a^2*b*c^2*tan(1/2*x)^3 - A*a*b^2*c^2*tan(1/2*x)^3 + 4*B*a*b^2*c^2*tan(1/2*x)^3 + 3*A*b^3*c^2*tan(1/2*x)^3 - 4*B*b^3*c^2*tan(1/2*x)^3 - 2*A*a*c^4*tan(1/2*x)^3 + 2*B*a*c^4*tan(1/2*x)^3 + 2*A*b*c^4*tan(1/2*x)^3 - 2*B*b*c^4*tan(1/2*x)^3 + 4*A*a^4*c*tan(1/2*x)^2 + 2*B*a^4*c*tan(1/2*x)^2 - 12*A*a^3*b*c*tan(1/2*x)^2 - 9*B*a^3*b*c*tan(1/2*x)^2 + 13*A*a^2*b^2*c*tan(1/2*x)^2 + 14*B*a^2*b^2*c*tan(1/2*x)^2 - 6*A*a*b^3*c*tan(1/2*x)^2 - 9*B*a*b^3*c*tan(1/2*x)^2 + A*b^4*c*tan(1/2*x)^2 + 2*B*b^4*c*tan(1/2*x)^2 + 7*A*a^2*c^3*tan(1/2*x)^2 - 4*B*a^2*c^3*tan(1/2*x)^2 - 6*A*a*b*c^3*tan(1/2*x)^2 - A*b^2*c^3*tan(1/2*x)^2 + 4*B*b^2*c^3*tan(1/2*x)^2 - 2*A*c^5*tan(1/2*x)^2 + 2*B*c^5*tan(1/2*x)^2 + 2*B*a^5*tan(1/2*x) - 4*A*a^4*b*tan(1/2*x) - 3*B*a^4*b*tan(1/2*x) + 5*A*a^3*b^2*tan(1/2*x) + B*a^3*b^2*tan(1/2*x) + 3*A*a^2*b^3*tan(1/2*x) + B*a^2*b^3*tan(1/2*x) - 5*A*a*b^4*tan(1/2*x) - 3*B*a*b^4*tan(1/2*x) + A*b^5*tan(1/2*x) + 2*B*b^5*tan(1/2*x) + 11*A*a^3*c^2*tan(1/2*x) - 4*B*a^3*c^2*tan(1/2*x) - 3*A*a^2*b*c^2*tan(1/2*x) - 8*B*a^2*b*c^2*tan(1/2*x) - 7*A*a*b^2*c^2*tan(1/2*x) + 8*B*a*b^2*c^2*tan(1/2*x) - A*b^3*c^2*tan(1/2*x) + 4*B*b^3*c^2*tan(1/2*x) - 2*A*a*c^4*tan(1/2*x) + 2*B*a*c^4*tan(1/2*x) - 2*A*b*c^4*tan(1/2*x) + 2*B*b*c^4*tan(1/2*x) + 4*A*a^4*c - 5*B*a^3*b*c - 3*A*a^2*b^2*c + 5*B*a*b^3*c - A*b^4*c - A*a^2*c^3 + 2*B*a*b*c^3 - A*b^2*c^3)/((a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^4*c^2 + 4*a^3*b*c^2 - 4*a*b^3*c^2 + 2*b^4*c^2 + a^2*c^4 - 2*a*b*c^4 + b^2*c^4)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b)^2)","B",0
538,1,168,0,0.161510," ","integrate((A+B*cos(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(-2 i \, A a + i \, B b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(2 i \, A a - i \, B b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} - 2 \, A a b + B b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{-i \, a \cos\left(x\right) - a \sin\left(x\right) - i \, a}{a \cos\left(x\right) - i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{-2 i \, A a \tan\left(\frac{1}{2} \, x\right) + i \, B b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a - 2 \, B a + B b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}}"," ",0,"-1/4*(-2*I*A*a + I*B*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(2*I*A*a - I*B*b)*log(tan(1/2*x) - I)/a^2 + 1/4*(2*B*a^2 - 2*A*a*b + B*b^2)*(x + 2*arctan((-I*a*cos(x) - a*sin(x) - I*a)/(a*cos(x) - I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(-2*I*A*a*tan(1/2*x) + I*B*b*tan(1/2*x) - 2*A*a - 2*B*a + B*b)/(a^2*(tan(1/2*x) - I))","B",0
539,1,168,0,0.155216," ","integrate((A+B*cos(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(2 i \, A a - i \, B b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(-2 i \, A a + i \, B b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} - 2 \, A a b + B b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{i \, a \cos\left(x\right) - a \sin\left(x\right) + i \, a}{a \cos\left(x\right) + i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{2 i \, A a \tan\left(\frac{1}{2} \, x\right) - i \, B b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a - 2 \, B a + B b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}}"," ",0,"-1/4*(2*I*A*a - I*B*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 + 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(-2*I*A*a + I*B*b)*log(tan(1/2*x) + I)/a^2 + 1/4*(2*B*a^2 - 2*A*a*b + B*b^2)*(x + 2*arctan((I*a*cos(x) - a*sin(x) + I*a)/(a*cos(x) + I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(2*I*A*a*tan(1/2*x) - I*B*b*tan(1/2*x) - 2*A*a - 2*B*a + B*b)/(a^2*(tan(1/2*x) + I))","B",0
540,1,177,0,0.185050," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{C c x}{b^{2} + c^{2}} - \frac{C b \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - a - b\right)}{b^{2} + c^{2}} + \frac{C b \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} - \frac{2 \, {\left(A b^{2} - C a c + A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2} - c^{2}} {\left(b^{2} + c^{2}\right)}}"," ",0,"C*c*x/(b^2 + c^2) - C*b*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - a - b)/(b^2 + c^2) + C*b*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) - 2*(A*b^2 - C*a*c + A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/(sqrt(a^2 - b^2 - c^2)*(b^2 + c^2))","A",0
541,1,206,0,0.200674," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} {\left(A a - C c\right)}}{{\left(a^{2} - b^{2} - c^{2}\right)}^{\frac{3}{2}}} - \frac{2 \, {\left(A a b \tan\left(\frac{1}{2} \, x\right) - A b^{2} \tan\left(\frac{1}{2} \, x\right) + C a c \tan\left(\frac{1}{2} \, x\right) - C b c \tan\left(\frac{1}{2} \, x\right) - A c^{2} \tan\left(\frac{1}{2} \, x\right) + C a^{2} - C b^{2} - A a c\right)}}{{\left(a^{3} - a^{2} b - a b^{2} + b^{3} - a c^{2} + b c^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*(A*a - C*c)/(a^2 - b^2 - c^2)^(3/2) - 2*(A*a*b*tan(1/2*x) - A*b^2*tan(1/2*x) + C*a*c*tan(1/2*x) - C*b*c*tan(1/2*x) - A*c^2*tan(1/2*x) + C*a^2 - C*b^2 - A*a*c)/((a^3 - a^2*b - a*b^2 + b^3 - a*c^2 + b*c^2)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b))","A",0
542,1,1054,0,0.520274," ","integrate((A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(2 \, A a^{2} + A b^{2} - 3 \, C a c + A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} + 2 \, b^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} - \frac{4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} - 11 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 9 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - A a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - A b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{3} + 9 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 7 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, C a^{5} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C a^{4} b \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C a b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C b^{5} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, A a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 12 \, A a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} - 13 \, A a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, A a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} - A b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 5 \, C a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 14 \, C a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 13 \, C a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, C b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 7 \, A a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 6 \, A a b c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C a c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C b c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, A c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right) - 5 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) + 5 \, A a b^{4} \tan\left(\frac{1}{2} \, x\right) - A b^{5} \tan\left(\frac{1}{2} \, x\right) + 5 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right) - 5 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right) - 5 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right) + 5 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right) - 11 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) + 3 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) + 7 \, A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) + A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) + 4 \, C a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right) - 4 \, C a b c^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, C a^{5} - 4 \, C a^{3} b^{2} + 2 \, C a b^{4} - 4 \, A a^{4} c + 3 \, A a^{2} b^{2} c + A b^{4} c + C a^{3} c^{2} - C a b^{2} c^{2} + A a^{2} c^{3} + A b^{2} c^{3}}{{\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - 2 \, a^{4} c^{2} + 4 \, a^{3} b c^{2} - 4 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + a^{2} c^{4} - 2 \, a b c^{4} + b^{2} c^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}^{2}}"," ",0,"-(2*A*a^2 + A*b^2 - 3*C*a*c + A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/((a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4)*sqrt(a^2 - b^2 - c^2)) - (4*A*a^4*b*tan(1/2*x)^3 - 11*A*a^3*b^2*tan(1/2*x)^3 + 9*A*a^2*b^3*tan(1/2*x)^3 - A*a*b^4*tan(1/2*x)^3 - A*b^5*tan(1/2*x)^3 + 3*C*a^4*c*tan(1/2*x)^3 - 9*C*a^3*b*c*tan(1/2*x)^3 + 9*C*a^2*b^2*c*tan(1/2*x)^3 - 3*C*a*b^3*c*tan(1/2*x)^3 - 5*A*a^3*c^2*tan(1/2*x)^3 + 7*A*a^2*b*c^2*tan(1/2*x)^3 + A*a*b^2*c^2*tan(1/2*x)^3 - 3*A*b^3*c^2*tan(1/2*x)^3 + 2*A*a*c^4*tan(1/2*x)^3 - 2*A*b*c^4*tan(1/2*x)^3 + 2*C*a^5*tan(1/2*x)^2 - 2*C*a^4*b*tan(1/2*x)^2 - 4*C*a^3*b^2*tan(1/2*x)^2 + 4*C*a^2*b^3*tan(1/2*x)^2 + 2*C*a*b^4*tan(1/2*x)^2 - 2*C*b^5*tan(1/2*x)^2 - 4*A*a^4*c*tan(1/2*x)^2 + 12*A*a^3*b*c*tan(1/2*x)^2 - 13*A*a^2*b^2*c*tan(1/2*x)^2 + 6*A*a*b^3*c*tan(1/2*x)^2 - A*b^4*c*tan(1/2*x)^2 + 5*C*a^3*c^2*tan(1/2*x)^2 - 14*C*a^2*b*c^2*tan(1/2*x)^2 + 13*C*a*b^2*c^2*tan(1/2*x)^2 - 4*C*b^3*c^2*tan(1/2*x)^2 - 7*A*a^2*c^3*tan(1/2*x)^2 + 6*A*a*b*c^3*tan(1/2*x)^2 + A*b^2*c^3*tan(1/2*x)^2 + 2*C*a*c^4*tan(1/2*x)^2 - 2*C*b*c^4*tan(1/2*x)^2 + 2*A*c^5*tan(1/2*x)^2 + 4*A*a^4*b*tan(1/2*x) - 5*A*a^3*b^2*tan(1/2*x) - 3*A*a^2*b^3*tan(1/2*x) + 5*A*a*b^4*tan(1/2*x) - A*b^5*tan(1/2*x) + 5*C*a^4*c*tan(1/2*x) - 5*C*a^3*b*c*tan(1/2*x) - 5*C*a^2*b^2*c*tan(1/2*x) + 5*C*a*b^3*c*tan(1/2*x) - 11*A*a^3*c^2*tan(1/2*x) + 3*A*a^2*b*c^2*tan(1/2*x) + 7*A*a*b^2*c^2*tan(1/2*x) + A*b^3*c^2*tan(1/2*x) + 4*C*a^2*c^3*tan(1/2*x) - 4*C*a*b*c^3*tan(1/2*x) + 2*A*a*c^4*tan(1/2*x) + 2*A*b*c^4*tan(1/2*x) + 2*C*a^5 - 4*C*a^3*b^2 + 2*C*a*b^4 - 4*A*a^4*c + 3*A*a^2*b^2*c + A*b^4*c + C*a^3*c^2 - C*a*b^2*c^2 + A*a^2*c^3 + A*b^2*c^3)/((a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^4*c^2 + 4*a^3*b*c^2 - 4*a*b^3*c^2 + 2*b^4*c^2 + a^2*c^4 - 2*a*b*c^4 + b^2*c^4)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b)^2)","B",0
543,1,169,0,0.155120," ","integrate((A+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(-2 i \, A a - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(2 i \, A a + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}{2 \, a^{2}} - \frac{{\left(2 i \, C a^{2} + 2 \, A a b - i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{-i \, a \cos\left(x\right) - a \sin\left(x\right) - i \, a}{a \cos\left(x\right) - i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{-2 i \, A a \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a - 2 i \, C a + i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}}"," ",0,"-1/4*(-2*I*A*a - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(2*I*A*a + C*b)*log(tan(1/2*x) - I)/a^2 - 1/4*(2*I*C*a^2 + 2*A*a*b - I*C*b^2)*(x + 2*arctan((-I*a*cos(x) - a*sin(x) - I*a)/(a*cos(x) - I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(-2*I*A*a*tan(1/2*x) - C*b*tan(1/2*x) - 2*A*a - 2*I*C*a + I*C*b)/(a^2*(tan(1/2*x) - I))","B",0
544,1,169,0,0.175522," ","integrate((A+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(2 i \, A a - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(-2 i \, A a + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}{2 \, a^{2}} - \frac{{\left(-2 i \, C a^{2} + 2 \, A a b + i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{i \, a \cos\left(x\right) - a \sin\left(x\right) + i \, a}{a \cos\left(x\right) + i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{2 i \, A a \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a + 2 i \, C a - i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}}"," ",0,"-1/4*(2*I*A*a - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 + 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(-2*I*A*a + C*b)*log(tan(1/2*x) + I)/a^2 - 1/4*(-2*I*C*a^2 + 2*A*a*b + I*C*b^2)*(x + 2*arctan((I*a*cos(x) - a*sin(x) + I*a)/(a*cos(x) + I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(2*I*A*a*tan(1/2*x) - C*b*tan(1/2*x) - 2*A*a + 2*I*C*a - I*C*b)/(a^2*(tan(1/2*x) + I))","B",0
545,1,187,0,0.150431," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{{\left(B b + C c\right)} x}{b^{2} + c^{2}} - \frac{{\left(C b - B c\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - a - b\right)}{b^{2} + c^{2}} + \frac{{\left(C b - B c\right)} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} + \frac{2 \, {\left(B a b + C a c\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2} - c^{2}} {\left(b^{2} + c^{2}\right)}}"," ",0,"(B*b + C*c)*x/(b^2 + c^2) - (C*b - B*c)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - a - b)/(b^2 + c^2) + (C*b - B*c)*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) + 2*(B*a*b + C*a*c)*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x) + c)/sqrt(a^2 - b^2 - c^2)))/(sqrt(a^2 - b^2 - c^2)*(b^2 + c^2))","A",0
546,1,205,0,0.184151," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} {\left(B b + C c\right)}}{{\left(a^{2} - b^{2} - c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, x\right) - B a b \tan\left(\frac{1}{2} \, x\right) - C a c \tan\left(\frac{1}{2} \, x\right) + C b c \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) - C a^{2} + C b^{2} - B b c\right)}}{{\left(a^{3} - a^{2} b - a b^{2} + b^{3} - a c^{2} + b c^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*(B*b + C*c)/(a^2 - b^2 - c^2)^(3/2) + 2*(B*a^2*tan(1/2*x) - B*a*b*tan(1/2*x) - C*a*c*tan(1/2*x) + C*b*c*tan(1/2*x) - B*c^2*tan(1/2*x) - C*a^2 + C*b^2 - B*b*c)/((a^3 - a^2*b - a*b^2 + b^3 - a*c^2 + b*c^2)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b))","A",0
547,1,1034,0,0.511717," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","\frac{3 \, {\left(B a b + C a c\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} + 2 \, b^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} + \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right)^{3} + 9 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C a^{4} b \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C a b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} + 14 \, B a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} - 5 \, C a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 14 \, C a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 13 \, C a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, C b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, B a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, B b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C a c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right) + B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) + B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) - 3 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right) - 5 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right) + 5 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right) + 5 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right) - 5 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right) - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 8 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) + 8 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) + 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 4 \, C a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right) + 4 \, C a b c^{3} \tan\left(\frac{1}{2} \, x\right) + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right) - 2 \, C a^{5} + 4 \, C a^{3} b^{2} - 2 \, C a b^{4} - 5 \, B a^{3} b c + 5 \, B a b^{3} c - C a^{3} c^{2} + C a b^{2} c^{2} + 2 \, B a b c^{3}}{{\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - 2 \, a^{4} c^{2} + 4 \, a^{3} b c^{2} - 4 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + a^{2} c^{4} - 2 \, a b c^{4} + b^{2} c^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}^{2}}"," ",0,"3*(B*a*b + C*a*c)*(pi*floor(1/2*x/pi + 1/2)*sgn(-2*a + 2*b) + arctan(-(a*tan(1/2*x) - b*tan(1/2*x) + c)/sqrt(a^2 - b^2 - c^2)))/((a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4)*sqrt(a^2 - b^2 - c^2)) + (2*B*a^5*tan(1/2*x)^3 - 5*B*a^4*b*tan(1/2*x)^3 + 5*B*a^3*b^2*tan(1/2*x)^3 - 5*B*a^2*b^3*tan(1/2*x)^3 + 5*B*a*b^4*tan(1/2*x)^3 - 2*B*b^5*tan(1/2*x)^3 - 3*C*a^4*c*tan(1/2*x)^3 + 9*C*a^3*b*c*tan(1/2*x)^3 - 9*C*a^2*b^2*c*tan(1/2*x)^3 + 3*C*a*b^3*c*tan(1/2*x)^3 - 4*B*a^3*c^2*tan(1/2*x)^3 + 4*B*a^2*b*c^2*tan(1/2*x)^3 + 4*B*a*b^2*c^2*tan(1/2*x)^3 - 4*B*b^3*c^2*tan(1/2*x)^3 + 2*B*a*c^4*tan(1/2*x)^3 - 2*B*b*c^4*tan(1/2*x)^3 - 2*C*a^5*tan(1/2*x)^2 + 2*C*a^4*b*tan(1/2*x)^2 + 4*C*a^3*b^2*tan(1/2*x)^2 - 4*C*a^2*b^3*tan(1/2*x)^2 - 2*C*a*b^4*tan(1/2*x)^2 + 2*C*b^5*tan(1/2*x)^2 + 2*B*a^4*c*tan(1/2*x)^2 - 9*B*a^3*b*c*tan(1/2*x)^2 + 14*B*a^2*b^2*c*tan(1/2*x)^2 - 9*B*a*b^3*c*tan(1/2*x)^2 + 2*B*b^4*c*tan(1/2*x)^2 - 5*C*a^3*c^2*tan(1/2*x)^2 + 14*C*a^2*b*c^2*tan(1/2*x)^2 - 13*C*a*b^2*c^2*tan(1/2*x)^2 + 4*C*b^3*c^2*tan(1/2*x)^2 - 4*B*a^2*c^3*tan(1/2*x)^2 + 4*B*b^2*c^3*tan(1/2*x)^2 - 2*C*a*c^4*tan(1/2*x)^2 + 2*C*b*c^4*tan(1/2*x)^2 + 2*B*c^5*tan(1/2*x)^2 + 2*B*a^5*tan(1/2*x) - 3*B*a^4*b*tan(1/2*x) + B*a^3*b^2*tan(1/2*x) + B*a^2*b^3*tan(1/2*x) - 3*B*a*b^4*tan(1/2*x) + 2*B*b^5*tan(1/2*x) - 5*C*a^4*c*tan(1/2*x) + 5*C*a^3*b*c*tan(1/2*x) + 5*C*a^2*b^2*c*tan(1/2*x) - 5*C*a*b^3*c*tan(1/2*x) - 4*B*a^3*c^2*tan(1/2*x) - 8*B*a^2*b*c^2*tan(1/2*x) + 8*B*a*b^2*c^2*tan(1/2*x) + 4*B*b^3*c^2*tan(1/2*x) - 4*C*a^2*c^3*tan(1/2*x) + 4*C*a*b*c^3*tan(1/2*x) + 2*B*a*c^4*tan(1/2*x) + 2*B*b*c^4*tan(1/2*x) - 2*C*a^5 + 4*C*a^3*b^2 - 2*C*a*b^4 - 5*B*a^3*b*c + 5*B*a*b^3*c - C*a^3*c^2 + C*a*b^2*c^2 + 2*B*a*b*c^3)/((a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^4*c^2 + 4*a^3*b*c^2 - 4*a*b^3*c^2 + 2*b^4*c^2 + a^2*c^4 - 2*a*b*c^4 + b^2*c^4)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b)^2)","B",0
548,1,178,0,0.160296," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(i \, B b - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(-i \, B b + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} - 2 i \, C a^{2} + B b^{2} + i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{-i \, a \cos\left(x\right) - a \sin\left(x\right) - i \, a}{a \cos\left(x\right) - i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{i \, B b \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, B a - 2 i \, C a + B b + i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}}"," ",0,"-1/4*(I*B*b - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(-I*B*b + C*b)*log(tan(1/2*x) - I)/a^2 + 1/4*(2*B*a^2 - 2*I*C*a^2 + B*b^2 + I*C*b^2)*(x + 2*arctan((-I*a*cos(x) - a*sin(x) - I*a)/(a*cos(x) - I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(I*B*b*tan(1/2*x) - C*b*tan(1/2*x) - 2*B*a - 2*I*C*a + B*b + I*C*b)/(a^2*(tan(1/2*x) - I))","B",0
549,1,178,0,0.158756," ","integrate((B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(-i \, B b - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(i \, B b + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} + 2 i \, C a^{2} + B b^{2} - i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{i \, a \cos\left(x\right) - a \sin\left(x\right) + i \, a}{a \cos\left(x\right) + i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{-i \, B b \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, B a + 2 i \, C a + B b - i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}}"," ",0,"-1/4*(-I*B*b - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 + 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(I*B*b + C*b)*log(tan(1/2*x) + I)/a^2 + 1/4*(2*B*a^2 + 2*I*C*a^2 + B*b^2 - I*C*b^2)*(x + 2*arctan((I*a*cos(x) - a*sin(x) + I*a)/(a*cos(x) + I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(-I*B*b*tan(1/2*x) - C*b*tan(1/2*x) - 2*B*a + 2*I*C*a + B*b - I*C*b)/(a^2*(tan(1/2*x) + I))","B",0
550,1,199,0,0.184384," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)),x, algorithm=""giac"")","\frac{{\left(B b + C c\right)} x}{b^{2} + c^{2}} - \frac{{\left(C b - B c\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, c \tan\left(\frac{1}{2} \, x\right) - a - b\right)}{b^{2} + c^{2}} + \frac{{\left(C b - B c\right)} \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}{b^{2} + c^{2}} + \frac{2 \, {\left(B a b - A b^{2} + C a c - A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{\sqrt{a^{2} - b^{2} - c^{2}} {\left(b^{2} + c^{2}\right)}}"," ",0,"(B*b + C*c)*x/(b^2 + c^2) - (C*b - B*c)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*c*tan(1/2*x) - a - b)/(b^2 + c^2) + (C*b - B*c)*log(tan(1/2*x)^2 + 1)/(b^2 + c^2) + 2*(B*a*b - A*b^2 + C*a*c - A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/(sqrt(a^2 - b^2 - c^2)*(b^2 + c^2))","A",0
551,1,241,0,0.166758," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2,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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)} {\left(A a - B b - C c\right)}}{{\left(a^{2} - b^{2} - c^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left(B a^{2} \tan\left(\frac{1}{2} \, x\right) - A a b \tan\left(\frac{1}{2} \, x\right) - B a b \tan\left(\frac{1}{2} \, x\right) + A b^{2} \tan\left(\frac{1}{2} \, x\right) - C a c \tan\left(\frac{1}{2} \, x\right) + C b c \tan\left(\frac{1}{2} \, x\right) + A c^{2} \tan\left(\frac{1}{2} \, x\right) - B c^{2} \tan\left(\frac{1}{2} \, x\right) - C a^{2} + C b^{2} + A a c - B b c\right)}}{{\left(a^{3} - a^{2} b - a b^{2} + b^{3} - a c^{2} + b c^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}}"," ",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) + c)/sqrt(a^2 - b^2 - c^2)))*(A*a - B*b - C*c)/(a^2 - b^2 - c^2)^(3/2) + 2*(B*a^2*tan(1/2*x) - A*a*b*tan(1/2*x) - B*a*b*tan(1/2*x) + A*b^2*tan(1/2*x) - C*a*c*tan(1/2*x) + C*b*c*tan(1/2*x) + A*c^2*tan(1/2*x) - B*c^2*tan(1/2*x) - C*a^2 + C*b^2 + A*a*c - B*b*c)/((a^3 - a^2*b - a*b^2 + b^3 - a*c^2 + b*c^2)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b))","A",0
552,1,1506,0,0.542512," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3,x, algorithm=""giac"")","-\frac{{\left(2 \, A a^{2} - 3 \, B a b + A b^{2} - 3 \, C a c + A c^{2}\right)} {\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) + c}{\sqrt{a^{2} - b^{2} - c^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, a^{2} c^{2} + 2 \, b^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - b^{2} - c^{2}}} + \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right)^{3} + 11 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} - 5 \, B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{3} + A a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + A b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right)^{3} - 3 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right)^{3} + 9 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{3} - 9 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{3} + 5 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 7 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 4 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 3 \, A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C a^{4} b \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, C a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, C a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C a b^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, A a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} - 12 \, A a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a^{3} b c \tan\left(\frac{1}{2} \, x\right)^{2} + 13 \, A a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} + 14 \, B a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, A a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} - 9 \, B a b^{3} c \tan\left(\frac{1}{2} \, x\right)^{2} + A b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B b^{4} c \tan\left(\frac{1}{2} \, x\right)^{2} - 5 \, C a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 14 \, C a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 13 \, C a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, C b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 7 \, A a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, B a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 6 \, A a b c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - A b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, B b^{2} c^{3} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, C a c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, C b c^{4} \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, A c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B c^{5} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, B a^{5} \tan\left(\frac{1}{2} \, x\right) - 4 \, A a^{4} b \tan\left(\frac{1}{2} \, x\right) - 3 \, B a^{4} b \tan\left(\frac{1}{2} \, x\right) + 5 \, A a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) + B a^{3} b^{2} \tan\left(\frac{1}{2} \, x\right) + 3 \, A a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) + B a^{2} b^{3} \tan\left(\frac{1}{2} \, x\right) - 5 \, A a b^{4} \tan\left(\frac{1}{2} \, x\right) - 3 \, B a b^{4} \tan\left(\frac{1}{2} \, x\right) + A b^{5} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b^{5} \tan\left(\frac{1}{2} \, x\right) - 5 \, C a^{4} c \tan\left(\frac{1}{2} \, x\right) + 5 \, C a^{3} b c \tan\left(\frac{1}{2} \, x\right) + 5 \, C a^{2} b^{2} c \tan\left(\frac{1}{2} \, x\right) - 5 \, C a b^{3} c \tan\left(\frac{1}{2} \, x\right) + 11 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 3 \, A a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) - 8 \, B a^{2} b c^{2} \tan\left(\frac{1}{2} \, x\right) - 7 \, A a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) + 8 \, B a b^{2} c^{2} \tan\left(\frac{1}{2} \, x\right) - A b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) + 4 \, B b^{3} c^{2} \tan\left(\frac{1}{2} \, x\right) - 4 \, C a^{2} c^{3} \tan\left(\frac{1}{2} \, x\right) + 4 \, C a b c^{3} \tan\left(\frac{1}{2} \, x\right) - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x\right) - 2 \, A b c^{4} \tan\left(\frac{1}{2} \, x\right) + 2 \, B b c^{4} \tan\left(\frac{1}{2} \, x\right) - 2 \, C a^{5} + 4 \, C a^{3} b^{2} - 2 \, C a b^{4} + 4 \, A a^{4} c - 5 \, B a^{3} b c - 3 \, A a^{2} b^{2} c + 5 \, B a b^{3} c - A b^{4} c - C a^{3} c^{2} + C a b^{2} c^{2} - A a^{2} c^{3} + 2 \, B a b c^{3} - A b^{2} c^{3}}{{\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - a^{2} b^{4} - 2 \, a b^{5} + b^{6} - 2 \, a^{4} c^{2} + 4 \, a^{3} b c^{2} - 4 \, a b^{3} c^{2} + 2 \, b^{4} c^{2} + a^{2} c^{4} - 2 \, a b c^{4} + b^{2} c^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)}^{2}}"," ",0,"-(2*A*a^2 - 3*B*a*b + A*b^2 - 3*C*a*c + A*c^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) + c)/sqrt(a^2 - b^2 - c^2)))/((a^4 - 2*a^2*b^2 + b^4 - 2*a^2*c^2 + 2*b^2*c^2 + c^4)*sqrt(a^2 - b^2 - c^2)) + (2*B*a^5*tan(1/2*x)^3 - 4*A*a^4*b*tan(1/2*x)^3 - 5*B*a^4*b*tan(1/2*x)^3 + 11*A*a^3*b^2*tan(1/2*x)^3 + 5*B*a^3*b^2*tan(1/2*x)^3 - 9*A*a^2*b^3*tan(1/2*x)^3 - 5*B*a^2*b^3*tan(1/2*x)^3 + A*a*b^4*tan(1/2*x)^3 + 5*B*a*b^4*tan(1/2*x)^3 + A*b^5*tan(1/2*x)^3 - 2*B*b^5*tan(1/2*x)^3 - 3*C*a^4*c*tan(1/2*x)^3 + 9*C*a^3*b*c*tan(1/2*x)^3 - 9*C*a^2*b^2*c*tan(1/2*x)^3 + 3*C*a*b^3*c*tan(1/2*x)^3 + 5*A*a^3*c^2*tan(1/2*x)^3 - 4*B*a^3*c^2*tan(1/2*x)^3 - 7*A*a^2*b*c^2*tan(1/2*x)^3 + 4*B*a^2*b*c^2*tan(1/2*x)^3 - A*a*b^2*c^2*tan(1/2*x)^3 + 4*B*a*b^2*c^2*tan(1/2*x)^3 + 3*A*b^3*c^2*tan(1/2*x)^3 - 4*B*b^3*c^2*tan(1/2*x)^3 - 2*A*a*c^4*tan(1/2*x)^3 + 2*B*a*c^4*tan(1/2*x)^3 + 2*A*b*c^4*tan(1/2*x)^3 - 2*B*b*c^4*tan(1/2*x)^3 - 2*C*a^5*tan(1/2*x)^2 + 2*C*a^4*b*tan(1/2*x)^2 + 4*C*a^3*b^2*tan(1/2*x)^2 - 4*C*a^2*b^3*tan(1/2*x)^2 - 2*C*a*b^4*tan(1/2*x)^2 + 2*C*b^5*tan(1/2*x)^2 + 4*A*a^4*c*tan(1/2*x)^2 + 2*B*a^4*c*tan(1/2*x)^2 - 12*A*a^3*b*c*tan(1/2*x)^2 - 9*B*a^3*b*c*tan(1/2*x)^2 + 13*A*a^2*b^2*c*tan(1/2*x)^2 + 14*B*a^2*b^2*c*tan(1/2*x)^2 - 6*A*a*b^3*c*tan(1/2*x)^2 - 9*B*a*b^3*c*tan(1/2*x)^2 + A*b^4*c*tan(1/2*x)^2 + 2*B*b^4*c*tan(1/2*x)^2 - 5*C*a^3*c^2*tan(1/2*x)^2 + 14*C*a^2*b*c^2*tan(1/2*x)^2 - 13*C*a*b^2*c^2*tan(1/2*x)^2 + 4*C*b^3*c^2*tan(1/2*x)^2 + 7*A*a^2*c^3*tan(1/2*x)^2 - 4*B*a^2*c^3*tan(1/2*x)^2 - 6*A*a*b*c^3*tan(1/2*x)^2 - A*b^2*c^3*tan(1/2*x)^2 + 4*B*b^2*c^3*tan(1/2*x)^2 - 2*C*a*c^4*tan(1/2*x)^2 + 2*C*b*c^4*tan(1/2*x)^2 - 2*A*c^5*tan(1/2*x)^2 + 2*B*c^5*tan(1/2*x)^2 + 2*B*a^5*tan(1/2*x) - 4*A*a^4*b*tan(1/2*x) - 3*B*a^4*b*tan(1/2*x) + 5*A*a^3*b^2*tan(1/2*x) + B*a^3*b^2*tan(1/2*x) + 3*A*a^2*b^3*tan(1/2*x) + B*a^2*b^3*tan(1/2*x) - 5*A*a*b^4*tan(1/2*x) - 3*B*a*b^4*tan(1/2*x) + A*b^5*tan(1/2*x) + 2*B*b^5*tan(1/2*x) - 5*C*a^4*c*tan(1/2*x) + 5*C*a^3*b*c*tan(1/2*x) + 5*C*a^2*b^2*c*tan(1/2*x) - 5*C*a*b^3*c*tan(1/2*x) + 11*A*a^3*c^2*tan(1/2*x) - 4*B*a^3*c^2*tan(1/2*x) - 3*A*a^2*b*c^2*tan(1/2*x) - 8*B*a^2*b*c^2*tan(1/2*x) - 7*A*a*b^2*c^2*tan(1/2*x) + 8*B*a*b^2*c^2*tan(1/2*x) - A*b^3*c^2*tan(1/2*x) + 4*B*b^3*c^2*tan(1/2*x) - 4*C*a^2*c^3*tan(1/2*x) + 4*C*a*b*c^3*tan(1/2*x) - 2*A*a*c^4*tan(1/2*x) + 2*B*a*c^4*tan(1/2*x) - 2*A*b*c^4*tan(1/2*x) + 2*B*b*c^4*tan(1/2*x) - 2*C*a^5 + 4*C*a^3*b^2 - 2*C*a*b^4 + 4*A*a^4*c - 5*B*a^3*b*c - 3*A*a^2*b^2*c + 5*B*a*b^3*c - A*b^4*c - C*a^3*c^2 + C*a*b^2*c^2 - A*a^2*c^3 + 2*B*a*b*c^3 - A*b^2*c^3)/((a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - a^2*b^4 - 2*a*b^5 + b^6 - 2*a^4*c^2 + 4*a^3*b*c^2 - 4*a*b^3*c^2 + 2*b^4*c^2 + a^2*c^4 - 2*a*b*c^4 + b^2*c^4)*(a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b)^2)","B",0
553,1,203,0,0.148144," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)+I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(-2 i \, A a + i \, B b - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} - 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(2 i \, A a - i \, B b + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} - 2 i \, C a^{2} - 2 \, A a b + B b^{2} + i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{-i \, a \cos\left(x\right) - a \sin\left(x\right) - i \, a}{a \cos\left(x\right) - i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{-2 i \, A a \tan\left(\frac{1}{2} \, x\right) + i \, B b \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a - 2 \, B a - 2 i \, C a + B b + i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) - i\right)}}"," ",0,"-1/4*(-2*I*A*a + I*B*b - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 - 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(2*I*A*a - I*B*b + C*b)*log(tan(1/2*x) - I)/a^2 + 1/4*(2*B*a^2 - 2*I*C*a^2 - 2*A*a*b + B*b^2 + I*C*b^2)*(x + 2*arctan((-I*a*cos(x) - a*sin(x) - I*a)/(a*cos(x) - I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(-2*I*A*a*tan(1/2*x) + I*B*b*tan(1/2*x) - C*b*tan(1/2*x) - 2*A*a - 2*B*a - 2*I*C*a + B*b + I*C*b)/(a^2*(tan(1/2*x) - I))","B",0
554,1,203,0,0.151208," ","integrate((A+B*cos(x)+C*sin(x))/(a+b*cos(x)-I*b*sin(x)),x, algorithm=""giac"")","-\frac{{\left(2 i \, A a - i \, B b - C b\right)} \log\left(-a \tan\left(\frac{1}{2} \, x\right)^{2} + b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 i \, a \tan\left(\frac{1}{2} \, x\right) + a + b\right)}{4 \, a^{2}} - \frac{{\left(-2 i \, A a + i \, B b + C b\right)} \log\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}{2 \, a^{2}} + \frac{{\left(2 \, B a^{2} + 2 i \, C a^{2} - 2 \, A a b + B b^{2} - i \, C b^{2}\right)} {\left(x + 2 \, \arctan\left(\frac{i \, a \cos\left(x\right) - a \sin\left(x\right) + i \, a}{a \cos\left(x\right) + i \, a \sin\left(x\right) - a + 2 \, b}\right)\right)}}{4 \, a^{2} b} - \frac{2 i \, A a \tan\left(\frac{1}{2} \, x\right) - i \, B b \tan\left(\frac{1}{2} \, x\right) - C b \tan\left(\frac{1}{2} \, x\right) - 2 \, A a - 2 \, B a + 2 i \, C a + B b - i \, C b}{2 \, a^{2} {\left(\tan\left(\frac{1}{2} \, x\right) + i\right)}}"," ",0,"-1/4*(2*I*A*a - I*B*b - C*b)*log(-a*tan(1/2*x)^2 + b*tan(1/2*x)^2 + 2*I*a*tan(1/2*x) + a + b)/a^2 - 1/2*(-2*I*A*a + I*B*b + C*b)*log(tan(1/2*x) + I)/a^2 + 1/4*(2*B*a^2 + 2*I*C*a^2 - 2*A*a*b + B*b^2 - I*C*b^2)*(x + 2*arctan((I*a*cos(x) - a*sin(x) + I*a)/(a*cos(x) + I*a*sin(x) - a + 2*b)))/(a^2*b) - 1/2*(2*I*A*a*tan(1/2*x) - I*B*b*tan(1/2*x) - C*b*tan(1/2*x) - 2*A*a - 2*B*a + 2*I*C*a + B*b - I*C*b)/(a^2*(tan(1/2*x) + I))","B",0
555,1,68,0,0.178527," ","integrate((b^2+c^2+a*b*cos(x)+a*c*sin(x))/(a+b*cos(x)+c*sin(x))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a b \tan\left(\frac{1}{2} \, x\right) - b^{2} \tan\left(\frac{1}{2} \, x\right) - c^{2} \tan\left(\frac{1}{2} \, x\right) - a c\right)}}{{\left(a \tan\left(\frac{1}{2} \, x\right)^{2} - b \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x\right) + a + b\right)} {\left(a - b\right)}}"," ",0,"2*(a*b*tan(1/2*x) - b^2*tan(1/2*x) - c^2*tan(1/2*x) - a*c)/((a*tan(1/2*x)^2 - b*tan(1/2*x)^2 + 2*c*tan(1/2*x) + a + b)*(a - b))","B",0
556,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(5/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""giac"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} {\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*(b*cos(x) + c*sin(x) + a)^(5/2), x)","F",0
557,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(3/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""giac"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} {\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*(b*cos(x) + c*sin(x) + a)^(3/2), x)","F",0
558,0,0,0,0.000000," ","integrate((a+b*cos(x)+c*sin(x))^(1/2)*(d+b*e*cos(x)+c*e*sin(x)),x, algorithm=""giac"")","\int {\left(b e \cos\left(x\right) + c e \sin\left(x\right) + d\right)} \sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)*sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
559,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{\sqrt{b \cos\left(x\right) + c \sin\left(x\right) + a}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/sqrt(b*cos(x) + c*sin(x) + a), x)","F",0
560,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(3/2),x, algorithm=""giac"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{{\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/(b*cos(x) + c*sin(x) + a)^(3/2), x)","F",0
561,0,0,0,0.000000," ","integrate((d+b*e*cos(x)+c*e*sin(x))/(a+b*cos(x)+c*sin(x))^(5/2),x, algorithm=""giac"")","\int \frac{b e \cos\left(x\right) + c e \sin\left(x\right) + d}{{\left(b \cos\left(x\right) + c \sin\left(x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*e*cos(x) + c*e*sin(x) + d)/(b*cos(x) + c*sin(x) + a)^(5/2), x)","F",0
562,1,141,0,0.180335," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d)),x, algorithm=""giac"")","{\left(\frac{{\left(x e + d\right)} C}{c} + \frac{B \log\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}{c} - \frac{B \log\left(\tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 1\right)}{c} - \frac{2 \, {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c}{\sqrt{a^{2} - c^{2}}}\right)\right)} {\left(C a - A c\right)}}{\sqrt{a^{2} - c^{2}} c}\right)} e^{\left(-1\right)}"," ",0,"((x*e + d)*C/c + B*log(a*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a)/c - B*log(tan(1/2*x*e + 1/2*d)^2 + 1)/c - 2*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x*e + 1/2*d) + c)/sqrt(a^2 - c^2)))*(C*a - A*c)/(sqrt(a^2 - c^2)*c))*e^(-1)","A",0
563,1,187,0,0.198340," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(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(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c}{\sqrt{a^{2} - c^{2}}}\right)\right)} {\left(A a - C c\right)}}{{\left(a^{2} - c^{2}\right)}^{\frac{3}{2}}} + \frac{B a^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - C a c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + A c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - B c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - C a^{2} + A a c}{{\left(a^{3} - a c^{2}\right)} {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}}\right)} e^{\left(-1\right)}"," ",0,"2*((pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x*e + 1/2*d) + c)/sqrt(a^2 - c^2)))*(A*a - C*c)/(a^2 - c^2)^(3/2) + (B*a^2*tan(1/2*x*e + 1/2*d) - C*a*c*tan(1/2*x*e + 1/2*d) + A*c^2*tan(1/2*x*e + 1/2*d) - B*c^2*tan(1/2*x*e + 1/2*d) - C*a^2 + A*a*c)/((a^3 - a*c^2)*(a*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a)))*e^(-1)","A",0
564,1,596,0,0.265447," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^3,x, algorithm=""giac"")","{\left(\frac{{\left(2 \, A a^{2} - 3 \, C a c + A c^{2}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c}{\sqrt{a^{2} - c^{2}}}\right)\right)}}{{\left(a^{4} - 2 \, a^{2} c^{2} + c^{4}\right)} \sqrt{a^{2} - c^{2}}} + \frac{2 \, B a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 3 \, C a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 5 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 2 \, C a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 4 \, A a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, B a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 5 \, C a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 7 \, A a^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 4 \, B a^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, C a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 2 \, A c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, B c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, B a^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 5 \, C a^{4} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 11 \, A a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, B a^{3} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 4 \, C a^{2} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 2 \, A a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 2 \, B a c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 2 \, C a^{5} + 4 \, A a^{4} c - C a^{3} c^{2} - A a^{2} c^{3}}{{\left(a^{6} - 2 \, a^{4} c^{2} + a^{2} c^{4}\right)} {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}^{2}}\right)} e^{\left(-1\right)}"," ",0,"((2*A*a^2 - 3*C*a*c + A*c^2)*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x*e + 1/2*d) + c)/sqrt(a^2 - c^2)))/((a^4 - 2*a^2*c^2 + c^4)*sqrt(a^2 - c^2)) + (2*B*a^5*tan(1/2*x*e + 1/2*d)^3 - 3*C*a^4*c*tan(1/2*x*e + 1/2*d)^3 + 5*A*a^3*c^2*tan(1/2*x*e + 1/2*d)^3 - 4*B*a^3*c^2*tan(1/2*x*e + 1/2*d)^3 - 2*A*a*c^4*tan(1/2*x*e + 1/2*d)^3 + 2*B*a*c^4*tan(1/2*x*e + 1/2*d)^3 - 2*C*a^5*tan(1/2*x*e + 1/2*d)^2 + 4*A*a^4*c*tan(1/2*x*e + 1/2*d)^2 + 2*B*a^4*c*tan(1/2*x*e + 1/2*d)^2 - 5*C*a^3*c^2*tan(1/2*x*e + 1/2*d)^2 + 7*A*a^2*c^3*tan(1/2*x*e + 1/2*d)^2 - 4*B*a^2*c^3*tan(1/2*x*e + 1/2*d)^2 - 2*C*a*c^4*tan(1/2*x*e + 1/2*d)^2 - 2*A*c^5*tan(1/2*x*e + 1/2*d)^2 + 2*B*c^5*tan(1/2*x*e + 1/2*d)^2 + 2*B*a^5*tan(1/2*x*e + 1/2*d) - 5*C*a^4*c*tan(1/2*x*e + 1/2*d) + 11*A*a^3*c^2*tan(1/2*x*e + 1/2*d) - 4*B*a^3*c^2*tan(1/2*x*e + 1/2*d) - 4*C*a^2*c^3*tan(1/2*x*e + 1/2*d) - 2*A*a*c^4*tan(1/2*x*e + 1/2*d) + 2*B*a*c^4*tan(1/2*x*e + 1/2*d) - 2*C*a^5 + 4*A*a^4*c - C*a^3*c^2 - A*a^2*c^3)/((a^6 - 2*a^4*c^2 + a^2*c^4)*(a*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a)^2))*e^(-1)","B",0
565,1,1340,0,0.307027," ","integrate((A+B*cos(e*x+d)+C*sin(e*x+d))/(a+c*sin(e*x+d))^4,x, algorithm=""giac"")","\frac{1}{3} \, {\left(\frac{3 \, {\left(2 \, A a^{3} - 4 \, C a^{2} c + 3 \, A a c^{2} - C c^{3}\right)} {\left(\pi \left \lfloor \frac{x e + d}{2 \, \pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + c}{\sqrt{a^{2} - c^{2}}}\right)\right)}}{{\left(a^{6} - 3 \, a^{4} c^{2} + 3 \, a^{2} c^{4} - c^{6}\right)} \sqrt{a^{2} - c^{2}}} + \frac{6 \, B a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 12 \, C a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 27 \, A a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, B a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 3 \, C a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 18 \, A a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 18 \, B a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} + 6 \, A a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, B a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{5} - 6 \, C a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 18 \, A a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, B a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 42 \, C a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 81 \, A a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 36 \, B a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 33 \, C a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 36 \, A a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 36 \, B a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 6 \, C a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, A a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} - 12 \, B a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{4} + 12 \, B a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 36 \, C a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 108 \, A a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 28 \, B a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 84 \, C a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 42 \, A a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 12 \, B a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 34 \, C a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 8 \, A a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 12 \, B a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 4 \, C a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} + 8 \, A c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 8 \, B c^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{3} - 12 \, C a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 36 \, A a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, B a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 60 \, C a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 120 \, A a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 36 \, B a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 84 \, C a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 18 \, A a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 36 \, B a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, C a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 12 \, A a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} - 12 \, B a c^{7} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 6 \, B a^{8} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 24 \, C a^{7} c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 81 \, A a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 18 \, B a^{6} c^{2} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 57 \, C a^{5} c^{3} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 12 \, A a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 18 \, B a^{4} c^{4} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 6 \, C a^{3} c^{5} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + 6 \, A a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, B a^{2} c^{6} \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) - 6 \, C a^{8} + 18 \, A a^{7} c - 10 \, C a^{6} c^{2} - 5 \, A a^{5} c^{3} + C a^{4} c^{4} + 2 \, A a^{3} c^{5}}{{\left(a^{9} - 3 \, a^{7} c^{2} + 3 \, a^{5} c^{4} - a^{3} c^{6}\right)} {\left(a \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right)^{2} + 2 \, c \tan\left(\frac{1}{2} \, x e + \frac{1}{2} \, d\right) + a\right)}^{3}}\right)} e^{\left(-1\right)}"," ",0,"1/3*(3*(2*A*a^3 - 4*C*a^2*c + 3*A*a*c^2 - C*c^3)*(pi*floor(1/2*(x*e + d)/pi + 1/2)*sgn(a) + arctan((a*tan(1/2*x*e + 1/2*d) + c)/sqrt(a^2 - c^2)))/((a^6 - 3*a^4*c^2 + 3*a^2*c^4 - c^6)*sqrt(a^2 - c^2)) + (6*B*a^8*tan(1/2*x*e + 1/2*d)^5 - 12*C*a^7*c*tan(1/2*x*e + 1/2*d)^5 + 27*A*a^6*c^2*tan(1/2*x*e + 1/2*d)^5 - 18*B*a^6*c^2*tan(1/2*x*e + 1/2*d)^5 - 3*C*a^5*c^3*tan(1/2*x*e + 1/2*d)^5 - 18*A*a^4*c^4*tan(1/2*x*e + 1/2*d)^5 + 18*B*a^4*c^4*tan(1/2*x*e + 1/2*d)^5 + 6*A*a^2*c^6*tan(1/2*x*e + 1/2*d)^5 - 6*B*a^2*c^6*tan(1/2*x*e + 1/2*d)^5 - 6*C*a^8*tan(1/2*x*e + 1/2*d)^4 + 18*A*a^7*c*tan(1/2*x*e + 1/2*d)^4 + 12*B*a^7*c*tan(1/2*x*e + 1/2*d)^4 - 42*C*a^6*c^2*tan(1/2*x*e + 1/2*d)^4 + 81*A*a^5*c^3*tan(1/2*x*e + 1/2*d)^4 - 36*B*a^5*c^3*tan(1/2*x*e + 1/2*d)^4 - 33*C*a^4*c^4*tan(1/2*x*e + 1/2*d)^4 - 36*A*a^3*c^5*tan(1/2*x*e + 1/2*d)^4 + 36*B*a^3*c^5*tan(1/2*x*e + 1/2*d)^4 + 6*C*a^2*c^6*tan(1/2*x*e + 1/2*d)^4 + 12*A*a*c^7*tan(1/2*x*e + 1/2*d)^4 - 12*B*a*c^7*tan(1/2*x*e + 1/2*d)^4 + 12*B*a^8*tan(1/2*x*e + 1/2*d)^3 - 36*C*a^7*c*tan(1/2*x*e + 1/2*d)^3 + 108*A*a^6*c^2*tan(1/2*x*e + 1/2*d)^3 - 28*B*a^6*c^2*tan(1/2*x*e + 1/2*d)^3 - 84*C*a^5*c^3*tan(1/2*x*e + 1/2*d)^3 + 42*A*a^4*c^4*tan(1/2*x*e + 1/2*d)^3 + 12*B*a^4*c^4*tan(1/2*x*e + 1/2*d)^3 - 34*C*a^3*c^5*tan(1/2*x*e + 1/2*d)^3 - 8*A*a^2*c^6*tan(1/2*x*e + 1/2*d)^3 + 12*B*a^2*c^6*tan(1/2*x*e + 1/2*d)^3 + 4*C*a*c^7*tan(1/2*x*e + 1/2*d)^3 + 8*A*c^8*tan(1/2*x*e + 1/2*d)^3 - 8*B*c^8*tan(1/2*x*e + 1/2*d)^3 - 12*C*a^8*tan(1/2*x*e + 1/2*d)^2 + 36*A*a^7*c*tan(1/2*x*e + 1/2*d)^2 + 12*B*a^7*c*tan(1/2*x*e + 1/2*d)^2 - 60*C*a^6*c^2*tan(1/2*x*e + 1/2*d)^2 + 120*A*a^5*c^3*tan(1/2*x*e + 1/2*d)^2 - 36*B*a^5*c^3*tan(1/2*x*e + 1/2*d)^2 - 84*C*a^4*c^4*tan(1/2*x*e + 1/2*d)^2 - 18*A*a^3*c^5*tan(1/2*x*e + 1/2*d)^2 + 36*B*a^3*c^5*tan(1/2*x*e + 1/2*d)^2 + 6*C*a^2*c^6*tan(1/2*x*e + 1/2*d)^2 + 12*A*a*c^7*tan(1/2*x*e + 1/2*d)^2 - 12*B*a*c^7*tan(1/2*x*e + 1/2*d)^2 + 6*B*a^8*tan(1/2*x*e + 1/2*d) - 24*C*a^7*c*tan(1/2*x*e + 1/2*d) + 81*A*a^6*c^2*tan(1/2*x*e + 1/2*d) - 18*B*a^6*c^2*tan(1/2*x*e + 1/2*d) - 57*C*a^5*c^3*tan(1/2*x*e + 1/2*d) - 12*A*a^4*c^4*tan(1/2*x*e + 1/2*d) + 18*B*a^4*c^4*tan(1/2*x*e + 1/2*d) + 6*C*a^3*c^5*tan(1/2*x*e + 1/2*d) + 6*A*a^2*c^6*tan(1/2*x*e + 1/2*d) - 6*B*a^2*c^6*tan(1/2*x*e + 1/2*d) - 6*C*a^8 + 18*A*a^7*c - 10*C*a^6*c^2 - 5*A*a^5*c^3 + C*a^4*c^4 + 2*A*a^3*c^5)/((a^9 - 3*a^7*c^2 + 3*a^5*c^4 - a^3*c^6)*(a*tan(1/2*x*e + 1/2*d)^2 + 2*c*tan(1/2*x*e + 1/2*d) + a)^3))*e^(-1)","B",0
566,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^m,x, algorithm=""giac"")","\int {\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^m, x)","F",0
567,1,75,0,0.187154," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{b^{3} \cos\left(6 \, d x + 6 \, c\right)}{192 \, d} - \frac{3 \, a b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} + \frac{1}{8} \, {\left(8 \, a^{3} + 3 \, a b^{2}\right)} x - \frac{3 \, {\left(16 \, a^{2} b + b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)}{64 \, d}"," ",0,"1/192*b^3*cos(6*d*x + 6*c)/d - 3/32*a*b^2*sin(4*d*x + 4*c)/d + 1/8*(8*a^3 + 3*a*b^2)*x - 3/64*(16*a^2*b + b^3)*cos(2*d*x + 2*c)/d","A",0
568,1,46,0,0.155249," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(8 \, a^{2} + b^{2}\right)} x - \frac{a b \cos\left(2 \, d x + 2 \, c\right)}{2 \, d} - \frac{b^{2} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d}"," ",0,"1/8*(8*a^2 + b^2)*x - 1/2*a*b*cos(2*d*x + 2*c)/d - 1/32*b^2*sin(4*d*x + 4*c)/d","A",0
569,1,18,0,0.134922," ","integrate(a+b*cos(d*x+c)*sin(d*x+c),x, algorithm=""giac"")","a x + \frac{b \sin\left(d x + c\right)^{2}}{2 \, d}"," ",0,"a*x + 1/2*b*sin(d*x + c)^2/d","A",0
570,1,61,0,0.163086," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c)),x, algorithm=""giac"")","\frac{2 \, {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{2 \, a \tan\left(d x + c\right) + b}{\sqrt{4 \, a^{2} - b^{2}}}\right)\right)}}{\sqrt{4 \, a^{2} - b^{2}} d}"," ",0,"2*(pi*floor((d*x + c)/pi + 1/2)*sgn(a) + arctan((2*a*tan(d*x + c) + b)/sqrt(4*a^2 - b^2)))/(sqrt(4*a^2 - b^2)*d)","A",0
571,1,116,0,0.177064," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{2 \, a \tan\left(d x + c\right) + b}{\sqrt{4 \, a^{2} - b^{2}}}\right)\right)} a}{{\left(4 \, a^{2} - b^{2}\right)}^{\frac{3}{2}}} + \frac{b^{2} \tan\left(d x + c\right) + 2 \, a b}{{\left(4 \, a^{3} - a b^{2}\right)} {\left(a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}}}{d}"," ",0,"(8*(pi*floor((d*x + c)/pi + 1/2)*sgn(a) + arctan((2*a*tan(d*x + c) + b)/sqrt(4*a^2 - b^2)))*a/(4*a^2 - b^2)^(3/2) + (b^2*tan(d*x + c) + 2*a*b)/((4*a^3 - a*b^2)*(a*tan(d*x + c)^2 + b*tan(d*x + c) + a)))/d","A",0
572,1,252,0,0.190116," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{8 \, {\left(\pi \left \lfloor \frac{d x + c}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{2 \, a \tan\left(d x + c\right) + b}{\sqrt{4 \, a^{2} - b^{2}}}\right)\right)} {\left(8 \, a^{2} + b^{2}\right)}}{{\left(16 \, a^{4} - 8 \, a^{2} b^{2} + b^{4}\right)} \sqrt{4 \, a^{2} - b^{2}}} + \frac{20 \, a^{3} b^{2} \tan\left(d x + c\right)^{3} - 2 \, a b^{4} \tan\left(d x + c\right)^{3} + 32 \, a^{4} b \tan\left(d x + c\right)^{2} + 14 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - b^{5} \tan\left(d x + c\right)^{2} + 44 \, a^{3} b^{2} \tan\left(d x + c\right) - 2 \, a b^{4} \tan\left(d x + c\right) + 32 \, a^{4} b - 2 \, a^{2} b^{3}}{{\left(16 \, a^{6} - 8 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(a \tan\left(d x + c\right)^{2} + b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(8*(pi*floor((d*x + c)/pi + 1/2)*sgn(a) + arctan((2*a*tan(d*x + c) + b)/sqrt(4*a^2 - b^2)))*(8*a^2 + b^2)/((16*a^4 - 8*a^2*b^2 + b^4)*sqrt(4*a^2 - b^2)) + (20*a^3*b^2*tan(d*x + c)^3 - 2*a*b^4*tan(d*x + c)^3 + 32*a^4*b*tan(d*x + c)^2 + 14*a^2*b^3*tan(d*x + c)^2 - b^5*tan(d*x + c)^2 + 44*a^3*b^2*tan(d*x + c) - 2*a*b^4*tan(d*x + c) + 32*a^4*b - 2*a^2*b^3)/((16*a^6 - 8*a^4*b^2 + a^2*b^4)*(a*tan(d*x + c)^2 + b*tan(d*x + c) + a)^2))/d","A",0
573,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,0,0,0,0.000000," ","integrate((a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
576,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b \cos\left(d x + c\right) \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(b*cos(d*x + c)*sin(d*x + c) + a), x)","F",0
577,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(-3/2), x)","F",0
578,0,0,0,0.000000," ","integrate(1/(a+b*cos(d*x+c)*sin(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(d x + c\right) \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*cos(d*x + c)*sin(d*x + c) + a)^(-5/2), x)","F",0
579,0,0,0,0.000000," ","integrate(x^3/(a+b*cos(x)*sin(x)),x, algorithm=""giac"")","\int \frac{x^{3}}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x^3/(b*cos(x)*sin(x) + a), x)","F",0
580,0,0,0,0.000000," ","integrate(x^2/(a+b*cos(x)*sin(x)),x, algorithm=""giac"")","\int \frac{x^{2}}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x^2/(b*cos(x)*sin(x) + a), x)","F",0
581,0,0,0,0.000000," ","integrate(x/(a+b*cos(x)*sin(x)),x, algorithm=""giac"")","\int \frac{x}{b \cos\left(x\right) \sin\left(x\right) + a}\,{d x}"," ",0,"integrate(x/(b*cos(x)*sin(x) + a), x)","F",0
582,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)*sin(x)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(x\right) \sin\left(x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*cos(x)*sin(x) + a)*x), x)","F",0
583,0,0,0,0.000000," ","integrate((b*x)^(2-n)*sin(a*x)^n/(a*c*x*cos(a*x)-c*sin(a*x))^2,x, algorithm=""giac"")","\int \frac{\left(b x\right)^{-n + 2} \sin\left(a x\right)^{n}}{{\left(a c x \cos\left(a x\right) - c \sin\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate((b*x)^(-n + 2)*sin(a*x)^n/(a*c*x*cos(a*x) - c*sin(a*x))^2, x)","F",0
584,0,0,0,0.000000," ","integrate((b*x)^(2-n)*cos(a*x)^n/(c*cos(a*x)+a*c*x*sin(a*x))^2,x, algorithm=""giac"")","\int \frac{\left(b x\right)^{-n + 2} \cos\left(a x\right)^{n}}{{\left(a c x \sin\left(a x\right) + c \cos\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate((b*x)^(-n + 2)*cos(a*x)^n/(a*c*x*sin(a*x) + c*cos(a*x))^2, x)","F",0
585,1,7347,0,1.202288," ","integrate(sin(a*x)^6/x^4/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\frac{32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 12 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} - 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 12 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 20 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 20 \, a^{7} x^{7} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 4 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) + 32 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) - 64 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) + 8 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 24 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 20 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} - 20 \, a^{7} x^{7} \tan\left(a x\right)^{2} + 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 12 \, a^{7} x^{7} \tan\left(\frac{1}{2} \, a x\right)^{2} - 24 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} - 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 8 \, a^{6} x^{6} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 40 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 40 \, a^{6} x^{6} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{6} x^{6} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{6} x^{6} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 12 \, a^{7} x^{7} + 24 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 36 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 36 \, a^{5} x^{5} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 8 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) + 64 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) - 128 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) + 16 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) - 8 \, a^{6} x^{6} \tan\left(2 \, a x\right) + 4 \, a^{6} x^{6} \tan\left(a x\right) - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 24 \, a^{6} x^{6} \tan\left(\frac{1}{2} \, a x\right) - 48 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 13 \, a^{4} x^{4} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 36 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} - 36 \, a^{5} x^{5} \tan\left(a x\right)^{2} + 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{5} x^{5} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{5} x^{5} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{2} - 3 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} + 2 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} - 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 13 \, a^{4} x^{4} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 72 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 72 \, a^{4} x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 13 \, a^{4} x^{4} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{4} x^{4} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 24 \, a^{5} x^{5} + 3 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 26 \, a^{3} x^{3} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 15 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 24 \, a^{3} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) + 32 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) - 64 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) + 8 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) - 13 \, a^{4} x^{4} \tan\left(2 \, a x\right) + 2 \, a^{4} x^{4} \tan\left(a x\right) + 48 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right) - 30 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 10 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 5 \, a^{2} x^{2} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 15 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} - 24 \, a^{3} x^{3} \tan\left(a x\right)^{2} + 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 26 \, a^{3} x^{3} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{3} x^{3} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 12 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{2} - 3 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 10 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) - 5 \, a^{2} x^{2} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 54 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{2} x^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 5 \, a^{2} x^{2} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 10 \, a^{2} x^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 12 \, a^{3} x^{3} + 3 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 20 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 10 \, a x \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a x \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a x \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 5 \, a^{2} x^{2} \tan\left(2 \, a x\right) + 10 \, a^{2} x^{2} \tan\left(a x\right) - 6 \, \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x \tan\left(2 \, a x\right)^{2} + 4 \, a x \tan\left(a x\right)^{2} + 10 \, a x \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 20 \, a x \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)}{12 \, {\left(a^{5} x^{8} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{5} x^{8} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + a^{5} x^{8} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{5} x^{8} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{5} x^{8} \tan\left(2 \, a x\right)^{2} - a^{5} x^{8} \tan\left(a x\right)^{2} + a^{5} x^{8} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{4} x^{7} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{5} x^{8} - 2 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 2 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{3} x^{6} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{7} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} - 2 \, a^{3} x^{6} \tan\left(a x\right)^{2} + 2 \, a^{3} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{2} + a x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{5} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{3} x^{6} - a x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + a x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{2} x^{5} \tan\left(\frac{1}{2} \, a x\right) + 2 \, x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x^{4} \tan\left(2 \, a x\right)^{2} - a x^{4} \tan\left(a x\right)^{2} + a x^{4} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x^{4} + 2 \, x^{3} \tan\left(\frac{1}{2} \, a x\right)\right)}}"," ",0,"1/12*(32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 64*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 8*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 64*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^8*x^8*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^8*x^8*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 8*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 8*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 64*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 128*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 16*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 12*a^7*x^7*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 - 64*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2 + 8*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 - 64*a^8*x^8*sin_integral(4*a*x)*tan(a*x)^2 + 8*a^8*x^8*sin_integral(2*a*x)*tan(a*x)^2 + 32*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 4*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 4*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 + 64*a^8*x^8*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 8*a^8*x^8*sin_integral(2*a*x)*tan(1/2*a*x)^2 + 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 128*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 16*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 12*a^7*x^7*tan(2*a*x)^2*tan(a*x)^2 + 64*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 8*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 8*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 64*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 128*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) - 16*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 64*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) - 8*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 8*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 64*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 128*a^7*x^7*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) - 16*a^7*x^7*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - 20*a^7*x^7*tan(2*a*x)^2*tan(1/2*a*x)^2 + 20*a^7*x^7*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^8*x^8*imag_part(cos_integral(4*a*x)) + 4*a^8*x^8*imag_part(cos_integral(2*a*x)) - 4*a^8*x^8*imag_part(cos_integral(-2*a*x)) + 32*a^8*x^8*imag_part(cos_integral(-4*a*x)) - 64*a^8*x^8*sin_integral(4*a*x) + 8*a^8*x^8*sin_integral(2*a*x) - 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 128*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 16*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 - 24*a^6*x^6*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 128*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 16*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^6*x^6*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 + 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 128*a^6*x^6*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 16*a^6*x^6*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 8*a^6*x^6*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 20*a^7*x^7*tan(2*a*x)^2 - 20*a^7*x^7*tan(a*x)^2 + 64*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) - 8*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) + 8*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 64*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 128*a^7*x^7*sin_integral(4*a*x)*tan(1/2*a*x) - 16*a^7*x^7*sin_integral(2*a*x)*tan(1/2*a*x) + 128*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 16*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 16*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 128*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 256*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 32*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 12*a^7*x^7*tan(1/2*a*x)^2 - 24*a^5*x^5*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 + 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 - 128*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2 + 16*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2 + 4*a^6*x^6*tan(2*a*x)^2*tan(a*x) - 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 + 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 - 128*a^6*x^6*sin_integral(4*a*x)*tan(a*x)^2 + 16*a^6*x^6*sin_integral(2*a*x)*tan(a*x)^2 - 8*a^6*x^6*tan(2*a*x)*tan(a*x)^2 - 40*a^6*x^6*tan(2*a*x)^2*tan(1/2*a*x) + 40*a^6*x^6*tan(a*x)^2*tan(1/2*a*x) + 64*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 8*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 8*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 + 128*a^6*x^6*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 16*a^6*x^6*sin_integral(2*a*x)*tan(1/2*a*x)^2 + 8*a^6*x^6*tan(2*a*x)*tan(1/2*a*x)^2 - 4*a^6*x^6*tan(a*x)*tan(1/2*a*x)^2 + 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 12*a^7*x^7 + 24*a^5*x^5*tan(2*a*x)^2*tan(a*x)^2 + 128*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 16*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 16*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 128*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 256*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) - 32*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) - 8*a^5*x^5*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 128*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) - 16*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 16*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 128*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 256*a^5*x^5*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) - 32*a^5*x^5*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 16*a^5*x^5*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - 36*a^5*x^5*tan(2*a*x)^2*tan(1/2*a*x)^2 + 36*a^5*x^5*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^6*x^6*imag_part(cos_integral(4*a*x)) + 8*a^6*x^6*imag_part(cos_integral(2*a*x)) - 8*a^6*x^6*imag_part(cos_integral(-2*a*x)) + 64*a^6*x^6*imag_part(cos_integral(-4*a*x)) - 128*a^6*x^6*sin_integral(4*a*x) + 16*a^6*x^6*sin_integral(2*a*x) - 8*a^6*x^6*tan(2*a*x) + 4*a^6*x^6*tan(a*x) - 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 64*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 8*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 24*a^6*x^6*tan(1/2*a*x) - 48*a^4*x^4*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 64*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 2*a^4*x^4*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 + 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^4*x^4*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 13*a^4*x^4*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 36*a^5*x^5*tan(2*a*x)^2 - 36*a^5*x^5*tan(a*x)^2 + 128*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) - 16*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) + 16*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 128*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 256*a^5*x^5*sin_integral(4*a*x)*tan(1/2*a*x) - 32*a^5*x^5*sin_integral(2*a*x)*tan(1/2*a*x) + 16*a^5*x^5*tan(2*a*x)*tan(1/2*a*x) - 8*a^5*x^5*tan(a*x)*tan(1/2*a*x) + 64*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 8*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 8*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 64*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 128*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 16*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 24*a^5*x^5*tan(1/2*a*x)^2 - 3*a^3*x^3*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 + 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 - 64*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2 + 8*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2 + 2*a^4*x^4*tan(2*a*x)^2*tan(a*x) - 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 + 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 - 64*a^4*x^4*sin_integral(4*a*x)*tan(a*x)^2 + 8*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2 - 13*a^4*x^4*tan(2*a*x)*tan(a*x)^2 - 72*a^4*x^4*tan(2*a*x)^2*tan(1/2*a*x) + 72*a^4*x^4*tan(a*x)^2*tan(1/2*a*x) + 32*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 4*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 4*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 + 64*a^4*x^4*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 8*a^4*x^4*sin_integral(2*a*x)*tan(1/2*a*x)^2 + 13*a^4*x^4*tan(2*a*x)*tan(1/2*a*x)^2 - 2*a^4*x^4*tan(a*x)*tan(1/2*a*x)^2 - 24*a^5*x^5 + 3*a^3*x^3*tan(2*a*x)^2*tan(a*x)^2 + 64*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 8*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 8*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 64*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 128*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) - 16*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) - 4*a^3*x^3*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 64*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) - 8*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 8*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 64*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 128*a^3*x^3*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) - 16*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 26*a^3*x^3*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - 15*a^3*x^3*tan(2*a*x)^2*tan(1/2*a*x)^2 + 24*a^3*x^3*tan(a*x)^2*tan(1/2*a*x)^2 - 32*a^4*x^4*imag_part(cos_integral(4*a*x)) + 4*a^4*x^4*imag_part(cos_integral(2*a*x)) - 4*a^4*x^4*imag_part(cos_integral(-2*a*x)) + 32*a^4*x^4*imag_part(cos_integral(-4*a*x)) - 64*a^4*x^4*sin_integral(4*a*x) + 8*a^4*x^4*sin_integral(2*a*x) - 13*a^4*x^4*tan(2*a*x) + 2*a^4*x^4*tan(a*x) + 48*a^4*x^4*tan(1/2*a*x) - 30*a^2*x^2*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 10*a^2*x^2*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 + 5*a^2*x^2*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 15*a^3*x^3*tan(2*a*x)^2 - 24*a^3*x^3*tan(a*x)^2 + 64*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) - 8*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) + 8*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 64*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 128*a^3*x^3*sin_integral(4*a*x)*tan(1/2*a*x) - 16*a^3*x^3*sin_integral(2*a*x)*tan(1/2*a*x) + 26*a^3*x^3*tan(2*a*x)*tan(1/2*a*x) - 4*a^3*x^3*tan(a*x)*tan(1/2*a*x) + 12*a^3*x^3*tan(1/2*a*x)^2 - 3*a*x*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 10*a^2*x^2*tan(2*a*x)^2*tan(a*x) - 5*a^2*x^2*tan(2*a*x)*tan(a*x)^2 - 54*a^2*x^2*tan(2*a*x)^2*tan(1/2*a*x) + 24*a^2*x^2*tan(a*x)^2*tan(1/2*a*x) + 5*a^2*x^2*tan(2*a*x)*tan(1/2*a*x)^2 - 10*a^2*x^2*tan(a*x)*tan(1/2*a*x)^2 - 12*a^3*x^3 + 3*a*x*tan(2*a*x)^2*tan(a*x)^2 - 20*a*x*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 10*a*x*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + a*x*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a*x*tan(a*x)^2*tan(1/2*a*x)^2 - 5*a^2*x^2*tan(2*a*x) + 10*a^2*x^2*tan(a*x) - 6*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - a*x*tan(2*a*x)^2 + 4*a*x*tan(a*x)^2 + 10*a*x*tan(2*a*x)*tan(1/2*a*x) - 20*a*x*tan(a*x)*tan(1/2*a*x) + 2*tan(2*a*x)^2*tan(1/2*a*x) - 8*tan(a*x)^2*tan(1/2*a*x))/(a^5*x^8*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - a^5*x^8*tan(2*a*x)^2*tan(a*x)^2 + a^5*x^8*tan(2*a*x)^2*tan(1/2*a*x)^2 + a^5*x^8*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^4*x^7*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - a^5*x^8*tan(2*a*x)^2 - a^5*x^8*tan(a*x)^2 + a^5*x^8*tan(1/2*a*x)^2 + 2*a^3*x^6*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^4*x^7*tan(2*a*x)^2*tan(1/2*a*x) + 2*a^4*x^7*tan(a*x)^2*tan(1/2*a*x) - a^5*x^8 - 2*a^3*x^6*tan(2*a*x)^2*tan(a*x)^2 + 2*a^3*x^6*tan(2*a*x)^2*tan(1/2*a*x)^2 + 2*a^3*x^6*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^4*x^7*tan(1/2*a*x) + 4*a^2*x^5*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 2*a^3*x^6*tan(2*a*x)^2 - 2*a^3*x^6*tan(a*x)^2 + 2*a^3*x^6*tan(1/2*a*x)^2 + a*x^4*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^2*x^5*tan(2*a*x)^2*tan(1/2*a*x) + 4*a^2*x^5*tan(a*x)^2*tan(1/2*a*x) - 2*a^3*x^6 - a*x^4*tan(2*a*x)^2*tan(a*x)^2 + a*x^4*tan(2*a*x)^2*tan(1/2*a*x)^2 + a*x^4*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^2*x^5*tan(1/2*a*x) + 2*x^3*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - a*x^4*tan(2*a*x)^2 - a*x^4*tan(a*x)^2 + a*x^4*tan(1/2*a*x)^2 + 2*x^3*tan(2*a*x)^2*tan(1/2*a*x) + 2*x^3*tan(a*x)^2*tan(1/2*a*x) - a*x^4 + 2*x^3*tan(1/2*a*x))","C",0
586,1,4175,0,0.810537," ","integrate(sin(a*x)^5/x^3/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\frac{27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{7} x^{7} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{7} x^{7} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{7} x^{7} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{7} x^{7} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{7} x^{7} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{7} x^{7} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{6} x^{6} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{6} x^{6} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 16 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{7} x^{7} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 54 \, a^{7} x^{7} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{7} x^{7} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 108 \, a^{5} x^{5} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 4 \, a^{5} x^{5} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{6} x^{6} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{6} x^{6} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{6} x^{6} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{6} x^{6} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 20 \, a^{6} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) + a^{7} x^{7} \Im \left( \operatorname{Ci}\left(a x\right) \right) - a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-a x\right) \right) + 27 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 54 \, a^{7} x^{7} \operatorname{Si}\left(3 \, a x\right) + 2 \, a^{7} x^{7} \operatorname{Si}\left(a x\right) - 36 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 108 \, a^{5} x^{5} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 4 \, a^{5} x^{5} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 12 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 20 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} + 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 54 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{6} x^{6} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{6} x^{6} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{6} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{2} + 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 216 \, a^{4} x^{4} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 8 \, a^{4} x^{4} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 32 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 108 \, a^{5} x^{5} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 4 \, a^{5} x^{5} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 36 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 36 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{3} + 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{3} x^{3} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 16 \, a^{6} x^{6} + 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 216 \, a^{4} x^{4} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 216 \, a^{4} x^{4} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 8 \, a^{4} x^{4} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 24 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 32 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) + 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(a x\right) \right) - 2 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-a x\right) \right) + 54 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 108 \, a^{5} x^{5} \operatorname{Si}\left(3 \, a x\right) + 4 \, a^{5} x^{5} \operatorname{Si}\left(a x\right) - 12 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right) + 36 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right) - 48 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{3} x^{3} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 16 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 32 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} + 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 108 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 216 \, a^{4} x^{4} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{2} + 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{2} x^{2} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 32 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 54 \, a^{3} x^{3} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 80 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 80 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{3} - 32 \, a^{4} x^{4} + 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{2} x^{2} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 60 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{2} x^{2} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 32 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) + 27 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 54 \, a^{3} x^{3} \operatorname{Si}\left(3 \, a x\right) + 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) - 16 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right) + 48 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right) - 12 \, a x \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a x \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 4 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} + 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 54 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{2} x^{2} \operatorname{Si}\left(3 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 60 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 44 \, a x \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 44 \, a x \tan\left(\frac{1}{2} \, a x\right)^{3} - 32 \, a^{2} x^{2} - 24 \, \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a x \tan\left(\frac{3}{2} \, a x\right) + 12 \, a x \tan\left(\frac{1}{2} \, a x\right) + 8 \, \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) - 24 \, \tan\left(\frac{1}{2} \, a x\right)^{2}}{16 \, {\left(a^{5} x^{7} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + a^{5} x^{7} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{4} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{5} x^{7} \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{3} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{4} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{4} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{5} x^{7} + 2 \, a^{3} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{4} x^{6} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{3} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} + a x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 4 \, a^{2} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{3} x^{5} + a x^{3} \tan\left(\frac{1}{2} \, a x\right)^{4} + 4 \, a^{2} x^{4} \tan\left(\frac{1}{2} \, a x\right) + 2 \, x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - a x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, x^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - a x^{3} + 2 \, x^{2} \tan\left(\frac{1}{2} \, a x\right)\right)}}"," ",0,"1/16*(27*a^7*x^7*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^7*x^7*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + a^7*x^7*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^7*x^7*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 54*a^7*x^7*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 2*a^7*x^7*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 27*a^7*x^7*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - a^7*x^7*imag_part(cos_integral(a*x))*tan(1/2*a*x)^4 + a^7*x^7*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 27*a^7*x^7*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 54*a^7*x^7*sin_integral(3*a*x)*tan(1/2*a*x)^4 - 2*a^7*x^7*sin_integral(a*x)*tan(1/2*a*x)^4 + 54*a^6*x^6*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 2*a^6*x^6*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^6*x^6*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 54*a^6*x^6*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 108*a^6*x^6*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 4*a^6*x^6*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 16*a^6*x^6*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^7*x^7*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + a^7*x^7*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2 - a^7*x^7*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 27*a^7*x^7*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 - 54*a^7*x^7*sin_integral(3*a*x)*tan(3/2*a*x)^2 + 2*a^7*x^7*sin_integral(a*x)*tan(3/2*a*x)^2 + 54*a^5*x^5*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 2*a^5*x^5*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 2*a^5*x^5*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 54*a^5*x^5*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 108*a^5*x^5*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 4*a^5*x^5*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 54*a^6*x^6*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 2*a^6*x^6*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^6*x^6*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 54*a^6*x^6*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 108*a^6*x^6*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 4*a^6*x^6*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 4*a^6*x^6*tan(3/2*a*x)^2*tan(1/2*a*x)^2 + 54*a^6*x^6*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 - 2*a^6*x^6*imag_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a^6*x^6*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^3 - 54*a^6*x^6*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 + 108*a^6*x^6*sin_integral(3*a*x)*tan(1/2*a*x)^3 - 4*a^6*x^6*sin_integral(a*x)*tan(1/2*a*x)^3 + 20*a^6*x^6*tan(1/2*a*x)^4 - 27*a^7*x^7*imag_part(cos_integral(3*a*x)) + a^7*x^7*imag_part(cos_integral(a*x)) - a^7*x^7*imag_part(cos_integral(-a*x)) + 27*a^7*x^7*imag_part(cos_integral(-3*a*x)) - 54*a^7*x^7*sin_integral(3*a*x) + 2*a^7*x^7*sin_integral(a*x) - 36*a^5*x^5*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 54*a^5*x^5*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - 2*a^5*x^5*imag_part(cos_integral(a*x))*tan(1/2*a*x)^4 + 2*a^5*x^5*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 54*a^5*x^5*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 108*a^5*x^5*sin_integral(3*a*x)*tan(1/2*a*x)^4 - 4*a^5*x^5*sin_integral(a*x)*tan(1/2*a*x)^4 + 12*a^5*x^5*tan(3/2*a*x)*tan(1/2*a*x)^4 + 20*a^6*x^6*tan(3/2*a*x)^2 + 54*a^6*x^6*imag_part(cos_integral(3*a*x))*tan(1/2*a*x) - 2*a^6*x^6*imag_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a^6*x^6*imag_part(cos_integral(-a*x))*tan(1/2*a*x) - 54*a^6*x^6*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x) + 108*a^6*x^6*sin_integral(3*a*x)*tan(1/2*a*x) - 4*a^6*x^6*sin_integral(a*x)*tan(1/2*a*x) - 4*a^6*x^6*tan(1/2*a*x)^2 + 108*a^4*x^4*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 4*a^4*x^4*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 4*a^4*x^4*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 108*a^4*x^4*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 216*a^4*x^4*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 8*a^4*x^4*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 32*a^4*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 54*a^5*x^5*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + 2*a^5*x^5*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2 - 2*a^5*x^5*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 54*a^5*x^5*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 - 108*a^5*x^5*sin_integral(3*a*x)*tan(3/2*a*x)^2 + 4*a^5*x^5*sin_integral(a*x)*tan(3/2*a*x)^2 - 36*a^5*x^5*tan(3/2*a*x)^2*tan(1/2*a*x) + 36*a^5*x^5*tan(1/2*a*x)^3 + 27*a^3*x^3*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^3*x^3*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + a^3*x^3*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^3*x^3*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 54*a^3*x^3*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 2*a^3*x^3*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 16*a^6*x^6 + 108*a^4*x^4*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 4*a^4*x^4*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 4*a^4*x^4*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 108*a^4*x^4*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 216*a^4*x^4*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 8*a^4*x^4*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 8*a^4*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^2 + 108*a^4*x^4*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 - 4*a^4*x^4*imag_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 4*a^4*x^4*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^3 - 108*a^4*x^4*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 + 216*a^4*x^4*sin_integral(3*a*x)*tan(1/2*a*x)^3 - 8*a^4*x^4*sin_integral(a*x)*tan(1/2*a*x)^3 + 24*a^4*x^4*tan(3/2*a*x)*tan(1/2*a*x)^3 + 32*a^4*x^4*tan(1/2*a*x)^4 - 54*a^5*x^5*imag_part(cos_integral(3*a*x)) + 2*a^5*x^5*imag_part(cos_integral(a*x)) - 2*a^5*x^5*imag_part(cos_integral(-a*x)) + 54*a^5*x^5*imag_part(cos_integral(-3*a*x)) - 108*a^5*x^5*sin_integral(3*a*x) + 4*a^5*x^5*sin_integral(a*x) - 12*a^5*x^5*tan(3/2*a*x) + 36*a^5*x^5*tan(1/2*a*x) - 48*a^3*x^3*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 27*a^3*x^3*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - a^3*x^3*imag_part(cos_integral(a*x))*tan(1/2*a*x)^4 + a^3*x^3*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 27*a^3*x^3*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 54*a^3*x^3*sin_integral(3*a*x)*tan(1/2*a*x)^4 - 2*a^3*x^3*sin_integral(a*x)*tan(1/2*a*x)^4 + 16*a^3*x^3*tan(3/2*a*x)*tan(1/2*a*x)^4 + 32*a^4*x^4*tan(3/2*a*x)^2 + 108*a^4*x^4*imag_part(cos_integral(3*a*x))*tan(1/2*a*x) - 4*a^4*x^4*imag_part(cos_integral(a*x))*tan(1/2*a*x) + 4*a^4*x^4*imag_part(cos_integral(-a*x))*tan(1/2*a*x) - 108*a^4*x^4*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x) + 216*a^4*x^4*sin_integral(3*a*x)*tan(1/2*a*x) - 8*a^4*x^4*sin_integral(a*x)*tan(1/2*a*x) + 24*a^4*x^4*tan(3/2*a*x)*tan(1/2*a*x) - 8*a^4*x^4*tan(1/2*a*x)^2 + 54*a^2*x^2*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 54*a^2*x^2*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 108*a^2*x^2*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 4*a^2*x^2*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 32*a^2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^3*x^3*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + a^3*x^3*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2 - a^3*x^3*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 27*a^3*x^3*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 - 54*a^3*x^3*sin_integral(3*a*x)*tan(3/2*a*x)^2 + 2*a^3*x^3*sin_integral(a*x)*tan(3/2*a*x)^2 - 80*a^3*x^3*tan(3/2*a*x)^2*tan(1/2*a*x) + 80*a^3*x^3*tan(1/2*a*x)^3 - 32*a^4*x^4 + 54*a^2*x^2*imag_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 54*a^2*x^2*imag_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 108*a^2*x^2*sin_integral(3*a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 4*a^2*x^2*sin_integral(a*x)*tan(3/2*a*x)^2*tan(1/2*a*x) - 60*a^2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^2 + 54*a^2*x^2*imag_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 - 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^3 - 54*a^2*x^2*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 + 108*a^2*x^2*sin_integral(3*a*x)*tan(1/2*a*x)^3 - 4*a^2*x^2*sin_integral(a*x)*tan(1/2*a*x)^3 + 32*a^2*x^2*tan(3/2*a*x)*tan(1/2*a*x)^3 - 4*a^2*x^2*tan(1/2*a*x)^4 - 27*a^3*x^3*imag_part(cos_integral(3*a*x)) + a^3*x^3*imag_part(cos_integral(a*x)) - a^3*x^3*imag_part(cos_integral(-a*x)) + 27*a^3*x^3*imag_part(cos_integral(-3*a*x)) - 54*a^3*x^3*sin_integral(3*a*x) + 2*a^3*x^3*sin_integral(a*x) - 16*a^3*x^3*tan(3/2*a*x) + 48*a^3*x^3*tan(1/2*a*x) - 12*a*x*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 4*a*x*tan(3/2*a*x)*tan(1/2*a*x)^4 - 4*a^2*x^2*tan(3/2*a*x)^2 + 54*a^2*x^2*imag_part(cos_integral(3*a*x))*tan(1/2*a*x) - 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(1/2*a*x) - 54*a^2*x^2*imag_part(cos_integral(-3*a*x))*tan(1/2*a*x) + 108*a^2*x^2*sin_integral(3*a*x)*tan(1/2*a*x) - 4*a^2*x^2*sin_integral(a*x)*tan(1/2*a*x) + 32*a^2*x^2*tan(3/2*a*x)*tan(1/2*a*x) - 60*a^2*x^2*tan(1/2*a*x)^2 - 44*a*x*tan(3/2*a*x)^2*tan(1/2*a*x) + 44*a*x*tan(1/2*a*x)^3 - 32*a^2*x^2 - 24*tan(3/2*a*x)^2*tan(1/2*a*x)^2 + 8*tan(3/2*a*x)*tan(1/2*a*x)^3 - 4*a*x*tan(3/2*a*x) + 12*a*x*tan(1/2*a*x) + 8*tan(3/2*a*x)*tan(1/2*a*x) - 24*tan(1/2*a*x)^2)/(a^5*x^7*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + a^5*x^7*tan(1/2*a*x)^4 + 2*a^4*x^6*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - a^5*x^7*tan(3/2*a*x)^2 + 2*a^3*x^5*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 2*a^4*x^6*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^4*x^6*tan(1/2*a*x)^3 - a^5*x^7 + 2*a^3*x^5*tan(1/2*a*x)^4 + 2*a^4*x^6*tan(1/2*a*x) + 4*a^2*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 2*a^3*x^5*tan(3/2*a*x)^2 + a*x^3*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 4*a^2*x^4*tan(3/2*a*x)^2*tan(1/2*a*x) + 4*a^2*x^4*tan(1/2*a*x)^3 - 2*a^3*x^5 + a*x^3*tan(1/2*a*x)^4 + 4*a^2*x^4*tan(1/2*a*x) + 2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - a*x^3*tan(3/2*a*x)^2 + 2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*x^2*tan(1/2*a*x)^3 - a*x^3 + 2*x^2*tan(1/2*a*x))","C",0
587,1,1033,0,0.477278," ","integrate(sin(a*x)^4/x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\frac{a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} + a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} - 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} + a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{3} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) + a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) - 2 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) + a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{3} x^{3} \tan\left(a x\right)^{2} + 2 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} + a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} - 2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 2 \, a^{2} x^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{2} x^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{3} x^{3} + 2 \, a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a x \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) + a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) - 2 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) - a^{2} x^{2} \tan\left(a x\right) + 2 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a x \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + a x \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x}{a^{3} x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{3} x^{4} \tan\left(a x\right)^{2} + a^{3} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{2} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{3} x^{4} + a x^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{2} x^{3} \tan\left(\frac{1}{2} \, a x\right) - a x^{2} \tan\left(a x\right)^{2} + a x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, x \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x^{2} + 2 \, x \tan\left(\frac{1}{2} \, a x\right)}"," ",0,"(a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2 + a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 - 2*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2 + a^4*x^4*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 - a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 + 2*a^4*x^4*sin_integral(2*a*x)*tan(1/2*a*x)^2 + 2*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 2*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 4*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - a^3*x^3*tan(a*x)^2*tan(1/2*a*x)^2 - a^4*x^4*imag_part(cos_integral(2*a*x)) + a^4*x^4*imag_part(cos_integral(-2*a*x)) - 2*a^4*x^4*sin_integral(2*a*x) + a^2*x^2*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - a^2*x^2*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^2*x^2*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + a^3*x^3*tan(a*x)^2 + 2*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 2*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) + 4*a^3*x^3*sin_integral(2*a*x)*tan(1/2*a*x) + a^3*x^3*tan(1/2*a*x)^2 - a^2*x^2*imag_part(cos_integral(2*a*x))*tan(a*x)^2 + a^2*x^2*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 - 2*a^2*x^2*sin_integral(2*a*x)*tan(a*x)^2 - 2*a^2*x^2*tan(a*x)^2*tan(1/2*a*x) + a^2*x^2*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 - a^2*x^2*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 + 2*a^2*x^2*sin_integral(2*a*x)*tan(1/2*a*x)^2 + a^2*x^2*tan(a*x)*tan(1/2*a*x)^2 - a^3*x^3 + 2*a*x*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 2*a*x*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 4*a*x*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - a^2*x^2*imag_part(cos_integral(2*a*x)) + a^2*x^2*imag_part(cos_integral(-2*a*x)) - 2*a^2*x^2*sin_integral(2*a*x) - a^2*x^2*tan(a*x) + 2*a^2*x^2*tan(1/2*a*x) + 2*a*x*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 2*a*x*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) + 4*a*x*sin_integral(2*a*x)*tan(1/2*a*x) + 2*a*x*tan(a*x)*tan(1/2*a*x) + a*x*tan(1/2*a*x)^2 - 2*tan(a*x)^2*tan(1/2*a*x) - a*x)/(a^3*x^4*tan(a*x)^2*tan(1/2*a*x)^2 - a^3*x^4*tan(a*x)^2 + a^3*x^4*tan(1/2*a*x)^2 + 2*a^2*x^3*tan(a*x)^2*tan(1/2*a*x) - a^3*x^4 + a*x^2*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^2*x^3*tan(1/2*a*x) - a*x^2*tan(a*x)^2 + a*x^2*tan(1/2*a*x)^2 + 2*x*tan(a*x)^2*tan(1/2*a*x) - a*x^2 + 2*x*tan(1/2*a*x))","C",0
588,1,496,0,0.368703," ","integrate(sin(a*x)^3/x/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\frac{a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(a x\right) \right) + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-a x\right) \right) - 2 \, a^{3} x^{3} \operatorname{Si}\left(a x\right) + a x \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a x \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a x \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{2} \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{2} x^{2} + 2 \, \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 2 \, \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, \tan\left(\frac{1}{2} \, a x\right)^{4} - a x \Im \left( \operatorname{Ci}\left(a x\right) \right) + a x \Im \left( \operatorname{Ci}\left(-a x\right) \right) - 2 \, a x \operatorname{Si}\left(a x\right) + 2 \, \Im \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, \Im \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, \operatorname{Si}\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) - 4}{2 \, {\left(a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{3} x^{3} + a x \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, \tan\left(\frac{1}{2} \, a x\right)^{3} - a x + 2 \, \tan\left(\frac{1}{2} \, a x\right)\right)}}"," ",0,"1/2*(a^3*x^3*imag_part(cos_integral(a*x))*tan(1/2*a*x)^4 - a^3*x^3*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^4 + 2*a^3*x^3*sin_integral(a*x)*tan(1/2*a*x)^4 + 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(1/2*a*x)^3 - 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + 4*a^2*x^2*sin_integral(a*x)*tan(1/2*a*x)^3 - 2*a^2*x^2*tan(1/2*a*x)^4 - a^3*x^3*imag_part(cos_integral(a*x)) + a^3*x^3*imag_part(cos_integral(-a*x)) - 2*a^3*x^3*sin_integral(a*x) + a*x*imag_part(cos_integral(a*x))*tan(1/2*a*x)^4 - a*x*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^4 + 2*a*x*sin_integral(a*x)*tan(1/2*a*x)^4 + 2*a^2*x^2*imag_part(cos_integral(a*x))*tan(1/2*a*x) - 2*a^2*x^2*imag_part(cos_integral(-a*x))*tan(1/2*a*x) + 4*a^2*x^2*sin_integral(a*x)*tan(1/2*a*x) + 4*a^2*x^2*tan(1/2*a*x)^2 - 2*a^2*x^2 + 2*imag_part(cos_integral(a*x))*tan(1/2*a*x)^3 - 2*imag_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + 4*sin_integral(a*x)*tan(1/2*a*x)^3 - 4*tan(1/2*a*x)^4 - a*x*imag_part(cos_integral(a*x)) + a*x*imag_part(cos_integral(-a*x)) - 2*a*x*sin_integral(a*x) + 2*imag_part(cos_integral(a*x))*tan(1/2*a*x) - 2*imag_part(cos_integral(-a*x))*tan(1/2*a*x) + 4*sin_integral(a*x)*tan(1/2*a*x) - 4)/(a^3*x^3*tan(1/2*a*x)^4 + 2*a^2*x^2*tan(1/2*a*x)^3 - a^3*x^3 + a*x*tan(1/2*a*x)^4 + 2*a^2*x^2*tan(1/2*a*x) + 2*tan(1/2*a*x)^3 - a*x + 2*tan(1/2*a*x))","C",0
589,1,39,0,0.193308," ","integrate(sin(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\frac{\tan\left(\frac{1}{2} \, a x\right)^{2} - 1}{a^{2} x \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{2} x + 2 \, a \tan\left(\frac{1}{2} \, a x\right)}"," ",0,"(tan(1/2*a*x)^2 - 1)/(a^2*x*tan(1/2*a*x)^2 - a^2*x + 2*a*tan(1/2*a*x))","A",0
590,1,42,0,0.176877," ","integrate(x*sin(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, a x\right)^{2} + 1\right)}}{a^{3} x \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{3} x + 2 \, a^{2} \tan\left(\frac{1}{2} \, a x\right)}"," ",0,"-2*(tan(1/2*a*x)^2 + 1)/(a^3*x*tan(1/2*a*x)^2 - a^3*x + 2*a^2*tan(1/2*a*x))","B",0
591,1,53,0,0.147703," ","integrate(x^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","-\frac{2 \, a x \tan\left(\frac{1}{2} \, a x\right) - \tan\left(\frac{1}{2} \, a x\right)^{2} + 1}{a^{4} x \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x + 2 \, a^{3} \tan\left(\frac{1}{2} \, a x\right)}"," ",0,"-(2*a*x*tan(1/2*a*x) - tan(1/2*a*x)^2 + 1)/(a^4*x*tan(1/2*a*x)^2 - a^4*x + 2*a^3*tan(1/2*a*x))","A",0
592,0,0,0,0.000000," ","integrate(x^3*csc(a*x)/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\int \frac{x^{3} \csc\left(a x\right)}{{\left(a x \cos\left(a x\right) - \sin\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*csc(a*x)/(a*x*cos(a*x) - sin(a*x))^2, x)","F",0
593,0,0,0,0.000000," ","integrate(x^4*csc(a*x)^2/(a*x*cos(a*x)-sin(a*x))^2,x, algorithm=""giac"")","\int \frac{x^{4} \csc\left(a x\right)^{2}}{{\left(a x \cos\left(a x\right) - \sin\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate(x^4*csc(a*x)^2/(a*x*cos(a*x) - sin(a*x))^2, x)","F",0
594,1,7279,0,1.209257," ","integrate(cos(a*x)^6/x^4/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\frac{64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 40 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{8} x^{8} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{8} x^{8} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{8} x^{8} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 20 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} + 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 24 \, a^{7} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{7} x^{7} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 20 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 12 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 12 \, a^{6} x^{6} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 4 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) - 32 \, a^{7} x^{7} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) + 64 \, a^{7} x^{7} \operatorname{Si}\left(4 \, a x\right) + 8 \, a^{7} x^{7} \operatorname{Si}\left(2 \, a x\right) + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 40 \, a^{7} x^{7} \tan\left(\frac{1}{2} \, a x\right) - 72 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 12 \, a^{6} x^{6} \tan\left(2 \, a x\right)^{2} + 12 \, a^{6} x^{6} \tan\left(a x\right)^{2} + 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 16 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 128 \, a^{6} x^{6} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 256 \, a^{6} x^{6} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{6} x^{6} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{6} x^{6} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{6} x^{6} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 20 \, a^{6} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{2} + 36 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} + 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} + 8 \, a^{5} x^{5} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 48 \, a^{5} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 48 \, a^{5} x^{5} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{5} x^{5} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{5} x^{5} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 20 \, a^{6} x^{6} - 36 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 26 \, a^{4} x^{4} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 24 \, a^{4} x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 8 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) - 64 \, a^{5} x^{5} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) + 128 \, a^{5} x^{5} \operatorname{Si}\left(4 \, a x\right) + 16 \, a^{5} x^{5} \operatorname{Si}\left(2 \, a x\right) + 8 \, a^{5} x^{5} \tan\left(2 \, a x\right) + 4 \, a^{5} x^{5} \tan\left(a x\right) + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 72 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right) - 30 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 13 \, a^{3} x^{3} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 24 \, a^{4} x^{4} \tan\left(2 \, a x\right)^{2} + 24 \, a^{4} x^{4} \tan\left(a x\right)^{2} + 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 64 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 128 \, a^{4} x^{4} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 16 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 26 \, a^{4} x^{4} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) - 36 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{2} + 27 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(2 \, a x\right)^{2} + 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(2 \, a x\right)^{2} + 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(2 \, a x\right)^{2} + 2 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(a x\right)^{2} + 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(a x\right)^{2} + 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} + 13 \, a^{3} x^{3} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 6 \, a^{3} x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{3} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 13 \, a^{3} x^{3} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{3} x^{3} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 36 \, a^{4} x^{4} - 27 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 20 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) + 10 \, a^{2} x^{2} \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 15 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(4 \, a x\right) \right) + 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - 4 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) - 32 \, a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-4 \, a x\right) \right) + 64 \, a^{3} x^{3} \operatorname{Si}\left(4 \, a x\right) + 8 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) + 13 \, a^{3} x^{3} \tan\left(2 \, a x\right) + 2 \, a^{3} x^{3} \tan\left(a x\right) + 48 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 10 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 5 \, a x \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 15 \, a^{2} x^{2} \tan\left(2 \, a x\right)^{2} + 10 \, a^{2} x^{2} \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 20 \, a^{2} x^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) - 12 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 10 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(a x\right) + 5 \, a x \tan\left(2 \, a x\right) \tan\left(a x\right)^{2} - 6 \, a x \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 5 \, a x \tan\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 10 \, a x \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 12 \, a^{2} x^{2} + \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} + 3 \, \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 5 \, a x \tan\left(2 \, a x\right) + 10 \, a x \tan\left(a x\right) - 8 \, a x \tan\left(\frac{1}{2} \, a x\right) - 3 \, \tan\left(2 \, a x\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a x\right)^{2} - 4}{12 \, {\left(2 \, a^{5} x^{8} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{4} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{5} x^{8} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{5} x^{8} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{4} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - a^{4} x^{7} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{4} x^{7} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{5} x^{8} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{4} x^{7} \tan\left(2 \, a x\right)^{2} + a^{4} x^{7} \tan\left(a x\right)^{2} - a^{4} x^{7} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{6} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{6} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{4} x^{7} + 2 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - 2 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{2} x^{5} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, a^{3} x^{6} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{2} x^{5} \tan\left(2 \, a x\right)^{2} + 2 \, a^{2} x^{5} \tan\left(a x\right)^{2} - 2 \, a^{2} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{2} - x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a x^{4} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{2} x^{5} + x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(a x\right)^{2} - x^{3} \tan\left(2 \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a x^{4} \tan\left(\frac{1}{2} \, a x\right) + x^{3} \tan\left(2 \, a x\right)^{2} + x^{3} \tan\left(a x\right)^{2} - x^{3} \tan\left(\frac{1}{2} \, a x\right)^{2} + x^{3}\right)}}"," ",0,"1/12*(64*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 8*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 8*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 64*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 128*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 16*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 8*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 8*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 64*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 128*a^8*x^8*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 16*a^8*x^8*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 64*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 8*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 8*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 64*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 128*a^8*x^8*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) + 16*a^8*x^8*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 64*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 8*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 - 40*a^7*x^7*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 64*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^7*x^7*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^7*x^7*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^8*x^8*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) + 8*a^8*x^8*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 8*a^8*x^8*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 64*a^8*x^8*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 128*a^8*x^8*sin_integral(4*a*x)*tan(1/2*a*x) + 16*a^8*x^8*sin_integral(2*a*x)*tan(1/2*a*x) + 128*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 16*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 16*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 128*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 256*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 32*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 20*a^6*x^6*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 - 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 + 64*a^7*x^7*sin_integral(4*a*x)*tan(2*a*x)^2 + 8*a^7*x^7*sin_integral(2*a*x)*tan(2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 - 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 + 64*a^7*x^7*sin_integral(4*a*x)*tan(a*x)^2 + 8*a^7*x^7*sin_integral(2*a*x)*tan(a*x)^2 - 24*a^7*x^7*tan(2*a*x)^2*tan(1/2*a*x) + 24*a^7*x^7*tan(a*x)^2*tan(1/2*a*x) - 32*a^7*x^7*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 4*a^7*x^7*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 4*a^7*x^7*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 - 64*a^7*x^7*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 8*a^7*x^7*sin_integral(2*a*x)*tan(1/2*a*x)^2 - 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 128*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 16*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 20*a^6*x^6*tan(2*a*x)^2*tan(a*x)^2 + 128*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 16*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 16*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 128*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 256*a^6*x^6*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 32*a^6*x^6*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 8*a^6*x^6*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 128*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 16*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 16*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 128*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 256*a^6*x^6*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) + 32*a^6*x^6*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 16*a^6*x^6*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 12*a^6*x^6*tan(2*a*x)^2*tan(1/2*a*x)^2 - 12*a^6*x^6*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^7*x^7*imag_part(cos_integral(4*a*x)) + 4*a^7*x^7*imag_part(cos_integral(2*a*x)) - 4*a^7*x^7*imag_part(cos_integral(-2*a*x)) - 32*a^7*x^7*imag_part(cos_integral(-4*a*x)) + 64*a^7*x^7*sin_integral(4*a*x) + 8*a^7*x^7*sin_integral(2*a*x) + 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 128*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 16*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 40*a^7*x^7*tan(1/2*a*x) - 72*a^5*x^5*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 128*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 16*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^5*x^5*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 - 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 128*a^5*x^5*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 16*a^5*x^5*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^5*x^5*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 12*a^6*x^6*tan(2*a*x)^2 + 12*a^6*x^6*tan(a*x)^2 + 128*a^6*x^6*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) + 16*a^6*x^6*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 16*a^6*x^6*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 128*a^6*x^6*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 256*a^6*x^6*sin_integral(4*a*x)*tan(1/2*a*x) + 32*a^6*x^6*sin_integral(2*a*x)*tan(1/2*a*x) + 16*a^6*x^6*tan(2*a*x)*tan(1/2*a*x) + 8*a^6*x^6*tan(a*x)*tan(1/2*a*x) + 64*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 8*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 8*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 64*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 128*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 16*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 20*a^6*x^6*tan(1/2*a*x)^2 + 36*a^4*x^4*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 - 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 + 128*a^5*x^5*sin_integral(4*a*x)*tan(2*a*x)^2 + 16*a^5*x^5*sin_integral(2*a*x)*tan(2*a*x)^2 + 4*a^5*x^5*tan(2*a*x)^2*tan(a*x) + 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 - 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 + 128*a^5*x^5*sin_integral(4*a*x)*tan(a*x)^2 + 16*a^5*x^5*sin_integral(2*a*x)*tan(a*x)^2 + 8*a^5*x^5*tan(2*a*x)*tan(a*x)^2 - 48*a^5*x^5*tan(2*a*x)^2*tan(1/2*a*x) + 48*a^5*x^5*tan(a*x)^2*tan(1/2*a*x) - 64*a^5*x^5*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 8*a^5*x^5*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 8*a^5*x^5*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 - 128*a^5*x^5*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 16*a^5*x^5*sin_integral(2*a*x)*tan(1/2*a*x)^2 - 8*a^5*x^5*tan(2*a*x)*tan(1/2*a*x)^2 - 4*a^5*x^5*tan(a*x)*tan(1/2*a*x)^2 - 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 20*a^6*x^6 - 36*a^4*x^4*tan(2*a*x)^2*tan(a*x)^2 + 64*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 8*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 8*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x) - 64*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x) + 128*a^4*x^4*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 16*a^4*x^4*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x) + 4*a^4*x^4*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 64*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 8*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 8*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 64*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x) + 128*a^4*x^4*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x) + 16*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 26*a^4*x^4*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 24*a^4*x^4*tan(2*a*x)^2*tan(1/2*a*x)^2 - 24*a^4*x^4*tan(a*x)^2*tan(1/2*a*x)^2 + 64*a^5*x^5*imag_part(cos_integral(4*a*x)) + 8*a^5*x^5*imag_part(cos_integral(2*a*x)) - 8*a^5*x^5*imag_part(cos_integral(-2*a*x)) - 64*a^5*x^5*imag_part(cos_integral(-4*a*x)) + 128*a^5*x^5*sin_integral(4*a*x) + 16*a^5*x^5*sin_integral(2*a*x) + 8*a^5*x^5*tan(2*a*x) + 4*a^5*x^5*tan(a*x) + 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(a*x)^2 - 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(a*x)^2 + 64*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 8*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2*tan(a*x)^2 + 72*a^5*x^5*tan(1/2*a*x) - 30*a^3*x^3*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2*tan(1/2*a*x)^2 - 64*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 8*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2*tan(1/2*a*x)^2 - 2*a^3*x^3*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 - 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 64*a^3*x^3*sin_integral(4*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 8*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 13*a^3*x^3*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 24*a^4*x^4*tan(2*a*x)^2 + 24*a^4*x^4*tan(a*x)^2 + 64*a^4*x^4*imag_part(cos_integral(4*a*x))*tan(1/2*a*x) + 8*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 8*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) - 64*a^4*x^4*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x) + 128*a^4*x^4*sin_integral(4*a*x)*tan(1/2*a*x) + 16*a^4*x^4*sin_integral(2*a*x)*tan(1/2*a*x) + 26*a^4*x^4*tan(2*a*x)*tan(1/2*a*x) + 4*a^4*x^4*tan(a*x)*tan(1/2*a*x) - 36*a^4*x^4*tan(1/2*a*x)^2 + 27*a^2*x^2*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(2*a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(2*a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(2*a*x)^2 - 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(2*a*x)^2 + 64*a^3*x^3*sin_integral(4*a*x)*tan(2*a*x)^2 + 8*a^3*x^3*sin_integral(2*a*x)*tan(2*a*x)^2 + 2*a^3*x^3*tan(2*a*x)^2*tan(a*x) + 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 - 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(a*x)^2 + 64*a^3*x^3*sin_integral(4*a*x)*tan(a*x)^2 + 8*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2 + 13*a^3*x^3*tan(2*a*x)*tan(a*x)^2 - 6*a^3*x^3*tan(2*a*x)^2*tan(1/2*a*x) + 24*a^3*x^3*tan(a*x)^2*tan(1/2*a*x) - 32*a^3*x^3*imag_part(cos_integral(4*a*x))*tan(1/2*a*x)^2 - 4*a^3*x^3*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + 4*a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(-4*a*x))*tan(1/2*a*x)^2 - 64*a^3*x^3*sin_integral(4*a*x)*tan(1/2*a*x)^2 - 8*a^3*x^3*sin_integral(2*a*x)*tan(1/2*a*x)^2 - 13*a^3*x^3*tan(2*a*x)*tan(1/2*a*x)^2 - 2*a^3*x^3*tan(a*x)*tan(1/2*a*x)^2 + 36*a^4*x^4 - 27*a^2*x^2*tan(2*a*x)^2*tan(a*x)^2 + 20*a^2*x^2*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x) + 10*a^2*x^2*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + 15*a^2*x^2*tan(2*a*x)^2*tan(1/2*a*x)^2 + 32*a^3*x^3*imag_part(cos_integral(4*a*x)) + 4*a^3*x^3*imag_part(cos_integral(2*a*x)) - 4*a^3*x^3*imag_part(cos_integral(-2*a*x)) - 32*a^3*x^3*imag_part(cos_integral(-4*a*x)) + 64*a^3*x^3*sin_integral(4*a*x) + 8*a^3*x^3*sin_integral(2*a*x) + 13*a^3*x^3*tan(2*a*x) + 2*a^3*x^3*tan(a*x) + 48*a^3*x^3*tan(1/2*a*x) + 2*a*x*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - 10*a*x*tan(2*a*x)^2*tan(a*x)*tan(1/2*a*x)^2 - 5*a*x*tan(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - 15*a^2*x^2*tan(2*a*x)^2 + 10*a^2*x^2*tan(2*a*x)*tan(1/2*a*x) + 20*a^2*x^2*tan(a*x)*tan(1/2*a*x) - 12*a^2*x^2*tan(1/2*a*x)^2 - tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 10*a*x*tan(2*a*x)^2*tan(a*x) + 5*a*x*tan(2*a*x)*tan(a*x)^2 - 6*a*x*tan(2*a*x)^2*tan(1/2*a*x) - 5*a*x*tan(2*a*x)*tan(1/2*a*x)^2 - 10*a*x*tan(a*x)*tan(1/2*a*x)^2 + 12*a^2*x^2 + tan(2*a*x)^2*tan(a*x)^2 + 3*tan(2*a*x)^2*tan(1/2*a*x)^2 + 5*a*x*tan(2*a*x) + 10*a*x*tan(a*x) - 8*a*x*tan(1/2*a*x) - 3*tan(2*a*x)^2 + 4*tan(1/2*a*x)^2 - 4)/(2*a^5*x^8*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) - a^4*x^7*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^5*x^8*tan(2*a*x)^2*tan(1/2*a*x) + 2*a^5*x^8*tan(a*x)^2*tan(1/2*a*x) + a^4*x^7*tan(2*a*x)^2*tan(a*x)^2 - a^4*x^7*tan(2*a*x)^2*tan(1/2*a*x)^2 - a^4*x^7*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^5*x^8*tan(1/2*a*x) + 4*a^3*x^6*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + a^4*x^7*tan(2*a*x)^2 + a^4*x^7*tan(a*x)^2 - a^4*x^7*tan(1/2*a*x)^2 - 2*a^2*x^5*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^3*x^6*tan(2*a*x)^2*tan(1/2*a*x) + 4*a^3*x^6*tan(a*x)^2*tan(1/2*a*x) + a^4*x^7 + 2*a^2*x^5*tan(2*a*x)^2*tan(a*x)^2 - 2*a^2*x^5*tan(2*a*x)^2*tan(1/2*a*x)^2 - 2*a^2*x^5*tan(a*x)^2*tan(1/2*a*x)^2 + 4*a^3*x^6*tan(1/2*a*x) + 2*a*x^4*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x) + 2*a^2*x^5*tan(2*a*x)^2 + 2*a^2*x^5*tan(a*x)^2 - 2*a^2*x^5*tan(1/2*a*x)^2 - x^3*tan(2*a*x)^2*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a*x^4*tan(2*a*x)^2*tan(1/2*a*x) + 2*a*x^4*tan(a*x)^2*tan(1/2*a*x) + 2*a^2*x^5 + x^3*tan(2*a*x)^2*tan(a*x)^2 - x^3*tan(2*a*x)^2*tan(1/2*a*x)^2 - x^3*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a*x^4*tan(1/2*a*x) + x^3*tan(2*a*x)^2 + x^3*tan(a*x)^2 - x^3*tan(1/2*a*x)^2 + x^3)","C",0
595,1,3130,0,0.691293," ","integrate(cos(a*x)^5/x^3/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","-\frac{54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{6} x^{6} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{6} x^{6} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{7} x^{7} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 72 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{6} x^{6} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} - 12 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 36 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 72 \, a^{6} x^{6} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{6} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{2} + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 8 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) + a^{6} x^{6} \Re \left( \operatorname{Ci}\left(a x\right) \right) + a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-a x\right) \right) + 27 \, a^{6} x^{6} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 12 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 12 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{3} - 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 108 \, a^{5} x^{5} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 128 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - 4 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{4} - 36 \, a^{5} x^{5} \tan\left(\frac{3}{2} \, a x\right) + 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 12 \, a^{5} x^{5} \tan\left(\frac{1}{2} \, a x\right) + 64 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 4 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} - 128 \, a^{4} x^{4} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 4 \, a^{4} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{2} + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 32 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) + 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(a x\right) \right) + 2 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-a x\right) \right) + 54 \, a^{4} x^{4} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 32 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 32 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{3} - 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 8 \, a^{4} x^{4} + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 54 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 56 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 16 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} - 64 \, a^{3} x^{3} \tan\left(\frac{3}{2} \, a x\right) + 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) \tan\left(\frac{3}{2} \, a x\right)^{2} + 12 \, a x \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 28 \, a x \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 16 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} - 56 \, a^{2} x^{2} \tan\left(\frac{3}{2} \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 24 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 8 \, \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(3 \, a x\right) \right) + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) + 27 \, a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-3 \, a x\right) \right) - 20 \, a x \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 20 \, a x \tan\left(\frac{1}{2} \, a x\right)^{3} + 32 \, a^{2} x^{2} - 12 \, \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 4 \, \tan\left(\frac{1}{2} \, a x\right)^{4} - 28 \, a x \tan\left(\frac{3}{2} \, a x\right) - 12 \, a x \tan\left(\frac{1}{2} \, a x\right) + 4 \, \tan\left(\frac{3}{2} \, a x\right)^{2} - 12 \, \tan\left(\frac{1}{2} \, a x\right)^{2} + 8}{16 \, {\left(2 \, a^{5} x^{7} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{4} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{5} x^{7} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{5} x^{7} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{4} x^{6} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{5} x^{7} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + a^{4} x^{6} \tan\left(\frac{3}{2} \, a x\right)^{2} - 2 \, a^{2} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 4 \, a^{3} x^{5} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{3} x^{5} \tan\left(\frac{1}{2} \, a x\right)^{3} + a^{4} x^{6} - 2 \, a^{2} x^{4} \tan\left(\frac{1}{2} \, a x\right)^{4} + 4 \, a^{3} x^{5} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{2} x^{4} \tan\left(\frac{3}{2} \, a x\right)^{2} - x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a x^{3} \tan\left(\frac{3}{2} \, a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x^{3} \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{2} x^{4} - x^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a x^{3} \tan\left(\frac{1}{2} \, a x\right) + x^{2} \tan\left(\frac{3}{2} \, a x\right)^{2} + x^{2}\right)}}"," ",0,"-1/16*(54*a^7*x^7*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^7*x^7*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^7*x^7*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 54*a^7*x^7*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 27*a^6*x^6*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^6*x^6*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^6*x^6*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^6*x^6*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 54*a^7*x^7*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^7*x^7*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^7*x^7*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 54*a^7*x^7*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 54*a^7*x^7*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 + 2*a^7*x^7*real_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a^7*x^7*real_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + 54*a^7*x^7*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 - 27*a^6*x^6*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - a^6*x^6*real_part(cos_integral(a*x))*tan(1/2*a*x)^4 - a^6*x^6*real_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 27*a^6*x^6*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 54*a^7*x^7*real_part(cos_integral(3*a*x))*tan(1/2*a*x) + 2*a^7*x^7*real_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a^7*x^7*real_part(cos_integral(-a*x))*tan(1/2*a*x) + 54*a^7*x^7*real_part(cos_integral(-3*a*x))*tan(1/2*a*x) - 8*a^6*x^6*tan(3/2*a*x)^2*tan(1/2*a*x)^2 - 72*a^6*x^6*tan(3/2*a*x)*tan(1/2*a*x)^3 + 108*a^5*x^5*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 4*a^5*x^5*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 4*a^5*x^5*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 108*a^5*x^5*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 27*a^6*x^6*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + a^6*x^6*real_part(cos_integral(a*x))*tan(3/2*a*x)^2 + a^6*x^6*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 27*a^6*x^6*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 - 12*a^5*x^5*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 36*a^5*x^5*tan(3/2*a*x)*tan(1/2*a*x)^4 - 54*a^4*x^4*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 2*a^4*x^4*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 2*a^4*x^4*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 54*a^4*x^4*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 72*a^6*x^6*tan(3/2*a*x)*tan(1/2*a*x) + 108*a^5*x^5*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 4*a^5*x^5*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 4*a^5*x^5*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 108*a^5*x^5*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 8*a^6*x^6*tan(1/2*a*x)^2 + 108*a^5*x^5*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 + 4*a^5*x^5*real_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 4*a^5*x^5*real_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + 108*a^5*x^5*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 + 8*a^4*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 27*a^6*x^6*real_part(cos_integral(3*a*x)) + a^6*x^6*real_part(cos_integral(a*x)) + a^6*x^6*real_part(cos_integral(-a*x)) + 27*a^6*x^6*real_part(cos_integral(-3*a*x)) - 12*a^5*x^5*tan(3/2*a*x)^2*tan(1/2*a*x) + 12*a^5*x^5*tan(1/2*a*x)^3 - 54*a^4*x^4*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - 2*a^4*x^4*real_part(cos_integral(a*x))*tan(1/2*a*x)^4 - 2*a^4*x^4*real_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 54*a^4*x^4*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 108*a^5*x^5*real_part(cos_integral(3*a*x))*tan(1/2*a*x) + 4*a^5*x^5*real_part(cos_integral(a*x))*tan(1/2*a*x) + 4*a^5*x^5*real_part(cos_integral(-a*x))*tan(1/2*a*x) + 108*a^5*x^5*real_part(cos_integral(-3*a*x))*tan(1/2*a*x) - 4*a^4*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^2 - 128*a^4*x^4*tan(3/2*a*x)*tan(1/2*a*x)^3 + 54*a^3*x^3*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^3*x^3*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 54*a^3*x^3*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - 4*a^4*x^4*tan(1/2*a*x)^4 - 36*a^5*x^5*tan(3/2*a*x) + 54*a^4*x^4*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + 2*a^4*x^4*real_part(cos_integral(a*x))*tan(3/2*a*x)^2 + 2*a^4*x^4*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 54*a^4*x^4*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 + 12*a^5*x^5*tan(1/2*a*x) + 64*a^3*x^3*tan(3/2*a*x)*tan(1/2*a*x)^4 - 27*a^2*x^2*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^2*x^2*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - a^2*x^2*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 27*a^2*x^2*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x)^4 - 4*a^4*x^4*tan(3/2*a*x)^2 - 128*a^4*x^4*tan(3/2*a*x)*tan(1/2*a*x) + 54*a^3*x^3*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^3*x^3*real_part(cos_integral(a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) + 54*a^3*x^3*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2*tan(1/2*a*x) - 4*a^4*x^4*tan(1/2*a*x)^2 + 54*a^3*x^3*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^3 + 2*a^3*x^3*real_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + 54*a^3*x^3*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^3 + 32*a^2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 54*a^4*x^4*real_part(cos_integral(3*a*x)) + 2*a^4*x^4*real_part(cos_integral(a*x)) + 2*a^4*x^4*real_part(cos_integral(-a*x)) + 54*a^4*x^4*real_part(cos_integral(-3*a*x)) - 32*a^3*x^3*tan(3/2*a*x)^2*tan(1/2*a*x) + 32*a^3*x^3*tan(1/2*a*x)^3 - 27*a^2*x^2*real_part(cos_integral(3*a*x))*tan(1/2*a*x)^4 - a^2*x^2*real_part(cos_integral(a*x))*tan(1/2*a*x)^4 - a^2*x^2*real_part(cos_integral(-a*x))*tan(1/2*a*x)^4 - 27*a^2*x^2*real_part(cos_integral(-3*a*x))*tan(1/2*a*x)^4 + 8*a^4*x^4 + 54*a^3*x^3*real_part(cos_integral(3*a*x))*tan(1/2*a*x) + 2*a^3*x^3*real_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(1/2*a*x) + 54*a^3*x^3*real_part(cos_integral(-3*a*x))*tan(1/2*a*x) + 24*a^2*x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^2 - 56*a^2*x^2*tan(3/2*a*x)*tan(1/2*a*x)^3 + 16*a^2*x^2*tan(1/2*a*x)^4 - 64*a^3*x^3*tan(3/2*a*x) + 27*a^2*x^2*real_part(cos_integral(3*a*x))*tan(3/2*a*x)^2 + a^2*x^2*real_part(cos_integral(a*x))*tan(3/2*a*x)^2 + a^2*x^2*real_part(cos_integral(-a*x))*tan(3/2*a*x)^2 + 27*a^2*x^2*real_part(cos_integral(-3*a*x))*tan(3/2*a*x)^2 + 12*a*x*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 28*a*x*tan(3/2*a*x)*tan(1/2*a*x)^4 + 16*a^2*x^2*tan(3/2*a*x)^2 - 56*a^2*x^2*tan(3/2*a*x)*tan(1/2*a*x) + 24*a^2*x^2*tan(1/2*a*x)^2 + 8*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 27*a^2*x^2*real_part(cos_integral(3*a*x)) + a^2*x^2*real_part(cos_integral(a*x)) + a^2*x^2*real_part(cos_integral(-a*x)) + 27*a^2*x^2*real_part(cos_integral(-3*a*x)) - 20*a*x*tan(3/2*a*x)^2*tan(1/2*a*x) + 20*a*x*tan(1/2*a*x)^3 + 32*a^2*x^2 - 12*tan(3/2*a*x)^2*tan(1/2*a*x)^2 + 4*tan(1/2*a*x)^4 - 28*a*x*tan(3/2*a*x) - 12*a*x*tan(1/2*a*x) + 4*tan(3/2*a*x)^2 - 12*tan(1/2*a*x)^2 + 8)/(2*a^5*x^7*tan(3/2*a*x)^2*tan(1/2*a*x)^3 - a^4*x^6*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 2*a^5*x^7*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a^5*x^7*tan(1/2*a*x)^3 - a^4*x^6*tan(1/2*a*x)^4 + 2*a^5*x^7*tan(1/2*a*x) + 4*a^3*x^5*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + a^4*x^6*tan(3/2*a*x)^2 - 2*a^2*x^4*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 4*a^3*x^5*tan(3/2*a*x)^2*tan(1/2*a*x) + 4*a^3*x^5*tan(1/2*a*x)^3 + a^4*x^6 - 2*a^2*x^4*tan(1/2*a*x)^4 + 4*a^3*x^5*tan(1/2*a*x) + 2*a*x^3*tan(3/2*a*x)^2*tan(1/2*a*x)^3 + 2*a^2*x^4*tan(3/2*a*x)^2 - x^2*tan(3/2*a*x)^2*tan(1/2*a*x)^4 + 2*a*x^3*tan(3/2*a*x)^2*tan(1/2*a*x) + 2*a*x^3*tan(1/2*a*x)^3 + 2*a^2*x^4 - x^2*tan(1/2*a*x)^4 + 2*a*x^3*tan(1/2*a*x) + x^2*tan(3/2*a*x)^2 + x^2)","C",0
596,1,997,0,0.488576," ","integrate(cos(a*x)^4/x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","-\frac{2 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{4} x^{4} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{4} x^{4} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} + 2 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 2 \, a^{3} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{2} x^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{3} x^{3} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - a^{3} x^{3} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) + 2 \, a^{3} x^{3} \operatorname{Si}\left(2 \, a x\right) + 2 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right) - a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a x \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} - a^{2} x^{2} \tan\left(a x\right)^{2} + 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, a^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 4 \, a^{2} x^{2} \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{2} x^{2} \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right) - a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(a x\right)^{2} - a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(a x\right)^{2} + 2 \, a x \operatorname{Si}\left(2 \, a x\right) \tan\left(a x\right)^{2} - 2 \, a x \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} + a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{2} - 2 \, a x \operatorname{Si}\left(2 \, a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} - a x \tan\left(a x\right) \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{2} x^{2} + a x \Im \left( \operatorname{Ci}\left(2 \, a x\right) \right) - a x \Im \left( \operatorname{Ci}\left(-2 \, a x\right) \right) + 2 \, a x \operatorname{Si}\left(2 \, a x\right) + a x \tan\left(a x\right) - \tan\left(\frac{1}{2} \, a x\right)^{2} + 1}{2 \, a^{3} x^{4} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) - a^{2} x^{3} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a^{3} x^{4} \tan\left(\frac{1}{2} \, a x\right) + a^{2} x^{3} \tan\left(a x\right)^{2} - a^{2} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a x^{2} \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right) + a^{2} x^{3} - x \tan\left(a x\right)^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a x^{2} \tan\left(\frac{1}{2} \, a x\right) + x \tan\left(a x\right)^{2} - x \tan\left(\frac{1}{2} \, a x\right)^{2} + x}"," ",0,"-(2*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 2*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 4*a^4*x^4*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) - a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 2*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^4*x^4*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 2*a^4*x^4*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) + 4*a^4*x^4*sin_integral(2*a*x)*tan(1/2*a*x) + a^3*x^3*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 + 2*a^3*x^3*sin_integral(2*a*x)*tan(a*x)^2 - 2*a^3*x^3*tan(a*x)^2*tan(1/2*a*x) - a^3*x^3*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + a^3*x^3*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 - 2*a^3*x^3*sin_integral(2*a*x)*tan(1/2*a*x)^2 + 2*a^2*x^2*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x) - 2*a^2*x^2*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x) + 4*a^2*x^2*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x) + a^2*x^2*tan(a*x)^2*tan(1/2*a*x)^2 + a^3*x^3*imag_part(cos_integral(2*a*x)) - a^3*x^3*imag_part(cos_integral(-2*a*x)) + 2*a^3*x^3*sin_integral(2*a*x) + 2*a^3*x^3*tan(1/2*a*x) - a*x*imag_part(cos_integral(2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 + a*x*imag_part(cos_integral(-2*a*x))*tan(a*x)^2*tan(1/2*a*x)^2 - 2*a*x*sin_integral(2*a*x)*tan(a*x)^2*tan(1/2*a*x)^2 - a^2*x^2*tan(a*x)^2 + 2*a^2*x^2*imag_part(cos_integral(2*a*x))*tan(1/2*a*x) - 2*a^2*x^2*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x) + 4*a^2*x^2*sin_integral(2*a*x)*tan(1/2*a*x) + 2*a^2*x^2*tan(a*x)*tan(1/2*a*x) - a^2*x^2*tan(1/2*a*x)^2 + a*x*imag_part(cos_integral(2*a*x))*tan(a*x)^2 - a*x*imag_part(cos_integral(-2*a*x))*tan(a*x)^2 + 2*a*x*sin_integral(2*a*x)*tan(a*x)^2 - 2*a*x*tan(a*x)^2*tan(1/2*a*x) - a*x*imag_part(cos_integral(2*a*x))*tan(1/2*a*x)^2 + a*x*imag_part(cos_integral(-2*a*x))*tan(1/2*a*x)^2 - 2*a*x*sin_integral(2*a*x)*tan(1/2*a*x)^2 - a*x*tan(a*x)*tan(1/2*a*x)^2 + a^2*x^2 + a*x*imag_part(cos_integral(2*a*x)) - a*x*imag_part(cos_integral(-2*a*x)) + 2*a*x*sin_integral(2*a*x) + a*x*tan(a*x) - tan(1/2*a*x)^2 + 1)/(2*a^3*x^4*tan(a*x)^2*tan(1/2*a*x) - a^2*x^3*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a^3*x^4*tan(1/2*a*x) + a^2*x^3*tan(a*x)^2 - a^2*x^3*tan(1/2*a*x)^2 + 2*a*x^2*tan(a*x)^2*tan(1/2*a*x) + a^2*x^3 - x*tan(a*x)^2*tan(1/2*a*x)^2 + 2*a*x^2*tan(1/2*a*x) + x*tan(a*x)^2 - x*tan(1/2*a*x)^2 + x)","C",0
597,1,366,0,0.353396," ","integrate(cos(a*x)^3/x/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\frac{2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a^{3} x^{3} \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 8 \, a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + 2 \, a x \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + 2 \, a x \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{3} + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(a x\right) \right) + a^{2} x^{2} \Re \left( \operatorname{Ci}\left(-a x\right) \right) - \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} - \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a x \Re \left( \operatorname{Ci}\left(a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x \Re \left( \operatorname{Ci}\left(-a x\right) \right) \tan\left(\frac{1}{2} \, a x\right) - 2 \, \tan\left(\frac{1}{2} \, a x\right)^{4} - 12 \, \tan\left(\frac{1}{2} \, a x\right)^{2} + \Re \left( \operatorname{Ci}\left(a x\right) \right) + \Re \left( \operatorname{Ci}\left(-a x\right) \right) - 2}{2 \, {\left(2 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right)^{3} - a^{2} x^{2} \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a^{3} x^{3} \tan\left(\frac{1}{2} \, a x\right) + 2 \, a x \tan\left(\frac{1}{2} \, a x\right)^{3} + a^{2} x^{2} - \tan\left(\frac{1}{2} \, a x\right)^{4} + 2 \, a x \tan\left(\frac{1}{2} \, a x\right) + 1\right)}}"," ",0,"1/2*(2*a^3*x^3*real_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(1/2*a*x)^3 - a^2*x^2*real_part(cos_integral(a*x))*tan(1/2*a*x)^4 - a^2*x^2*real_part(cos_integral(-a*x))*tan(1/2*a*x)^4 + 2*a^3*x^3*real_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a^3*x^3*real_part(cos_integral(-a*x))*tan(1/2*a*x) - 8*a^2*x^2*tan(1/2*a*x)^2 + 2*a*x*real_part(cos_integral(a*x))*tan(1/2*a*x)^3 + 2*a*x*real_part(cos_integral(-a*x))*tan(1/2*a*x)^3 + a^2*x^2*real_part(cos_integral(a*x)) + a^2*x^2*real_part(cos_integral(-a*x)) - real_part(cos_integral(a*x))*tan(1/2*a*x)^4 - real_part(cos_integral(-a*x))*tan(1/2*a*x)^4 + 2*a*x*real_part(cos_integral(a*x))*tan(1/2*a*x) + 2*a*x*real_part(cos_integral(-a*x))*tan(1/2*a*x) - 2*tan(1/2*a*x)^4 - 12*tan(1/2*a*x)^2 + real_part(cos_integral(a*x)) + real_part(cos_integral(-a*x)) - 2)/(2*a^3*x^3*tan(1/2*a*x)^3 - a^2*x^2*tan(1/2*a*x)^4 + 2*a^3*x^3*tan(1/2*a*x) + 2*a*x*tan(1/2*a*x)^3 + a^2*x^2 - tan(1/2*a*x)^4 + 2*a*x*tan(1/2*a*x) + 1)","C",0
598,1,32,0,0.167062," ","integrate(cos(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\frac{2 \, \tan\left(\frac{1}{2} \, a x\right)}{2 \, a^{2} x \tan\left(\frac{1}{2} \, a x\right) - a \tan\left(\frac{1}{2} \, a x\right)^{2} + a}"," ",0,"2*tan(1/2*a*x)/(2*a^2*x*tan(1/2*a*x) - a*tan(1/2*a*x)^2 + a)","A",0
599,1,40,0,0.176886," ","integrate(x*cos(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, a x\right)^{2} + 1\right)}}{2 \, a^{3} x \tan\left(\frac{1}{2} \, a x\right) - a^{2} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{2}}"," ",0,"-2*(tan(1/2*a*x)^2 + 1)/(2*a^3*x*tan(1/2*a*x) - a^2*tan(1/2*a*x)^2 + a^2)","B",0
600,1,52,0,0.152888," ","integrate(x^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\frac{a x \tan\left(\frac{1}{2} \, a x\right)^{2} - a x + 2 \, \tan\left(\frac{1}{2} \, a x\right)}{2 \, a^{4} x \tan\left(\frac{1}{2} \, a x\right) - a^{3} \tan\left(\frac{1}{2} \, a x\right)^{2} + a^{3}}"," ",0,"(a*x*tan(1/2*a*x)^2 - a*x + 2*tan(1/2*a*x))/(2*a^4*x*tan(1/2*a*x) - a^3*tan(1/2*a*x)^2 + a^3)","A",0
601,0,0,0,0.000000," ","integrate(x^3*sec(a*x)/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\int \frac{x^{3} \sec\left(a x\right)}{{\left(a x \sin\left(a x\right) + \cos\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*sec(a*x)/(a*x*sin(a*x) + cos(a*x))^2, x)","F",0
602,0,0,0,0.000000," ","integrate(x^4*sec(a*x)^2/(cos(a*x)+a*x*sin(a*x))^2,x, algorithm=""giac"")","\int \frac{x^{4} \sec\left(a x\right)^{2}}{{\left(a x \sin\left(a x\right) + \cos\left(a x\right)\right)}^{2}}\,{d x}"," ",0,"integrate(x^4*sec(a*x)^2/(a*x*sin(a*x) + cos(a*x))^2, x)","F",0
603,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\int \sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)\,{d x}"," ",0,"integrate(sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a))*cos(2*b*x + 2*a), x)","F",0
609,0,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\int \sqrt{c \tan\left(2 \, b x + 2 \, a\right) \tan\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2}\,{d x}"," ",0,"integrate(sqrt(c*tan(2*b*x + 2*a)*tan(b*x + a))*cos(2*b*x + 2*a)^2, x)","F",0
610,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate((c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^3*(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^4/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^3/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate(sec(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(1/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cos(2*b*x+2*a)^2/(c*tan(b*x+a)*tan(2*b*x+2*a))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate(cot(x)*csc(x)/sin(2*x)^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(x\right) \csc\left(x\right)}{\sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(cot(x)*csc(x)/sqrt(sin(2*x)), x)","F",0
634,0,0,0,0.000000," ","integrate(csc(x)^2*sec(x)/sin(2*x)^(1/2)/(-2+tan(x)),x, algorithm=""giac"")","\int \frac{\csc\left(x\right)^{2} \sec\left(x\right)}{{\left(\tan\left(x\right) - 2\right)} \sqrt{\sin\left(2 \, x\right)}}\,{d x}"," ",0,"integrate(csc(x)^2*sec(x)/((tan(x) - 2)*sqrt(sin(2*x))), x)","F",0
635,0,0,0,0.000000," ","integrate(cos(x)^2*sin(x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(x\right)^{2} \sin\left(x\right)}{{\left(\sin\left(x\right)^{2} - \sin\left(2 \, x\right)\right)} \sin\left(2 \, x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(x)^2*sin(x)/((sin(x)^2 - sin(2*x))*sin(2*x)^(5/2)), x)","F",0
636,0,0,0,0.000000," ","integrate(cos(x)^3*cos(2*x)/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(2 \, x\right) \cos\left(x\right)^{3}}{{\left(\sin\left(x\right)^{2} - \sin\left(2 \, x\right)\right)} \sin\left(2 \, x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(2*x)*cos(x)^3/((sin(x)^2 - sin(2*x))*sin(2*x)^(5/2)), x)","F",0
637,0,0,0,0.000000," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^n*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \sec\left(d x + c\right) \tan\left(d x + c\right) + a \cos\left(d x + c\right)\right)} {\left(b \sec\left(d x + c\right) + a \sin\left(d x + c\right)\right)}^{n}\,{d x}"," ",0,"integrate((b*sec(d*x + c)*tan(d*x + c) + a*cos(d*x + c))*(b*sec(d*x + c) + a*sin(d*x + c))^n, x)","F",0
638,1,142,0,1.953853," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^3*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{4} + 4 \, a b^{3} \tan\left(d x + c\right)^{3} + 6 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} + 2 \, b^{4} \tan\left(d x + c\right)^{2} + 4 \, a^{3} b \tan\left(d x + c\right) + 4 \, a b^{3} \tan\left(d x + c\right) - \frac{4 \, a^{3} b \tan\left(d x + c\right)^{3} + 2 \, a^{4} \tan\left(d x + c\right)^{2} + 4 \, a^{3} b \tan\left(d x + c\right) + a^{4}}{{\left(\tan\left(d x + c\right)^{2} + 1\right)}^{2}}}{4 \, d}"," ",0,"1/4*(b^4*tan(d*x + c)^4 + 4*a*b^3*tan(d*x + c)^3 + 6*a^2*b^2*tan(d*x + c)^2 + 2*b^4*tan(d*x + c)^2 + 4*a^3*b*tan(d*x + c) + 4*a*b^3*tan(d*x + c) - (4*a^3*b*tan(d*x + c)^3 + 2*a^4*tan(d*x + c)^2 + 4*a^3*b*tan(d*x + c) + a^4)/(tan(d*x + c)^2 + 1)^2)/d","B",0
639,-1,0,0,0.000000," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))^2*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,1,45,0,2.670670," ","integrate((b*sec(d*x+c)+a*sin(d*x+c))*(a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c)),x, algorithm=""giac"")","\frac{b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) - \frac{a^{2}}{\tan\left(d x + c\right)^{2} + 1}}{2 \, d}"," ",0,"1/2*(b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) - a^2/(tan(d*x + c)^2 + 1))/d","A",0
641,-2,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c)),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 0.56gen.cc:simplify/tmp.type!=_EXT Error: Bad Argument Value","F(-2)",0
642,1,108,0,0.725910," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - b\right)}}{{\left(b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + b\right)} b d}"," ",0,"2*(a*tan(1/2*d*x + 1/2*c)^3 - b*tan(1/2*d*x + 1/2*c)^2 - a*tan(1/2*d*x + 1/2*c) - b)/((b*tan(1/2*d*x + 1/2*c)^4 - 2*a*tan(1/2*d*x + 1/2*c)^3 + 2*b*tan(1/2*d*x + 1/2*c)^2 + 2*a*tan(1/2*d*x + 1/2*c) + b)*b*d)","B",0
643,-2,0,0,0.000000," ","integrate((a*cos(d*x+c)+b*sec(d*x+c)*tan(d*x+c))/(b*sec(d*x+c)+a*sin(d*x+c))^3,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Evaluation time: 52.12gen.cc:simplify/tmp.type!=_EXT Error: Bad Argument Value","F(-2)",0
644,0,0,0,0.000000," ","integrate(F(c,d,cos(b*x+a),r,s)*sin(b*x+a),x, algorithm=""giac"")","\int F\left(c, d, \cos\left(b x + a\right), r, s\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(F(c, d, cos(b*x + a), r, s)*sin(b*x + a), x)","F",0
645,0,0,0,0.000000," ","integrate(cos(b*x+a)*F(c,d,sin(b*x+a),r,s),x, algorithm=""giac"")","\int F\left(c, d, \sin\left(b x + a\right), r, s\right) \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(F(c, d, sin(b*x + a), r, s)*cos(b*x + a), x)","F",0
646,0,0,0,0.000000," ","integrate(F(c,d,tan(b*x+a),r,s)*sec(b*x+a)^2,x, algorithm=""giac"")","\int F\left(c, d, \tan\left(b x + a\right), r, s\right) \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(F(c, d, tan(b*x + a), r, s)*sec(b*x + a)^2, x)","F",0
647,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*F(c,d,cot(b*x+a),r,s),x, algorithm=""giac"")","\int F\left(c, d, \cot\left(b x + a\right), r, s\right) \csc\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(F(c, d, cot(b*x + a), r, s)*csc(b*x + a)^2, x)","F",0
648,1,13,0,0.131040," ","integrate(sin(x)/(a+b*cos(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| b \cos\left(x\right) + a \right|}\right)}{b}"," ",0,"-log(abs(b*cos(x) + a))/b","A",0
649,1,20,0,0.138919," ","integrate((a+b*cos(x))^n*sin(x),x, algorithm=""giac"")","-\frac{{\left(b \cos\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"-(b*cos(x) + a)^(n + 1)/(b*(n + 1))","A",0
650,1,14,0,0.125297," ","integrate(sin(x)/(1+cos(x)^2)^(1/2),x, algorithm=""giac"")","\log\left(\sqrt{\cos\left(x\right)^{2} + 1} - \cos\left(x\right)\right)"," ",0,"log(sqrt(cos(x)^2 + 1) - cos(x))","B",0
651,1,5,0,0.139701," ","integrate(cos(cos(x))*sin(x),x, algorithm=""giac"")","-\sin\left(\cos\left(x\right)\right)"," ",0,"-sin(cos(x))","A",0
652,1,17,0,0.140262," ","integrate(cos(x)*cos(cos(x))*sin(x)*sin(cos(x)),x, algorithm=""giac"")","\frac{1}{4} \, \cos\left(x\right) \cos\left(2 \, \cos\left(x\right)\right) - \frac{1}{8} \, \sin\left(2 \, \cos\left(x\right)\right)"," ",0,"1/4*cos(x)*cos(2*cos(x)) - 1/8*sin(2*cos(x))","A",0
653,1,20,0,0.151835," ","integrate(cos(cos(x))*sin(x)*sin(6*cos(x))^2,x, algorithm=""giac"")","\frac{1}{52} \, \sin\left(13 \, \cos\left(x\right)\right) + \frac{1}{44} \, \sin\left(11 \, \cos\left(x\right)\right) - \frac{1}{2} \, \sin\left(\cos\left(x\right)\right)"," ",0,"1/52*sin(13*cos(x)) + 1/44*sin(11*cos(x)) - 1/2*sin(cos(x))","A",0
654,1,39,0,0.130302," ","integrate(cos(x)^3*(a+b*cos(x)^2)^3*sin(x),x, algorithm=""giac"")","-\frac{1}{10} \, b^{3} \cos\left(x\right)^{10} - \frac{3}{8} \, a b^{2} \cos\left(x\right)^{8} - \frac{1}{2} \, a^{2} b \cos\left(x\right)^{6} - \frac{1}{4} \, a^{3} \cos\left(x\right)^{4}"," ",0,"-1/10*b^3*cos(x)^10 - 3/8*a*b^2*cos(x)^8 - 1/2*a^2*b*cos(x)^6 - 1/4*a^3*cos(x)^4","A",0
655,1,7,0,0.158478," ","integrate(sin(3*x)*sin(cos(3*x)),x, algorithm=""giac"")","\frac{1}{3} \, \cos\left(\cos\left(3 \, x\right)\right)"," ",0,"1/3*cos(cos(3*x))","A",0
656,1,17,0,0.148787," ","integrate(exp(cos(1+3*x))*cos(1+3*x)*sin(1+3*x),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(\cos\left(3 \, x + 1\right) - 1\right)} e^{\left(\cos\left(3 \, x + 1\right)\right)}"," ",0,"-1/3*(cos(3*x + 1) - 1)*e^(cos(3*x + 1))","A",0
657,1,7,0,0.153705," ","integrate(cos(x)^2*sin(x)/(1-cos(x)^6)^(1/2),x, algorithm=""giac"")","-\frac{1}{3} \, \arcsin\left(\cos\left(x\right)^{3}\right)"," ",0,"-1/3*arcsin(cos(x)^3)","A",0
658,1,75,0,0.136457," ","integrate(sin(x)^5/(1-5*cos(x))^(1/2),x, algorithm=""giac"")","\frac{2}{28125} \, {\left(5 \, \cos\left(x\right) - 1\right)}^{4} \sqrt{-5 \, \cos\left(x\right) + 1} + \frac{8}{21875} \, {\left(5 \, \cos\left(x\right) - 1\right)}^{3} \sqrt{-5 \, \cos\left(x\right) + 1} - \frac{88}{15625} \, {\left(5 \, \cos\left(x\right) - 1\right)}^{2} \sqrt{-5 \, \cos\left(x\right) + 1} + \frac{64}{3125} \, {\left(-5 \, \cos\left(x\right) + 1\right)}^{\frac{3}{2}} + \frac{1152}{3125} \, \sqrt{-5 \, \cos\left(x\right) + 1}"," ",0,"2/28125*(5*cos(x) - 1)^4*sqrt(-5*cos(x) + 1) + 8/21875*(5*cos(x) - 1)^3*sqrt(-5*cos(x) + 1) - 88/15625*(5*cos(x) - 1)^2*sqrt(-5*cos(x) + 1) + 64/3125*(-5*cos(x) + 1)^(3/2) + 1152/3125*sqrt(-5*cos(x) + 1)","A",0
659,1,17,0,0.142672," ","integrate(exp(n*cos(b*x+a))*sin(b*x+a),x, algorithm=""giac"")","-\frac{e^{\left(n \cos\left(b x + a\right)\right)}}{b n}"," ",0,"-e^(n*cos(b*x + a))/(b*n)","A",0
660,1,23,0,0.151735," ","integrate(exp(n*cos(b*c*x+a*c))*sin(c*(b*x+a)),x, algorithm=""giac"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
661,1,23,0,0.148170," ","integrate(exp(n*cos(c*(b*x+a)))*sin(b*c*x+a*c),x, algorithm=""giac"")","-\frac{e^{\left(n \cos\left(b c x + a c\right)\right)}}{b c n}"," ",0,"-e^(n*cos(b*c*x + a*c))/(b*c*n)","A",0
662,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*tan(b*x+a),x, algorithm=""giac"")","\int e^{\left(n \cos\left(b x + a\right)\right)} \tan\left(b x + a\right)\,{d x}"," ",0,"integrate(e^(n*cos(b*x + a))*tan(b*x + a), x)","F",0
663,0,0,0,0.000000," ","integrate(exp(n*cos(b*c*x+a*c))*tan(c*(b*x+a)),x, algorithm=""giac"")","\int e^{\left(n \cos\left(b c x + a c\right)\right)} \tan\left({\left(b x + a\right)} c\right)\,{d x}"," ",0,"integrate(e^(n*cos(b*c*x + a*c))*tan((b*x + a)*c), x)","F",0
664,0,0,0,0.000000," ","integrate(exp(n*cos(c*(b*x+a)))*tan(b*c*x+a*c),x, algorithm=""giac"")","\int e^{\left(n \cos\left({\left(b x + a\right)} c\right)\right)} \tan\left(b c x + a c\right)\,{d x}"," ",0,"integrate(e^(n*cos((b*x + a)*c))*tan(b*c*x + a*c), x)","F",0
665,1,12,0,0.141193," ","integrate(cos(x)/(a+b*sin(x)),x, algorithm=""giac"")","\frac{\log\left({\left| b \sin\left(x\right) + a \right|}\right)}{b}"," ",0,"log(abs(b*sin(x) + a))/b","A",0
666,1,19,0,0.148230," ","integrate(cos(x)*(a+b*sin(x))^n,x, algorithm=""giac"")","\frac{{\left(b \sin\left(x\right) + a\right)}^{n + 1}}{b {\left(n + 1\right)}}"," ",0,"(b*sin(x) + a)^(n + 1)/(b*(n + 1))","A",0
667,1,16,0,0.128262," ","integrate(cos(x)/(1+sin(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left(\sqrt{\sin\left(x\right)^{2} + 1} - \sin\left(x\right)\right)"," ",0,"-log(sqrt(sin(x)^2 + 1) - sin(x))","B",0
668,1,5,0,0.154466," ","integrate(cos(x)/(4-sin(x)^2)^(1/2),x, algorithm=""giac"")","\arcsin\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"arcsin(1/2*sin(x))","A",0
669,1,9,0,0.223804," ","integrate(cos(3*x)/(4-sin(3*x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \arcsin\left(\frac{1}{2} \, \sin\left(3 \, x\right)\right)"," ",0,"1/3*arcsin(1/2*sin(3*x))","A",0
670,1,38,0,0.150007," ","integrate(cos(x)*(1+csc(x))^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, {\left(2 \, \sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \log\left({\left| 2 \, \sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - 2 \, \sin\left(x\right) - 1 \right|}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/2*(2*sqrt(sin(x)^2 + sin(x)) - log(abs(2*sqrt(sin(x)^2 + sin(x)) - 2*sin(x) - 1)))*sgn(sin(x))","B",0
671,1,22,0,0.141023," ","integrate(cos(x)*(4-sin(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-\sin\left(x\right)^{2} + 4} \sin\left(x\right) + 2 \, \arcsin\left(\frac{1}{2} \, \sin\left(x\right)\right)"," ",0,"1/2*sqrt(-sin(x)^2 + 4)*sin(x) + 2*arcsin(1/2*sin(x))","A",0
672,1,10,0,0.133315," ","integrate(cos(x)*sin(x)*(1+sin(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\sin\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(sin(x)^2 + 1)^(3/2)","A",0
673,1,20,0,0.155857," ","integrate(cos(x)/(2*sin(x)+sin(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left(-\sqrt{\sin\left(x\right)^{2} + 2 \, \sin\left(x\right)} + \sin\left(x\right) + 1\right)"," ",0,"-log(-sqrt(sin(x)^2 + 2*sin(x)) + sin(x) + 1)","A",0
674,1,3,0,0.142497," ","integrate(cos(x)*cos(sin(x)),x, algorithm=""giac"")","\sin\left(\sin\left(x\right)\right)"," ",0,"sin(sin(x))","A",0
675,1,4,0,0.132390," ","integrate(cos(x)*cos(sin(x))*cos(sin(sin(x))),x, algorithm=""giac"")","\sin\left(\sin\left(\sin\left(x\right)\right)\right)"," ",0,"sin(sin(sin(x)))","A",0
676,1,29,0,0.144868," ","integrate(cos(x)*sec(sin(x)),x, algorithm=""giac"")","\frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(\sin\left(x\right)\right)} + \sin\left(\sin\left(x\right)\right) + 2 \right|}\right) - \frac{1}{4} \, \log\left({\left| \frac{1}{\sin\left(\sin\left(x\right)\right)} + \sin\left(\sin\left(x\right)\right) - 2 \right|}\right)"," ",0,"1/4*log(abs(1/sin(sin(x)) + sin(sin(x)) + 2)) - 1/4*log(abs(1/sin(sin(x)) + sin(sin(x)) - 2))","B",0
677,1,39,0,0.122524," ","integrate(cos(x)*sin(x)^3*(a+b*sin(x)^2)^3,x, algorithm=""giac"")","\frac{1}{10} \, b^{3} \sin\left(x\right)^{10} + \frac{3}{8} \, a b^{2} \sin\left(x\right)^{8} + \frac{1}{2} \, a^{2} b \sin\left(x\right)^{6} + \frac{1}{4} \, a^{3} \sin\left(x\right)^{4}"," ",0,"1/10*b^3*sin(x)^10 + 3/8*a*b^2*sin(x)^8 + 1/2*a^2*b*sin(x)^6 + 1/4*a^3*sin(x)^4","A",0
678,1,8,0,0.137731," ","integrate(exp(sin(x))*cos(x)*sin(x),x, algorithm=""giac"")","{\left(\sin\left(x\right) - 1\right)} e^{\sin\left(x\right)}"," ",0,"(sin(x) - 1)*e^sin(x)","A",0
679,1,13,0,0.129901," ","integrate(cos(x)^3/(sin(x)^3)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \sin\left(x\right)^{\frac{3}{2}} - \frac{2}{\sqrt{\sin\left(x\right)}}"," ",0,"-2/3*sin(x)^(3/2) - 2/sqrt(sin(x))","A",0
680,1,7,0,0.148703," ","integrate(exp(sin(x)^(1/2))*cos(x)/sin(x)^(1/2),x, algorithm=""giac"")","2 \, e^{\sqrt{\sin\left(x\right)}}"," ",0,"2*e^sqrt(sin(x))","A",0
681,1,5,0,0.120577," ","integrate(exp(4+sin(x))*cos(x),x, algorithm=""giac"")","e^{\left(\sin\left(x\right) + 4\right)}"," ",0,"e^(sin(x) + 4)","A",0
682,1,12,0,0.148101," ","integrate(exp(cos(x)*sin(x))*cos(2*x),x, algorithm=""giac"")","e^{\left(\frac{\tan\left(x\right)}{\tan\left(x\right)^{2} + 1}\right)}"," ",0,"e^(tan(x)/(tan(x)^2 + 1))","A",0
683,1,18,0,0.144891," ","integrate(exp(cos(1/2*x)*sin(1/2*x))*cos(x),x, algorithm=""giac"")","2 \, e^{\left(\frac{\tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}"," ",0,"2*e^(tan(1/2*x)/(tan(1/2*x)^2 + 1))","B",0
684,1,16,0,0.130554," ","integrate(exp(n*sin(b*x+a))*cos(b*x+a),x, algorithm=""giac"")","\frac{e^{\left(n \sin\left(b x + a\right)\right)}}{b n}"," ",0,"e^(n*sin(b*x + a))/(b*n)","A",0
685,1,22,0,0.131771," ","integrate(exp(n*sin(b*c*x+a*c))*cos(c*(b*x+a)),x, algorithm=""giac"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
686,1,22,0,0.146710," ","integrate(exp(n*sin(c*(b*x+a)))*cos(b*c*x+a*c),x, algorithm=""giac"")","\frac{e^{\left(n \sin\left(b c x + a c\right)\right)}}{b c n}"," ",0,"e^(n*sin(b*c*x + a*c))/(b*c*n)","A",0
687,1,13,0,0.141502," ","integrate(exp(n*sin(b*x+a))*cot(b*x+a),x, algorithm=""giac"")","\frac{{\rm Ei}\left(n \sin\left(b x + a\right)\right)}{b}"," ",0,"Ei(n*sin(b*x + a))/b","A",0
688,0,0,0,0.000000," ","integrate(exp(n*sin(b*c*x+a*c))*cot(c*(b*x+a)),x, algorithm=""giac"")","\int \cot\left({\left(b x + a\right)} c\right) e^{\left(n \sin\left(b c x + a c\right)\right)}\,{d x}"," ",0,"integrate(cot((b*x + a)*c)*e^(n*sin(b*c*x + a*c)), x)","F",0
689,0,0,0,0.000000," ","integrate(exp(n*sin(c*(b*x+a)))*cot(b*c*x+a*c),x, algorithm=""giac"")","\int \cot\left(b c x + a c\right) e^{\left(n \sin\left({\left(b x + a\right)} c\right)\right)}\,{d x}"," ",0,"integrate(cot(b*c*x + a*c)*e^(n*sin((b*x + a)*c)), x)","F",0
690,1,12,0,0.121593," ","integrate(sec(x)^2/(a+b*tan(x)),x, algorithm=""giac"")","\frac{\log\left({\left| b \tan\left(x\right) + a \right|}\right)}{b}"," ",0,"log(abs(b*tan(x) + a))/b","A",0
691,1,17,0,0.155600," ","integrate(sec(x)^2/(1-tan(x)^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \tan\left(x\right) + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| \tan\left(x\right) - 1 \right|}\right)"," ",0,"1/2*log(abs(tan(x) + 1)) - 1/2*log(abs(tan(x) - 1))","A",0
692,1,7,0,0.152338," ","integrate(sec(x)^2/(9+tan(x)^2),x, algorithm=""giac"")","\frac{1}{3} \, \arctan\left(\frac{1}{3} \, \tan\left(x\right)\right)"," ",0,"1/3*arctan(1/3*tan(x))","A",0
693,-2,0,0,0.000000," ","integrate(sec(x)^2*(a+b*tan(x))^n,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to divide, perhaps due to rounding error%%%{1,[0,1,0]%%%} / %%%{1,[0,0,1]%%%} Error: Bad Argument Value","F(-2)",0
694,1,4,0,0.126501," ","integrate(sec(x)^2*(1+1/(1+tan(x)^2)),x, algorithm=""giac"")","x + \tan\left(x\right)"," ",0,"x + tan(x)","A",0
695,1,4,0,0.123691," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^2),x, algorithm=""giac"")","x + \tan\left(x\right)"," ",0,"x + tan(x)","A",0
696,1,5,0,0.125501," ","integrate(sec(x)^2/(2+2*tan(x)+tan(x)^2),x, algorithm=""giac"")","\arctan\left(\tan\left(x\right) + 1\right)"," ",0,"arctan(tan(x) + 1)","A",0
697,1,19,0,0.138979," ","integrate(sec(x)^2/(tan(x)^2+tan(x)^3),x, algorithm=""giac"")","-\frac{1}{\tan\left(x\right)} + \log\left({\left| \tan\left(x\right) + 1 \right|}\right) - \log\left({\left| \tan\left(x\right) \right|}\right)"," ",0,"-1/tan(x) + log(abs(tan(x) + 1)) - log(abs(tan(x)))","A",0
698,1,17,0,0.158801," ","integrate(sec(x)^2/(-tan(x)^2+tan(x)^3),x, algorithm=""giac"")","\frac{1}{\tan\left(x\right)} + \log\left({\left| \tan\left(x\right) - 1 \right|}\right) - \log\left({\left| \tan\left(x\right) \right|}\right)"," ",0,"1/tan(x) + log(abs(tan(x) - 1)) - log(abs(tan(x)))","A",0
699,1,61,0,0.167180," ","integrate(sec(x)^2/(3-4*tan(x)^3),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{3} \left(\frac{3}{4}\right)^{\frac{1}{3}} \arctan\left(\frac{4}{9} \, \sqrt{3} \left(\frac{3}{4}\right)^{\frac{2}{3}} {\left(\left(\frac{3}{4}\right)^{\frac{1}{3}} + 2 \, \tan\left(x\right)\right)}\right) + \frac{1}{36} \cdot 6^{\frac{1}{3}} \log\left(\tan\left(x\right)^{2} + \left(\frac{3}{4}\right)^{\frac{1}{3}} \tan\left(x\right) + \left(\frac{3}{4}\right)^{\frac{2}{3}}\right) - \frac{1}{9} \, \left(\frac{3}{4}\right)^{\frac{1}{3}} \log\left({\left| -\left(\frac{3}{4}\right)^{\frac{1}{3}} + \tan\left(x\right) \right|}\right)"," ",0,"1/9*sqrt(3)*(3/4)^(1/3)*arctan(4/9*sqrt(3)*(3/4)^(2/3)*((3/4)^(1/3) + 2*tan(x))) + 1/36*6^(1/3)*log(tan(x)^2 + (3/4)^(1/3)*tan(x) + (3/4)^(2/3)) - 1/9*(3/4)^(1/3)*log(abs(-(3/4)^(1/3) + tan(x)))","A",0
700,1,17,0,0.126188," ","integrate(sec(x)^2/(11-5*tan(x)+5*tan(x)^2),x, algorithm=""giac"")","\frac{2}{195} \, \sqrt{195} \arctan\left(\frac{1}{39} \, \sqrt{195} {\left(2 \, \tan\left(x\right) - 1\right)}\right)"," ",0,"2/195*sqrt(195)*arctan(1/39*sqrt(195)*(2*tan(x) - 1))","A",0
701,1,29,0,0.144920," ","integrate(sec(x)^2*(a+b*tan(x))/(c+d*tan(x)),x, algorithm=""giac"")","\frac{b \tan\left(x\right)}{d} - \frac{{\left(b c - a d\right)} \log\left({\left| d \tan\left(x\right) + c \right|}\right)}{d^{2}}"," ",0,"b*tan(x)/d - (b*c - a*d)*log(abs(d*tan(x) + c))/d^2","A",0
702,1,64,0,0.149212," ","integrate(sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)),x, algorithm=""giac"")","\frac{b^{2} d \tan\left(x\right)^{2} - 2 \, b^{2} c \tan\left(x\right) + 4 \, a b d \tan\left(x\right)}{2 \, d^{2}} + \frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d \tan\left(x\right) + c \right|}\right)}{d^{3}}"," ",0,"1/2*(b^2*d*tan(x)^2 - 2*b^2*c*tan(x) + 4*a*b*d*tan(x))/d^2 + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*tan(x) + c))/d^3","A",0
703,1,123,0,0.148272," ","integrate(sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)),x, algorithm=""giac"")","\frac{2 \, b^{3} d^{2} \tan\left(x\right)^{3} - 3 \, b^{3} c d \tan\left(x\right)^{2} + 9 \, a b^{2} d^{2} \tan\left(x\right)^{2} + 6 \, b^{3} c^{2} \tan\left(x\right) - 18 \, a b^{2} c d \tan\left(x\right) + 18 \, a^{2} b d^{2} \tan\left(x\right)}{6 \, d^{3}} - \frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| d \tan\left(x\right) + c \right|}\right)}{d^{4}}"," ",0,"1/6*(2*b^3*d^2*tan(x)^3 - 3*b^3*c*d*tan(x)^2 + 9*a*b^2*d^2*tan(x)^2 + 6*b^3*c^2*tan(x) - 18*a*b^2*c*d*tan(x) + 18*a^2*b*d^2*tan(x))/d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(d*tan(x) + c))/d^4","A",0
704,1,10,0,0.148617," ","integrate(sec(x)^2*tan(x)^2/(2+tan(x)^3)^2,x, algorithm=""giac"")","-\frac{1}{3 \, {\left(\tan\left(x\right)^{3} + 2\right)}}"," ",0,"-1/3/(tan(x)^3 + 2)","A",0
705,1,25,0,0.139026," ","integrate(sec(x)^2*tan(x)^6*(1+tan(x)^2)^3,x, algorithm=""giac"")","\frac{1}{13} \, \tan\left(x\right)^{13} + \frac{3}{11} \, \tan\left(x\right)^{11} + \frac{1}{3} \, \tan\left(x\right)^{9} + \frac{1}{7} \, \tan\left(x\right)^{7}"," ",0,"1/13*tan(x)^13 + 3/11*tan(x)^11 + 1/3*tan(x)^9 + 1/7*tan(x)^7","A",0
706,1,24,0,0.158010," ","integrate(sec(x)^2*(2+tan(x)^2)/(1+tan(x)^3),x, algorithm=""giac"")","\frac{2}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, \tan\left(x\right) - 1\right)}\right) + \log\left({\left| \tan\left(x\right) + 1 \right|}\right)"," ",0,"2/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*tan(x) - 1)) + log(abs(tan(x) + 1))","A",0
707,1,15,0,0.192601," ","integrate((1+cos(x)^2)*sec(x)^2,x, algorithm=""giac"")","-\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + x + \tan\left(x\right)"," ",0,"-pi*floor(x/pi + 1/2) + x + tan(x)","B",0
708,1,15,0,0.155758," ","integrate(sec(x)^2/(1+sec(x)^2-3*tan(x)),x, algorithm=""giac"")","-\log\left({\left| \tan\left(x\right) - 1 \right|}\right) + \log\left({\left| \tan\left(x\right) - 2 \right|}\right)"," ",0,"-log(abs(tan(x) - 1)) + log(abs(tan(x) - 2))","A",0
709,0,0,0,0.000000," ","integrate(sec(x)^2/(4-sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{\sec\left(x\right)^{2}}{\sqrt{-\sec\left(x\right)^{2} + 4}}\,{d x}"," ",0,"integrate(sec(x)^2/sqrt(-sec(x)^2 + 4), x)","F",0
710,1,7,0,0.171643," ","integrate(sec(x)^2/(1-4*tan(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \arcsin\left(2 \, \tan\left(x\right)\right)"," ",0,"1/2*arcsin(2*tan(x))","A",0
711,1,17,0,0.177043," ","integrate(sec(x)^2/(-4+tan(x)^2)^(1/2),x, algorithm=""giac"")","-\log\left({\left| \sqrt{\tan\left(x\right)^{2} - 4} - \tan\left(x\right) \right|}\right)"," ",0,"-log(abs(sqrt(tan(x)^2 - 4) - tan(x)))","A",0
712,1,142,0,0.202092," ","integrate(sec(x)^2*(1-cot(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, {\left(\pi + 2 \, \arctan\left(-i\right) + 2 i\right)} \mathrm{sgn}\left(\sin\left(x\right)\right) + \frac{1}{4} \, {\left(2 \, \pi \mathrm{sgn}\left(\cos\left(x\right)\right) + \sqrt{2} {\left(\frac{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}{\cos\left(x\right)} - \frac{4 \, \cos\left(x\right)}{\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}}\right)} + 4 \, \arctan\left(-\frac{\sqrt{2} {\left(\frac{{\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}^{2}}{\cos\left(x\right)^{2}} - 4\right)} \cos\left(x\right)}{4 \, {\left(\sqrt{2} \sqrt{-2 \, \cos\left(x\right)^{2} + 1} - \sqrt{2}\right)}}\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-1/2*(pi + 2*arctan(-I) + 2*I)*sgn(sin(x)) + 1/4*(2*pi*sgn(cos(x)) + sqrt(2)*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))/cos(x) - 4*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))) + 4*arctan(-1/4*sqrt(2)*((sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))^2/cos(x)^2 - 4)*cos(x)/(sqrt(2)*sqrt(-2*cos(x)^2 + 1) - sqrt(2))))*sgn(sin(x))","C",0
713,1,20,0,0.146537," ","integrate(sec(x)^2*(1-tan(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{-\tan\left(x\right)^{2} + 1} \tan\left(x\right) + \frac{1}{2} \, \arcsin\left(\tan\left(x\right)\right)"," ",0,"1/2*sqrt(-tan(x)^2 + 1)*tan(x) + 1/2*arcsin(tan(x))","A",0
714,1,3,0,0.132292," ","integrate(exp(tan(x))*sec(x)^2,x, algorithm=""giac"")","e^{\tan\left(x\right)}"," ",0,"e^tan(x)","A",0
715,1,20,0,0.149582," ","integrate(sec(x)^4*(-1+sec(x)^2)^2*tan(x),x, algorithm=""giac"")","\frac{6 \, \cos\left(x\right)^{4} - 8 \, \cos\left(x\right)^{2} + 3}{24 \, \cos\left(x\right)^{8}}"," ",0,"1/24*(6*cos(x)^4 - 8*cos(x)^2 + 3)/cos(x)^8","A",0
716,1,22,0,0.166682," ","integrate(csc(x)^2/(a+b*cot(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| a \tan\left(x\right) + b \right|}\right)}{b} + \frac{\log\left({\left| \tan\left(x\right) \right|}\right)}{b}"," ",0,"-log(abs(a*tan(x) + b))/b + log(abs(tan(x)))/b","A",0
717,0,0,0,0.000000," ","integrate((a+b*cot(x))^n*csc(x)^2,x, algorithm=""giac"")","\int {\left(b \cot\left(x\right) + a\right)}^{n} \csc\left(x\right)^{2}\,{d x}"," ",0,"integrate((b*cot(x) + a)^n*csc(x)^2, x)","F",0
718,1,16,0,0.147037," ","integrate(csc(x)^2*(1+sin(x)^2),x, algorithm=""giac"")","x - \frac{1}{2 \, \tan\left(\frac{1}{2} \, x\right)} + \frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"x - 1/2/tan(1/2*x) + 1/2*tan(1/2*x)","B",0
719,1,16,0,0.141464," ","integrate((1+1/(1+cot(x)^2))*csc(x)^2,x, algorithm=""giac"")","x - \frac{1}{2 \, \tan\left(\frac{1}{2} \, x\right)} + \frac{1}{2} \, \tan\left(\frac{1}{2} \, x\right)"," ",0,"x - 1/2/tan(1/2*x) + 1/2*tan(1/2*x)","B",0
720,1,68,0,0.151919," ","integrate((a+b*cot(x))*csc(x)^2/(c+d*cot(x)),x, algorithm=""giac"")","-\frac{{\left(b c - a d\right)} \log\left({\left| \tan\left(x\right) \right|}\right)}{d^{2}} + \frac{{\left(b c^{2} - a c d\right)} \log\left({\left| c \tan\left(x\right) + d \right|}\right)}{c d^{2}} + \frac{b c \tan\left(x\right) - a d \tan\left(x\right) - b d}{d^{2} \tan\left(x\right)}"," ",0,"-(b*c - a*d)*log(abs(tan(x)))/d^2 + (b*c^2 - a*c*d)*log(abs(c*tan(x) + d))/(c*d^2) + (b*c*tan(x) - a*d*tan(x) - b*d)/(d^2*tan(x))","B",0
721,1,139,0,0.164689," ","integrate((a+b*cot(x))^2*csc(x)^2/(c+d*cot(x)),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| \tan\left(x\right) \right|}\right)}{d^{3}} - \frac{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \log\left({\left| c \tan\left(x\right) + d \right|}\right)}{c d^{3}} - \frac{3 \, b^{2} c^{2} \tan\left(x\right)^{2} - 6 \, a b c d \tan\left(x\right)^{2} + 3 \, a^{2} d^{2} \tan\left(x\right)^{2} - 2 \, b^{2} c d \tan\left(x\right) + 4 \, a b d^{2} \tan\left(x\right) + b^{2} d^{2}}{2 \, d^{3} \tan\left(x\right)^{2}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(tan(x)))/d^3 - (b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*log(abs(c*tan(x) + d))/(c*d^3) - 1/2*(3*b^2*c^2*tan(x)^2 - 6*a*b*c*d*tan(x)^2 + 3*a^2*d^2*tan(x)^2 - 2*b^2*c*d*tan(x) + 4*a*b*d^2*tan(x) + b^2*d^2)/(d^3*tan(x)^2)","B",0
722,1,232,0,0.172421," ","integrate((a+b*cot(x))^3*csc(x)^2/(c+d*cot(x)),x, algorithm=""giac"")","-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| \tan\left(x\right) \right|}\right)}{d^{4}} + \frac{{\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \log\left({\left| c \tan\left(x\right) + d \right|}\right)}{c d^{4}} + \frac{11 \, b^{3} c^{3} \tan\left(x\right)^{3} - 33 \, a b^{2} c^{2} d \tan\left(x\right)^{3} + 33 \, a^{2} b c d^{2} \tan\left(x\right)^{3} - 11 \, a^{3} d^{3} \tan\left(x\right)^{3} - 6 \, b^{3} c^{2} d \tan\left(x\right)^{2} + 18 \, a b^{2} c d^{2} \tan\left(x\right)^{2} - 18 \, a^{2} b d^{3} \tan\left(x\right)^{2} + 3 \, b^{3} c d^{2} \tan\left(x\right) - 9 \, a b^{2} d^{3} \tan\left(x\right) - 2 \, b^{3} d^{3}}{6 \, d^{4} \tan\left(x\right)^{3}}"," ",0,"-(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(tan(x)))/d^4 + (b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*log(abs(c*tan(x) + d))/(c*d^4) + 1/6*(11*b^3*c^3*tan(x)^3 - 33*a*b^2*c^2*d*tan(x)^3 + 33*a^2*b*c*d^2*tan(x)^3 - 11*a^3*d^3*tan(x)^3 - 6*b^3*c^2*d*tan(x)^2 + 18*a*b^2*c*d^2*tan(x)^2 - 18*a^2*b*d^3*tan(x)^2 + 3*b^3*c*d^2*tan(x) - 9*a*b^2*d^3*tan(x) - 2*b^3*d^3)/(d^4*tan(x)^3)","B",0
723,0,0,0,0.000000," ","integrate(csc(x)^2/exp(cot(x)),x, algorithm=""giac"")","\int \csc\left(x\right)^{2} e^{\left(-\cot\left(x\right)\right)}\,{d x}"," ",0,"integrate(csc(x)^2*e^(-cot(x)), x)","F",0
724,1,22,0,0.142323," ","integrate(sec(x)*tan(x)/(a+b*sec(x)),x, algorithm=""giac"")","\frac{\log\left({\left| a \cos\left(x\right) + b \right|}\right)}{b} - \frac{\log\left({\left| \cos\left(x\right) \right|}\right)}{b}"," ",0,"log(abs(a*cos(x) + b))/b - log(abs(cos(x)))/b","A",0
725,1,5,0,0.142077," ","integrate(sec(x)*tan(x)/(1+sec(x)^2),x, algorithm=""giac"")","-\arctan\left(\cos\left(x\right)\right)"," ",0,"-arctan(cos(x))","A",0
726,1,7,0,0.132193," ","integrate(sec(x)*tan(x)/(9+4*sec(x)^2),x, algorithm=""giac"")","-\frac{1}{6} \, \arctan\left(\frac{3}{2} \, \cos\left(x\right)\right)"," ",0,"-1/6*arctan(3/2*cos(x))","A",0
727,1,7,0,0.145263," ","integrate(sec(x)*tan(x)/(sec(x)+sec(x)^2),x, algorithm=""giac"")","-\log\left(\cos\left(x\right) + 1\right)"," ",0,"-log(cos(x) + 1)","A",0
728,1,36,0,0.150357," ","integrate(sec(x)*tan(x)/(4+sec(x)^2)^(1/2),x, algorithm=""giac"")","\frac{\log\left(\sqrt{4 \, \cos\left(x\right)^{2} + 1} + 1\right) - \log\left(\sqrt{4 \, \cos\left(x\right)^{2} + 1} - 1\right)}{2 \, \mathrm{sgn}\left(\cos\left(x\right)\right)}"," ",0,"1/2*(log(sqrt(4*cos(x)^2 + 1) + 1) - log(sqrt(4*cos(x)^2 + 1) - 1))/sgn(cos(x))","B",0
729,1,21,0,0.150491," ","integrate(sec(x)*tan(x)/(1+cos(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{2}{{\left(\sqrt{\cos\left(x\right)^{2} + 1} - \cos\left(x\right)\right)}^{2} - 1}"," ",0,"-2/((sqrt(cos(x)^2 + 1) - cos(x))^2 - 1)","A",0
730,1,5,0,0.140185," ","integrate(exp(sec(x))*sec(x)*tan(x),x, algorithm=""giac"")","e^{\frac{1}{\cos\left(x\right)}}"," ",0,"e^(1/cos(x))","A",0
731,1,11,0,0.145727," ","integrate(2^sec(x)*sec(x)*tan(x),x, algorithm=""giac"")","\frac{2^{\left(\frac{1}{\cos\left(x\right)}\right)}}{\log\left(2\right)}"," ",0,"2^(1/cos(x))/log(2)","A",0
732,1,37,0,0.165754," ","integrate(sec(2*x)*tan(2*x)/(1+sec(2*x))^(3/2),x, algorithm=""giac"")","\frac{1}{{\left(\sqrt{\cos\left(2 \, x\right)^{2} + \cos\left(2 \, x\right)} - \cos\left(2 \, x\right) - 1\right)} \mathrm{sgn}\left(\cos\left(2 \, x\right)\right)} + \mathrm{sgn}\left(\cos\left(2 \, x\right)\right)"," ",0,"1/((sqrt(cos(2*x)^2 + cos(2*x)) - cos(2*x) - 1)*sgn(cos(2*x))) + sgn(cos(2*x))","B",0
733,0,0,0,0.000000," ","integrate(sec(3*x)*(1+5*cos(3*x)^2)^(1/2)*tan(3*x),x, algorithm=""giac"")","\int \sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1} \sec\left(3 \, x\right) \tan\left(3 \, x\right)\,{d x}"," ",0,"integrate(sqrt(5*cos(3*x)^2 + 1)*sec(3*x)*tan(3*x), x)","F",0
734,1,34,0,0.154172," ","integrate(sec(3*x)*tan(3*x)/(1+5*cos(3*x)^2)^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{5}}{3 \, {\left({\left(\sqrt{5} \cos\left(3 \, x\right) - \sqrt{5 \, \cos\left(3 \, x\right)^{2} + 1}\right)}^{2} - 1\right)}}"," ",0,"-2/3*sqrt(5)/((sqrt(5)*cos(3*x) - sqrt(5*cos(3*x)^2 + 1))^2 - 1)","A",0
735,1,22,0,0.129787," ","integrate(cot(x)*csc(x)/(a+b*csc(x)),x, algorithm=""giac"")","-\frac{\log\left({\left| a \sin\left(x\right) + b \right|}\right)}{b} + \frac{\log\left({\left| \sin\left(x\right) \right|}\right)}{b}"," ",0,"-log(abs(a*sin(x) + b))/b + log(abs(sin(x)))/b","A",0
736,1,14,0,0.250461," ","integrate(5^csc(3*x)*cot(3*x)*csc(3*x),x, algorithm=""giac"")","-\frac{5^{\left(\frac{1}{\sin\left(3 \, x\right)}\right)}}{3 \, \log\left(5\right)}"," ",0,"-1/3*5^(1/sin(3*x))/log(5)","A",0
737,1,3,0,0.147788," ","integrate(cot(x)*csc(x)/(1+csc(x)^2),x, algorithm=""giac"")","\arctan\left(\sin\left(x\right)\right)"," ",0,"arctan(sin(x))","A",0
738,1,48,0,0.243638," ","integrate(cot(6*x)*csc(6*x)/(5-11*csc(6*x)^2)^2,x, algorithm=""giac"")","\frac{1}{6600} \, \sqrt{55} \log\left(\frac{\sqrt{55} - 5 \, \sin\left(6 \, x\right)}{\sqrt{55} + 5 \, \sin\left(6 \, x\right)}\right) - \frac{\sin\left(6 \, x\right)}{60 \, {\left(5 \, \sin\left(6 \, x\right)^{2} - 11\right)}}"," ",0,"1/6600*sqrt(55)*log((sqrt(55) - 5*sin(6*x))/(sqrt(55) + 5*sin(6*x))) - 1/60*sin(6*x)/(5*sin(6*x)^2 - 11)","A",0
739,1,21,0,0.151100," ","integrate(cot(x)*csc(x)/(1+sin(x)^2)^(1/2),x, algorithm=""giac"")","\frac{2}{{\left(\sqrt{\sin\left(x\right)^{2} + 1} - \sin\left(x\right)\right)}^{2} - 1}"," ",0,"2/((sqrt(sin(x)^2 + 1) - sin(x))^2 - 1)","A",0
740,1,48,0,0.506640," ","integrate(cot(5*x)*csc(5*x)^3/(1+sin(5*x)^2)^(1/2),x, algorithm=""giac"")","\frac{4 \, {\left(3 \, {\left(\sqrt{\sin\left(5 \, x\right)^{2} + 1} - \sin\left(5 \, x\right)\right)}^{2} - 1\right)}}{15 \, {\left({\left(\sqrt{\sin\left(5 \, x\right)^{2} + 1} - \sin\left(5 \, x\right)\right)}^{2} - 1\right)}^{3}}"," ",0,"4/15*(3*(sqrt(sin(5*x)^2 + 1) - sin(5*x))^2 - 1)/((sqrt(sin(5*x)^2 + 1) - sin(5*x))^2 - 1)^3","A",0
741,0,0,0,0.000000," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""giac"")","\int e^{\left(n \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\,{d x}"," ",0,"integrate(e^(n*sin(b*x + a))*sin(2*b*x + 2*a), x)","F",0
742,0,0,0,0.000000," ","integrate(exp(n*sin(b*x+a))*sin(2*b*x+2*a),x, algorithm=""giac"")","\int e^{\left(n \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\,{d x}"," ",0,"integrate(e^(n*sin(b*x + a))*sin(2*b*x + 2*a), x)","F",0
743,1,138,0,0.231321," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(2 \, n e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right) - e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)}\right)}}{b n^{2} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + b n^{2}}"," ",0,"4*(2*n*e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a) - e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 - e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1)))/(b*n^2*tan(1/4*b*x + 1/4*a)^2 + b*n^2)","B",0
744,1,138,0,0.235381," ","integrate(exp(n*sin(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(2 \, n e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right) - e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - e^{\left(\frac{2 \, n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)}\right)}}{b n^{2} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + b n^{2}}"," ",0,"4*(2*n*e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a) - e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 - e^(2*n*tan(1/4*b*x + 1/4*a)/(tan(1/4*b*x + 1/4*a)^2 + 1)))/(b*n^2*tan(1/4*b*x + 1/4*a)^2 + b*n^2)","B",0
745,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""giac"")","\int e^{\left(n \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\,{d x}"," ",0,"integrate(e^(n*cos(b*x + a))*sin(2*b*x + 2*a), x)","F",0
746,0,0,0,0.000000," ","integrate(exp(n*cos(b*x+a))*sin(2*b*x+2*a),x, algorithm=""giac"")","\int e^{\left(n \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\,{d x}"," ",0,"integrate(e^(n*cos(b*x + a))*sin(2*b*x + 2*a), x)","F",0
747,1,195,0,0.215501," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(n e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} + e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)}\right)}}{b n^{2} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + b n^{2}}"," ",0,"4*(n*e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 + e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 - n*e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1)) + e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1)))/(b*n^2*tan(1/4*b*x + 1/4*a)^2 + b*n^2)","B",0
748,1,195,0,0.219604," ","integrate(exp(n*cos(1/2*a+1/2*b*x))*sin(b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(n e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)} + e^{\left(-\frac{n \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} - n}{\tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + 1}\right)}\right)}}{b n^{2} \tan\left(\frac{1}{4} \, b x + \frac{1}{4} \, a\right)^{2} + b n^{2}}"," ",0,"4*(n*e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 + e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1))*tan(1/4*b*x + 1/4*a)^2 - n*e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1)) + e^(-(n*tan(1/4*b*x + 1/4*a)^2 - n)/(tan(1/4*b*x + 1/4*a)^2 + 1)))/(b*n^2*tan(1/4*b*x + 1/4*a)^2 + b*n^2)","B",0
749,1,7,0,0.144455," ","integrate(csc(x)*log(tan(x))*sec(x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(\tan\left(x\right)\right)^{2}"," ",0,"1/2*log(tan(x))^2","A",0
750,0,0,0,0.000000," ","integrate(csc(2*x)*log(tan(x)),x, algorithm=""giac"")","\int \csc\left(2 \, x\right) \log\left(\tan\left(x\right)\right)\,{d x}"," ",0,"integrate(csc(2*x)*log(tan(x)), x)","F",0
751,0,0,0,0.000000," ","integrate(exp(cos(x)^2+sin(x)^2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
752,1,103,0,0.156791," ","integrate(x*sec(x)^2,x, algorithm=""giac"")","\frac{\log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} - 4 \, x \tan\left(\frac{1}{2} \, x\right) - \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}}"," ",0,"1/2*(log(4*(tan(1/2*x)^4 - 2*tan(1/2*x)^2 + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - 4*x*tan(1/2*x) - log(4*(tan(1/2*x)^4 - 2*tan(1/2*x)^2 + 1)/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1)))/(tan(1/2*x)^2 - 1)","B",0
753,1,22,0,0.132836," ","integrate(x*cos(x^2)^4,x, algorithm=""giac"")","\frac{3}{16} \, x^{2} + \frac{1}{64} \, \sin\left(4 \, x^{2}\right) + \frac{1}{8} \, \sin\left(2 \, x^{2}\right)"," ",0,"3/16*x^2 + 1/64*sin(4*x^2) + 1/8*sin(2*x^2)","A",0
754,1,6,0,0.137049," ","integrate(sin(x)*cos(x)^(1/2),x, algorithm=""giac"")","-\frac{2}{3} \, \cos\left(x\right)^{\frac{3}{2}}"," ",0,"-2/3*cos(x)^(3/2)","A",0
755,1,9,0,0.132128," ","integrate(tan(exp(-2*x))/exp(2*x),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \cos\left(e^{\left(-2 \, x\right)}\right) \right|}\right)"," ",0,"1/2*log(abs(cos(e^(-2*x))))","A",0
756,1,7,0,0.140304," ","integrate(sec(x)*sin(2*x)/(1+cos(x)),x, algorithm=""giac"")","-2 \, \log\left(\cos\left(x\right) + 1\right)"," ",0,"-2*log(cos(x) + 1)","A",0
757,1,103,0,0.176286," ","integrate(x*sec(3*x)^2,x, algorithm=""giac"")","\frac{\log\left(\frac{4 \, {\left(\tan\left(\frac{3}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} + 1\right)}}{\tan\left(\frac{3}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{3}{2} \, x\right)^{2} - 12 \, x \tan\left(\frac{3}{2} \, x\right) - \log\left(\frac{4 \, {\left(\tan\left(\frac{3}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} + 1\right)}}{\tan\left(\frac{3}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} + 1}\right)}{18 \, {\left(\tan\left(\frac{3}{2} \, x\right)^{2} - 1\right)}}"," ",0,"1/18*(log(4*(tan(3/2*x)^4 - 2*tan(3/2*x)^2 + 1)/(tan(3/2*x)^4 + 2*tan(3/2*x)^2 + 1))*tan(3/2*x)^2 - 12*x*tan(3/2*x) - log(4*(tan(3/2*x)^4 - 2*tan(3/2*x)^2 + 1)/(tan(3/2*x)^4 + 2*tan(3/2*x)^2 + 1)))/(tan(3/2*x)^2 - 1)","B",0
758,1,27,0,0.125325," ","integrate(cos(2*pi*x)/exp(2*pi*x),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(\frac{\cos\left(2 \, \pi x\right)}{\pi} - \frac{\sin\left(2 \, \pi x\right)}{\pi}\right)} e^{\left(-2 \, \pi x\right)}"," ",0,"-1/4*(cos(2*pi*x)/pi - sin(2*pi*x)/pi)*e^(-2*pi*x)","A",0
759,1,37,0,0.145110," ","integrate(cos(x)^12*sin(x)^10-cos(x)^10*sin(x)^12,x, algorithm=""giac"")","-\frac{1}{23068672} \, \sin\left(22 \, x\right) + \frac{1}{2097152} \, \sin\left(18 \, x\right) - \frac{5}{2097152} \, \sin\left(14 \, x\right) + \frac{15}{2097152} \, \sin\left(10 \, x\right) - \frac{15}{1048576} \, \sin\left(6 \, x\right) + \frac{21}{1048576} \, \sin\left(2 \, x\right)"," ",0,"-1/23068672*sin(22*x) + 1/2097152*sin(18*x) - 5/2097152*sin(14*x) + 15/2097152*sin(10*x) - 15/1048576*sin(6*x) + 21/1048576*sin(2*x)","B",0
760,1,8,0,0.151138," ","integrate(x*cot(x^2),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \sin\left(x^{2}\right) \right|}\right)"," ",0,"1/2*log(abs(sin(x^2)))","A",0
761,1,6,0,0.117656," ","integrate(x*sec(x^2)^2,x, algorithm=""giac"")","\frac{1}{2} \, \tan\left(x^{2}\right)"," ",0,"1/2*tan(x^2)","A",0
762,1,15,0,0.657033," ","integrate(sin(8*x)/(9+sin(4*x)^4),x, algorithm=""giac"")","\frac{1}{12} \, \arctan\left(\frac{3}{\cos\left(4 \, x\right)^{2} - 1}\right)"," ",0,"1/12*arctan(3/(cos(4*x)^2 - 1))","A",0
763,1,15,0,0.148185," ","integrate(cos(2*x)/(8+sin(2*x)^2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} \sin\left(2 \, x\right)\right)"," ",0,"1/8*sqrt(2)*arctan(1/4*sqrt(2)*sin(2*x))","A",0
764,1,29,0,0.125289," ","integrate(x*(cos(x^2)^3-sin(x^2)^3),x, algorithm=""giac"")","-\frac{1}{6} \, \cos\left(x^{2}\right)^{3} - \frac{1}{6} \, \sin\left(x^{2}\right)^{3} + \frac{1}{2} \, \cos\left(x^{2}\right) + \frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"-1/6*cos(x^2)^3 - 1/6*sin(x^2)^3 + 1/2*cos(x^2) + 1/2*sin(x^2)","A",0
765,1,10,0,0.144517," ","integrate(cos(x)*sin(x)/(1-cos(x)),x, algorithm=""giac"")","\cos\left(x\right) + \log\left(-\cos\left(x\right) + 1\right)"," ",0,"cos(x) + log(-cos(x) + 1)","A",0
766,1,6,0,0.126677," ","integrate(x*cos(x^2),x, algorithm=""giac"")","\frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"1/2*sin(x^2)","A",0
767,1,8,0,0.122742," ","integrate(x^2*cos(4*x^3),x, algorithm=""giac"")","\frac{1}{12} \, \sin\left(4 \, x^{3}\right)"," ",0,"1/12*sin(4*x^3)","A",0
768,1,6,0,0.138076," ","integrate(x^3*cos(x^4),x, algorithm=""giac"")","\frac{1}{4} \, \sin\left(x^{4}\right)"," ",0,"1/4*sin(x^4)","A",0
769,1,8,0,0.117599," ","integrate(x*sin(1/2*x^2),x, algorithm=""giac"")","-\cos\left(\frac{1}{2} \, x^{2}\right)"," ",0,"-cos(1/2*x^2)","A",0
770,1,8,0,0.119101," ","integrate(x*sec(x^2)*tan(x^2),x, algorithm=""giac"")","\frac{1}{2 \, \cos\left(x^{2}\right)}"," ",0,"1/2/cos(x^2)","A",0
771,1,10,0,0.139634," ","integrate(tan(1/x)^2/x^2,x, algorithm=""giac"")","\frac{1}{x} - \tan\left(\frac{1}{x}\right)"," ",0,"1/x - tan(1/x)","A",0
772,1,10,0,0.172432," ","integrate(x*tan(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left({\left| \cos\left(x^{2} + 1\right) \right|}\right)"," ",0,"-1/2*log(abs(cos(x^2 + 1)))","A",0
773,1,10,0,0.140467," ","integrate(sin(pi*(1+2*x)),x, algorithm=""giac"")","\frac{\cos\left(2 \, \pi x\right)}{2 \, \pi}"," ",0,"1/2*cos(2*pi*x)/pi","A",0
774,1,18,0,0.153184," ","integrate((cot(x)+csc(x)^2)/(1-cos(x)^2),x, algorithm=""giac"")","-\frac{6 \, \tan\left(x\right)^{2} + 3 \, \tan\left(x\right) + 2}{6 \, \tan\left(x\right)^{3}}"," ",0,"-1/6*(6*tan(x)^2 + 3*tan(x) + 2)/tan(x)^3","A",0
775,1,39,0,0.141352," ","integrate(x^2*cos(4*x^3)*cos(5*x^3),x, algorithm=""giac"")","\frac{128}{27} \, \sin\left(x^{3}\right)^{9} - \frac{32}{3} \, \sin\left(x^{3}\right)^{7} + 8 \, \sin\left(x^{3}\right)^{5} - \frac{20}{9} \, \sin\left(x^{3}\right)^{3} + \frac{1}{3} \, \sin\left(x^{3}\right)"," ",0,"128/27*sin(x^3)^9 - 32/3*sin(x^3)^7 + 8*sin(x^3)^5 - 20/9*sin(x^3)^3 + 1/3*sin(x^3)","B",0
776,1,32,0,0.123653," ","integrate(x^14*sin(x^3),x, algorithm=""giac"")","-\frac{1}{3} \, {\left(x^{12} - 12 \, x^{6} + 24\right)} \cos\left(x^{3}\right) + \frac{4}{3} \, {\left(x^{9} - 6 \, x^{3}\right)} \sin\left(x^{3}\right)"," ",0,"-1/3*(x^12 - 12*x^6 + 24)*cos(x^3) + 4/3*(x^9 - 6*x^3)*sin(x^3)","A",0
777,1,25,0,0.147739," ","integrate(x^2*sin(2*x^3)/exp(3*x^3),x, algorithm=""giac"")","-\frac{1}{39} \, {\left(2 \, \cos\left(2 \, x^{3}\right) + 3 \, \sin\left(2 \, x^{3}\right)\right)} e^{\left(-3 \, x^{3}\right)}"," ",0,"-1/39*(2*cos(2*x^3) + 3*sin(2*x^3))*e^(-3*x^3)","A",0
778,1,4,0,0.135658," ","integrate(2*x*cos(x^2),x, algorithm=""giac"")","\sin\left(x^{2}\right)"," ",0,"sin(x^2)","A",0
779,1,6,0,0.119365," ","integrate(3*x^2*cos(x^3+7),x, algorithm=""giac"")","\sin\left(x^{3} + 7\right)"," ",0,"sin(x^3 + 7)","A",0
780,1,7,0,0.119748," ","integrate(1/(x^2+1)+sin(x),x, algorithm=""giac"")","\arctan\left(x\right) - \cos\left(x\right)"," ",0,"arctan(x) - cos(x)","A",0
781,1,8,0,0.122781," ","integrate(x*sin(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \cos\left(x^{2} + 1\right)"," ",0,"-1/2*cos(x^2 + 1)","A",0
782,1,8,0,0.136338," ","integrate(x*cos(x^2+1),x, algorithm=""giac"")","\frac{1}{2} \, \sin\left(x^{2} + 1\right)"," ",0,"1/2*sin(x^2 + 1)","A",0
783,1,8,0,0.141561," ","integrate(1+x^2*cos(x^3),x, algorithm=""giac"")","x + \frac{1}{3} \, \sin\left(x^{3}\right)"," ",0,"x + 1/3*sin(x^3)","A",0
784,1,8,0,0.139285," ","integrate(x^2*sin(x^3+1),x, algorithm=""giac"")","-\frac{1}{3} \, \cos\left(x^{3} + 1\right)"," ",0,"-1/3*cos(x^3 + 1)","A",0
785,1,6,0,0.137302," ","integrate(12*x^2*cos(x^3),x, algorithm=""giac"")","4 \, \sin\left(x^{3}\right)"," ",0,"4*sin(x^3)","A",0
786,1,14,0,0.137800," ","integrate((1+x)*sin(1+x),x, algorithm=""giac"")","-{\left(x + 1\right)} \cos\left(x + 1\right) + \sin\left(x + 1\right)"," ",0,"-(x + 1)*cos(x + 1) + sin(x + 1)","A",0
787,1,16,0,0.137140," ","integrate(x^5*cos(x^3),x, algorithm=""giac"")","\frac{1}{3} \, x^{3} \sin\left(x^{3}\right) + \frac{1}{3} \, \cos\left(x^{3}\right)"," ",0,"1/3*x^3*sin(x^3) + 1/3*cos(x^3)","A",0
788,1,15,0,0.135118," ","integrate(cos(x)/exp(3*x),x, algorithm=""giac"")","-\frac{1}{10} \, {\left(3 \, \cos\left(x\right) - \sin\left(x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/10*(3*cos(x) - sin(x))*e^(-3*x)","A",0
789,1,16,0,0.139735," ","integrate(x^3*sin(x^2),x, algorithm=""giac"")","-\frac{1}{2} \, x^{2} \cos\left(x^{2}\right) + \frac{1}{2} \, \sin\left(x^{2}\right)"," ",0,"-1/2*x^2*cos(x^2) + 1/2*sin(x^2)","A",0
790,1,16,0,0.136838," ","integrate(x^3*cos(x^2),x, algorithm=""giac"")","\frac{1}{2} \, x^{2} \sin\left(x^{2}\right) + \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"1/2*x^2*sin(x^2) + 1/2*cos(x^2)","A",0
791,1,7,0,0.135991," ","integrate(cos(x)*cos(2*sin(x)),x, algorithm=""giac"")","\frac{1}{2} \, \sin\left(2 \, \sin\left(x\right)\right)"," ",0,"1/2*sin(2*sin(x))","A",0
792,1,9,0,0.118674," ","integrate(cos(x)*sin(x)/(1+cos(x)^2),x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\cos\left(x\right)^{2} + 1\right)"," ",0,"-1/2*log(cos(x)^2 + 1)","A",0
793,1,61,0,0.149845," ","integrate((1+cos(x))*(x+sin(x))^3,x, algorithm=""giac"")","\frac{1}{4} \, x^{4} + \frac{3}{4} \, x^{2} - \frac{1}{4} \, {\left(3 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - \frac{1}{4} \, x \sin\left(3 \, x\right) + \frac{1}{4} \, {\left(4 \, x^{3} - 21 \, x\right)} \sin\left(x\right) + 6 \, x \sin\left(x\right) + \frac{1}{32} \, \cos\left(4 \, x\right) - \frac{3}{8} \, \cos\left(2 \, x\right)"," ",0,"1/4*x^4 + 3/4*x^2 - 1/4*(3*x^2 - 1)*cos(2*x) - 1/4*x*sin(3*x) + 1/4*(4*x^3 - 21*x)*sin(x) + 6*x*sin(x) + 1/32*cos(4*x) - 3/8*cos(2*x)","B",0
794,1,8,0,0.144413," ","integrate((1+cos(x))*csc(x)^2,x, algorithm=""giac"")","-\frac{1}{\tan\left(\frac{1}{2} \, x\right)}"," ",0,"-1/tan(1/2*x)","A",0
795,1,7,0,0.140923," ","integrate(sin(x)*tan(x)^2,x, algorithm=""giac"")","\frac{1}{\cos\left(x\right)} + \cos\left(x\right)"," ",0,"1/cos(x) + cos(x)","A",0
796,1,794,0,0.201287," ","integrate(exp(sin(x))*sec(x)^2*(x*cos(x)^3-sin(x)),x, algorithm=""giac"")","\frac{x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{8} + e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{8} - 16 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{6} + 12 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{7} - x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{8} - 14 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{6} + 12 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{7} - e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{8} + 30 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 52 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{5} + 16 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{6} - 28 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{5} + 14 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{6} - 16 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 52 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{3} - 30 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{4} + 14 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - 28 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right)^{3} + x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} - 12 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right) + 16 \, x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right)^{2} + 12 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{3}{2} \, x\right) \tan\left(\frac{1}{2} \, x\right) - 14 \, e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} \tan\left(\frac{1}{2} \, x\right)^{2} - x e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)} + e^{\left(\frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)}}{\tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{8} + 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{6} + \tan\left(\frac{1}{2} \, x\right)^{8} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{6} - 2 \, \tan\left(\frac{3}{2} \, x\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{3}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 1}"," ",0,"(x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^8 + e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^8 - 16*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^6 + 12*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^7 - x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8 - 14*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^6 + 12*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^7 - e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^8 + 30*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^4 - 52*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^5 + 16*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 - 28*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^5 + 14*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^6 - 16*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^2 + 52*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^3 - 30*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^4 + 14*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2*tan(1/2*x)^2 - 28*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x)^3 + x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2 - 12*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x) + 16*x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)^2 + 12*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(3/2*x)*tan(1/2*x) - 14*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 - x*e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1)) + e^(2*tan(1/2*x)/(tan(1/2*x)^2 + 1)))/(tan(3/2*x)^2*tan(1/2*x)^8 + 2*tan(3/2*x)^2*tan(1/2*x)^6 + tan(1/2*x)^8 + 2*tan(1/2*x)^6 - 2*tan(3/2*x)^2*tan(1/2*x)^2 - tan(3/2*x)^2 - 2*tan(1/2*x)^2 - 1)","B",0
797,1,52,0,0.188912," ","integrate(x*csc(x)^2,x, algorithm=""giac"")","\frac{x \tan\left(\frac{1}{2} \, x\right)^{2} + \log\left(\frac{16 \, \tan\left(\frac{1}{2} \, x\right)^{2}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right) - x}{2 \, \tan\left(\frac{1}{2} \, x\right)}"," ",0,"1/2*(x*tan(1/2*x)^2 + log(16*tan(1/2*x)^2/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))*tan(1/2*x) - x)/tan(1/2*x)","B",0
798,1,14,0,0.155632," ","integrate(cos(x)*sin(1/6*pi+x),x, algorithm=""giac"")","\frac{1}{4} \, x - \frac{1}{4} \, \cos\left(\frac{1}{6} \, \pi + 2 \, x\right)"," ",0,"1/4*x - 1/4*cos(1/6*pi + 2*x)","A",0
799,1,15,0,0.136184," ","integrate(x*sin(x^2)^3,x, algorithm=""giac"")","\frac{1}{6} \, \cos\left(x^{2}\right)^{3} - \frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"1/6*cos(x^2)^3 - 1/2*cos(x^2)","A",0
800,1,18,0,0.125083," ","integrate(sin(x)^2*tan(x),x, algorithm=""giac"")","-\frac{1}{2} \, \sin\left(x\right)^{2} - \frac{1}{2} \, \log\left(-\sin\left(x\right)^{2} + 1\right)"," ",0,"-1/2*sin(x)^2 - 1/2*log(-sin(x)^2 + 1)","A",0
801,1,28,0,0.127797," ","integrate(cos(x)^2*cot(x)^3,x, algorithm=""giac"")","-\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2 \, {\left(\cos\left(x\right)^{2} - 1\right)}} - \log\left(-\cos\left(x\right)^{2} + 1\right)"," ",0,"-1/2*cos(x)^2 + 1/2/(cos(x)^2 - 1) - log(-cos(x)^2 + 1)","A",0
802,1,5,0,0.142961," ","integrate(sec(x)*(1-sin(x)),x, algorithm=""giac"")","\log\left(\sin\left(x\right) + 1\right)"," ",0,"log(sin(x) + 1)","A",0
803,1,7,0,0.130453," ","integrate((1+cos(x))*csc(x),x, algorithm=""giac"")","\log\left(-\cos\left(x\right) + 1\right)"," ",0,"log(-cos(x) + 1)","A",0
804,1,9,0,0.150641," ","integrate(cos(x)^2*(1-tan(x)^2),x, algorithm=""giac"")","\frac{1}{\frac{1}{\tan\left(x\right)} + \tan\left(x\right)}"," ",0,"1/(1/tan(x) + tan(x))","A",0
805,1,29,0,0.148067," ","integrate(csc(2*x)*(cos(x)+sin(x)),x, algorithm=""giac"")","\frac{1}{2} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) - \frac{1}{2} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right) + \frac{1}{2} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) \right|}\right)"," ",0,"1/2*log(abs(tan(1/2*x) + 1)) - 1/2*log(abs(tan(1/2*x) - 1)) + 1/2*log(abs(tan(1/2*x)))","B",0
806,1,15,0,0.133376," ","integrate(cos(x)*(-3+2*sin(x))/(2-3*sin(x)+sin(x)^2),x, algorithm=""giac"")","\log\left(-\sin\left(x\right) + 2\right) + \log\left(-\sin\left(x\right) + 1\right)"," ",0,"log(-sin(x) + 2) + log(-sin(x) + 1)","A",0
807,1,17,0,0.124832," ","integrate(cos(x)^2*sin(x)/(5+cos(x)^2),x, algorithm=""giac"")","\sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} \cos\left(x\right)\right) - \cos\left(x\right)"," ",0,"sqrt(5)*arctan(1/5*sqrt(5)*cos(x)) - cos(x)","A",0
808,1,12,0,0.151784," ","integrate(cos(x)/(sin(x)+sin(x)^2),x, algorithm=""giac"")","-\log\left(\sin\left(x\right) + 1\right) + \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"-log(sin(x) + 1) + log(abs(sin(x)))","A",0
809,0,0,0,0.000000," ","integrate(cos(x)/(sin(x)+sin(x)^(2^(1/2))),x, algorithm=""giac"")","\int \frac{\cos\left(x\right)}{\sin\left(x\right)^{\left(\sqrt{2}\right)} + \sin\left(x\right)}\,{d x}"," ",0,"integrate(cos(x)/(sin(x)^sqrt(2) + sin(x)), x)","F",0
810,1,28,0,0.138198," ","integrate(1/(2*sin(x)+sin(2*x)),x, algorithm=""giac"")","-\frac{\cos\left(x\right) - 1}{8 \, {\left(\cos\left(x\right) + 1\right)}} + \frac{1}{8} \, \log\left(-\frac{\cos\left(x\right) - 1}{\cos\left(x\right) + 1}\right)"," ",0,"-1/8*(cos(x) - 1)/(cos(x) + 1) + 1/8*log(-(cos(x) - 1)/(cos(x) + 1))","A",0
811,1,26,0,0.125307," ","integrate((x^2+4*x-3)*sin(2*x),x, algorithm=""giac"")","-\frac{1}{4} \, {\left(2 \, x^{2} + 8 \, x - 7\right)} \cos\left(2 \, x\right) + \frac{1}{2} \, {\left(x + 2\right)} \sin\left(2 \, x\right)"," ",0,"-1/4*(2*x^2 + 8*x - 7)*cos(2*x) + 1/2*(x + 2)*sin(2*x)","A",0
812,1,19,0,0.135708," ","integrate(cos(4*x)/exp(3*x),x, algorithm=""giac"")","-\frac{1}{25} \, {\left(3 \, \cos\left(4 \, x\right) - 4 \, \sin\left(4 \, x\right)\right)} e^{\left(-3 \, x\right)}"," ",0,"-1/25*(3*cos(4*x) - 4*sin(4*x))*e^(-3*x)","A",0
813,1,17,0,0.132829," ","integrate(cos(x)*sin(x)/(1+sin(x))^(1/2),x, algorithm=""giac"")","\frac{2}{3} \, {\left(\sin\left(x\right) + 1\right)}^{\frac{3}{2}} - 2 \, \sqrt{\sin\left(x\right) + 1}"," ",0,"2/3*(sin(x) + 1)^(3/2) - 2*sqrt(sin(x) + 1)","A",0
814,1,24,0,0.141032," ","integrate(x+60*cos(x)^5*sin(x)^4,x, algorithm=""giac"")","\frac{20}{3} \, \sin\left(x\right)^{9} - \frac{120}{7} \, \sin\left(x\right)^{7} + 12 \, \sin\left(x\right)^{5} + \frac{1}{2} \, x^{2}"," ",0,"20/3*sin(x)^9 - 120/7*sin(x)^7 + 12*sin(x)^5 + 1/2*x^2","A",0
815,1,14,0,0.130089," ","integrate(cos(x)*(sec(x)+tan(x)),x, algorithm=""giac"")","x - \frac{2}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"x - 2/(tan(1/2*x)^2 + 1)","B",0
816,1,30,0,0.135096," ","integrate(cos(x)*(sec(x)^3+tan(x)),x, algorithm=""giac"")","-\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right) - 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} - 1}"," ",0,"-2*(tan(1/2*x)^3 + tan(1/2*x)^2 + tan(1/2*x) - 1)/(tan(1/2*x)^4 - 1)","B",0
817,1,13,0,0.149043," ","integrate(-1/2*cot(x)*csc(x)+1/2*csc(x)^2,x, algorithm=""giac"")","\frac{1}{2 \, \sin\left(x\right)} - \frac{1}{2 \, \tan\left(x\right)}"," ",0,"1/2/sin(x) - 1/2/tan(x)","A",0
818,1,11,0,0.127167," ","integrate(-csc(x)^2+sin(2*x),x, algorithm=""giac"")","\frac{1}{\tan\left(x\right)} - \frac{1}{2} \, \cos\left(2 \, x\right)"," ",0,"1/tan(x) - 1/2*cos(2*x)","A",0
819,1,11,0,0.146256," ","integrate(2*cot(2*x)-3*sin(3*x),x, algorithm=""giac"")","\cos\left(3 \, x\right) + \log\left({\left| \sin\left(2 \, x\right) \right|}\right)"," ",0,"cos(3*x) + log(abs(sin(2*x)))","A",0
820,1,8,0,0.139544," ","integrate(x*sin(2*x^2),x, algorithm=""giac"")","-\frac{1}{4} \, \cos\left(2 \, x^{2}\right)"," ",0,"-1/4*cos(2*x^2)","A",0
821,1,12,0,0.127706," ","integrate(cos(-1+x)*sin(-1+x)*(1+sin(-1+x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, {\left(\sin\left(x - 1\right)^{2} + 1\right)}^{\frac{3}{2}}"," ",0,"1/3*(sin(x - 1)^2 + 1)^(3/2)","A",0
822,1,8,0,0.134549," ","integrate(cos(1/x)*sin(1/x)/x^2,x, algorithm=""giac"")","\frac{1}{2} \, \cos\left(\frac{1}{x}\right)^{2}"," ",0,"1/2*cos(1/x)^2","A",0
823,1,10,0,0.204931," ","integrate(cos(1/2+3/2*x)*sin(1/2+3/2*x)^3,x, algorithm=""giac"")","\frac{1}{6} \, \sin\left(\frac{3}{2} \, x + \frac{1}{2}\right)^{4}"," ",0,"1/6*sin(3/2*x + 1/2)^4","A",0
824,1,9,0,0.138320," ","integrate(4*x*tan(x^2),x, algorithm=""giac"")","\log\left(\tan\left(x^{2}\right)^{2} + 1\right)"," ",0,"log(tan(x^2)^2 + 1)","A",0
825,1,41,0,0.159122," ","integrate(x*sec(x^2-5),x, algorithm=""giac"")","\frac{1}{8} \, \log\left({\left| \frac{1}{\sin\left(x^{2} - 5\right)} + \sin\left(x^{2} - 5\right) + 2 \right|}\right) - \frac{1}{8} \, \log\left({\left| \frac{1}{\sin\left(x^{2} - 5\right)} + \sin\left(x^{2} - 5\right) - 2 \right|}\right)"," ",0,"1/8*log(abs(1/sin(x^2 - 5) + sin(x^2 - 5) + 2)) - 1/8*log(abs(1/sin(x^2 - 5) + sin(x^2 - 5) - 2))","B",0
826,1,43,0,0.137322," ","integrate(csc(1/x)/x^2,x, algorithm=""giac"")","-\frac{1}{2} \, \log\left(\frac{4 \, \tan\left(\frac{1}{2 \, x}\right)^{2}}{\tan\left(\frac{1}{2 \, x}\right)^{2} + 1}\right) + \frac{1}{2} \, \log\left(\frac{4}{\tan\left(\frac{1}{2 \, x}\right)^{2} + 1}\right)"," ",0,"-1/2*log(4*tan(1/2/x)^2/(tan(1/2/x)^2 + 1)) + 1/2*log(4/(tan(1/2/x)^2 + 1))","B",0
827,1,16,0,0.151847," ","integrate((csc(x)-sec(x))*(cos(x)+sin(x)),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(-\cos\left(x\right)^{2} + 1\right) + \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"1/2*log(-cos(x)^2 + 1) + log(abs(cos(x)))","B",0
828,1,4,0,0.143441," ","integrate(-cos(3*x)*sin(2*x)+cos(2*x)*sin(3*x),x, algorithm=""giac"")","-\cos\left(x\right)"," ",0,"-cos(x)","A",0
829,1,81,0,0.170946," ","integrate(4*x*sec(2*x)^2,x, algorithm=""giac"")","\frac{\log\left(\frac{4 \, {\left(\tan\left(x\right)^{4} - 2 \, \tan\left(x\right)^{2} + 1\right)}}{\tan\left(x\right)^{4} + 2 \, \tan\left(x\right)^{2} + 1}\right) \tan\left(x\right)^{2} - 8 \, x \tan\left(x\right) - \log\left(\frac{4 \, {\left(\tan\left(x\right)^{4} - 2 \, \tan\left(x\right)^{2} + 1\right)}}{\tan\left(x\right)^{4} + 2 \, \tan\left(x\right)^{2} + 1}\right)}{2 \, {\left(\tan\left(x\right)^{2} - 1\right)}}"," ",0,"1/2*(log(4*(tan(x)^4 - 2*tan(x)^2 + 1)/(tan(x)^4 + 2*tan(x)^2 + 1))*tan(x)^2 - 8*x*tan(x) - log(4*(tan(x)^4 - 2*tan(x)^2 + 1)/(tan(x)^4 + 2*tan(x)^2 + 1)))/(tan(x)^2 - 1)","B",0
830,1,20,0,0.140667," ","integrate(4*sin(x)^2*tan(x)^2,x, algorithm=""giac"")","-6 \, x + \frac{2 \, \tan\left(x\right)}{\tan\left(x\right)^{2} + 1} + 4 \, \tan\left(x\right)"," ",0,"-6*x + 2*tan(x)/(tan(x)^2 + 1) + 4*tan(x)","A",0
831,1,31,0,0.131502," ","integrate(cos(x)^4*cot(x)^2,x, algorithm=""giac"")","-\frac{15}{8} \, x - \frac{7 \, \tan\left(x\right)^{3} + 9 \, \tan\left(x\right)}{8 \, {\left(\tan\left(x\right)^{2} + 1\right)}^{2}} - \frac{1}{\tan\left(x\right)}"," ",0,"-15/8*x - 1/8*(7*tan(x)^3 + 9*tan(x))/(tan(x)^2 + 1)^2 - 1/tan(x)","A",0
832,1,10,0,0.136951," ","integrate(16*cos(x)^2*sin(x)^2,x, algorithm=""giac"")","2 \, x - \frac{1}{2} \, \sin\left(4 \, x\right)"," ",0,"2*x - 1/2*sin(4*x)","A",0
833,1,22,0,0.120844," ","integrate(8*cos(x)^2*sin(x)^4,x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{24} \, \sin\left(6 \, x\right) - \frac{1}{8} \, \sin\left(4 \, x\right) - \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/2*x + 1/24*sin(6*x) - 1/8*sin(4*x) - 1/8*sin(2*x)","A",0
834,1,13,0,0.128874," ","integrate(35*cos(x)^3*sin(x)^4,x, algorithm=""giac"")","-5 \, \sin\left(x\right)^{7} + 7 \, \sin\left(x\right)^{5}"," ",0,"-5*sin(x)^7 + 7*sin(x)^5","A",0
835,1,16,0,0.138591," ","integrate(4*cos(x)^4*sin(x)^4,x, algorithm=""giac"")","\frac{3}{32} \, x + \frac{1}{256} \, \sin\left(8 \, x\right) - \frac{1}{32} \, \sin\left(4 \, x\right)"," ",0,"3/32*x + 1/256*sin(8*x) - 1/32*sin(4*x)","A",0
836,1,18,0,0.125419," ","integrate(cos(x)/(-sin(x)+sin(x)^3),x, algorithm=""giac"")","\frac{1}{2} \, \log\left(-\sin\left(x\right)^{2} + 1\right) - \log\left({\left| \sin\left(x\right) \right|}\right)"," ",0,"1/2*log(-sin(x)^2 + 1) - log(abs(sin(x)))","A",0
837,1,13,0,0.143191," ","integrate(-1+2*cos(x)^2+cos(x)*sin(x),x, algorithm=""giac"")","-\frac{1}{2} \, \cos\left(x\right)^{2} + \frac{1}{2} \, \sin\left(2 \, x\right)"," ",0,"-1/2*cos(x)^2 + 1/2*sin(2*x)","A",0
838,1,1,0,0.137107," ","integrate(cos(x)^2+sin(x)^2,x, algorithm=""giac"")","x"," ",0,"x","A",0
839,1,6,0,0.120098," ","integrate(-cos(x)^2+sin(x)^2,x, algorithm=""giac"")","-\frac{1}{2} \, \sin\left(2 \, x\right)"," ",0,"-1/2*sin(2*x)","A",0
840,1,9,0,0.125274," ","integrate(2^sin(x)*cos(x),x, algorithm=""giac"")","\frac{2^{\sin\left(x\right)}}{\log\left(2\right)}"," ",0,"2^sin(x)/log(2)","A",0
841,1,6,0,0.141313," ","integrate(tan(x)^3+tan(x)^5,x, algorithm=""giac"")","\frac{1}{4} \, \tan\left(x\right)^{4}"," ",0,"1/4*tan(x)^4","A",0
842,1,26,0,0.152950," ","integrate(x*sec(x)*(2+x*tan(x)),x, algorithm=""giac"")","-\frac{x^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + x^{2}}{\tan\left(\frac{1}{2} \, x\right)^{2} - 1}"," ",0,"-(x^2*tan(1/2*x)^2 + x^2)/(tan(1/2*x)^2 - 1)","B",0
843,1,8,0,0.119297," ","integrate(cot(x^(1/2))*csc(x^(1/2))/x^(1/2),x, algorithm=""giac"")","-\frac{2}{\sin\left(\sqrt{x}\right)}"," ",0,"-2/sin(sqrt(x))","A",0
844,1,6,0,0.120327," ","integrate(cos(x^(1/2))*sin(x^(1/2))/x^(1/2),x, algorithm=""giac"")","\sin\left(\sqrt{x}\right)^{2}"," ",0,"sin(sqrt(x))^2","A",0
845,1,8,0,0.136050," ","integrate(sec(x^(1/2))*tan(x^(1/2))/x^(1/2),x, algorithm=""giac"")","\frac{2}{\cos\left(\sqrt{x}\right)}"," ",0,"2/cos(sqrt(x))","A",0
846,1,77,0,0.156833," ","integrate(sin(x)^2/(a+b*sin(2*x)),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{2 \, \sqrt{a^{2} - b^{2}}} - \frac{\log\left(a \tan\left(x\right)^{2} + 2 \, b \tan\left(x\right) + a\right)}{4 \, b} + \frac{\log\left(\tan\left(x\right)^{2} + 1\right)}{4 \, b}"," ",0,"1/2*(pi*floor(x/pi + 1/2)*sgn(a) + arctan((a*tan(x) + b)/sqrt(a^2 - b^2)))/sqrt(a^2 - b^2) - 1/4*log(a*tan(x)^2 + 2*b*tan(x) + a)/b + 1/4*log(tan(x)^2 + 1)/b","A",0
847,1,77,0,0.158038," ","integrate(cos(x)^2/(a+b*sin(2*x)),x, algorithm=""giac"")","\frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor \mathrm{sgn}\left(a\right) + \arctan\left(\frac{a \tan\left(x\right) + b}{\sqrt{a^{2} - b^{2}}}\right)}{2 \, \sqrt{a^{2} - b^{2}}} + \frac{\log\left(a \tan\left(x\right)^{2} + 2 \, b \tan\left(x\right) + a\right)}{4 \, b} - \frac{\log\left(\tan\left(x\right)^{2} + 1\right)}{4 \, b}"," ",0,"1/2*(pi*floor(x/pi + 1/2)*sgn(a) + arctan((a*tan(x) + b)/sqrt(a^2 - b^2)))/sqrt(a^2 - b^2) + 1/4*log(a*tan(x)^2 + 2*b*tan(x) + a)/b - 1/4*log(tan(x)^2 + 1)/b","A",0
848,1,141,0,0.171787," ","integrate(sin(x)^2/(a+b*cos(2*x)),x, algorithm=""giac"")","\frac{\sqrt{a^{2} - b^{2}} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a + \sqrt{-16 \, {\left(a + b\right)} {\left(a - b\right)} + 16 \, a^{2}}}{a - b}}}\right)\right)} {\left| a - b \right|}}{2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} {\left| b \right|}} - \frac{\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a - \sqrt{-16 \, {\left(a + b\right)} {\left(a - b\right)} + 16 \, a^{2}}}{a - b}}}\right)}{2 \, {\left| b \right|}}"," ",0,"1/2*sqrt(a^2 - b^2)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a + sqrt(-16*(a + b)*(a - b) + 16*a^2))/(a - b))))*abs(a - b)/((a^2 - 2*a*b + b^2)*abs(b)) - 1/2*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a - sqrt(-16*(a + b)*(a - b) + 16*a^2))/(a - b))))/abs(b)","B",0
849,1,159,0,0.148089," ","integrate(cos(x)^2/(a+b*cos(2*x)),x, algorithm=""giac"")","-\frac{\sqrt{a^{2} - b^{2}} {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a + \sqrt{-16 \, {\left(a + b\right)} {\left(a - b\right)} + 16 \, a^{2}}}{a - b}}}\right)\right)} {\left| a - b \right|}}{2 \, {\left({\left(a - b\right)} b^{2} + {\left(a^{2} - a b\right)} {\left| b \right|}\right)}} - \frac{{\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor + \arctan\left(\frac{2 \, \tan\left(x\right)}{\sqrt{\frac{4 \, a - \sqrt{-16 \, {\left(a + b\right)} {\left(a - b\right)} + 16 \, a^{2}}}{a - b}}}\right)\right)} {\left(a - b\right)}}{2 \, {\left(b^{2} - a {\left| b \right|}\right)}}"," ",0,"-1/2*sqrt(a^2 - b^2)*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a + sqrt(-16*(a + b)*(a - b) + 16*a^2))/(a - b))))*abs(a - b)/((a - b)*b^2 + (a^2 - a*b)*abs(b)) - 1/2*(pi*floor(x/pi + 1/2) + arctan(2*tan(x)/sqrt((4*a - sqrt(-16*(a + b)*(a - b) + 16*a^2))/(a - b))))*(a - b)/(b^2 - a*abs(b))","B",0
850,1,61,0,0.345420," ","integrate(tan(d*x+c)/(a*sin(d*x+c)^2)^(1/2),x, algorithm=""giac"")","\frac{\frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1 \right|}\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1 \right|}\right)}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{\sqrt{a} d}"," ",0,"(log(abs(tan(1/2*d*x + 1/2*c) + 1))/sgn(tan(1/2*d*x + 1/2*c)) - log(abs(tan(1/2*d*x + 1/2*c) - 1))/sgn(tan(1/2*d*x + 1/2*c)))/(sqrt(a)*d)","B",0
851,1,31,0,0.247316," ","integrate(cot(d*x+c)/(a*cos(d*x+c)^2)^(1/2),x, algorithm=""giac"")","\frac{\arctan\left(\frac{\sqrt{-a \sin\left(d x + c\right)^{2} + a}}{\sqrt{-a}}\right)}{\sqrt{-a} d}"," ",0,"arctan(sqrt(-a*sin(d*x + c)^2 + a)/sqrt(-a))/(sqrt(-a)*d)","A",0
852,1,6,0,0.138049," ","integrate(x*cos(x^2)/sin(x^2)^(1/2),x, algorithm=""giac"")","\sqrt{\sin\left(x^{2}\right)}"," ",0,"sqrt(sin(x^2))","A",0
853,1,14,0,0.157951," ","integrate(cos(x)/(1-cos(2*x))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left({\left| \sin\left(x\right) \right|}\right)}{2 \, \mathrm{sgn}\left(\sin\left(x\right)\right)}"," ",0,"1/2*sqrt(2)*log(abs(sin(x)))/sgn(sin(x))","A",0
854,1,12,0,0.126752," ","integrate(cos(log(x))^2*sin(log(x))^2/x,x, algorithm=""giac"")","\frac{1}{8} \, \log\left(x\right) - \frac{1}{32} \, \sin\left(4 \, \log\left(x\right)\right)"," ",0,"1/8*log(x) - 1/32*sin(4*log(x))","A",0
855,1,34,0,0.167387," ","integrate(sin(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{3} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right) - \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) - \frac{1}{6} \, \log\left({\left| \tan\left(x\right) + 1 \right|}\right)"," ",0,"1/2*x + 1/3*log(tan(x)^2 - tan(x) + 1) - 1/4*log(tan(x)^2 + 1) - 1/6*log(abs(tan(x) + 1))","A",0
856,1,34,0,0.165158," ","integrate(cos(x)^3/(cos(x)^3+sin(x)^3),x, algorithm=""giac"")","\frac{1}{2} \, x - \frac{1}{3} \, \log\left(\tan\left(x\right)^{2} - \tan\left(x\right) + 1\right) + \frac{1}{4} \, \log\left(\tan\left(x\right)^{2} + 1\right) + \frac{1}{6} \, \log\left({\left| \tan\left(x\right) + 1 \right|}\right)"," ",0,"1/2*x - 1/3*log(tan(x)^2 - tan(x) + 1) + 1/4*log(tan(x)^2 + 1) + 1/6*log(abs(tan(x) + 1))","A",0
857,1,34,0,0.120633," ","integrate(sec(x)/(-5+cos(x)^2+4*sin(x)),x, algorithm=""giac"")","-\frac{1}{3 \, {\left(\sin\left(x\right) - 2\right)}} - \frac{1}{18} \, \log\left(\sin\left(x\right) + 1\right) - \frac{4}{9} \, \log\left(-\sin\left(x\right) + 2\right) + \frac{1}{2} \, \log\left(-\sin\left(x\right) + 1\right)"," ",0,"-1/3/(sin(x) - 2) - 1/18*log(sin(x) + 1) - 4/9*log(-sin(x) + 2) + 1/2*log(-sin(x) + 1)","A",0
858,0,0,0,0.000000," ","integrate(1/cos(x)^(3/2)/(3*cos(x)+sin(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \cos\left(x\right) + \sin\left(x\right)} \cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(3*cos(x) + sin(x))*cos(x)^(3/2)), x)","F",0
859,0,0,0,0.000000," ","integrate(csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(x\right) + \sin\left(x\right)} \csc\left(x\right)}{\cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cos(x) + sin(x))*csc(x)/cos(x)^(3/2), x)","F",0
860,1,42,0,0.167839," ","integrate((cos(x)+sin(x))/(1+sin(2*x))^(1/2),x, algorithm=""giac"")","\frac{2 \, \pi \left \lfloor \frac{x}{2 \, \pi} + \frac{1}{2} \right \rfloor - x}{\mathrm{sgn}\left(\tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, x\right) - 1\right)}"," ",0,"(2*pi*floor(1/2*x/pi + 1/2) - x)/sgn(tan(1/2*x)^4 - 2*tan(1/2*x)^3 - 2*tan(1/2*x) - 1)","B",0
861,1,55,0,0.322575," ","integrate(sec(x)*(sec(x)+tan(x))^(1/2),x, algorithm=""giac"")","-\frac{4 \, \mathrm{sgn}\left(-\tan\left(\frac{1}{2} \, x\right)^{3} - \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2} \, x\right) - 1\right) \mathrm{sgn}\left(\cos\left(x\right)\right)}{\frac{\sqrt{-\tan\left(\frac{1}{2} \, x\right)^{2} + 1} - 1}{\tan\left(\frac{1}{2} \, x\right)} + 1}"," ",0,"-4*sgn(-tan(1/2*x)^3 - tan(1/2*x)^2 - tan(1/2*x) - 1)*sgn(cos(x))/((sqrt(-tan(1/2*x)^2 + 1) - 1)/tan(1/2*x) + 1)","B",0
862,1,68,0,0.159529," ","integrate(sec(x)*(4+3*sec(x))^(1/2)*tan(x),x, algorithm=""giac"")","\frac{2 \, {\left(4 \, {\left(\sqrt{4 \, \cos\left(x\right)^{2} + 3 \, \cos\left(x\right)} - 2 \, \cos\left(x\right)\right)}^{2} - 6 \, \sqrt{4 \, \cos\left(x\right)^{2} + 3 \, \cos\left(x\right)} + 12 \, \cos\left(x\right) + 3\right)} \mathrm{sgn}\left(\cos\left(x\right)\right)}{{\left(\sqrt{4 \, \cos\left(x\right)^{2} + 3 \, \cos\left(x\right)} - 2 \, \cos\left(x\right)\right)}^{3}}"," ",0,"2*(4*(sqrt(4*cos(x)^2 + 3*cos(x)) - 2*cos(x))^2 - 6*sqrt(4*cos(x)^2 + 3*cos(x)) + 12*cos(x) + 3)*sgn(cos(x))/(sqrt(4*cos(x)^2 + 3*cos(x)) - 2*cos(x))^3","B",0
863,1,128,0,0.168931," ","integrate(sec(x)*(1+sec(x))^(1/2)*tan(x)^3,x, algorithm=""giac"")","-\frac{2 \, {\left(35 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{6} - 35 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{5} - 35 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{4} + 105 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{3} - 91 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{2} + 35 \, \sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - 35 \, \cos\left(x\right) - 5\right)} \mathrm{sgn}\left(\cos\left(x\right)\right)}{35 \, {\left(\sqrt{\cos\left(x\right)^{2} + \cos\left(x\right)} - \cos\left(x\right)\right)}^{7}}"," ",0,"-2/35*(35*(sqrt(cos(x)^2 + cos(x)) - cos(x))^6 - 35*(sqrt(cos(x)^2 + cos(x)) - cos(x))^5 - 35*(sqrt(cos(x)^2 + cos(x)) - cos(x))^4 + 105*(sqrt(cos(x)^2 + cos(x)) - cos(x))^3 - 91*(sqrt(cos(x)^2 + cos(x)) - cos(x))^2 + 35*sqrt(cos(x)^2 + cos(x)) - 35*cos(x) - 5)*sgn(cos(x))/(sqrt(cos(x)^2 + cos(x)) - cos(x))^7","B",0
864,1,128,0,0.142895," ","integrate(cot(x)^3*csc(x)*(1+csc(x))^(1/2),x, algorithm=""giac"")","\frac{2 \, {\left(35 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{6} - 35 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{5} - 35 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{4} + 105 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{3} - 91 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{2} + 35 \, \sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - 35 \, \sin\left(x\right) - 5\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)}{35 \, {\left(\sqrt{\sin\left(x\right)^{2} + \sin\left(x\right)} - \sin\left(x\right)\right)}^{7}}"," ",0,"2/35*(35*(sqrt(sin(x)^2 + sin(x)) - sin(x))^6 - 35*(sqrt(sin(x)^2 + sin(x)) - sin(x))^5 - 35*(sqrt(sin(x)^2 + sin(x)) - sin(x))^4 + 105*(sqrt(sin(x)^2 + sin(x)) - sin(x))^3 - 91*(sqrt(sin(x)^2 + sin(x)) - sin(x))^2 + 35*sqrt(sin(x)^2 + sin(x)) - 35*sin(x) - 5)*sgn(sin(x))/(sqrt(sin(x)^2 + sin(x)) - sin(x))^7","B",0
865,0,0,0,0.000000," ","integrate(csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)),x, algorithm=""giac"")","\int {\left(x \cos\left(x\right) - 4 \, \sec\left(x\right) \tan\left(x\right)\right)} \sqrt{\csc\left(x\right)}\,{d x}"," ",0,"integrate((x*cos(x) - 4*sec(x)*tan(x))*sqrt(csc(x)), x)","F",0
866,1,97,0,0.153190," ","integrate(cot(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""giac"")","-\frac{1}{48} \, {\left({\left(2 \, {\left(4 \, \sin\left(x\right)^{2} - 19\right)} \sin\left(x\right)^{2} + 87\right)} \sqrt{-\sin\left(x\right)^{2} + 1} \sin\left(x\right) - 105 \, {\left(\pi \left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor - x\right)} \left(-1\right)^{\left \lfloor \frac{x}{\pi} + \frac{1}{2} \right \rfloor} + \frac{24 \, {\left(\sqrt{-\sin\left(x\right)^{2} + 1} - 1\right)}}{\sin\left(x\right)} - \frac{24 \, \sin\left(x\right)}{\sqrt{-\sin\left(x\right)^{2} + 1} - 1}\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"-1/48*((2*(4*sin(x)^2 - 19)*sin(x)^2 + 87)*sqrt(-sin(x)^2 + 1)*sin(x) - 105*(pi*floor(x/pi + 1/2) - x)*(-1)^floor(x/pi + 1/2) + 24*(sqrt(-sin(x)^2 + 1) - 1)/sin(x) - 24*sin(x)/(sqrt(-sin(x)^2 + 1) - 1))*sgn(sin(x))","A",0
867,1,44,0,0.150647," ","integrate(cos(x)*(1-sin(x)^2)^3*(-1+csc(x)^2)^(1/2),x, algorithm=""giac"")","\frac{1}{210} \, {\left(30 \, \cos\left(x\right)^{7} + 42 \, \cos\left(x\right)^{5} + 70 \, \cos\left(x\right)^{3} + 210 \, \cos\left(x\right) - 105 \, \log\left(\cos\left(x\right) + 1\right) + 105 \, \log\left(-\cos\left(x\right) + 1\right)\right)} \mathrm{sgn}\left(\sin\left(x\right)\right)"," ",0,"1/210*(30*cos(x)^7 + 42*cos(x)^5 + 70*cos(x)^3 + 210*cos(x) - 105*log(cos(x) + 1) + 105*log(-cos(x) + 1))*sgn(sin(x))","A",0
868,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{x \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{2}}}\,{d x}"," ",0,"integrate(x*csc(x)*sec(x)/sqrt(a*sec(x)^2), x)","F",0
869,0,0,0,0.000000," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{2}}}\,{d x}"," ",0,"integrate(x^2*csc(x)*sec(x)/sqrt(a*sec(x)^2), x)","F",0
870,0,0,0,0.000000," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{2}}}\,{d x}"," ",0,"integrate(x^3*csc(x)*sec(x)/sqrt(a*sec(x)^2), x)","F",0
871,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{x \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{4}}}\,{d x}"," ",0,"integrate(x*csc(x)*sec(x)/sqrt(a*sec(x)^4), x)","F",0
872,0,0,0,0.000000," ","integrate(x^2*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{4}}}\,{d x}"," ",0,"integrate(x^2*csc(x)*sec(x)/sqrt(a*sec(x)^4), x)","F",0
873,0,0,0,0.000000," ","integrate(x^3*csc(x)*sec(x)/(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \frac{x^{3} \csc\left(x\right) \sec\left(x\right)}{\sqrt{a \sec\left(x\right)^{4}}}\,{d x}"," ",0,"integrate(x^3*csc(x)*sec(x)/sqrt(a*sec(x)^4), x)","F",0
874,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{2}} x \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^2)*x*csc(x)*sec(x), x)","F",0
875,0,0,0,0.000000," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{2}} x^{2} \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^2)*x^2*csc(x)*sec(x), x)","F",0
876,0,0,0,0.000000," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^2)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{2}} x^{3} \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^2)*x^3*csc(x)*sec(x), x)","F",0
877,0,0,0,0.000000," ","integrate(x*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{4}} x \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^4)*x*csc(x)*sec(x), x)","F",0
878,0,0,0,0.000000," ","integrate(x^2*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{4}} x^{2} \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^4)*x^2*csc(x)*sec(x), x)","F",0
879,0,0,0,0.000000," ","integrate(x^3*csc(x)*sec(x)*(a*sec(x)^4)^(1/2),x, algorithm=""giac"")","\int \sqrt{a \sec\left(x\right)^{4}} x^{3} \csc\left(x\right) \sec\left(x\right)\,{d x}"," ",0,"integrate(sqrt(a*sec(x)^4)*x^3*csc(x)*sec(x), x)","F",0
880,1,13,0,0.121660," ","integrate(sin(x)*sin(2*x)*sin(3*x),x, algorithm=""giac"")","-\frac{4}{3} \, \sin\left(x\right)^{6} + \frac{3}{2} \, \sin\left(x\right)^{4}"," ",0,"-4/3*sin(x)^6 + 3/2*sin(x)^4","A",0
881,1,22,0,0.147387," ","integrate(cos(x)*cos(2*x)*cos(3*x),x, algorithm=""giac"")","\frac{1}{4} \, x + \frac{1}{24} \, \sin\left(6 \, x\right) + \frac{1}{16} \, \sin\left(4 \, x\right) + \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/4*x + 1/24*sin(6*x) + 1/16*sin(4*x) + 1/8*sin(2*x)","A",0
882,1,22,0,0.131666," ","integrate(cos(x)*sin(2*x)*sin(3*x),x, algorithm=""giac"")","\frac{1}{4} \, x - \frac{1}{24} \, \sin\left(6 \, x\right) - \frac{1}{16} \, \sin\left(4 \, x\right) + \frac{1}{8} \, \sin\left(2 \, x\right)"," ",0,"1/4*x - 1/24*sin(6*x) - 1/16*sin(4*x) + 1/8*sin(2*x)","A",0
883,1,19,0,0.131447," ","integrate(cos(2*x)*cos(3*x)*sin(x),x, algorithm=""giac"")","\frac{4}{3} \, \sin\left(x\right)^{6} - \frac{3}{2} \, \sin\left(x\right)^{4} + \frac{1}{2} \, \sin\left(x\right)^{2}"," ",0,"4/3*sin(x)^6 - 3/2*sin(x)^4 + 1/2*sin(x)^2","A",0
884,1,6,0,0.134846," ","integrate(x*sin(x^2),x, algorithm=""giac"")","-\frac{1}{2} \, \cos\left(x^{2}\right)"," ",0,"-1/2*cos(x^2)","A",0
885,1,19,0,0.127181," ","integrate((-cos(x)+sin(x))*(cos(x)+sin(x))^5,x, algorithm=""giac"")","\frac{1}{4} \, \cos\left(4 \, x\right) + \frac{1}{24} \, \sin\left(6 \, x\right) - \frac{5}{8} \, \sin\left(2 \, x\right)"," ",0,"1/4*cos(4*x) + 1/24*sin(6*x) - 5/8*sin(2*x)","B",0
886,1,52,0,0.132730," ","integrate(2*x*sec(x)^2*tan(x),x, algorithm=""giac"")","\frac{x \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, x \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + x - 2 \, \tan\left(\frac{1}{2} \, x\right)}{\tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}"," ",0,"(x*tan(1/2*x)^4 + 2*x*tan(1/2*x)^2 + 2*tan(1/2*x)^3 + x - 2*tan(1/2*x))/(tan(1/2*x)^4 - 2*tan(1/2*x)^2 + 1)","B",0
887,1,8,0,0.152875," ","integrate((1+cos(x)^2)/(1+cos(2*x)),x, algorithm=""giac"")","\frac{1}{2} \, x + \frac{1}{2} \, \tan\left(x\right)"," ",0,"1/2*x + 1/2*tan(x)","A",0
888,1,24,0,0.142877," ","integrate(sin(x)/(cos(x)^3-cos(x)^5),x, algorithm=""giac"")","\frac{1}{2 \, \cos\left(x\right)^{2}} + \frac{1}{2} \, \log\left(-\cos\left(x\right)^{2} + 1\right) - \log\left({\left| \cos\left(x\right) \right|}\right)"," ",0,"1/2/cos(x)^2 + 1/2*log(-cos(x)^2 + 1) - log(abs(cos(x)))","B",0
889,1,20,0,0.139430," ","integrate(sec(x)*(5-11*sec(x)^5)^2*tan(x),x, algorithm=""giac"")","\frac{75 \, \cos\left(x\right)^{10} - 55 \, \cos\left(x\right)^{5} + 33}{3 \, \cos\left(x\right)^{11}}"," ",0,"1/3*(75*cos(x)^10 - 55*cos(x)^5 + 33)/cos(x)^11","A",0
890,1,51,0,0.299432," ","integrate(sin(5*x)^3*tan(5*x)^3,x, algorithm=""giac"")","\frac{1}{15} \, \sin\left(5 \, x\right)^{3} - \frac{\sin\left(5 \, x\right)}{10 \, {\left(\sin\left(5 \, x\right)^{2} - 1\right)}} - \frac{1}{4} \, \log\left(\sin\left(5 \, x\right) + 1\right) + \frac{1}{4} \, \log\left(-\sin\left(5 \, x\right) + 1\right) + \frac{2}{5} \, \sin\left(5 \, x\right)"," ",0,"1/15*sin(5*x)^3 - 1/10*sin(5*x)/(sin(5*x)^2 - 1) - 1/4*log(sin(5*x) + 1) + 1/4*log(-sin(5*x) + 1) + 2/5*sin(5*x)","A",0
891,1,33,0,0.757167," ","integrate(sin(5*x)^3*tan(5*x)^4,x, algorithm=""giac"")","\frac{1}{15} \, \cos\left(5 \, x\right)^{3} - \frac{9 \, \cos\left(5 \, x\right)^{2} - 1}{15 \, \cos\left(5 \, x\right)^{3}} - \frac{3}{5} \, \cos\left(5 \, x\right)"," ",0,"1/15*cos(5*x)^3 - 1/15*(9*cos(5*x)^2 - 1)/cos(5*x)^3 - 3/5*cos(5*x)","A",0
892,1,59,0,0.423309," ","integrate(sin(6*x)^5*tan(6*x)^3,x, algorithm=""giac"")","\frac{1}{30} \, \sin\left(6 \, x\right)^{5} + \frac{1}{9} \, \sin\left(6 \, x\right)^{3} - \frac{\sin\left(6 \, x\right)}{12 \, {\left(\sin\left(6 \, x\right)^{2} - 1\right)}} - \frac{7}{24} \, \log\left(\sin\left(6 \, x\right) + 1\right) + \frac{7}{24} \, \log\left(-\sin\left(6 \, x\right) + 1\right) + \frac{1}{2} \, \sin\left(6 \, x\right)"," ",0,"1/30*sin(6*x)^5 + 1/9*sin(6*x)^3 - 1/12*sin(6*x)/(sin(6*x)^2 - 1) - 7/24*log(sin(6*x) + 1) + 7/24*log(-sin(6*x) + 1) + 1/2*sin(6*x)","A",0
893,1,33,0,0.144629," ","integrate((-1+sec(2*x)^2)^3*sin(2*x),x, algorithm=""giac"")","\frac{15 \, \cos\left(2 \, x\right)^{4} - 5 \, \cos\left(2 \, x\right)^{2} + 1}{10 \, \cos\left(2 \, x\right)^{5}} + \frac{1}{2} \, \cos\left(2 \, x\right)"," ",0,"1/10*(15*cos(2*x)^4 - 5*cos(2*x)^2 + 1)/cos(2*x)^5 + 1/2*cos(2*x)","A",0
894,1,42,0,0.147147," ","integrate(sin(x)*tan(x)^5,x, algorithm=""giac"")","\frac{9 \, \sin\left(x\right)^{3} - 7 \, \sin\left(x\right)}{8 \, {\left(\sin\left(x\right)^{2} - 1\right)}^{2}} + \frac{15}{16} \, \log\left(\sin\left(x\right) + 1\right) - \frac{15}{16} \, \log\left(-\sin\left(x\right) + 1\right) - \sin\left(x\right)"," ",0,"1/8*(9*sin(x)^3 - 7*sin(x))/(sin(x)^2 - 1)^2 + 15/16*log(sin(x) + 1) - 15/16*log(-sin(x) + 1) - sin(x)","A",0
895,1,41,0,0.159779," ","integrate(cos(2*x)^5*cot(2*x)^4,x, algorithm=""giac"")","\frac{1}{10} \, \sin\left(2 \, x\right)^{5} - \frac{2}{3} \, \sin\left(2 \, x\right)^{3} + \frac{12 \, \sin\left(2 \, x\right)^{2} - 1}{6 \, \sin\left(2 \, x\right)^{3}} + 3 \, \sin\left(2 \, x\right)"," ",0,"1/10*sin(2*x)^5 - 2/3*sin(2*x)^3 + 1/6*(12*sin(2*x)^2 - 1)/sin(2*x)^3 + 3*sin(2*x)","A",0
896,1,73,0,0.488871," ","integrate(cos(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^5,x, algorithm=""giac"")","\frac{1}{33} \, \sin\left(3 \, x\right)^{11} - \frac{8}{27} \, \sin\left(3 \, x\right)^{9} + \frac{4}{3} \, \sin\left(3 \, x\right)^{7} - \frac{56}{15} \, \sin\left(3 \, x\right)^{5} + \frac{70}{9} \, \sin\left(3 \, x\right)^{3} - \frac{420 \, \sin\left(3 \, x\right)^{4} - 40 \, \sin\left(3 \, x\right)^{2} + 3}{45 \, \sin\left(3 \, x\right)^{5}} - \frac{56}{3} \, \sin\left(3 \, x\right)"," ",0,"1/33*sin(3*x)^11 - 8/27*sin(3*x)^9 + 4/3*sin(3*x)^7 - 56/15*sin(3*x)^5 + 70/9*sin(3*x)^3 - 1/45*(420*sin(3*x)^4 - 40*sin(3*x)^2 + 3)/sin(3*x)^5 - 56/3*sin(3*x)","A",0
897,1,52,0,0.143544," ","integrate(cot(2*x)*(-1+csc(2*x)^2)^2*(1-sin(2*x)^2)^2,x, algorithm=""giac"")","\frac{1}{8} \, \cos\left(2 \, x\right)^{4} + \frac{3}{4} \, \cos\left(2 \, x\right)^{2} - \frac{8 \, \cos\left(2 \, x\right)^{2} - 7}{8 \, {\left(\cos\left(2 \, x\right)^{2} - 1\right)}^{2}} + \frac{3}{2} \, \log\left(-\cos\left(2 \, x\right)^{2} + 1\right)"," ",0,"1/8*cos(2*x)^4 + 3/4*cos(2*x)^2 - 1/8*(8*cos(2*x)^2 - 7)/(cos(2*x)^2 - 1)^2 + 3/2*log(-cos(2*x)^2 + 1)","A",0
898,1,57,0,0.164677," ","integrate(cos(2*x)*(-1+csc(2*x)^2)^4*(1-sin(2*x)^2)^2,x, algorithm=""giac"")","\frac{1}{10} \, \sin\left(2 \, x\right)^{5} - \sin\left(2 \, x\right)^{3} + \frac{700 \, \sin\left(2 \, x\right)^{6} - 175 \, \sin\left(2 \, x\right)^{4} + 42 \, \sin\left(2 \, x\right)^{2} - 5}{70 \, \sin\left(2 \, x\right)^{7}} + \frac{15}{2} \, \sin\left(2 \, x\right)"," ",0,"1/10*sin(2*x)^5 - sin(2*x)^3 + 1/70*(700*sin(2*x)^6 - 175*sin(2*x)^4 + 42*sin(2*x)^2 - 5)/sin(2*x)^7 + 15/2*sin(2*x)","A",0
899,1,60,0,0.248682," ","integrate(cot(3*x)*(-1+csc(3*x)^2)^3*(1-sin(3*x)^2)^2,x, algorithm=""giac"")","-\frac{1}{12} \, \sin\left(3 \, x\right)^{4} + \frac{5}{6} \, \sin\left(3 \, x\right)^{2} + \frac{110 \, \sin\left(3 \, x\right)^{6} - 60 \, \sin\left(3 \, x\right)^{4} + 15 \, \sin\left(3 \, x\right)^{2} - 2}{36 \, \sin\left(3 \, x\right)^{6}} - \frac{5}{3} \, \log\left(\sin\left(3 \, x\right)^{2}\right)"," ",0,"-1/12*sin(3*x)^4 + 5/6*sin(3*x)^2 + 1/36*(110*sin(3*x)^6 - 60*sin(3*x)^4 + 15*sin(3*x)^2 - 2)/sin(3*x)^6 - 5/3*log(sin(3*x)^2)","A",0
900,-1,0,0,0.000000," ","integrate((1+cot(9*x)^2)^2*(1+tan(9*x)^2)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,1,39,0,6.000680," ","integrate(cos(x)*(9-7*sin(x)^3)^2/(1-sin(x)^2),x, algorithm=""giac"")","-\frac{49}{5} \, \sin\left(x\right)^{5} - \frac{49}{3} \, \sin\left(x\right)^{3} + 63 \, \sin\left(x\right)^{2} + 128 \, \log\left(\sin\left(x\right) + 1\right) - 2 \, \log\left(-\sin\left(x\right) + 1\right) - 49 \, \sin\left(x\right)"," ",0,"-49/5*sin(x)^5 - 49/3*sin(x)^3 + 63*sin(x)^2 + 128*log(sin(x) + 1) - 2*log(-sin(x) + 1) - 49*sin(x)","A",0
902,1,52,0,0.147297," ","integrate(cos(2*x)^4*cot(2*x)^5,x, algorithm=""giac"")","\frac{1}{8} \, \cos\left(2 \, x\right)^{4} + \frac{3}{4} \, \cos\left(2 \, x\right)^{2} - \frac{8 \, \cos\left(2 \, x\right)^{2} - 7}{8 \, {\left(\cos\left(2 \, x\right)^{2} - 1\right)}^{2}} + \frac{3}{2} \, \log\left(-\cos\left(2 \, x\right)^{2} + 1\right)"," ",0,"1/8*cos(2*x)^4 + 3/4*cos(2*x)^2 - 1/8*(8*cos(2*x)^2 - 7)/(cos(2*x)^2 - 1)^2 + 3/2*log(-cos(2*x)^2 + 1)","A",0
903,1,72,0,0.228202," ","integrate(sec(x)*tan(x)^2/(4+3*sec(x)),x, algorithm=""giac"")","-\frac{1}{9} \, \sqrt{7} \log\left(\frac{{\left| -2 \, \sqrt{7} + 2 \, \tan\left(\frac{1}{2} \, x\right) \right|}}{{\left| 2 \, \sqrt{7} + 2 \, \tan\left(\frac{1}{2} \, x\right) \right|}}\right) - \frac{2 \, \tan\left(\frac{1}{2} \, x\right)}{3 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 1\right)}} - \frac{4}{9} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) + 1 \right|}\right) + \frac{4}{9} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"-1/9*sqrt(7)*log(abs(-2*sqrt(7) + 2*tan(1/2*x))/abs(2*sqrt(7) + 2*tan(1/2*x))) - 2/3*tan(1/2*x)/(tan(1/2*x)^2 - 1) - 4/9*log(abs(tan(1/2*x) + 1)) + 4/9*log(abs(tan(1/2*x) - 1))","A",0
904,1,1179,0,0.522375," ","integrate(x*sec(1+x)*tan(1+x),x, algorithm=""giac"")","\frac{2 \, x \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2}\right) - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2}\right) + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, x \tan\left(\frac{1}{2}\right)^{2} - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2}\right) - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2}\right) + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} - 4 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2}\right) - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right) + 4 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2}\right) + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right) + 2 \, x \tan\left(\frac{1}{2} \, x\right)^{2} - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2}\right) - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2}\right) + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, x + \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) - 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2}\right) - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right) - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{3} - 2 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right) + 2 \, \tan\left(\frac{1}{2} \, x\right)^{3} + \tan\left(\frac{1}{2}\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2}\right) + 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{2} + 1}\right)}{2 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(\frac{1}{2} \, x\right)^{2} - \tan\left(\frac{1}{2}\right)^{2} - 4 \, \tan\left(\frac{1}{2}\right) \tan\left(\frac{1}{2} \, x\right) - \tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"1/2*(2*x*tan(1/2)^2*tan(1/2*x)^2 + log(2*(tan(1/2)^2*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^3 + 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x) - 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 - 2*tan(1/2) - 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)^2*tan(1/2*x)^2 - log(2*(tan(1/2)^2*tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x)^3 - 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x) + 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 + 2*tan(1/2) + 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)^2*tan(1/2*x)^2 + 2*x*tan(1/2)^2 - log(2*(tan(1/2)^2*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^3 + 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x) - 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 - 2*tan(1/2) - 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)^2 + log(2*(tan(1/2)^2*tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x)^3 - 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x) + 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 + 2*tan(1/2) + 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)^2 - 4*log(2*(tan(1/2)^2*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^3 + 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x) - 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 - 2*tan(1/2) - 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)*tan(1/2*x) + 4*log(2*(tan(1/2)^2*tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x)^3 - 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x) + 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 + 2*tan(1/2) + 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2)*tan(1/2*x) + 2*x*tan(1/2*x)^2 - log(2*(tan(1/2)^2*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^3 + 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x) - 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 - 2*tan(1/2) - 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2*x)^2 + log(2*(tan(1/2)^2*tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x)^3 - 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x) + 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 + 2*tan(1/2) + 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1))*tan(1/2*x)^2 + 2*x + log(2*(tan(1/2)^2*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^3 + 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x) - 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 - 2*tan(1/2) - 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1)) - log(2*(tan(1/2)^2*tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x)^3 - 2*tan(1/2)*tan(1/2*x)^4 + 2*tan(1/2)^2*tan(1/2*x)^2 + tan(1/2*x)^4 - 2*tan(1/2)^2*tan(1/2*x) + 2*tan(1/2*x)^3 + tan(1/2)^2 + 2*tan(1/2*x)^2 + 2*tan(1/2) + 2*tan(1/2*x) + 1)/(tan(1/2)^2 + 1)))/(tan(1/2)^2*tan(1/2*x)^2 - tan(1/2)^2 - 4*tan(1/2)*tan(1/2*x) - tan(1/2*x)^2 + 1)","B",0
905,1,12,0,0.137361," ","integrate(sin(2*x)/(9-sin(x)^2)^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{-\sin\left(x\right)^{2} + 9}"," ",0,"-2*sqrt(-sin(x)^2 + 9)","A",0
906,1,9,0,0.148253," ","integrate(sin(2*x)/(9-cos(x)^4)^(1/2),x, algorithm=""giac"")","-\arcsin\left(\frac{1}{3} \, \cos\left(x\right)^{2}\right)"," ",0,"-arcsin(1/3*cos(x)^2)","A",0
907,1,34,0,0.144001," ","integrate(cos(1/x)/x^5,x, algorithm=""giac"")","\frac{6 \, \sin\left(\frac{1}{x}\right)}{x} - \frac{3 \, \cos\left(\frac{1}{x}\right)}{x^{2}} - \frac{\sin\left(\frac{1}{x}\right)}{x^{3}} + 6 \, \cos\left(\frac{1}{x}\right)"," ",0,"6*sin(1/x)/x - 3*cos(1/x)/x^2 - sin(1/x)/x^3 + 6*cos(1/x)","A",0
908,1,17,0,0.144991," ","integrate(cos(1+x)^3*sin(1+x)^3,x, algorithm=""giac"")","-\frac{1}{6} \, \sin\left(x + 1\right)^{6} + \frac{1}{4} \, \sin\left(x + 1\right)^{4}"," ",0,"-1/6*sin(x + 1)^6 + 1/4*sin(x + 1)^4","A",0
909,1,58,0,0.126951," ","integrate((1+2*x)^3*sin(1+2*x)^2,x, algorithm=""giac"")","x^{4} + 2 \, x^{3} + \frac{3}{2} \, x^{2} - \frac{3}{32} \, {\left(8 \, x^{2} + 8 \, x + 1\right)} \cos\left(4 \, x + 2\right) - \frac{1}{16} \, {\left(16 \, x^{3} + 24 \, x^{2} + 6 \, x - 1\right)} \sin\left(4 \, x + 2\right) + \frac{1}{2} \, x"," ",0,"x^4 + 2*x^3 + 3/2*x^2 - 3/32*(8*x^2 + 8*x + 1)*cos(4*x + 2) - 1/16*(16*x^3 + 24*x^2 + 6*x - 1)*sin(4*x + 2) + 1/2*x","A",0
910,1,70,0,0.204969," ","integrate((-1+sec(x))/(1-tan(x)),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 2 \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) + 2 \right|}}\right) - \frac{1}{2} \, x - \frac{1}{2} \, \log\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right) + \frac{1}{2} \, \log\left({\left| \tan\left(\frac{1}{2} \, x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, x\right) - 1 \right|}\right)"," ",0,"-1/2*sqrt(2)*log(abs(-2*sqrt(2) + 2*tan(1/2*x) + 2)/abs(2*sqrt(2) + 2*tan(1/2*x) + 2)) - 1/2*x - 1/2*log(tan(1/2*x)^2 + 1) + 1/2*log(abs(tan(1/2*x)^2 + 2*tan(1/2*x) - 1))","B",0
911,1,41,0,0.119763," ","integrate(x^2*cos(3*x)*cos(5*x),x, algorithm=""giac"")","\frac{1}{64} \, x \cos\left(8 \, x\right) + \frac{1}{4} \, x \cos\left(2 \, x\right) + \frac{1}{512} \, {\left(32 \, x^{2} - 1\right)} \sin\left(8 \, x\right) + \frac{1}{8} \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)"," ",0,"1/64*x*cos(8*x) + 1/4*x*cos(2*x) + 1/512*(32*x^2 - 1)*sin(8*x) + 1/8*(2*x^2 - 1)*sin(2*x)","A",0
912,0,0,0,0.000000," ","integrate((cos(x)+sin(x))/cos(x)^(1/2)/sin(x)^(1/2),x, algorithm=""giac"")","\int \frac{\cos\left(x\right) + \sin\left(x\right)}{\sqrt{\cos\left(x\right)} \sqrt{\sin\left(x\right)}}\,{d x}"," ",0,"integrate((cos(x) + sin(x))/(sqrt(cos(x))*sqrt(sin(x))), x)","F",0
913,1,10,0,0.125952," ","integrate(sec(x)^2*(1+sin(x)),x, algorithm=""giac"")","-\frac{2}{\tan\left(\frac{1}{2} \, x\right) - 1}"," ",0,"-2/(tan(1/2*x) - 1)","A",0
914,-1,0,0,0.000000," ","integrate(10*x^9*cos(x^5*log(x))-x^10*(x^4+5*x^4*log(x))*sin(x^5*log(x)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
915,1,93,0,3.119381," ","integrate(cos(1/2*x)^2*tan(1/4*pi+1/2*x),x, algorithm=""giac"")","\frac{x \tan\left(\frac{1}{2} \, x\right)^{2} - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, x\right)^{2} + \tan\left(\frac{1}{2} \, x\right)^{2} + x - \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, x\right) + 1\right)}}{\tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right) - 1}{2 \, {\left(\tan\left(\frac{1}{2} \, x\right)^{2} + 1\right)}}"," ",0,"1/2*(x*tan(1/2*x)^2 - log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1))*tan(1/2*x)^2 + tan(1/2*x)^2 + x - log(2*(tan(1/2*x)^2 - 2*tan(1/2*x) + 1)/(tan(1/2*x)^2 + 1)) - 1)/(tan(1/2*x)^2 + 1)","B",0
916,1,51,0,1.979068," ","integrate((2+3*x)^2*sin(x)^3,x, algorithm=""giac"")","\frac{1}{12} \, {\left(9 \, x^{2} + 12 \, x + 2\right)} \cos\left(3 \, x\right) - \frac{3}{4} \, {\left(9 \, x^{2} + 12 \, x - 14\right)} \cos\left(x\right) - \frac{1}{6} \, {\left(3 \, x + 2\right)} \sin\left(3 \, x\right) + \frac{9}{2} \, {\left(3 \, x + 2\right)} \sin\left(x\right)"," ",0,"1/12*(9*x^2 + 12*x + 2)*cos(3*x) - 3/4*(9*x^2 + 12*x - 14)*cos(x) - 1/6*(3*x + 2)*sin(3*x) + 9/2*(3*x + 2)*sin(x)","A",0
917,0,0,0,0.000000," ","integrate(sec(x)^(1+m)*sin(x),x, algorithm=""giac"")","\int \sec\left(x\right)^{m + 1} \sin\left(x\right)\,{d x}"," ",0,"integrate(sec(x)^(m + 1)*sin(x), x)","F",0
918,0,0,0,0.000000," ","integrate(cos(b*x+a)^n*sin(b*x+a)^(-2-n),x, algorithm=""giac"")","\int \cos\left(b x + a\right)^{n} \sin\left(b x + a\right)^{-n - 2}\,{d x}"," ",0,"integrate(cos(b*x + a)^n*sin(b*x + a)^(-n - 2), x)","F",0
919,1,3,0,0.117994," ","integrate(1/(sec(x)+sin(x)*tan(x)),x, algorithm=""giac"")","\arctan\left(\sin\left(x\right)\right)"," ",0,"arctan(sin(x))","A",0
920,1,27,0,0.123537," ","integrate((c*x^2+b*x+a)*sin(x),x, algorithm=""giac"")","-{\left(c x^{2} + b x + a - 2 \, c\right)} \cos\left(x\right) + {\left(2 \, c x + b\right)} \sin\left(x\right)"," ",0,"-(c*x^2 + b*x + a - 2*c)*cos(x) + (2*c*x + b)*sin(x)","A",0
921,1,6,0,0.130733," ","integrate(sin(x^5)/x,x, algorithm=""giac"")","\frac{1}{5} \, \operatorname{Si}\left(x^{5}\right)"," ",0,"1/5*sin_integral(x^5)","A",0
922,1,29,0,0.126479," ","integrate(sin(2^x)/(1+2^x),x, algorithm=""giac"")","\frac{\operatorname{Ci}\left(2^{x} + 1\right) \sin\left(1\right) - \cos\left(1\right) \operatorname{Si}\left(2^{x} + 1\right) + \operatorname{Si}\left(2^{x}\right)}{\log\left(2\right)}"," ",0,"(cos_integral(2^x + 1)*sin(1) - cos(1)*sin_integral(2^x + 1) + sin_integral(2^x))/log(2)","A",0
923,1,10,0,0.162780," ","integrate(x*cos(2*x^2)*sin(2*x^2)^(3/4),x, algorithm=""giac"")","\frac{1}{7} \, \sin\left(2 \, x^{2}\right)^{\frac{7}{4}}"," ",0,"1/7*sin(2*x^2)^(7/4)","A",0
924,1,8,0,0.138956," ","integrate(x*sec(x^2)^2*tan(x^2)^2,x, algorithm=""giac"")","\frac{1}{6} \, \tan\left(x^{2}\right)^{3}"," ",0,"1/6*tan(x^2)^3","A",0
925,1,15,0,0.179269," ","integrate(x^2*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""giac"")","-\frac{\cos\left(b x^{3} + a\right)^{8}}{24 \, b}"," ",0,"-1/24*cos(b*x^3 + a)^8/b","A",0
926,1,126,0,0.440524," ","integrate(x^5*cos(b*x^3+a)^7*sin(b*x^3+a),x, algorithm=""giac"")","-\frac{24 \, b x^{3} \cos\left(8 \, b x^{3} + 8 \, a\right) + 192 \, b x^{3} \cos\left(6 \, b x^{3} + 6 \, a\right) + 672 \, b x^{3} \cos\left(4 \, b x^{3} + 4 \, a\right) + 1344 \, b x^{3} \cos\left(2 \, b x^{3} + 2 \, a\right) - 3 \, \sin\left(8 \, b x^{3} + 8 \, a\right) - 32 \, \sin\left(6 \, b x^{3} + 6 \, a\right) - 168 \, \sin\left(4 \, b x^{3} + 4 \, a\right) - 672 \, \sin\left(2 \, b x^{3} + 2 \, a\right)}{73728 \, b^{2}}"," ",0,"-1/73728*(24*b*x^3*cos(8*b*x^3 + 8*a) + 192*b*x^3*cos(6*b*x^3 + 6*a) + 672*b*x^3*cos(4*b*x^3 + 4*a) + 1344*b*x^3*cos(2*b*x^3 + 2*a) - 3*sin(8*b*x^3 + 8*a) - 32*sin(6*b*x^3 + 6*a) - 168*sin(4*b*x^3 + 4*a) - 672*sin(2*b*x^3 + 2*a))/b^2","A",0
927,1,1455,0,1.641124," ","integrate(x^5*sec(b*x^3+a)^7*tan(b*x^3+a),x, algorithm=""giac"")","-\frac{96 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{14} - 96 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{14} + 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{14} - 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{14} + 672 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{12} - 672 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{12} - 105 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{12} + 105 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{12} + 132 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{13} + 2016 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{10} - 2016 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{10} + 315 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{10} - 315 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{10} - 112 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{11} + 3360 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{8} - 3360 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{8} - 525 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{8} + 525 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{8} + 340 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{9} + 3360 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{6} - 3360 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{6} + 525 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{6} - 525 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{6} + 2016 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{4} - 2016 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{4} - 315 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{4} + 315 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{4} - 340 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{5} + 96 \, b x^{3} + 672 \, {\left(b x^{3} + a\right)} \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 672 \, a \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 105 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 105 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 112 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{3} - 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) + 15 \, \log\left(\frac{2 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right) + 1\right)}}{\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} + 1}\right) - 132 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)}{2016 \, {\left(\tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{14} - 7 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{12} + 21 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{10} - 35 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{8} + 35 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{6} - 21 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{4} + 7 \, \tan\left(\frac{1}{2} \, b x^{3} + \frac{1}{2} \, a\right)^{2} - 1\right)} b^{2}}"," ",0,"-1/2016*(96*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^14 - 96*a*tan(1/2*b*x^3 + 1/2*a)^14 + 15*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^14 - 15*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^14 + 672*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^12 - 672*a*tan(1/2*b*x^3 + 1/2*a)^12 - 105*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^12 + 105*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^12 + 132*tan(1/2*b*x^3 + 1/2*a)^13 + 2016*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^10 - 2016*a*tan(1/2*b*x^3 + 1/2*a)^10 + 315*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^10 - 315*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^10 - 112*tan(1/2*b*x^3 + 1/2*a)^11 + 3360*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^8 - 3360*a*tan(1/2*b*x^3 + 1/2*a)^8 - 525*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^8 + 525*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^8 + 340*tan(1/2*b*x^3 + 1/2*a)^9 + 3360*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^6 - 3360*a*tan(1/2*b*x^3 + 1/2*a)^6 + 525*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^6 - 525*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^6 + 2016*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^4 - 2016*a*tan(1/2*b*x^3 + 1/2*a)^4 - 315*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^4 + 315*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^4 - 340*tan(1/2*b*x^3 + 1/2*a)^5 + 96*b*x^3 + 672*(b*x^3 + a)*tan(1/2*b*x^3 + 1/2*a)^2 - 672*a*tan(1/2*b*x^3 + 1/2*a)^2 + 105*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^2 - 105*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1))*tan(1/2*b*x^3 + 1/2*a)^2 + 112*tan(1/2*b*x^3 + 1/2*a)^3 - 15*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 + 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1)) + 15*log(2*(tan(1/2*b*x^3 + 1/2*a)^2 - 2*tan(1/2*b*x^3 + 1/2*a) + 1)/(tan(1/2*b*x^3 + 1/2*a)^2 + 1)) - 132*tan(1/2*b*x^3 + 1/2*a))/((tan(1/2*b*x^3 + 1/2*a)^14 - 7*tan(1/2*b*x^3 + 1/2*a)^12 + 21*tan(1/2*b*x^3 + 1/2*a)^10 - 35*tan(1/2*b*x^3 + 1/2*a)^8 + 35*tan(1/2*b*x^3 + 1/2*a)^6 - 21*tan(1/2*b*x^3 + 1/2*a)^4 + 7*tan(1/2*b*x^3 + 1/2*a)^2 - 1)*b^2)","B",0
928,1,20,0,0.126825," ","integrate(sec(1/x)^2/x^2,x, algorithm=""giac"")","\frac{2 \, \tan\left(\frac{1}{2 \, x}\right)}{\tan\left(\frac{1}{2 \, x}\right)^{2} - 1}"," ",0,"2*tan(1/2/x)/(tan(1/2/x)^2 - 1)","B",0
929,1,4,0,0.132307," ","integrate(3*x^2*cos(x^3),x, algorithm=""giac"")","\sin\left(x^{3}\right)"," ",0,"sin(x^3)","A",0
930,1,943,0,0.373540," ","integrate((1+2*x)*sec(1+2*x)^2,x, algorithm=""giac"")","\frac{\log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{8} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{7} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{8} - 2 \, \tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{4} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{5} + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{6} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{7} + \tan\left(x\right)^{8} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{3} + 36 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{5} + \tan\left(\frac{1}{2}\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right) + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{3} - 2 \, \tan\left(x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, x \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right) - 8 \, x \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{2} - \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{8} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{7} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{8} - 2 \, \tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{4} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{5} + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{6} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{7} + \tan\left(x\right)^{8} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{3} + 36 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{5} + \tan\left(\frac{1}{2}\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right) + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{3} - 2 \, \tan\left(x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right)^{2} - 4 \, \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{8} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{7} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{8} - 2 \, \tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{4} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{5} + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{6} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{7} + \tan\left(x\right)^{8} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{3} + 36 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{5} + \tan\left(\frac{1}{2}\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right) + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{3} - 2 \, \tan\left(x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(\frac{1}{2}\right) \tan\left(x\right) - 4 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right) - \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{8} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{7} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{8} - 2 \, \tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{4} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{5} + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{6} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{7} + \tan\left(x\right)^{8} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{3} + 36 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{5} + \tan\left(\frac{1}{2}\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right) + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{3} - 2 \, \tan\left(x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} + 1}\right) \tan\left(x\right)^{2} - 4 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{2} + 8 \, x \tan\left(\frac{1}{2}\right) + 8 \, x \tan\left(x\right) + \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{8} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{7} - 2 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{8} - 2 \, \tan\left(\frac{1}{2}\right)^{4} \tan\left(x\right)^{4} - 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{5} + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{6} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{7} + \tan\left(x\right)^{8} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right)^{3} + 36 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{5} + \tan\left(\frac{1}{2}\right)^{4} + 8 \, \tan\left(\frac{1}{2}\right)^{3} \tan\left(x\right) + 16 \, \tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right)^{3} - 2 \, \tan\left(x\right)^{4} - 2 \, \tan\left(\frac{1}{2}\right)^{2} - 8 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) + 1\right)}}{\tan\left(\frac{1}{2}\right)^{4} + 2 \, \tan\left(\frac{1}{2}\right)^{2} + 1}\right) + 4 \, \tan\left(\frac{1}{2}\right) + 4 \, \tan\left(x\right)}{4 \, {\left(\tan\left(\frac{1}{2}\right)^{2} \tan\left(x\right)^{2} - \tan\left(\frac{1}{2}\right)^{2} - 4 \, \tan\left(\frac{1}{2}\right) \tan\left(x\right) - \tan\left(x\right)^{2} + 1\right)}}"," ",0,"1/4*(log(4*(tan(1/2)^4*tan(x)^8 - 8*tan(1/2)^3*tan(x)^7 - 2*tan(1/2)^2*tan(x)^8 - 2*tan(1/2)^4*tan(x)^4 - 8*tan(1/2)^3*tan(x)^5 + 16*tan(1/2)^2*tan(x)^6 + 8*tan(1/2)*tan(x)^7 + tan(x)^8 + 8*tan(1/2)^3*tan(x)^3 + 36*tan(1/2)^2*tan(x)^4 + 8*tan(1/2)*tan(x)^5 + tan(1/2)^4 + 8*tan(1/2)^3*tan(x) + 16*tan(1/2)^2*tan(x)^2 - 8*tan(1/2)*tan(x)^3 - 2*tan(x)^4 - 2*tan(1/2)^2 - 8*tan(1/2)*tan(x) + 1)/(tan(1/2)^4 + 2*tan(1/2)^2 + 1))*tan(1/2)^2*tan(x)^2 - 8*x*tan(1/2)^2*tan(x) - 8*x*tan(1/2)*tan(x)^2 - log(4*(tan(1/2)^4*tan(x)^8 - 8*tan(1/2)^3*tan(x)^7 - 2*tan(1/2)^2*tan(x)^8 - 2*tan(1/2)^4*tan(x)^4 - 8*tan(1/2)^3*tan(x)^5 + 16*tan(1/2)^2*tan(x)^6 + 8*tan(1/2)*tan(x)^7 + tan(x)^8 + 8*tan(1/2)^3*tan(x)^3 + 36*tan(1/2)^2*tan(x)^4 + 8*tan(1/2)*tan(x)^5 + tan(1/2)^4 + 8*tan(1/2)^3*tan(x) + 16*tan(1/2)^2*tan(x)^2 - 8*tan(1/2)*tan(x)^3 - 2*tan(x)^4 - 2*tan(1/2)^2 - 8*tan(1/2)*tan(x) + 1)/(tan(1/2)^4 + 2*tan(1/2)^2 + 1))*tan(1/2)^2 - 4*log(4*(tan(1/2)^4*tan(x)^8 - 8*tan(1/2)^3*tan(x)^7 - 2*tan(1/2)^2*tan(x)^8 - 2*tan(1/2)^4*tan(x)^4 - 8*tan(1/2)^3*tan(x)^5 + 16*tan(1/2)^2*tan(x)^6 + 8*tan(1/2)*tan(x)^7 + tan(x)^8 + 8*tan(1/2)^3*tan(x)^3 + 36*tan(1/2)^2*tan(x)^4 + 8*tan(1/2)*tan(x)^5 + tan(1/2)^4 + 8*tan(1/2)^3*tan(x) + 16*tan(1/2)^2*tan(x)^2 - 8*tan(1/2)*tan(x)^3 - 2*tan(x)^4 - 2*tan(1/2)^2 - 8*tan(1/2)*tan(x) + 1)/(tan(1/2)^4 + 2*tan(1/2)^2 + 1))*tan(1/2)*tan(x) - 4*tan(1/2)^2*tan(x) - log(4*(tan(1/2)^4*tan(x)^8 - 8*tan(1/2)^3*tan(x)^7 - 2*tan(1/2)^2*tan(x)^8 - 2*tan(1/2)^4*tan(x)^4 - 8*tan(1/2)^3*tan(x)^5 + 16*tan(1/2)^2*tan(x)^6 + 8*tan(1/2)*tan(x)^7 + tan(x)^8 + 8*tan(1/2)^3*tan(x)^3 + 36*tan(1/2)^2*tan(x)^4 + 8*tan(1/2)*tan(x)^5 + tan(1/2)^4 + 8*tan(1/2)^3*tan(x) + 16*tan(1/2)^2*tan(x)^2 - 8*tan(1/2)*tan(x)^3 - 2*tan(x)^4 - 2*tan(1/2)^2 - 8*tan(1/2)*tan(x) + 1)/(tan(1/2)^4 + 2*tan(1/2)^2 + 1))*tan(x)^2 - 4*tan(1/2)*tan(x)^2 + 8*x*tan(1/2) + 8*x*tan(x) + log(4*(tan(1/2)^4*tan(x)^8 - 8*tan(1/2)^3*tan(x)^7 - 2*tan(1/2)^2*tan(x)^8 - 2*tan(1/2)^4*tan(x)^4 - 8*tan(1/2)^3*tan(x)^5 + 16*tan(1/2)^2*tan(x)^6 + 8*tan(1/2)*tan(x)^7 + tan(x)^8 + 8*tan(1/2)^3*tan(x)^3 + 36*tan(1/2)^2*tan(x)^4 + 8*tan(1/2)*tan(x)^5 + tan(1/2)^4 + 8*tan(1/2)^3*tan(x) + 16*tan(1/2)^2*tan(x)^2 - 8*tan(1/2)*tan(x)^3 - 2*tan(x)^4 - 2*tan(1/2)^2 - 8*tan(1/2)*tan(x) + 1)/(tan(1/2)^4 + 2*tan(1/2)^2 + 1)) + 4*tan(1/2) + 4*tan(x))/(tan(1/2)^2*tan(x)^2 - tan(1/2)^2 - 4*tan(1/2)*tan(x) - tan(x)^2 + 1)","B",0
931,0,0,0,0.000000," ","integrate(x^4/b/(x^3+3*sin(b*x+a))^(1/2)+x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2)+4/3*x*(x^3+3*sin(b*x+a))^(1/2)/b,x, algorithm=""giac"")","\int \frac{x^{4}}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)} b} + \frac{x^{2} \cos\left(b x + a\right)}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)}} + \frac{4 \, \sqrt{x^{3} + 3 \, \sin\left(b x + a\right)} x}{3 \, b}\,{d x}"," ",0,"integrate(x^4/(sqrt(x^3 + 3*sin(b*x + a))*b) + x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)) + 4/3*sqrt(x^3 + 3*sin(b*x + a))*x/b, x)","F",0
932,0,0,0,0.000000," ","integrate(x^2*cos(b*x+a)/(x^3+3*sin(b*x+a))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2} \cos\left(b x + a\right)}{\sqrt{x^{3} + 3 \, \sin\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x^2*cos(b*x + a)/sqrt(x^3 + 3*sin(b*x + a)), x)","F",0
933,1,83,0,0.149867," ","integrate((cos(x)+sin(x))/(exp(-x)+sin(x)),x, algorithm=""giac"")","x + \frac{1}{2} \, \log\left(\frac{4 \, {\left(e^{\left(-2 \, x\right)} \tan\left(\frac{1}{2} \, x\right)^{4} + 4 \, e^{\left(-x\right)} \tan\left(\frac{1}{2} \, x\right)^{3} + 2 \, e^{\left(-2 \, x\right)} \tan\left(\frac{1}{2} \, x\right)^{2} + 4 \, e^{\left(-x\right)} \tan\left(\frac{1}{2} \, x\right) + 4 \, \tan\left(\frac{1}{2} \, x\right)^{2} + e^{\left(-2 \, x\right)}\right)}}{\tan\left(\frac{1}{2} \, x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, x\right)^{2} + 1}\right)"," ",0,"x + 1/2*log(4*(e^(-2*x)*tan(1/2*x)^4 + 4*e^(-x)*tan(1/2*x)^3 + 2*e^(-2*x)*tan(1/2*x)^2 + 4*e^(-x)*tan(1/2*x) + 4*tan(1/2*x)^2 + e^(-2*x))/(tan(1/2*x)^4 + 2*tan(1/2*x)^2 + 1))","B",0
934,1,62,0,0.129617," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3),x, algorithm=""giac"")","\frac{3}{8} \, b x + \frac{a \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{3 \, a \cos\left(d x + c\right)}{4 \, d} + \frac{b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{b \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"3/8*b*x + 1/12*a*cos(3*d*x + 3*c)/d - 3/4*a*cos(d*x + c)/d + 1/32*b*sin(4*d*x + 4*c)/d - 1/4*b*sin(2*d*x + 2*c)/d","A",0
935,1,143,0,0.191804," ","integrate(sin(d*x+c)*(a*sin(d*x+c)^2+b*sin(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{5}{8} \, a b x + \frac{b^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{a b \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} + \frac{3 \, a b \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{15 \, a b \sin\left(2 \, d x + 2 \, c\right)}{32 \, d} - \frac{{\left(4 \, a^{2} + 7 \, b^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(20 \, a^{2} + 21 \, b^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{5 \, {\left(8 \, a^{2} + 7 \, b^{2}\right)} \cos\left(d x + c\right)}{64 \, d}"," ",0,"5/8*a*b*x + 1/448*b^2*cos(7*d*x + 7*c)/d - 1/96*a*b*sin(6*d*x + 6*c)/d + 3/32*a*b*sin(4*d*x + 4*c)/d - 15/32*a*b*sin(2*d*x + 2*c)/d - 1/320*(4*a^2 + 7*b^2)*cos(5*d*x + 5*c)/d + 1/192*(20*a^2 + 21*b^2)*cos(3*d*x + 3*c)/d - 5/64*(8*a^2 + 7*b^2)*cos(d*x + c)/d","A",0
936,1,70,0,0.152566," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3),x, algorithm=""giac"")","\frac{1}{8} \, {\left(4 \, a + 3 \, c\right)} x + \frac{b \cos\left(3 \, d x + 3 \, c\right)}{12 \, d} - \frac{3 \, b \cos\left(d x + c\right)}{4 \, d} + \frac{c \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{{\left(a + c\right)} \sin\left(2 \, d x + 2 \, c\right)}{4 \, d}"," ",0,"1/8*(4*a + 3*c)*x + 1/12*b*cos(3*d*x + 3*c)/d - 3/4*b*cos(d*x + c)/d + 1/32*c*sin(4*d*x + 4*c)/d - 1/4*(a + c)*sin(2*d*x + 2*c)/d","A",0
937,1,186,0,0.177781," ","integrate(sin(d*x+c)*(a*sin(d*x+c)+b*sin(d*x+c)^2+c*sin(d*x+c)^3)^2,x, algorithm=""giac"")","\frac{1}{8} \, {\left(6 \, a b + 5 \, b c\right)} x + \frac{c^{2} \cos\left(7 \, d x + 7 \, c\right)}{448 \, d} - \frac{b c \sin\left(6 \, d x + 6 \, c\right)}{96 \, d} - \frac{{\left(4 \, b^{2} + 8 \, a c + 7 \, c^{2}\right)} \cos\left(5 \, d x + 5 \, c\right)}{320 \, d} + \frac{{\left(16 \, a^{2} + 20 \, b^{2} + 40 \, a c + 21 \, c^{2}\right)} \cos\left(3 \, d x + 3 \, c\right)}{192 \, d} - \frac{{\left(48 \, a^{2} + 40 \, b^{2} + 80 \, a c + 35 \, c^{2}\right)} \cos\left(d x + c\right)}{64 \, d} + \frac{{\left(2 \, a b + 3 \, b c\right)} \sin\left(4 \, d x + 4 \, c\right)}{32 \, d} - \frac{{\left(16 \, a b + 15 \, b c\right)} \sin\left(2 \, d x + 2 \, c\right)}{32 \, d}"," ",0,"1/8*(6*a*b + 5*b*c)*x + 1/448*c^2*cos(7*d*x + 7*c)/d - 1/96*b*c*sin(6*d*x + 6*c)/d - 1/320*(4*b^2 + 8*a*c + 7*c^2)*cos(5*d*x + 5*c)/d + 1/192*(16*a^2 + 20*b^2 + 40*a*c + 21*c^2)*cos(3*d*x + 3*c)/d - 1/64*(48*a^2 + 40*b^2 + 80*a*c + 35*c^2)*cos(d*x + c)/d + 1/32*(2*a*b + 3*b*c)*sin(4*d*x + 4*c)/d - 1/32*(16*a*b + 15*b*c)*sin(2*d*x + 2*c)/d","A",0
938,0,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2)),x, algorithm=""giac"")","\int {\left(c \sin\left(d x + c\right) + a + \frac{b}{\sqrt{\sin\left(d x + c\right)}}\right)} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((c*sin(d*x + c) + a + b/sqrt(sin(d*x + c)))*sin(d*x + c), x)","F",0
939,-2,0,0,0.000000," ","integrate(sin(d*x+c)*(a+c*sin(d*x+c)+b/sin(d*x+c)^(1/2))^2,x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, choosing root of [1,0,%%%{-2,[2]%%%}+%%%{-2,[1]%%%}+%%%{-2,[0]%%%},0,%%%{1,[4]%%%}+%%%{-2,[3]%%%}+%%%{3,[2]%%%}+%%%{-2,[1]%%%}+%%%{1,[0]%%%}] at parameters values [93.1017843988]Warning, choosing root of [1,0,%%%{-2,[2]%%%}+%%%{-2,[1]%%%}+%%%{-2,[0]%%%},0,%%%{1,[4]%%%}+%%%{-2,[3]%%%}+%%%{3,[2]%%%}+%%%{-2,[1]%%%}+%%%{1,[0]%%%}] at parameters values [2.14118046779]Warning, choosing root of [1,0,%%%{-2,[2]%%%}+%%%{-2,[1]%%%}+%%%{-2,[0]%%%},0,%%%{1,[4]%%%}+%%%{-2,[3]%%%}+%%%{3,[2]%%%}+%%%{-2,[1]%%%}+%%%{1,[0]%%%}] at parameters values [9.72821606882]int()  Error: Bad Argument Value","F(-2)",0
940,1,31,0,0.616370," ","integrate(f^(b*x+a)*(cos(d*x+c)+I*sin(d*x+c))^n,x, algorithm=""giac"")","\frac{f^{a} e^{\left(i \, d n x + b x \log\left(f\right) + i \, c n\right)}}{i \, d n + b \log\left(f\right)}"," ",0,"f^a*e^(I*d*n*x + b*x*log(f) + I*c*n)/(I*d*n + b*log(f))","A",0
941,1,31,0,0.834128," ","integrate(f^(b*x+a)*(cos(d*x+c)-I*sin(d*x+c))^n,x, algorithm=""giac"")","\frac{f^{a} e^{\left(-i \, d n x + b x \log\left(f\right) - i \, c n\right)}}{-i \, d n + b \log\left(f\right)}"," ",0,"f^a*e^(-I*d*n*x + b*x*log(f) - I*c*n)/(-I*d*n + b*log(f))","A",0
942,1,128,0,0.529130," ","integrate((cos(b*x+a)^5-sin(b*x+a)^5)/(cos(b*x+a)^5+sin(b*x+a)^5),x, algorithm=""giac"")","-\frac{2 \, \sqrt{5} \log\left(-\frac{1}{2} \, {\left(\sqrt{5} + 1\right)} \tan\left(b x + a\right) + \tan\left(b x + a\right)^{2} + 1\right) - 2 \, \sqrt{5} \log\left(\frac{1}{2} \, {\left(\sqrt{5} - 1\right)} \tan\left(b x + a\right) + \tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left(\tan\left(b x + a\right)^{4} - \tan\left(b x + a\right)^{3} + \tan\left(b x + a\right)^{2} - \tan\left(b x + a\right) + 1\right) + 5 \, \log\left(\tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(b x + a\right) + 1 \right|}\right)}{10 \, b}"," ",0,"-1/10*(2*sqrt(5)*log(-1/2*(sqrt(5) + 1)*tan(b*x + a) + tan(b*x + a)^2 + 1) - 2*sqrt(5)*log(1/2*(sqrt(5) - 1)*tan(b*x + a) + tan(b*x + a)^2 + 1) - 2*log(tan(b*x + a)^4 - tan(b*x + a)^3 + tan(b*x + a)^2 - tan(b*x + a) + 1) + 5*log(tan(b*x + a)^2 + 1) - 2*log(abs(tan(b*x + a) + 1)))/b","A",0
943,1,48,0,0.261282," ","integrate((cos(b*x+a)^4-sin(b*x+a)^4)/(cos(b*x+a)^4+sin(b*x+a)^4),x, algorithm=""giac"")","-\frac{\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right) \right|}}\right)}{4 \, b}"," ",0,"-1/4*sqrt(2)*log(abs(-2*sqrt(2) + 2*sin(2*b*x + 2*a))/abs(2*sqrt(2) + 2*sin(2*b*x + 2*a)))/b","A",0
944,1,52,0,0.286857," ","integrate((cos(b*x+a)^3-sin(b*x+a)^3)/(cos(b*x+a)^3+sin(b*x+a)^3),x, algorithm=""giac"")","-\frac{4 \, \log\left(\tan\left(b x + a\right)^{2} - \tan\left(b x + a\right) + 1\right) - 3 \, \log\left(\tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(b x + a\right) + 1 \right|}\right)}{6 \, b}"," ",0,"-1/6*(4*log(tan(b*x + a)^2 - tan(b*x + a) + 1) - 3*log(tan(b*x + a)^2 + 1) - 2*log(abs(tan(b*x + a) + 1)))/b","A",0
945,1,14,0,0.175539," ","integrate((cos(b*x+a)^2-sin(b*x+a)^2)/(cos(b*x+a)^2+sin(b*x+a)^2),x, algorithm=""giac"")","\frac{\sin\left(2 \, b x + 2 \, a\right)}{2 \, b}"," ",0,"1/2*sin(2*b*x + 2*a)/b","A",0
946,1,29,0,0.174700," ","integrate((cos(b*x+a)-sin(b*x+a))/(cos(b*x+a)+sin(b*x+a)),x, algorithm=""giac"")","-\frac{\log\left(\tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(b x + a\right) + 1 \right|}\right)}{2 \, b}"," ",0,"-1/2*(log(tan(b*x + a)^2 + 1) - 2*log(abs(tan(b*x + a) + 1)))/b","A",0
947,1,29,0,0.294414," ","integrate((-csc(b*x+a)+sec(b*x+a))/(csc(b*x+a)+sec(b*x+a)),x, algorithm=""giac"")","\frac{\log\left(\tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(b x + a\right) + 1 \right|}\right)}{2 \, b}"," ",0,"1/2*(log(tan(b*x + a)^2 + 1) - 2*log(abs(tan(b*x + a) + 1)))/b","A",0
948,1,14,0,0.243024," ","integrate((-csc(b*x+a)^2+sec(b*x+a)^2)/(csc(b*x+a)^2+sec(b*x+a)^2),x, algorithm=""giac"")","-\frac{\sin\left(2 \, b x + 2 \, a\right)}{2 \, b}"," ",0,"-1/2*sin(2*b*x + 2*a)/b","A",0
949,1,52,0,0.390254," ","integrate((-csc(b*x+a)^3+sec(b*x+a)^3)/(csc(b*x+a)^3+sec(b*x+a)^3),x, algorithm=""giac"")","\frac{4 \, \log\left(\tan\left(b x + a\right)^{2} - \tan\left(b x + a\right) + 1\right) - 3 \, \log\left(\tan\left(b x + a\right)^{2} + 1\right) - 2 \, \log\left({\left| \tan\left(b x + a\right) + 1 \right|}\right)}{6 \, b}"," ",0,"1/6*(4*log(tan(b*x + a)^2 - tan(b*x + a) + 1) - 3*log(tan(b*x + a)^2 + 1) - 2*log(abs(tan(b*x + a) + 1)))/b","A",0
950,1,48,0,0.386082," ","integrate((-csc(b*x+a)^4+sec(b*x+a)^4)/(csc(b*x+a)^4+sec(b*x+a)^4),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left(\frac{{\left| -2 \, \sqrt{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right) \right|}}{{\left| 2 \, \sqrt{2} + 2 \, \sin\left(2 \, b x + 2 \, a\right) \right|}}\right)}{4 \, b}"," ",0,"1/4*sqrt(2)*log(abs(-2*sqrt(2) + 2*sin(2*b*x + 2*a))/abs(2*sqrt(2) + 2*sin(2*b*x + 2*a)))/b","A",0
