1,1,120,0,0.322961," ","integrate(csc(x)^5/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{21 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{3 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{\sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}}{24 \, a} + \frac{\frac{2 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{18 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{69 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - 1}{24 \, {\left(\frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}\right)}} - \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a}"," ",0,"1/24*(21*sin(x)/(cos(x) + 1) - 3*sin(x)^2/(cos(x) + 1)^2 + sin(x)^3/(cos(x) + 1)^3)/a + 1/24*(2*sin(x)/(cos(x) + 1) - 18*sin(x)^2/(cos(x) + 1)^2 - 69*sin(x)^3/(cos(x) + 1)^3 - 1)/(a*sin(x)^3/(cos(x) + 1)^3 + a*sin(x)^4/(cos(x) + 1)^4) - 3/2*log(sin(x)/(cos(x) + 1))/a","B",0
2,1,97,0,0.329543," ","integrate(csc(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\frac{4 \, \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}}{8 \, a} + \frac{\frac{3 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{20 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - 1}{8 \, {\left(\frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}\right)}} + \frac{3 \, \log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{2 \, a}"," ",0,"-1/8*(4*sin(x)/(cos(x) + 1) - sin(x)^2/(cos(x) + 1)^2)/a + 1/8*(3*sin(x)/(cos(x) + 1) + 20*sin(x)^2/(cos(x) + 1)^2 - 1)/(a*sin(x)^2/(cos(x) + 1)^2 + a*sin(x)^3/(cos(x) + 1)^3) + 3/2*log(sin(x)/(cos(x) + 1))/a","B",0
3,1,68,0,0.330362," ","integrate(csc(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\frac{5 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + 1}{2 \, {\left(\frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}} - \frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{\sin\left(x\right)}{2 \, a {\left(\cos\left(x\right) + 1\right)}}"," ",0,"-1/2*(5*sin(x)/(cos(x) + 1) + 1)/(a*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2) - log(sin(x)/(cos(x) + 1))/a + 1/2*sin(x)/(a*(cos(x) + 1))","B",0
4,1,31,0,0.322673," ","integrate(csc(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\log\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}}"," ",0,"log(sin(x)/(cos(x) + 1))/a + 2/(a + a*sin(x)/(cos(x) + 1))","A",0
5,1,16,0,0.336277," ","integrate(csc(x)/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{2}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1}}"," ",0,"-2/(a + a*sin(x)/(cos(x) + 1))","A",0
6,1,50,0,0.416435," ","integrate(1/(a+a*csc(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)}}{d}"," ",0,"2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
7,1,78,0,0.425843," ","integrate(sin(x)/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 2\right)}}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}}} - \frac{2 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-2*(sin(x)/(cos(x) + 1) + sin(x)^2/(cos(x) + 1)^2 + 2)/(a + a*sin(x)/(cos(x) + 1) + a*sin(x)^2/(cos(x) + 1)^2 + a*sin(x)^3/(cos(x) + 1)^3) - 2*arctan(sin(x)/(cos(x) + 1))/a","B",0
8,1,128,0,0.429276," ","integrate(sin(x)^2/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{5 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{2 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"(sin(x)/(cos(x) + 1) + 5*sin(x)^2/(cos(x) + 1)^2 + 3*sin(x)^3/(cos(x) + 1)^3 + 3*sin(x)^4/(cos(x) + 1)^4 + 4)/(a + a*sin(x)/(cos(x) + 1) + 2*a*sin(x)^2/(cos(x) + 1)^2 + 2*a*sin(x)^3/(cos(x) + 1)^3 + a*sin(x)^4/(cos(x) + 1)^4 + a*sin(x)^5/(cos(x) + 1)^5) + 3*arctan(sin(x)/(cos(x) + 1))/a","B",0
9,1,180,0,0.427810," ","integrate(sin(x)^3/(a+a*csc(x)),x, algorithm=""maxima"")","-\frac{\frac{7 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{39 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + 16}{3 \, {\left(a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{3 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{3 \, a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{a \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}}\right)}} - \frac{3 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{a}"," ",0,"-1/3*(7*sin(x)/(cos(x) + 1) + 39*sin(x)^2/(cos(x) + 1)^2 + 24*sin(x)^3/(cos(x) + 1)^3 + 24*sin(x)^4/(cos(x) + 1)^4 + 9*sin(x)^5/(cos(x) + 1)^5 + 9*sin(x)^6/(cos(x) + 1)^6 + 16)/(a + a*sin(x)/(cos(x) + 1) + 3*a*sin(x)^2/(cos(x) + 1)^2 + 3*a*sin(x)^3/(cos(x) + 1)^3 + 3*a*sin(x)^4/(cos(x) + 1)^4 + 3*a*sin(x)^5/(cos(x) + 1)^5 + a*sin(x)^6/(cos(x) + 1)^6 + a*sin(x)^7/(cos(x) + 1)^7) - 3*arctan(sin(x)/(cos(x) + 1))/a","B",0
10,1,230,0,0.425404," ","integrate(sin(x)^4/(a+a*csc(x)),x, algorithm=""maxima"")","\frac{\frac{19 \, \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{211 \, \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{91 \, \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{219 \, \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{165 \, \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{165 \, \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{45 \, \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{45 \, \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + 64}{12 \, {\left(a + \frac{a \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{4 \, a \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{4 \, a \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{6 \, a \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{4 \, a \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}} + \frac{4 \, a \sin\left(x\right)^{7}}{{\left(\cos\left(x\right) + 1\right)}^{7}} + \frac{a \sin\left(x\right)^{8}}{{\left(\cos\left(x\right) + 1\right)}^{8}} + \frac{a \sin\left(x\right)^{9}}{{\left(\cos\left(x\right) + 1\right)}^{9}}\right)}} + \frac{15 \, \arctan\left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)}{4 \, a}"," ",0,"1/12*(19*sin(x)/(cos(x) + 1) + 211*sin(x)^2/(cos(x) + 1)^2 + 91*sin(x)^3/(cos(x) + 1)^3 + 219*sin(x)^4/(cos(x) + 1)^4 + 165*sin(x)^5/(cos(x) + 1)^5 + 165*sin(x)^6/(cos(x) + 1)^6 + 45*sin(x)^7/(cos(x) + 1)^7 + 45*sin(x)^8/(cos(x) + 1)^8 + 64)/(a + a*sin(x)/(cos(x) + 1) + 4*a*sin(x)^2/(cos(x) + 1)^2 + 4*a*sin(x)^3/(cos(x) + 1)^3 + 6*a*sin(x)^4/(cos(x) + 1)^4 + 6*a*sin(x)^5/(cos(x) + 1)^5 + 4*a*sin(x)^6/(cos(x) + 1)^6 + 4*a*sin(x)^7/(cos(x) + 1)^7 + a*sin(x)^8/(cos(x) + 1)^8 + a*sin(x)^9/(cos(x) + 1)^9) + 15/4*arctan(sin(x)/(cos(x) + 1))/a","B",0
11,1,142,0,0.426756," ","integrate(1/(a+a*csc(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 4}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{3 \, d}"," ",0,"2/3*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4)/(a^2 + 3*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
12,1,228,0,0.436249," ","integrate(1/(a+a*csc(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{95 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{145 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{75 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 22}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{15 \, d}"," ",0,"2/15*((95*sin(d*x + c)/(cos(d*x + c) + 1) + 145*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 75*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 22)/(a^3 + 5*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 10*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
13,1,417,0,0.473575," ","integrate((a+a*csc(x))^(5/2),x, algorithm=""maxima"")","\frac{1}{22} \, \sqrt{2} a^{\frac{5}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{11}{2}} + \frac{5}{18} \, \sqrt{2} a^{\frac{5}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{9}{2}} + \frac{9}{14} \, \sqrt{2} a^{\frac{5}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{7}{2}} + \frac{1}{2} \, \sqrt{2} a^{\frac{5}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{5}{2}} - \frac{2}{3} \, \sqrt{2} a^{\frac{5}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{3}{2}} + \sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right)\right)} a^{\frac{5}{2}} - 2 \, \sqrt{2} a^{\frac{5}{2}} \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}} - \frac{\frac{693 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{1155 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + \frac{1386 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} + \frac{990 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} + \frac{385 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} + \frac{63 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}}{1386 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}} - \frac{\frac{7 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{105 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{210 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{70 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}} - \frac{21 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{5}}{{\left(\cos\left(x\right) + 1\right)}^{5}} - \frac{3 \, \sqrt{2} a^{\frac{5}{2}} \sin\left(x\right)^{6}}{{\left(\cos\left(x\right) + 1\right)}^{6}}}{42 \, \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{5}{2}}}"," ",0,"1/22*sqrt(2)*a^(5/2)*(sin(x)/(cos(x) + 1))^(11/2) + 5/18*sqrt(2)*a^(5/2)*(sin(x)/(cos(x) + 1))^(9/2) + 9/14*sqrt(2)*a^(5/2)*(sin(x)/(cos(x) + 1))^(7/2) + 1/2*sqrt(2)*a^(5/2)*(sin(x)/(cos(x) + 1))^(5/2) - 2/3*sqrt(2)*a^(5/2)*(sin(x)/(cos(x) + 1))^(3/2) + sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(x)/(cos(x) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(x)/(cos(x) + 1)))))*a^(5/2) - 2*sqrt(2)*a^(5/2)*sqrt(sin(x)/(cos(x) + 1)) - 1/1386*(693*sqrt(2)*a^(5/2)*sin(x)/(cos(x) + 1) + 1155*sqrt(2)*a^(5/2)*sin(x)^2/(cos(x) + 1)^2 + 1386*sqrt(2)*a^(5/2)*sin(x)^3/(cos(x) + 1)^3 + 990*sqrt(2)*a^(5/2)*sin(x)^4/(cos(x) + 1)^4 + 385*sqrt(2)*a^(5/2)*sin(x)^5/(cos(x) + 1)^5 + 63*sqrt(2)*a^(5/2)*sin(x)^6/(cos(x) + 1)^6)/sqrt(sin(x)/(cos(x) + 1)) - 1/42*(7*sqrt(2)*a^(5/2)*sin(x)/(cos(x) + 1) + 105*sqrt(2)*a^(5/2)*sin(x)^2/(cos(x) + 1)^2 - 210*sqrt(2)*a^(5/2)*sin(x)^3/(cos(x) + 1)^3 - 70*sqrt(2)*a^(5/2)*sin(x)^4/(cos(x) + 1)^4 - 21*sqrt(2)*a^(5/2)*sin(x)^5/(cos(x) + 1)^5 - 3*sqrt(2)*a^(5/2)*sin(x)^6/(cos(x) + 1)^6)/(sin(x)/(cos(x) + 1))^(5/2)","B",0
14,1,200,0,0.445567," ","integrate((a+a*csc(x))^(3/2),x, algorithm=""maxima"")","\sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right)\right)} a^{\frac{3}{2}} - \frac{1}{5} \, \sqrt{2} {\left(a^{\frac{3}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{5}{2}} + 5 \, a^{\frac{3}{2}} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{3}{2}} + 10 \, a^{\frac{3}{2}} \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)} - \frac{\frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(x\right)}{\cos\left(x\right) + 1} - \frac{15 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} - \frac{5 \, \sqrt{2} a^{\frac{3}{2}} \sin\left(x\right)^{3}}{{\left(\cos\left(x\right) + 1\right)}^{3}} - \frac{\sqrt{2} a^{\frac{3}{2}} \sin\left(x\right)^{4}}{{\left(\cos\left(x\right) + 1\right)}^{4}}}{5 \, \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{3}{2}}}"," ",0,"sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(x)/(cos(x) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(x)/(cos(x) + 1)))))*a^(3/2) - 1/5*sqrt(2)*(a^(3/2)*(sin(x)/(cos(x) + 1))^(5/2) + 5*a^(3/2)*(sin(x)/(cos(x) + 1))^(3/2) + 10*a^(3/2)*sqrt(sin(x)/(cos(x) + 1))) - 1/5*(5*sqrt(2)*a^(3/2)*sin(x)/(cos(x) + 1) - 15*sqrt(2)*a^(3/2)*sin(x)^2/(cos(x) + 1)^2 - 5*sqrt(2)*a^(3/2)*sin(x)^3/(cos(x) + 1)^3 - sqrt(2)*a^(3/2)*sin(x)^4/(cos(x) + 1)^4)/(sin(x)/(cos(x) + 1))^(3/2)","B",0
15,1,148,0,0.441582," ","integrate((a+a*csc(x))^(1/2),x, algorithm=""maxima"")","-\frac{2}{3} \, \sqrt{2} \sqrt{a} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{3}{2}} + \sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right)\right)} \sqrt{a} - 2 \, \sqrt{2} \sqrt{a} \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}} + \frac{2 \, {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{\sqrt{2} \sqrt{a} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}}{3 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}}"," ",0,"-2/3*sqrt(2)*sqrt(a)*(sin(x)/(cos(x) + 1))^(3/2) + sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(x)/(cos(x) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(x)/(cos(x) + 1)))))*sqrt(a) - 2*sqrt(2)*sqrt(a)*sqrt(sin(x)/(cos(x) + 1)) + 2/3*(3*sqrt(2)*sqrt(a)*sin(x)/(cos(x) + 1) + sqrt(2)*sqrt(a)*sin(x)^2/(cos(x) + 1)^2)/sqrt(sin(x)/(cos(x) + 1))","B",0
16,1,83,0,0.452147," ","integrate(1/(a+a*csc(x))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right)\right)}}{\sqrt{a}} - \frac{2 \, \sqrt{2} \arctan\left(\sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}{\sqrt{a}}"," ",0,"sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(x)/(cos(x) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(x)/(cos(x) + 1)))))/sqrt(a) - 2*sqrt(2)*arctan(sqrt(sin(x)/(cos(x) + 1)))/sqrt(a)","A",0
17,1,150,0,0.451558," ","integrate(1/(a+a*csc(x))^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \left(\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}\right)^{\frac{3}{2}} - \sqrt{2} \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}}{2 \, {\left(a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(x\right)}{\cos\left(x\right) + 1} + \frac{a^{\frac{3}{2}} \sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}}\right)}} + \frac{\sqrt{2} {\left(\sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right) + \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}\right)\right)}}{a^{\frac{3}{2}}} - \frac{5 \, \sqrt{2} \arctan\left(\sqrt{\frac{\sin\left(x\right)}{\cos\left(x\right) + 1}}\right)}{2 \, a^{\frac{3}{2}}}"," ",0,"-1/2*(sqrt(2)*(sin(x)/(cos(x) + 1))^(3/2) - sqrt(2)*sqrt(sin(x)/(cos(x) + 1)))/(a^(3/2) + 2*a^(3/2)*sin(x)/(cos(x) + 1) + a^(3/2)*sin(x)^2/(cos(x) + 1)^2) + sqrt(2)*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(sin(x)/(cos(x) + 1)))) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(sin(x)/(cos(x) + 1)))))/a^(3/2) - 5/2*sqrt(2)*arctan(sqrt(sin(x)/(cos(x) + 1)))/a^(3/2)","B",0
18,0,0,0,0.000000," ","integrate(1/(a+a*csc(x))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \csc\left(x\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*csc(x) + a)^(-5/2), x)","F",0
19,0,0,0,0.000000," ","integrate(csc(f*x+e)^(1/2)*(a+a*csc(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(f x + e\right) + a} \sqrt{\csc\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*csc(f*x + e) + a)*sqrt(csc(f*x + e)), x)","F",0
20,0,0,0,0.000000," ","integrate((-csc(f*x+e))^(1/2)*(a-a*csc(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \csc\left(f x + e\right) + a} \sqrt{-\csc\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(-a*csc(f*x + e) + a)*sqrt(-csc(f*x + e)), x)","F",0
21,0,0,0,0.000000," ","integrate(csc(d*x+c)^(4/3)*(a+a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)*csc(d*x + c)^(4/3), x)","F",0
22,0,0,0,0.000000," ","integrate(csc(d*x+c)^(1/3)*(a+a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)*csc(d*x + c)^(1/3), x)","F",0
23,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \csc\left(d x + c\right) + a}}{\csc\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)/csc(d*x + c)^(2/3), x)","F",0
24,0,0,0,0.000000," ","integrate(csc(d*x+c)^(5/3)*(a+a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{\frac{5}{3}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)*csc(d*x + c)^(5/3), x)","F",0
25,0,0,0,0.000000," ","integrate(csc(d*x+c)^(2/3)*(a+a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)*csc(d*x + c)^(2/3), x)","F",0
26,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \csc\left(d x + c\right) + a}}{\csc\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)/csc(d*x + c)^(1/3), x)","F",0
27,0,0,0,0.000000," ","integrate((a+a*csc(d*x+c))^(1/2)/csc(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{\sqrt{a \csc\left(d x + c\right) + a}}{\csc\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)/csc(d*x + c)^(4/3), x)","F",0
28,0,0,0,0.000000," ","integrate(csc(d*x+c)^n*(a+a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{n}\,{d x}"," ",0,"integrate(sqrt(a*csc(d*x + c) + a)*csc(d*x + c)^n, x)","F",0
29,0,0,0,0.000000," ","integrate(csc(d*x+c)^n*(a-a*csc(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{-a \csc\left(d x + c\right) + a} \csc\left(d x + c\right)^{n}\,{d x}"," ",0,"integrate(sqrt(-a*csc(d*x + c) + a)*csc(d*x + c)^n, x)","F",0
30,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+a*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m*csc(f*x + e)^3, x)","F",0
31,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+a*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m*csc(f*x + e)^2, x)","F",0
32,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+a*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m*csc(f*x + e), x)","F",0
33,0,0,0,0.000000," ","integrate((a+a*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m, x)","F",0
34,0,0,0,0.000000," ","integrate((a+a*csc(f*x+e))^m*sin(f*x+e),x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m*sin(f*x + e), x)","F",0
35,0,0,0,0.000000," ","integrate((a+a*csc(f*x+e))^m*sin(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(a \csc\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*csc(f*x + e) + a)^m*sin(f*x + e)^2, x)","F",0
36,1,125,0,0.338716," ","integrate((a+b*csc(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{a b^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{d} - \frac{4 \, a^{3} b \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right)}{d} - \frac{6 \, a^{2} b^{2}}{d \tan\left(d x + c\right)} - \frac{{\left(3 \, \tan\left(d x + c\right)^{2} + 1\right)} b^{4}}{3 \, d \tan\left(d x + c\right)^{3}}"," ",0,"a^4*x + a*b^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1))/d - 4*a^3*b*log(cot(d*x + c) + csc(d*x + c))/d - 6*a^2*b^2/(d*tan(d*x + c)) - 1/3*(3*tan(d*x + c)^2 + 1)*b^4/(d*tan(d*x + c)^3)","A",0
37,1,95,0,0.335798," ","integrate((a+b*csc(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{b^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d} - \frac{3 \, a^{2} b \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right)}{d} - \frac{3 \, a b^{2}}{d \tan\left(d x + c\right)}"," ",0,"a^3*x + 1/4*b^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1))/d - 3*a^2*b*log(cot(d*x + c) + csc(d*x + c))/d - 3*a*b^2/(d*tan(d*x + c))","A",0
38,1,43,0,0.363253," ","integrate((a+b*csc(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x - \frac{2 \, a b \log\left(\cot\left(d x + c\right) + \csc\left(d x + c\right)\right)}{d} - \frac{b^{2}}{d \tan\left(d x + c\right)}"," ",0,"a^2*x - 2*a*b*log(cot(d*x + c) + csc(d*x + c))/d - b^2/(d*tan(d*x + c))","A",0
39,-2,0,0,0.000000," ","integrate(csc(x)^5/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
40,-2,0,0,0.000000," ","integrate(csc(x)^4/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
41,-2,0,0,0.000000," ","integrate(csc(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
42,-2,0,0,0.000000," ","integrate(csc(x)^2/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
43,-2,0,0,0.000000," ","integrate(csc(x)/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
44,-2,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
45,-2,0,0,0.000000," ","integrate(sin(x)/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
46,-2,0,0,0.000000," ","integrate(sin(x)^2/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
47,-2,0,0,0.000000," ","integrate(sin(x)^3/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
48,-2,0,0,0.000000," ","integrate(sin(x)^4/(a+b*csc(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
49,-2,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
50,-2,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
51,-2,0,0,0.000000," ","integrate(1/(a+b*csc(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
52,1,49,0,0.413388," ","integrate(1/(3+5*csc(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, \arctan\left(\frac{5 \, \sin\left(d x + c\right)}{4 \, {\left(\cos\left(d x + c\right) + 1\right)}} + \frac{3}{4}\right) - 4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{6 \, d}"," ",0,"-1/6*(5*arctan(5/4*sin(d*x + c)/(cos(d*x + c) + 1) + 3/4) - 4*arctan(sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
53,1,71,0,0.409539," ","integrate(1/(5+3*csc(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right) - 3 \, \log\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right) + 3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 3\right)}{20 \, d}"," ",0,"1/20*(8*arctan(sin(d*x + c)/(cos(d*x + c) + 1)) - 3*log(3*sin(d*x + c)/(cos(d*x + c) + 1) + 1) + 3*log(sin(d*x + c)/(cos(d*x + c) + 1) + 3))/d","A",0
54,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(a+b*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m*csc(f*x + e)^3, x)","F",0
55,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(a+b*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m*csc(f*x + e)^2, x)","F",0
56,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m} \csc\left(f x + e\right)\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m*csc(f*x + e), x)","F",0
57,0,0,0,0.000000," ","integrate((a+b*csc(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m, x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*csc(f*x+e))^m*sin(f*x+e),x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m*sin(f*x + e), x)","F",0
59,0,0,0,0.000000," ","integrate((a+b*csc(f*x+e))^m*sin(f*x+e)^2,x, algorithm=""maxima"")","\int {\left(b \csc\left(f x + e\right) + a\right)}^{m} \sin\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*csc(f*x + e) + a)^m*sin(f*x + e)^2, x)","F",0
