1,0,0,0,0.000000," ","integrate((a+I*a*cot(d*x+c))**n,x)","\int \left(i a \cot{\left(c + d x \right)} + a\right)^{n}\, dx"," ",0,"Integral((I*a*cot(c + d*x) + a)**n, x)","F",0
2,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)*(a+a*cot(d*x+c)),x)","a \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral((e*cot(c + d*x))**(5/2), x) + Integral((e*cot(c + d*x))**(5/2)*cot(c + d*x), x))","F",0
3,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+a*cot(d*x+c)),x)","a \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral((e*cot(c + d*x))**(3/2), x) + Integral((e*cot(c + d*x))**(3/2)*cot(c + d*x), x))","F",0
4,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+a*cot(d*x+c)),x)","a \left(\int \sqrt{e \cot{\left(c + d x \right)}}\, dx + \int \sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sqrt(e*cot(c + d*x)), x) + Integral(sqrt(e*cot(c + d*x))*cot(c + d*x), x))","F",0
5,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))**(1/2),x)","a \left(\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{\cot{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(1/sqrt(e*cot(c + d*x)), x) + Integral(cot(c + d*x)/sqrt(e*cot(c + d*x)), x))","F",0
6,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))**(3/2),x)","a \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a*(Integral((e*cot(c + d*x))**(-3/2), x) + Integral(cot(c + d*x)/(e*cot(c + d*x))**(3/2), x))","F",0
7,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))/(e*cot(d*x+c))**(5/2),x)","a \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a*(Integral((e*cot(c + d*x))**(-5/2), x) + Integral(cot(c + d*x)/(e*cot(c + d*x))**(5/2), x))","F",0
8,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)*(a+a*cot(d*x+c))**2,x)","a^{2} \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx + \int 2 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral((e*cot(c + d*x))**(5/2), x) + Integral(2*(e*cot(c + d*x))**(5/2)*cot(c + d*x), x) + Integral((e*cot(c + d*x))**(5/2)*cot(c + d*x)**2, x))","F",0
9,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+a*cot(d*x+c))**2,x)","a^{2} \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx + \int 2 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral((e*cot(c + d*x))**(3/2), x) + Integral(2*(e*cot(c + d*x))**(3/2)*cot(c + d*x), x) + Integral((e*cot(c + d*x))**(3/2)*cot(c + d*x)**2, x))","F",0
10,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+a*cot(d*x+c))**2,x)","a^{2} \left(\int \sqrt{e \cot{\left(c + d x \right)}}\, dx + \int 2 \sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx + \int \sqrt{e \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(sqrt(e*cot(c + d*x)), x) + Integral(2*sqrt(e*cot(c + d*x))*cot(c + d*x), x) + Integral(sqrt(e*cot(c + d*x))*cot(c + d*x)**2, x))","F",0
11,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**2/(e*cot(d*x+c))**(1/2),x)","a^{2} \left(\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{2 \cot{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{\cot^{2}{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**2*(Integral(1/sqrt(e*cot(c + d*x)), x) + Integral(2*cot(c + d*x)/sqrt(e*cot(c + d*x)), x) + Integral(cot(c + d*x)**2/sqrt(e*cot(c + d*x)), x))","F",0
12,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**2/(e*cot(d*x+c))**(3/2),x)","a^{2} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{2 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a**2*(Integral((e*cot(c + d*x))**(-3/2), x) + Integral(2*cot(c + d*x)/(e*cot(c + d*x))**(3/2), x) + Integral(cot(c + d*x)**2/(e*cot(c + d*x))**(3/2), x))","F",0
13,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**2/(e*cot(d*x+c))**(5/2),x)","a^{2} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{2 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a**2*(Integral((e*cot(c + d*x))**(-5/2), x) + Integral(2*cot(c + d*x)/(e*cot(c + d*x))**(5/2), x) + Integral(cot(c + d*x)**2/(e*cot(c + d*x))**(5/2), x))","F",0
14,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**2/(e*cot(d*x+c))**(7/2),x)","a^{2} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{2 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{\cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"a**2*(Integral((e*cot(c + d*x))**(-7/2), x) + Integral(2*cot(c + d*x)/(e*cot(c + d*x))**(7/2), x) + Integral(cot(c + d*x)**2/(e*cot(c + d*x))**(7/2), x))","F",0
15,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)*(a+a*cot(d*x+c))**3,x)","a^{3} \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx + \int 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)}\, dx + \int 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{2}{\left(c + d x \right)}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(5/2), x) + Integral(3*(e*cot(c + d*x))**(5/2)*cot(c + d*x), x) + Integral(3*(e*cot(c + d*x))**(5/2)*cot(c + d*x)**2, x) + Integral((e*cot(c + d*x))**(5/2)*cot(c + d*x)**3, x))","F",0
16,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+a*cot(d*x+c))**3,x)","a^{3} \left(\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx + \int 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)}\, dx + \int 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)}\, dx + \int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(3/2), x) + Integral(3*(e*cot(c + d*x))**(3/2)*cot(c + d*x), x) + Integral(3*(e*cot(c + d*x))**(3/2)*cot(c + d*x)**2, x) + Integral((e*cot(c + d*x))**(3/2)*cot(c + d*x)**3, x))","F",0
17,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+a*cot(d*x+c))**3,x)","a^{3} \left(\int \sqrt{e \cot{\left(c + d x \right)}}\, dx + \int 3 \sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx + \int 3 \sqrt{e \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\, dx + \int \sqrt{e \cot{\left(c + d x \right)}} \cot^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(sqrt(e*cot(c + d*x)), x) + Integral(3*sqrt(e*cot(c + d*x))*cot(c + d*x), x) + Integral(3*sqrt(e*cot(c + d*x))*cot(c + d*x)**2, x) + Integral(sqrt(e*cot(c + d*x))*cot(c + d*x)**3, x))","F",0
18,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**3/(e*cot(d*x+c))**(1/2),x)","a^{3} \left(\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{3 \cot{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{3 \cot^{2}{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx + \int \frac{\cot^{3}{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"a**3*(Integral(1/sqrt(e*cot(c + d*x)), x) + Integral(3*cot(c + d*x)/sqrt(e*cot(c + d*x)), x) + Integral(3*cot(c + d*x)**2/sqrt(e*cot(c + d*x)), x) + Integral(cot(c + d*x)**3/sqrt(e*cot(c + d*x)), x))","F",0
19,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**3/(e*cot(d*x+c))**(3/2),x)","a^{3} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{3 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{3 \cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\cot^{3}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(-3/2), x) + Integral(3*cot(c + d*x)/(e*cot(c + d*x))**(3/2), x) + Integral(3*cot(c + d*x)**2/(e*cot(c + d*x))**(3/2), x) + Integral(cot(c + d*x)**3/(e*cot(c + d*x))**(3/2), x))","F",0
20,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**3/(e*cot(d*x+c))**(5/2),x)","a^{3} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{3 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{3 \cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx + \int \frac{\cot^{3}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(-5/2), x) + Integral(3*cot(c + d*x)/(e*cot(c + d*x))**(5/2), x) + Integral(3*cot(c + d*x)**2/(e*cot(c + d*x))**(5/2), x) + Integral(cot(c + d*x)**3/(e*cot(c + d*x))**(5/2), x))","F",0
21,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**3/(e*cot(d*x+c))**(7/2),x)","a^{3} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{3 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{3 \cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx + \int \frac{\cot^{3}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(-7/2), x) + Integral(3*cot(c + d*x)/(e*cot(c + d*x))**(7/2), x) + Integral(3*cot(c + d*x)**2/(e*cot(c + d*x))**(7/2), x) + Integral(cot(c + d*x)**3/(e*cot(c + d*x))**(7/2), x))","F",0
22,0,0,0,0.000000," ","integrate((a+a*cot(d*x+c))**3/(e*cot(d*x+c))**(9/2),x)","a^{3} \left(\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{3 \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{3 \cot^{2}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{9}{2}}}\, dx + \int \frac{\cot^{3}{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{9}{2}}}\, dx\right)"," ",0,"a**3*(Integral((e*cot(c + d*x))**(-9/2), x) + Integral(3*cot(c + d*x)/(e*cot(c + d*x))**(9/2), x) + Integral(3*cot(c + d*x)**2/(e*cot(c + d*x))**(9/2), x) + Integral(cot(c + d*x)**3/(e*cot(c + d*x))**(9/2), x))","F",0
23,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\cot{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e*cot(c + d*x))**(5/2)/(cot(c + d*x) + 1), x)/a","F",0
24,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cot{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(cot(c + d*x) + 1), x)/a","F",0
25,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{\cot{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(e*cot(c + d*x))/(cot(c + d*x) + 1), x)/a","F",0
26,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)} + \sqrt{e \cot{\left(c + d x \right)}}}\, dx}{a}"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*cot(c + d*x) + sqrt(e*cot(c + d*x))), x)/a","F",0
27,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx}{a}"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*cot(c + d*x) + (e*cot(c + d*x))**(3/2)), x)/a","F",0
28,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c)),x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx}{a}"," ",0,"Integral(1/((e*cot(c + d*x))**(5/2)*cot(c + d*x) + (e*cot(c + d*x))**(5/2)), x)/a","F",0
29,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\cot^{2}{\left(c + d x \right)} + 2 \cot{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((e*cot(c + d*x))**(5/2)/(cot(c + d*x)**2 + 2*cot(c + d*x) + 1), x)/a**2","F",0
30,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cot^{2}{\left(c + d x \right)} + 2 \cot{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(cot(c + d*x)**2 + 2*cot(c + d*x) + 1), x)/a**2","F",0
31,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{\cot^{2}{\left(c + d x \right)} + 2 \cot{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sqrt(e*cot(c + d*x))/(cot(c + d*x)**2 + 2*cot(c + d*x) + 1), x)/a**2","F",0
32,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)} + 2 \sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)} + \sqrt{e \cot{\left(c + d x \right)}}}\, dx}{a^{2}}"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*cot(c + d*x)**2 + 2*sqrt(e*cot(c + d*x))*cot(c + d*x) + sqrt(e*cot(c + d*x))), x)/a**2","F",0
33,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)} + 2 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{2}}"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*cot(c + d*x)**2 + 2*(e*cot(c + d*x))**(3/2)*cot(c + d*x) + (e*cot(c + d*x))**(3/2)), x)/a**2","F",0
34,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c))**2,x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{2}{\left(c + d x \right)} + 2 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx}{a^{2}}"," ",0,"Integral(1/((e*cot(c + d*x))**(5/2)*cot(c + d*x)**2 + 2*(e*cot(c + d*x))**(5/2)*cot(c + d*x) + (e*cot(c + d*x))**(5/2)), x)/a**2","F",0
35,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\cot^{3}{\left(c + d x \right)} + 3 \cot^{2}{\left(c + d x \right)} + 3 \cot{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((e*cot(c + d*x))**(5/2)/(cot(c + d*x)**3 + 3*cot(c + d*x)**2 + 3*cot(c + d*x) + 1), x)/a**3","F",0
36,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\cot^{3}{\left(c + d x \right)} + 3 \cot^{2}{\left(c + d x \right)} + 3 \cot{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(cot(c + d*x)**3 + 3*cot(c + d*x)**2 + 3*cot(c + d*x) + 1), x)/a**3","F",0
37,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{\cot^{3}{\left(c + d x \right)} + 3 \cot^{2}{\left(c + d x \right)} + 3 \cot{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sqrt(e*cot(c + d*x))/(cot(c + d*x)**3 + 3*cot(c + d*x)**2 + 3*cot(c + d*x) + 1), x)/a**3","F",0
38,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \cot^{3}{\left(c + d x \right)} + 3 \sqrt{e \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)} + 3 \sqrt{e \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)} + \sqrt{e \cot{\left(c + d x \right)}}}\, dx}{a^{3}}"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*cot(c + d*x)**3 + 3*sqrt(e*cot(c + d*x))*cot(c + d*x)**2 + 3*sqrt(e*cot(c + d*x))*cot(c + d*x) + sqrt(e*cot(c + d*x))), x)/a**3","F",0
39,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{3}{\left(c + d x \right)} + 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(c + d x \right)} + 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx}{a^{3}}"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*cot(c + d*x)**3 + 3*(e*cot(c + d*x))**(3/2)*cot(c + d*x)**2 + 3*(e*cot(c + d*x))**(3/2)*cot(c + d*x) + (e*cot(c + d*x))**(3/2)), x)/a**3","F",0
40,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(5/2)/(a+a*cot(d*x+c))**3,x)","\frac{\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{3}{\left(c + d x \right)} + 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot^{2}{\left(c + d x \right)} + 3 \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \cot{\left(c + d x \right)} + \left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx}{a^{3}}"," ",0,"Integral(1/((e*cot(c + d*x))**(5/2)*cot(c + d*x)**3 + 3*(e*cot(c + d*x))**(5/2)*cot(c + d*x)**2 + 3*(e*cot(c + d*x))**(5/2)*cot(c + d*x) + (e*cot(c + d*x))**(5/2)), x)/a**3","F",0
41,0,0,0,0.000000," ","integrate(cot(x)**2*(1+cot(x))**(1/2),x)","\int \sqrt{\cot{\left(x \right)} + 1} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(cot(x) + 1)*cot(x)**2, x)","F",0
42,0,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))**(1/2),x)","\int \sqrt{\cot{\left(x \right)} + 1} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(cot(x) + 1)*cot(x), x)","F",0
43,0,0,0,0.000000," ","integrate(cot(x)**2*(1+cot(x))**(3/2),x)","\int \left(\cot{\left(x \right)} + 1\right)^{\frac{3}{2}} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral((cot(x) + 1)**(3/2)*cot(x)**2, x)","F",0
44,0,0,0,0.000000," ","integrate(cot(x)*(1+cot(x))**(3/2),x)","\int \left(\cot{\left(x \right)} + 1\right)^{\frac{3}{2}} \cot{\left(x \right)}\, dx"," ",0,"Integral((cot(x) + 1)**(3/2)*cot(x), x)","F",0
45,0,0,0,0.000000," ","integrate(cot(x)**2/(1+cot(x))**(1/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\sqrt{\cot{\left(x \right)} + 1}}\, dx"," ",0,"Integral(cot(x)**2/sqrt(cot(x) + 1), x)","F",0
46,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{\cot{\left(x \right)} + 1}}\, dx"," ",0,"Integral(cot(x)/sqrt(cot(x) + 1), x)","F",0
47,0,0,0,0.000000," ","integrate(cot(x)**2/(1+cot(x))**(3/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\left(\cot{\left(x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)**2/(cot(x) + 1)**(3/2), x)","F",0
48,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))**(3/2),x)","\int \frac{\cot{\left(x \right)}}{\left(\cot{\left(x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)/(cot(x) + 1)**(3/2), x)","F",0
49,0,0,0,0.000000," ","integrate(cot(x)**2/(1+cot(x))**(5/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\left(\cot{\left(x \right)} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)**2/(cot(x) + 1)**(5/2), x)","F",0
50,0,0,0,0.000000," ","integrate(cot(x)/(1+cot(x))**(5/2),x)","\int \frac{\cot{\left(x \right)}}{\left(\cot{\left(x \right)} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)/(cot(x) + 1)**(5/2), x)","F",0
51,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+b*cot(d*x+c)),x)","\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x)), x)","F",0
52,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+b*cot(d*x+c)),x)","\int \sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x)), x)","F",0
53,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))**(1/2),x)","\int \frac{a + b \cot{\left(c + d x \right)}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))/sqrt(e*cot(c + d*x)), x)","F",0
54,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))**(3/2),x)","\int \frac{a + b \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))/(e*cot(c + d*x))**(3/2), x)","F",0
55,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))/(e*cot(d*x+c))**(5/2),x)","\int \frac{a + b \cot{\left(c + d x \right)}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))/(e*cot(c + d*x))**(5/2), x)","F",0
56,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+b*cot(d*x+c))**2,x)","\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x))**2, x)","F",0
57,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+b*cot(d*x+c))**2,x)","\int \sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x))**2, x)","F",0
58,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**2/(e*cot(d*x+c))**(1/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**2/sqrt(e*cot(c + d*x)), x)","F",0
59,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**2/(e*cot(d*x+c))**(3/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**2/(e*cot(c + d*x))**(3/2), x)","F",0
60,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**2/(e*cot(d*x+c))**(5/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**2/(e*cot(c + d*x))**(5/2), x)","F",0
61,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**2/(e*cot(d*x+c))**(7/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**2/(e*cot(c + d*x))**(7/2), x)","F",0
62,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)*(a+b*cot(d*x+c))**3,x)","\int \left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x))**3, x)","F",0
63,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)*(a+b*cot(d*x+c))**3,x)","\int \sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x))**3, x)","F",0
64,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**3/(e*cot(d*x+c))**(1/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}{\sqrt{e \cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**3/sqrt(e*cot(c + d*x)), x)","F",0
65,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**3/(e*cot(d*x+c))**(3/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**3/(e*cot(c + d*x))**(3/2), x)","F",0
66,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**3/(e*cot(d*x+c))**(5/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**3/(e*cot(c + d*x))**(5/2), x)","F",0
67,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**3/(e*cot(d*x+c))**(7/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**3/(e*cot(c + d*x))**(7/2), x)","F",0
68,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**3/(e*cot(d*x+c))**(9/2),x)","\int \frac{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**3/(e*cot(c + d*x))**(9/2), x)","F",0
69,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+b*cot(d*x+c)),x)","\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}{a + b \cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*cot(c + d*x))**(5/2)/(a + b*cot(c + d*x)), x)","F",0
70,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c)),x)","\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{a + b \cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(a + b*cot(c + d*x)), x)","F",0
71,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c)),x)","\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{a + b \cot{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))/(a + b*cot(c + d*x)), x)","F",0
72,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c)),x)","\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x))), x)","F",0
73,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c)),x)","\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x))), x)","F",0
74,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(5/2)/(a+b*cot(d*x+c)),x)","\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}} \left(a + b \cot{\left(c + d x \right)}\right)}\, dx"," ",0,"Integral(1/((e*cot(c + d*x))**(5/2)*(a + b*cot(c + d*x))), x)","F",0
75,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))**(7/2)/(a+b*cot(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+b*cot(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c))**2,x)","\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(a + b*cot(c + d*x))**2, x)","F",0
78,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c))**2,x)","\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{\left(a + b \cot{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))/(a + b*cot(c + d*x))**2, x)","F",0
79,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c))**2,x)","\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x))**2), x)","F",0
80,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c))**2,x)","\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x))**2), x)","F",0
81,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))**(9/2)/(a+b*cot(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate((e*cot(d*x+c))**(7/2)/(a+b*cot(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(5/2)/(a+b*cot(d*x+c))**3,x)","\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((e*cot(c + d*x))**(5/2)/(a + b*cot(c + d*x))**3, x)","F",0
84,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c))**3,x)","\int \frac{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((e*cot(c + d*x))**(3/2)/(a + b*cot(c + d*x))**3, x)","F",0
85,0,0,0,0.000000," ","integrate((e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c))**3,x)","\int \frac{\sqrt{e \cot{\left(c + d x \right)}}}{\left(a + b \cot{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(e*cot(c + d*x))/(a + b*cot(c + d*x))**3, x)","F",0
86,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(1/2)/(a+b*cot(d*x+c))**3,x)","\int \frac{1}{\sqrt{e \cot{\left(c + d x \right)}} \left(a + b \cot{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/(sqrt(e*cot(c + d*x))*(a + b*cot(c + d*x))**3), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(e*cot(d*x+c))**(3/2)/(a+b*cot(d*x+c))**3,x)","\int \frac{1}{\left(e \cot{\left(c + d x \right)}\right)^{\frac{3}{2}} \left(a + b \cot{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(1/((e*cot(c + d*x))**(3/2)*(a + b*cot(c + d*x))**3), x)","F",0
88,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**n,x)","\int \left(a + b \cot{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((a + b*cot(c + d*x))**n, x)","F",0
89,0,0,0,0.000000," ","integrate((a+b*cot(f*x+e))**m*(d*tan(f*x+e))**n,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{n} \left(a + b \cot{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((d*tan(e + f*x))**n*(a + b*cot(e + f*x))**m, x)","F",0
90,0,0,0,0.000000," ","integrate((1+I*cot(d*x+c))/(a+b*cot(d*x+c))**(1/2),x)","i \left(\int \left(- \frac{i}{\sqrt{a + b \cot{\left(c + d x \right)}}}\right)\, dx + \int \frac{\cot{\left(c + d x \right)}}{\sqrt{a + b \cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"I*(Integral(-I/sqrt(a + b*cot(c + d*x)), x) + Integral(cot(c + d*x)/sqrt(a + b*cot(c + d*x)), x))","F",0
91,0,0,0,0.000000," ","integrate((1-I*cot(d*x+c))/(a+b*cot(d*x+c))**(1/2),x)","- i \left(\int \frac{i}{\sqrt{a + b \cot{\left(c + d x \right)}}}\, dx + \int \frac{\cot{\left(c + d x \right)}}{\sqrt{a + b \cot{\left(c + d x \right)}}}\, dx\right)"," ",0,"-I*(Integral(I/sqrt(a + b*cot(c + d*x)), x) + Integral(cot(c + d*x)/sqrt(a + b*cot(c + d*x)), x))","F",0
92,1,534,0,1.109183," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \cot{\left(c \right)}\right)}{\cot{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{\frac{A \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + B x}{b} & \text{for}\: a = 0 \\- \frac{i A d x \cot{\left(c + d x \right)}}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} - \frac{A d x}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} + \frac{i A}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} - \frac{B d x \cot{\left(c + d x \right)}}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} + \frac{i B d x}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} - \frac{B}{- 2 b d \cot{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\\frac{i A d x \cot{\left(c + d x \right)}}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} - \frac{A d x}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} - \frac{i A}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} - \frac{B d x \cot{\left(c + d x \right)}}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} - \frac{i B d x}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} - \frac{B}{- 2 b d \cot{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{x \left(A + B \cot{\left(c \right)}\right)}{a + b \cot{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 A a d x}{2 a^{2} d + 2 b^{2} d} - \frac{2 A b \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{A b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 B a \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 B b d x}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*cot(c))/cot(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((A*log(tan(c + d*x)**2 + 1)/(2*d) + B*x)/b, Eq(a, 0)), (-I*A*d*x*cot(c + d*x)/(-2*b*d*cot(c + d*x) + 2*I*b*d) - A*d*x/(-2*b*d*cot(c + d*x) + 2*I*b*d) + I*A/(-2*b*d*cot(c + d*x) + 2*I*b*d) - B*d*x*cot(c + d*x)/(-2*b*d*cot(c + d*x) + 2*I*b*d) + I*B*d*x/(-2*b*d*cot(c + d*x) + 2*I*b*d) - B/(-2*b*d*cot(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (I*A*d*x*cot(c + d*x)/(-2*b*d*cot(c + d*x) - 2*I*b*d) - A*d*x/(-2*b*d*cot(c + d*x) - 2*I*b*d) - I*A/(-2*b*d*cot(c + d*x) - 2*I*b*d) - B*d*x*cot(c + d*x)/(-2*b*d*cot(c + d*x) - 2*I*b*d) - I*B*d*x/(-2*b*d*cot(c + d*x) - 2*I*b*d) - B/(-2*b*d*cot(c + d*x) - 2*I*b*d), Eq(a, I*b)), (x*(A + B*cot(c))/(a + b*cot(c)), Eq(d, 0)), (2*A*a*d*x/(2*a**2*d + 2*b**2*d) - 2*A*b*log(tan(c + d*x) + b/a)/(2*a**2*d + 2*b**2*d) + A*b*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*B*a*log(tan(c + d*x) + b/a)/(2*a**2*d + 2*b**2*d) - B*a*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*B*b*d*x/(2*a**2*d + 2*b**2*d), True))","A",0
93,1,3966,0,4.232193," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \cot{\left(c \right)}\right)}{\cot^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- A x + \frac{A \tan{\left(c + d x \right)}}{d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d}}{b^{2}} & \text{for}\: a = 0 \\\frac{A d x \cot^{2}{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A d x \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{A d x}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{A \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B d x \cot^{2}{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B d x \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B d x}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - i b \\\frac{A d x \cot^{2}{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i A d x \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{A d x}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{A \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i A}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} + \frac{i B d x \cot^{2}{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 B d x \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B d x}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} - \frac{i B \cot{\left(c + d x \right)}}{- 4 b^{2} d \cot^{2}{\left(c + d x \right)} - 8 i b^{2} d \cot{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = i b \\\frac{A d x \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 A d x \tan^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{4 A d x \tan{\left(c + d x \right)} \cot{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 A d x \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{A d x}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{A \tan{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} - \frac{5 A \tan{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} - \frac{4 A \cot{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{2 B d x \tan^{2}{\left(c + d x \right)} \cot{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{2 B d x \tan{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} - \frac{2 B d x \tan{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} - \frac{2 B d x \cot{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 B \tan^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{B \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} + \frac{2 B}{8 b^{2} d \tan^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)} - 16 b^{2} d \tan{\left(c + d x \right)} \cot{\left(c + d x \right)} + 8 b^{2} d} & \text{for}\: a = - \frac{b}{\tan{\left(c + d x \right)}} \\\frac{x \left(A + B \cot{\left(c \right)}\right)}{\left(a + b \cot{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 A a^{4} d x \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 A a^{3} b d x}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{4 A a^{3} b \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 A a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 A a^{2} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{4 A a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 A a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 A a^{2} b^{2}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 A a b^{3} d x}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 A b^{4}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 B a^{4} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{4 B a^{3} b d x \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 B a^{3} b \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 B a^{3} b}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{4 B a^{2} b^{2} d x}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 B a^{2} b^{2} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} - \frac{2 B a b^{3} \log{\left(\tan{\left(c + d x \right)} + \frac{b}{a} \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} + \frac{2 B a b^{3}}{2 a^{6} d \tan{\left(c + d x \right)} + 2 a^{5} b d + 4 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 2 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*cot(c))/cot(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-A*x + A*tan(c + d*x)/d + B*log(tan(c + d*x)**2 + 1)/(2*d))/b**2, Eq(a, 0)), (A*d*x*cot(c + d*x)**2/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - 2*I*A*d*x*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - A*d*x/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - A*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) + 2*I*A/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - I*B*d*x*cot(c + d*x)**2/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - 2*B*d*x*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) + I*B*d*x/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) + I*B*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 + 8*I*b**2*d*cot(c + d*x) + 4*b**2*d), Eq(a, -I*b)), (A*d*x*cot(c + d*x)**2/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) + 2*I*A*d*x*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - A*d*x/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - A*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - 2*I*A/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) + I*B*d*x*cot(c + d*x)**2/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - 2*B*d*x*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - I*B*d*x/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d) - I*B*cot(c + d*x)/(-4*b**2*d*cot(c + d*x)**2 - 8*I*b**2*d*cot(c + d*x) + 4*b**2*d), Eq(a, I*b)), (A*d*x*tan(c + d*x)**2*cot(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 3*A*d*x*tan(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 4*A*d*x*tan(c + d*x)*cot(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 3*A*d*x*cot(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + A*d*x/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + A*tan(c + d*x)*cot(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) - 5*A*tan(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) - 4*A*cot(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 2*B*d*x*tan(c + d*x)**2*cot(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 2*B*d*x*tan(c + d*x)*cot(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) - 2*B*d*x*tan(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) - 2*B*d*x*cot(c + d*x)/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 3*B*tan(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + B*cot(c + d*x)**2/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d) + 2*B/(8*b**2*d*tan(c + d*x)**2*cot(c + d*x)**2 - 16*b**2*d*tan(c + d*x)*cot(c + d*x) + 8*b**2*d), Eq(a, -b/tan(c + d*x))), (x*(A + B*cot(c))/(a + b*cot(c))**2, Eq(d, 0)), (2*A*a**4*d*x*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*A*a**3*b*d*x/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 4*A*a**3*b*log(tan(c + d*x) + b/a)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*A*a**3*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*A*a**2*b**2*d*x*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 4*A*a**2*b**2*log(tan(c + d*x) + b/a)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*A*a**2*b**2*log(tan(c + d*x)**2 + 1)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*A*a**2*b**2/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*A*a*b**3*d*x/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*A*b**4/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*B*a**4*log(tan(c + d*x) + b/a)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - B*a**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 4*B*a**3*b*d*x*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*B*a**3*b*log(tan(c + d*x) + b/a)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - B*a**3*b*log(tan(c + d*x)**2 + 1)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*B*a**3*b/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 4*B*a**2*b**2*d*x/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*B*a**2*b**2*log(tan(c + d*x) + b/a)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + B*a**2*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) - 2*B*a*b**3*log(tan(c + d*x) + b/a)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + B*a*b**3*log(tan(c + d*x)**2 + 1)/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d) + 2*B*a*b**3/(2*a**6*d*tan(c + d*x) + 2*a**5*b*d + 4*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 2*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d), True))","A",0
94,-2,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
95,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**(5/2)*(A+B*cot(d*x+c)),x)","\int \left(A + B \cot{\left(c + d x \right)}\right) \left(a + b \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))*(a + b*cot(c + d*x))**(5/2), x)","F",0
96,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**(3/2)*(A+B*cot(d*x+c)),x)","\int \left(A + B \cot{\left(c + d x \right)}\right) \left(a + b \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))*(a + b*cot(c + d*x))**(3/2), x)","F",0
97,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c))**(1/2)*(A+B*cot(d*x+c)),x)","\int \left(A + B \cot{\left(c + d x \right)}\right) \sqrt{a + b \cot{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))*sqrt(a + b*cot(c + d*x)), x)","F",0
98,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))**(5/2),x)","- \int a^{3} \sqrt{a + b \cot{\left(c + d x \right)}}\, dx - \int \left(- b^{3} \sqrt{a + b \cot{\left(c + d x \right)}} \cot^{3}{\left(c + d x \right)}\right)\, dx - \int \left(- a b^{2} \sqrt{a + b \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\right)\, dx - \int a^{2} b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx"," ",0,"-Integral(a**3*sqrt(a + b*cot(c + d*x)), x) - Integral(-b**3*sqrt(a + b*cot(c + d*x))*cot(c + d*x)**3, x) - Integral(-a*b**2*sqrt(a + b*cot(c + d*x))*cot(c + d*x)**2, x) - Integral(a**2*b*sqrt(a + b*cot(c + d*x))*cot(c + d*x), x)","F",0
99,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))**(3/2),x)","- \int a^{2} \sqrt{a + b \cot{\left(c + d x \right)}}\, dx - \int \left(- b^{2} \sqrt{a + b \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(a**2*sqrt(a + b*cot(c + d*x)), x) - Integral(-b**2*sqrt(a + b*cot(c + d*x))*cot(c + d*x)**2, x)","F",0
100,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))*(a+b*cot(d*x+c))**(1/2),x)","- \int a \sqrt{a + b \cot{\left(c + d x \right)}}\, dx - \int \left(- b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}\right)\, dx"," ",0,"-Integral(a*sqrt(a + b*cot(c + d*x)), x) - Integral(-b*sqrt(a + b*cot(c + d*x))*cot(c + d*x), x)","F",0
101,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))**(1/2),x)","\int \frac{A + B \cot{\left(c + d x \right)}}{\sqrt{a + b \cot{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))/sqrt(a + b*cot(c + d*x)), x)","F",0
102,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))**(3/2),x)","\int \frac{A + B \cot{\left(c + d x \right)}}{\left(a + b \cot{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))/(a + b*cot(c + d*x))**(3/2), x)","F",0
103,0,0,0,0.000000," ","integrate((A+B*cot(d*x+c))/(a+b*cot(d*x+c))**(5/2),x)","\int \frac{A + B \cot{\left(c + d x \right)}}{\left(a + b \cot{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*cot(c + d*x))/(a + b*cot(c + d*x))**(5/2), x)","F",0
104,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))**(1/2),x)","- \int \frac{a}{\sqrt{a + b \cot{\left(c + d x \right)}}}\, dx - \int \left(- \frac{b \cot{\left(c + d x \right)}}{\sqrt{a + b \cot{\left(c + d x \right)}}}\right)\, dx"," ",0,"-Integral(a/sqrt(a + b*cot(c + d*x)), x) - Integral(-b*cot(c + d*x)/sqrt(a + b*cot(c + d*x)), x)","F",0
105,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))**(3/2),x)","- \int \frac{a}{a \sqrt{a + b \cot{\left(c + d x \right)}} + b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}}\, dx - \int \left(- \frac{b \cot{\left(c + d x \right)}}{a \sqrt{a + b \cot{\left(c + d x \right)}} + b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)}}\right)\, dx"," ",0,"-Integral(a/(a*sqrt(a + b*cot(c + d*x)) + b*sqrt(a + b*cot(c + d*x))*cot(c + d*x)), x) - Integral(-b*cot(c + d*x)/(a*sqrt(a + b*cot(c + d*x)) + b*sqrt(a + b*cot(c + d*x))*cot(c + d*x)), x)","F",0
106,0,0,0,0.000000," ","integrate((-a+b*cot(d*x+c))/(a+b*cot(d*x+c))**(5/2),x)","- \int \frac{a}{a^{2} \sqrt{a + b \cot{\left(c + d x \right)}} + 2 a b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)} + b^{2} \sqrt{a + b \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}}\, dx - \int \left(- \frac{b \cot{\left(c + d x \right)}}{a^{2} \sqrt{a + b \cot{\left(c + d x \right)}} + 2 a b \sqrt{a + b \cot{\left(c + d x \right)}} \cot{\left(c + d x \right)} + b^{2} \sqrt{a + b \cot{\left(c + d x \right)}} \cot^{2}{\left(c + d x \right)}}\right)\, dx"," ",0,"-Integral(a/(a**2*sqrt(a + b*cot(c + d*x)) + 2*a*b*sqrt(a + b*cot(c + d*x))*cot(c + d*x) + b**2*sqrt(a + b*cot(c + d*x))*cot(c + d*x)**2), x) - Integral(-b*cot(c + d*x)/(a**2*sqrt(a + b*cot(c + d*x)) + 2*a*b*sqrt(a + b*cot(c + d*x))*cot(c + d*x) + b**2*sqrt(a + b*cot(c + d*x))*cot(c + d*x)**2), x)","F",0
