1,0,0,0,0.000000," ","integrate((a*sin(x)**2)**(5/2),x)","\int \left(a \sin^{2}{\left(x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*sin(x)**2)**(5/2), x)","F",0
2,0,0,0,0.000000," ","integrate((a*sin(x)**2)**(3/2),x)","\int \left(a \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*sin(x)**2)**(3/2), x)","F",0
3,1,20,0,0.579085," ","integrate((a*sin(x)**2)**(1/2),x)","- \frac{\sqrt{a} \sqrt{\sin^{2}{\left(x \right)}} \cos{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"-sqrt(a)*sqrt(sin(x)**2)*cos(x)/sin(x)","A",0
4,0,0,0,0.000000," ","integrate(1/(a*sin(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{a \sin^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*sin(x)**2), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(a*sin(x)**2)**(3/2),x)","\int \frac{1}{\left(a \sin^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(x)**2)**(-3/2), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(a*sin(x)**2)**(5/2),x)","\int \frac{1}{\left(a \sin^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(x)**2)**(-5/2), x)","F",0
7,-1,0,0,0.000000," ","integrate((a*sin(x)**3)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,-1,0,0,0.000000," ","integrate((a*sin(x)**3)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,0,0,0,0.000000," ","integrate((a*sin(x)**3)**(1/2),x)","\int \sqrt{a \sin^{3}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a*sin(x)**3), x)","F",0
10,0,0,0,0.000000," ","integrate(1/(a*sin(x)**3)**(1/2),x)","\int \frac{1}{\sqrt{a \sin^{3}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*sin(x)**3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(a*sin(x)**3)**(3/2),x)","\int \frac{1}{\left(a \sin^{3}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(x)**3)**(-3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(a*sin(x)**3)**(5/2),x)","\int \frac{1}{\left(a \sin^{3}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(x)**3)**(-5/2), x)","F",0
13,0,0,0,0.000000," ","integrate((a*sin(x)**4)**(5/2),x)","\int \left(a \sin^{4}{\left(x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*sin(x)**4)**(5/2), x)","F",0
14,0,0,0,0.000000," ","integrate((a*sin(x)**4)**(3/2),x)","\int \left(a \sin^{4}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*sin(x)**4)**(3/2), x)","F",0
15,0,0,0,0.000000," ","integrate((a*sin(x)**4)**(1/2),x)","\int \sqrt{a \sin^{4}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a*sin(x)**4), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(a*sin(x)**4)**(1/2),x)","\int \frac{1}{\sqrt{a \sin^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a*sin(x)**4), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(a*sin(x)**4)**(3/2),x)","\int \frac{1}{\left(a \sin^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*sin(x)**4)**(-3/2), x)","F",0
18,0,0,0,0.000000," ","integrate(1/(a*sin(x)**4)**(5/2),x)","\int \frac{1}{\left(a \sin^{4}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*sin(x)**4)**(-5/2), x)","F",0
19,-1,0,0,0.000000," ","integrate((c*sin(b*x+a)**m)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,0,0,0,0.000000," ","integrate((c*sin(b*x+a)**m)**(3/2),x)","\int \left(c \sin^{m}{\left(a + b x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*sin(a + b*x)**m)**(3/2), x)","F",0
21,0,0,0,0.000000," ","integrate((c*sin(b*x+a)**m)**(1/2),x)","\int \sqrt{c \sin^{m}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x)**m), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)**m)**(1/2),x)","\int \frac{1}{\sqrt{c \sin^{m}{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*sin(a + b*x)**m), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)**m)**(3/2),x)","\int \frac{1}{\left(c \sin^{m}{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x)**m)**(-3/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a)**m)**(5/2),x)","\int \frac{1}{\left(c \sin^{m}{\left(a + b x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x)**m)**(-5/2), x)","F",0
25,0,0,0,0.000000," ","integrate((b*sin(d*x+c)**n)**p,x)","\int \left(b \sin^{n}{\left(c + d x \right)}\right)^{p}\, dx"," ",0,"Integral((b*sin(c + d*x)**n)**p, x)","F",0
26,0,0,0,0.000000," ","integrate((c*sin(b*x+a)**2)**p,x)","\int \left(c \sin^{2}{\left(a + b x \right)}\right)^{p}\, dx"," ",0,"Integral((c*sin(a + b*x)**2)**p, x)","F",0
27,0,0,0,0.000000," ","integrate((c*sin(b*x+a)**3)**p,x)","\int \left(c \sin^{3}{\left(a + b x \right)}\right)^{p}\, dx"," ",0,"Integral((c*sin(a + b*x)**3)**p, x)","F",0
28,0,0,0,0.000000," ","integrate((c*sin(b*x+a)**4)**p,x)","\int \left(c \sin^{4}{\left(a + b x \right)}\right)^{p}\, dx"," ",0,"Integral((c*sin(a + b*x)**4)**p, x)","F",0
29,1,61,0,2.106636," ","integrate((c*sin(b*x+a)**n)**(1/n),x)","\begin{cases} x \left(c \sin^{n}{\left(a \right)}\right)^{\frac{1}{n}} & \text{for}\: b = 0 \\x \left(0^{n} c\right)^{\frac{1}{n}} & \text{for}\: a = - b x \vee a = - b x + \pi \\- \frac{c^{\frac{1}{n}} \left(\sin^{n}{\left(a + b x \right)}\right)^{\frac{1}{n}} \cos{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c*sin(a)**n)**(1/n), Eq(b, 0)), (x*(0**n*c)**(1/n), Eq(a, -b*x) | Eq(a, -b*x + pi)), (-c**(1/n)*(sin(a + b*x)**n)**(1/n)*cos(a + b*x)/(b*sin(a + b*x)), True))","A",0
30,0,0,0,0.000000," ","integrate((a*(b*sin(d*x+c))**p)**n,x)","\int \left(a \left(b \sin{\left(c + d x \right)}\right)^{p}\right)^{n}\, dx"," ",0,"Integral((a*(b*sin(c + d*x))**p)**n, x)","F",0
31,1,15,0,0.099183," ","integrate(a-a*sin(x)**2,x)","a x - a \left(\frac{x}{2} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}\right)"," ",0,"a*x - a*(x/2 - sin(x)*cos(x)/2)","A",0
32,1,110,0,1.121519," ","integrate((a-a*sin(x)**2)**2,x)","\frac{3 a^{2} x \sin^{4}{\left(x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} - a^{2} x \sin^{2}{\left(x \right)} + \frac{3 a^{2} x \cos^{4}{\left(x \right)}}{8} - a^{2} x \cos^{2}{\left(x \right)} + a^{2} x - \frac{5 a^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{3 a^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} + a^{2} \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"3*a**2*x*sin(x)**4/8 + 3*a**2*x*sin(x)**2*cos(x)**2/4 - a**2*x*sin(x)**2 + 3*a**2*x*cos(x)**4/8 - a**2*x*cos(x)**2 + a**2*x - 5*a**2*sin(x)**3*cos(x)/8 - 3*a**2*sin(x)*cos(x)**3/8 + a**2*sin(x)*cos(x)","B",0
33,1,233,0,2.663400," ","integrate((a-a*sin(x)**2)**3,x)","- \frac{5 a^{3} x \sin^{6}{\left(x \right)}}{16} - \frac{15 a^{3} x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(x \right)}}{8} - \frac{15 a^{3} x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{16} + \frac{9 a^{3} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} - \frac{3 a^{3} x \sin^{2}{\left(x \right)}}{2} - \frac{5 a^{3} x \cos^{6}{\left(x \right)}}{16} + \frac{9 a^{3} x \cos^{4}{\left(x \right)}}{8} - \frac{3 a^{3} x \cos^{2}{\left(x \right)}}{2} + a^{3} x + \frac{11 a^{3} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{16} + \frac{5 a^{3} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{6} - \frac{15 a^{3} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 a^{3} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{16} - \frac{9 a^{3} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} + \frac{3 a^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"-5*a**3*x*sin(x)**6/16 - 15*a**3*x*sin(x)**4*cos(x)**2/16 + 9*a**3*x*sin(x)**4/8 - 15*a**3*x*sin(x)**2*cos(x)**4/16 + 9*a**3*x*sin(x)**2*cos(x)**2/4 - 3*a**3*x*sin(x)**2/2 - 5*a**3*x*cos(x)**6/16 + 9*a**3*x*cos(x)**4/8 - 3*a**3*x*cos(x)**2/2 + a**3*x + 11*a**3*sin(x)**5*cos(x)/16 + 5*a**3*sin(x)**3*cos(x)**3/6 - 15*a**3*sin(x)**3*cos(x)/8 + 5*a**3*sin(x)*cos(x)**5/16 - 9*a**3*sin(x)*cos(x)**3/8 + 3*a**3*sin(x)*cos(x)/2","B",0
34,1,376,0,7.316841," ","integrate((a-a*sin(x)**2)**4,x)","\frac{35 a^{4} x \sin^{8}{\left(x \right)}}{128} + \frac{35 a^{4} x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} - \frac{5 a^{4} x \sin^{6}{\left(x \right)}}{4} + \frac{105 a^{4} x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{64} - \frac{15 a^{4} x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{9 a^{4} x \sin^{4}{\left(x \right)}}{4} + \frac{35 a^{4} x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{32} - \frac{15 a^{4} x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{9 a^{4} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} - 2 a^{4} x \sin^{2}{\left(x \right)} + \frac{35 a^{4} x \cos^{8}{\left(x \right)}}{128} - \frac{5 a^{4} x \cos^{6}{\left(x \right)}}{4} + \frac{9 a^{4} x \cos^{4}{\left(x \right)}}{4} - 2 a^{4} x \cos^{2}{\left(x \right)} + a^{4} x - \frac{93 a^{4} \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{128} - \frac{511 a^{4} \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{384} + \frac{11 a^{4} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{385 a^{4} \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{384} + \frac{10 a^{4} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{15 a^{4} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{35 a^{4} \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{128} + \frac{5 a^{4} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{4} - \frac{9 a^{4} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{4} + 2 a^{4} \sin{\left(x \right)} \cos{\left(x \right)}"," ",0,"35*a**4*x*sin(x)**8/128 + 35*a**4*x*sin(x)**6*cos(x)**2/32 - 5*a**4*x*sin(x)**6/4 + 105*a**4*x*sin(x)**4*cos(x)**4/64 - 15*a**4*x*sin(x)**4*cos(x)**2/4 + 9*a**4*x*sin(x)**4/4 + 35*a**4*x*sin(x)**2*cos(x)**6/32 - 15*a**4*x*sin(x)**2*cos(x)**4/4 + 9*a**4*x*sin(x)**2*cos(x)**2/2 - 2*a**4*x*sin(x)**2 + 35*a**4*x*cos(x)**8/128 - 5*a**4*x*cos(x)**6/4 + 9*a**4*x*cos(x)**4/4 - 2*a**4*x*cos(x)**2 + a**4*x - 93*a**4*sin(x)**7*cos(x)/128 - 511*a**4*sin(x)**5*cos(x)**3/384 + 11*a**4*sin(x)**5*cos(x)/4 - 385*a**4*sin(x)**3*cos(x)**5/384 + 10*a**4*sin(x)**3*cos(x)**3/3 - 15*a**4*sin(x)**3*cos(x)/4 - 35*a**4*sin(x)*cos(x)**7/128 + 5*a**4*sin(x)*cos(x)**5/4 - 9*a**4*sin(x)*cos(x)**3/4 + 2*a**4*sin(x)*cos(x)","B",0
35,1,314,0,35.438357," ","integrate(sin(d*x+c)**7/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{160 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 25 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 20 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 5 a d} - \frac{128 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 25 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 20 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 5 a d} - \frac{32}{5 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 25 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 20 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 5 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{7}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-160*tan(c/2 + d*x/2)**4/(5*a*d*tan(c/2 + d*x/2)**12 + 20*a*d*tan(c/2 + d*x/2)**10 + 25*a*d*tan(c/2 + d*x/2)**8 - 25*a*d*tan(c/2 + d*x/2)**4 - 20*a*d*tan(c/2 + d*x/2)**2 - 5*a*d) - 128*tan(c/2 + d*x/2)**2/(5*a*d*tan(c/2 + d*x/2)**12 + 20*a*d*tan(c/2 + d*x/2)**10 + 25*a*d*tan(c/2 + d*x/2)**8 - 25*a*d*tan(c/2 + d*x/2)**4 - 20*a*d*tan(c/2 + d*x/2)**2 - 5*a*d) - 32/(5*a*d*tan(c/2 + d*x/2)**12 + 20*a*d*tan(c/2 + d*x/2)**10 + 25*a*d*tan(c/2 + d*x/2)**8 - 25*a*d*tan(c/2 + d*x/2)**4 - 20*a*d*tan(c/2 + d*x/2)**2 - 5*a*d), Ne(d, 0)), (x*sin(c)**7/(-a*sin(c)**2 + a), True))","A",0
36,1,143,0,14.348459," ","integrate(sin(d*x+c)**5/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{32 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a d} - \frac{16}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{5}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**8 + 6*a*d*tan(c/2 + d*x/2)**6 - 6*a*d*tan(c/2 + d*x/2)**2 - 3*a*d) - 16/(3*a*d*tan(c/2 + d*x/2)**8 + 6*a*d*tan(c/2 + d*x/2)**6 - 6*a*d*tan(c/2 + d*x/2)**2 - 3*a*d), Ne(d, 0)), (x*sin(c)**5/(-a*sin(c)**2 + a), True))","A",0
37,1,36,0,6.934512," ","integrate(sin(d*x+c)**3/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{4}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4/(a*d*tan(c/2 + d*x/2)**4 - a*d), Ne(d, 0)), (x*sin(c)**3/(-a*sin(c)**2 + a), True))","A",0
38,1,34,0,2.484521," ","integrate(sin(d*x+c)/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{2}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(a*d*tan(c/2 + d*x/2)**2 - a*d), Ne(d, 0)), (x*sin(c)/(-a*sin(c)**2 + a), True))","A",0
39,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)/(sin(c + d*x)**2 - 1), x)/a","F",0
40,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)**3/(sin(c + d*x)**2 - 1), x)/a","F",0
41,0,0,0,0.000000," ","integrate(csc(d*x+c)**5/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc^{5}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)**5/(sin(c + d*x)**2 - 1), x)/a","F",0
42,1,1161,0,28.492954," ","integrate(sin(d*x+c)**6/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{45 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{30 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} + \frac{30 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} + \frac{45 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} + \frac{15 d x}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{30 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{80 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{36 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{80 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} - \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 16 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 16 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 24 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 8 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{6}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**10/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 45*d*x*tan(c/2 + d*x/2)**8/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 30*d*x*tan(c/2 + d*x/2)**6/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) + 30*d*x*tan(c/2 + d*x/2)**4/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) + 45*d*x*tan(c/2 + d*x/2)**2/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) + 15*d*x/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 30*tan(c/2 + d*x/2)**9/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 80*tan(c/2 + d*x/2)**7/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 36*tan(c/2 + d*x/2)**5/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 80*tan(c/2 + d*x/2)**3/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d) - 30*tan(c/2 + d*x/2)/(8*a*d*tan(c/2 + d*x/2)**10 + 24*a*d*tan(c/2 + d*x/2)**8 + 16*a*d*tan(c/2 + d*x/2)**6 - 16*a*d*tan(c/2 + d*x/2)**4 - 24*a*d*tan(c/2 + d*x/2)**2 - 8*a*d), Ne(d, 0)), (x*sin(c)**6/(-a*sin(c)**2 + a), True))","A",0
43,1,502,0,12.748316," ","integrate(sin(d*x+c)**4/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{3 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} - \frac{3 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} + \frac{3 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} + \frac{3 d x}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} - \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} - \frac{4 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 2 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*d*x*tan(c/2 + d*x/2)**6/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) - 3*d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) + 3*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) + 3*d*x/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) - 6*tan(c/2 + d*x/2)**5/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) - 4*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d) - 6*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**6 + 2*a*d*tan(c/2 + d*x/2)**4 - 2*a*d*tan(c/2 + d*x/2)**2 - 2*a*d), Ne(d, 0)), (x*sin(c)**4/(-a*sin(c)**2 + a), True))","A",0
44,1,100,0,4.572306," ","integrate(sin(d*x+c)**2/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} + \frac{d x}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} - \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)}}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d*x*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**2 - a*d) + d*x/(a*d*tan(c/2 + d*x/2)**2 - a*d) - 2*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 - a*d), Ne(d, 0)), (x*sin(c)**2/(-a*sin(c)**2 + a), True))","A",0
45,1,41,0,1.887903," ","integrate(1/(a-a*sin(d*x+c)**2),x)","\begin{cases} - \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - a d} & \text{for}\: d \neq 0 \\\frac{x}{- a \sin^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**2 - a*d), Ne(d, 0)), (x/(-a*sin(c)**2 + a), True))","A",0
46,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)**2/(sin(c + d*x)**2 - 1), x)/a","F",0
47,0,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)**4/(sin(c + d*x)**2 - 1), x)/a","F",0
48,0,0,0,0.000000," ","integrate(csc(d*x+c)**6/(a-a*sin(d*x+c)**2),x)","- \frac{\int \frac{\csc^{6}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} - 1}\, dx}{a}"," ",0,"-Integral(csc(c + d*x)**6/(sin(c + d*x)**2 - 1), x)/a","F",0
49,1,156,0,106.836916," ","integrate(sin(d*x+c)**7/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{96 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{32}{3 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{7}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-96*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**12 - 9*a**2*d*tan(c/2 + d*x/2)**8 + 9*a**2*d*tan(c/2 + d*x/2)**4 - 3*a**2*d) + 32/(3*a**2*d*tan(c/2 + d*x/2)**12 - 9*a**2*d*tan(c/2 + d*x/2)**8 + 9*a**2*d*tan(c/2 + d*x/2)**4 - 3*a**2*d), Ne(d, 0)), (x*sin(c)**7/(-a*sin(c)**2 + a)**2, True))","A",0
50,1,156,0,49.027256," ","integrate(sin(d*x+c)**5/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{32 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{16}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{5}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-32*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**8 - 6*a**2*d*tan(c/2 + d*x/2)**6 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 16/(3*a**2*d*tan(c/2 + d*x/2)**8 - 6*a**2*d*tan(c/2 + d*x/2)**6 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x*sin(c)**5/(-a*sin(c)**2 + a)**2, True))","A",0
51,1,156,0,20.998589," ","integrate(sin(d*x+c)**3/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{12 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{4}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 4/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x*sin(c)**3/(-a*sin(c)**2 + a)**2, True))","A",0
52,1,156,0,9.724267," ","integrate(sin(d*x+c)/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{6 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} - \frac{2}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) - 2/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x*sin(c)/(-a*sin(c)**2 + a)**2, True))","A",0
53,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a-a*sin(d*x+c)**2)**2,x)","\frac{\int \frac{\csc{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} - 2 \sin^{2}{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)/(sin(c + d*x)**4 - 2*sin(c + d*x)**2 + 1), x)/a**2","F",0
54,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a-a*sin(d*x+c)**2)**2,x)","\frac{\int \frac{\csc^{3}{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} - 2 \sin^{2}{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)**3/(sin(c + d*x)**4 - 2*sin(c + d*x)**2 + 1), x)/a**2","F",0
55,1,1275,0,72.425427," ","integrate(sin(d*x+c)**6/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{15 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{30 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} + \frac{30 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} + \frac{15 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{15 d x}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} + \frac{30 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{40 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{44 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} - \frac{40 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 6 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{6}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c/2 + d*x/2)**10/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 15*d*x*tan(c/2 + d*x/2)**8/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 30*d*x*tan(c/2 + d*x/2)**6/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) + 30*d*x*tan(c/2 + d*x/2)**4/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) + 15*d*x*tan(c/2 + d*x/2)**2/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 15*d*x/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) + 30*tan(c/2 + d*x/2)**9/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 40*tan(c/2 + d*x/2)**7/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 44*tan(c/2 + d*x/2)**5/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) - 40*tan(c/2 + d*x/2)**3/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d) + 30*tan(c/2 + d*x/2)/(6*a**2*d*tan(c/2 + d*x/2)**10 - 6*a**2*d*tan(c/2 + d*x/2)**8 - 12*a**2*d*tan(c/2 + d*x/2)**6 + 12*a**2*d*tan(c/2 + d*x/2)**4 + 6*a**2*d*tan(c/2 + d*x/2)**2 - 6*a**2*d), Ne(d, 0)), (x*sin(c)**6/(-a*sin(c)**2 + a)**2, True))","A",0
56,1,551,0,29.677804," ","integrate(sin(d*x+c)**4/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} \frac{3 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} - \frac{9 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{9 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} - \frac{3 d x}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} - \frac{20 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) - 9*d*x*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 9*d*x*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) - 3*d*x/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 6*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) - 20*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 6*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x*sin(c)**4/(-a*sin(c)**2 + a)**2, True))","A",0
57,1,94,0,12.970652," ","integrate(sin(d*x+c)**2/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{8 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)}}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x*sin(c)**2/(-a*sin(c)**2 + a)**2, True))","A",0
58,1,238,0,5.171603," ","integrate(1/(a-a*sin(d*x+c)**2)**2,x)","\begin{cases} - \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} + \frac{4 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} - 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(- a \sin^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) + 4*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d) - 6*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**6 - 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 - 3*a**2*d), Ne(d, 0)), (x/(-a*sin(c)**2 + a)**2, True))","A",0
59,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a-a*sin(d*x+c)**2)**2,x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} - 2 \sin^{2}{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)**2/(sin(c + d*x)**4 - 2*sin(c + d*x)**2 + 1), x)/a**2","F",0
60,0,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a-a*sin(d*x+c)**2)**2,x)","\frac{\int \frac{\csc^{4}{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} - 2 \sin^{2}{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)**4/(sin(c + d*x)**4 - 2*sin(c + d*x)**2 + 1), x)/a**2","F",0
61,1,362,0,7.346830," ","integrate(1/(a-a*sin(x)**2)**3,x)","- \frac{30 \tan^{9}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} - 75 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} - 150 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} - 15 a^{3}} + \frac{40 \tan^{7}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} - 75 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} - 150 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} - 15 a^{3}} - \frac{116 \tan^{5}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} - 75 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} - 150 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} - 15 a^{3}} + \frac{40 \tan^{3}{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} - 75 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} - 150 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} - 15 a^{3}} - \frac{30 \tan{\left(\frac{x}{2} \right)}}{15 a^{3} \tan^{10}{\left(\frac{x}{2} \right)} - 75 a^{3} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{3} \tan^{6}{\left(\frac{x}{2} \right)} - 150 a^{3} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{3} \tan^{2}{\left(\frac{x}{2} \right)} - 15 a^{3}}"," ",0,"-30*tan(x/2)**9/(15*a**3*tan(x/2)**10 - 75*a**3*tan(x/2)**8 + 150*a**3*tan(x/2)**6 - 150*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**2 - 15*a**3) + 40*tan(x/2)**7/(15*a**3*tan(x/2)**10 - 75*a**3*tan(x/2)**8 + 150*a**3*tan(x/2)**6 - 150*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**2 - 15*a**3) - 116*tan(x/2)**5/(15*a**3*tan(x/2)**10 - 75*a**3*tan(x/2)**8 + 150*a**3*tan(x/2)**6 - 150*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**2 - 15*a**3) + 40*tan(x/2)**3/(15*a**3*tan(x/2)**10 - 75*a**3*tan(x/2)**8 + 150*a**3*tan(x/2)**6 - 150*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**2 - 15*a**3) - 30*tan(x/2)/(15*a**3*tan(x/2)**10 - 75*a**3*tan(x/2)**8 + 150*a**3*tan(x/2)**6 - 150*a**3*tan(x/2)**4 + 75*a**3*tan(x/2)**2 - 15*a**3)","B",0
62,1,675,0,22.196022," ","integrate(1/(a-a*sin(x)**2)**4,x)","- \frac{70 \tan^{13}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} + \frac{140 \tan^{11}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} - \frac{602 \tan^{9}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} + \frac{424 \tan^{7}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} - \frac{602 \tan^{5}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} + \frac{140 \tan^{3}{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}} - \frac{70 \tan{\left(\frac{x}{2} \right)}}{35 a^{4} \tan^{14}{\left(\frac{x}{2} \right)} - 245 a^{4} \tan^{12}{\left(\frac{x}{2} \right)} + 735 a^{4} \tan^{10}{\left(\frac{x}{2} \right)} - 1225 a^{4} \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a^{4} \tan^{6}{\left(\frac{x}{2} \right)} - 735 a^{4} \tan^{4}{\left(\frac{x}{2} \right)} + 245 a^{4} \tan^{2}{\left(\frac{x}{2} \right)} - 35 a^{4}}"," ",0,"-70*tan(x/2)**13/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) + 140*tan(x/2)**11/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) - 602*tan(x/2)**9/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) + 424*tan(x/2)**7/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) - 602*tan(x/2)**5/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) + 140*tan(x/2)**3/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4) - 70*tan(x/2)/(35*a**4*tan(x/2)**14 - 245*a**4*tan(x/2)**12 + 735*a**4*tan(x/2)**10 - 1225*a**4*tan(x/2)**8 + 1225*a**4*tan(x/2)**6 - 735*a**4*tan(x/2)**4 + 245*a**4*tan(x/2)**2 - 35*a**4)","B",0
63,1,1083,0,69.506930," ","integrate(1/(a-a*sin(x)**2)**5,x)","- \frac{630 \tan^{17}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} + \frac{1680 \tan^{15}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} - \frac{9576 \tan^{13}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} + \frac{10224 \tan^{11}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} - \frac{21316 \tan^{9}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} + \frac{10224 \tan^{7}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} - \frac{9576 \tan^{5}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} + \frac{1680 \tan^{3}{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}} - \frac{630 \tan{\left(\frac{x}{2} \right)}}{315 a^{5} \tan^{18}{\left(\frac{x}{2} \right)} - 2835 a^{5} \tan^{16}{\left(\frac{x}{2} \right)} + 11340 a^{5} \tan^{14}{\left(\frac{x}{2} \right)} - 26460 a^{5} \tan^{12}{\left(\frac{x}{2} \right)} + 39690 a^{5} \tan^{10}{\left(\frac{x}{2} \right)} - 39690 a^{5} \tan^{8}{\left(\frac{x}{2} \right)} + 26460 a^{5} \tan^{6}{\left(\frac{x}{2} \right)} - 11340 a^{5} \tan^{4}{\left(\frac{x}{2} \right)} + 2835 a^{5} \tan^{2}{\left(\frac{x}{2} \right)} - 315 a^{5}}"," ",0,"-630*tan(x/2)**17/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) + 1680*tan(x/2)**15/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) - 9576*tan(x/2)**13/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) + 10224*tan(x/2)**11/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) - 21316*tan(x/2)**9/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) + 10224*tan(x/2)**7/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) - 9576*tan(x/2)**5/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) + 1680*tan(x/2)**3/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5) - 630*tan(x/2)/(315*a**5*tan(x/2)**18 - 2835*a**5*tan(x/2)**16 + 11340*a**5*tan(x/2)**14 - 26460*a**5*tan(x/2)**12 + 39690*a**5*tan(x/2)**10 - 39690*a**5*tan(x/2)**8 + 26460*a**5*tan(x/2)**6 - 11340*a**5*tan(x/2)**4 + 2835*a**5*tan(x/2)**2 - 315*a**5)","B",0
64,1,107,0,3.315218," ","integrate(sin(d*x+c)**3*(a+b*sin(d*x+c)**2),x)","\begin{cases} - \frac{a \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 a \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{b \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 b \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 b \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin^{2}{\left(c \right)}\right) \sin^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sin(c + d*x)**2*cos(c + d*x)/d - 2*a*cos(c + d*x)**3/(3*d) - b*sin(c + d*x)**4*cos(c + d*x)/d - 4*b*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*b*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a + b*sin(c)**2)*sin(c)**3, True))","A",0
65,1,58,0,0.999148," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c)**2),x)","\begin{cases} - \frac{a \cos{\left(c + d x \right)}}{d} - \frac{b \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin^{2}{\left(c \right)}\right) \sin{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*cos(c + d*x)/d - b*sin(c + d*x)**2*cos(c + d*x)/d - 2*b*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a + b*sin(c)**2)*sin(c), True))","A",0
66,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c)**2),x)","\int \left(a + b \sin^{2}{\left(c + d x \right)}\right) \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**2)*csc(c + d*x), x)","F",0
67,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*(a+b*sin(d*x+c)**2),x)","\int \left(a + b \sin^{2}{\left(c + d x \right)}\right) \csc^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**2)*csc(c + d*x)**3, x)","F",0
68,1,258,0,5.372521," ","integrate(sin(d*x+c)**4*(a+b*sin(d*x+c)**2),x)","\begin{cases} \frac{3 a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{5 b x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 b x \cos^{6}{\left(c + d x \right)}}{16} - \frac{11 b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{5 b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{5 b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin^{2}{\left(c \right)}\right) \sin^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**4/8 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a*x*cos(c + d*x)**4/8 - 5*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) + 5*b*x*sin(c + d*x)**6/16 + 15*b*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*b*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*b*x*cos(c + d*x)**6/16 - 11*b*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 5*b*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 5*b*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*sin(c)**2)*sin(c)**4, True))","A",0
69,1,158,0,1.934344," ","integrate(sin(d*x+c)**2*(a+b*sin(d*x+c)**2),x)","\begin{cases} \frac{a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a x \cos^{2}{\left(c + d x \right)}}{2} - \frac{a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} + \frac{3 b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin^{2}{\left(c \right)}\right) \sin^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**2/2 + a*x*cos(c + d*x)**2/2 - a*sin(c + d*x)*cos(c + d*x)/(2*d) + 3*b*x*sin(c + d*x)**4/8 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b*x*cos(c + d*x)**4/8 - 5*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*sin(c)**2)*sin(c)**2, True))","A",0
70,1,51,0,0.348825," ","integrate(a+b*sin(d*x+c)**2,x)","a x + b \left(\begin{cases} \frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \sin^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 - sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*sin(c)**2, True))","A",0
71,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*(a+b*sin(d*x+c)**2),x)","\int \left(a + b \sin^{2}{\left(c + d x \right)}\right) \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**2)*csc(c + d*x)**2, x)","F",0
72,0,0,0,0.000000," ","integrate(csc(d*x+c)**4*(a+b*sin(d*x+c)**2),x)","\int \left(a + b \sin^{2}{\left(c + d x \right)}\right) \csc^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**2)*csc(c + d*x)**4, x)","F",0
73,-1,0,0,0.000000," ","integrate(csc(d*x+c)**6*(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,1,15,0,0.063344," ","integrate(a+b*sin(x)**2,x)","a x + b \left(\frac{x}{2} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{2}\right)"," ",0,"a*x + b*(x/2 - sin(x)*cos(x)/2)","A",0
75,1,110,0,0.757712," ","integrate((a+b*sin(x)**2)**2,x)","a^{2} x + a b x \sin^{2}{\left(x \right)} + a b x \cos^{2}{\left(x \right)} - a b \sin{\left(x \right)} \cos{\left(x \right)} + \frac{3 b^{2} x \sin^{4}{\left(x \right)}}{8} + \frac{3 b^{2} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{3 b^{2} x \cos^{4}{\left(x \right)}}{8} - \frac{5 b^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{3 b^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8}"," ",0,"a**2*x + a*b*x*sin(x)**2 + a*b*x*cos(x)**2 - a*b*sin(x)*cos(x) + 3*b**2*x*sin(x)**4/8 + 3*b**2*x*sin(x)**2*cos(x)**2/4 + 3*b**2*x*cos(x)**4/8 - 5*b**2*sin(x)**3*cos(x)/8 - 3*b**2*sin(x)*cos(x)**3/8","B",0
76,1,246,0,2.757044," ","integrate((a+b*sin(x)**2)**3,x)","a^{3} x + \frac{3 a^{2} b x \sin^{2}{\left(x \right)}}{2} + \frac{3 a^{2} b x \cos^{2}{\left(x \right)}}{2} - \frac{3 a^{2} b \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{9 a b^{2} x \sin^{4}{\left(x \right)}}{8} + \frac{9 a b^{2} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{9 a b^{2} x \cos^{4}{\left(x \right)}}{8} - \frac{15 a b^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{9 a b^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} + \frac{5 b^{3} x \sin^{6}{\left(x \right)}}{16} + \frac{15 b^{3} x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{16} + \frac{15 b^{3} x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{16} + \frac{5 b^{3} x \cos^{6}{\left(x \right)}}{16} - \frac{11 b^{3} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{16} - \frac{5 b^{3} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{6} - \frac{5 b^{3} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{16}"," ",0,"a**3*x + 3*a**2*b*x*sin(x)**2/2 + 3*a**2*b*x*cos(x)**2/2 - 3*a**2*b*sin(x)*cos(x)/2 + 9*a*b**2*x*sin(x)**4/8 + 9*a*b**2*x*sin(x)**2*cos(x)**2/4 + 9*a*b**2*x*cos(x)**4/8 - 15*a*b**2*sin(x)**3*cos(x)/8 - 9*a*b**2*sin(x)*cos(x)**3/8 + 5*b**3*x*sin(x)**6/16 + 15*b**3*x*sin(x)**4*cos(x)**2/16 + 15*b**3*x*sin(x)**2*cos(x)**4/16 + 5*b**3*x*cos(x)**6/16 - 11*b**3*sin(x)**5*cos(x)/16 - 5*b**3*sin(x)**3*cos(x)**3/6 - 5*b**3*sin(x)*cos(x)**5/16","B",0
77,1,410,0,7.521323," ","integrate((a+b*sin(x)**2)**4,x)","a^{4} x + 2 a^{3} b x \sin^{2}{\left(x \right)} + 2 a^{3} b x \cos^{2}{\left(x \right)} - 2 a^{3} b \sin{\left(x \right)} \cos{\left(x \right)} + \frac{9 a^{2} b^{2} x \sin^{4}{\left(x \right)}}{4} + \frac{9 a^{2} b^{2} x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{2} + \frac{9 a^{2} b^{2} x \cos^{4}{\left(x \right)}}{4} - \frac{15 a^{2} b^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{9 a^{2} b^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{4} + \frac{5 a b^{3} x \sin^{6}{\left(x \right)}}{4} + \frac{15 a b^{3} x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{15 a b^{3} x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{4} + \frac{5 a b^{3} x \cos^{6}{\left(x \right)}}{4} - \frac{11 a b^{3} \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{10 a b^{3} \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - \frac{5 a b^{3} \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{4} + \frac{35 b^{4} x \sin^{8}{\left(x \right)}}{128} + \frac{35 b^{4} x \sin^{6}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} + \frac{105 b^{4} x \sin^{4}{\left(x \right)} \cos^{4}{\left(x \right)}}{64} + \frac{35 b^{4} x \sin^{2}{\left(x \right)} \cos^{6}{\left(x \right)}}{32} + \frac{35 b^{4} x \cos^{8}{\left(x \right)}}{128} - \frac{93 b^{4} \sin^{7}{\left(x \right)} \cos{\left(x \right)}}{128} - \frac{511 b^{4} \sin^{5}{\left(x \right)} \cos^{3}{\left(x \right)}}{384} - \frac{385 b^{4} \sin^{3}{\left(x \right)} \cos^{5}{\left(x \right)}}{384} - \frac{35 b^{4} \sin{\left(x \right)} \cos^{7}{\left(x \right)}}{128}"," ",0,"a**4*x + 2*a**3*b*x*sin(x)**2 + 2*a**3*b*x*cos(x)**2 - 2*a**3*b*sin(x)*cos(x) + 9*a**2*b**2*x*sin(x)**4/4 + 9*a**2*b**2*x*sin(x)**2*cos(x)**2/2 + 9*a**2*b**2*x*cos(x)**4/4 - 15*a**2*b**2*sin(x)**3*cos(x)/4 - 9*a**2*b**2*sin(x)*cos(x)**3/4 + 5*a*b**3*x*sin(x)**6/4 + 15*a*b**3*x*sin(x)**4*cos(x)**2/4 + 15*a*b**3*x*sin(x)**2*cos(x)**4/4 + 5*a*b**3*x*cos(x)**6/4 - 11*a*b**3*sin(x)**5*cos(x)/4 - 10*a*b**3*sin(x)**3*cos(x)**3/3 - 5*a*b**3*sin(x)*cos(x)**5/4 + 35*b**4*x*sin(x)**8/128 + 35*b**4*x*sin(x)**6*cos(x)**2/32 + 105*b**4*x*sin(x)**4*cos(x)**4/64 + 35*b**4*x*sin(x)**2*cos(x)**6/32 + 35*b**4*x*cos(x)**8/128 - 93*b**4*sin(x)**7*cos(x)/128 - 511*b**4*sin(x)**5*cos(x)**3/384 - 385*b**4*sin(x)**3*cos(x)**5/384 - 35*b**4*sin(x)*cos(x)**7/128","B",0
78,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)**2),x)","\int \frac{\csc{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(a + b*sin(c + d*x)**2), x)","F",0
83,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+b*sin(d*x+c)**2),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**3/(a + b*sin(c + d*x)**2), x)","F",0
84,-1,0,0,0.000000," ","integrate(csc(d*x+c)**5/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(sin(d*x+c)**8/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)**2),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a + b*sin(c + d*x)**2), x)","F",0
91,0,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a+b*sin(d*x+c)**2),x)","\int \frac{\csc^{4}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**4/(a + b*sin(c + d*x)**2), x)","F",0
92,-1,0,0,0.000000," ","integrate(csc(d*x+c)**6/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(csc(d*x+c)**8/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a+b*sin(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a+b*sin(d*x+c)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+b*sin(d*x+c)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**2)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**2)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,0,0,0,0.000000," ","integrate(sin(x)/(1+sin(x)**2)**(1/2),x)","\int \frac{\sin{\left(x \right)}}{\sqrt{\sin^{2}{\left(x \right)} + 1}}\, dx"," ",0,"Integral(sin(x)/sqrt(sin(x)**2 + 1), x)","F",0
114,0,0,0,0.000000," ","integrate(sin(x)*(1+sin(x)**2)**(1/2),x)","\int \sqrt{\sin^{2}{\left(x \right)} + 1} \sin{\left(x \right)}\, dx"," ",0,"Integral(sqrt(sin(x)**2 + 1)*sin(x), x)","F",0
115,0,0,0,0.000000," ","integrate(sin(7+3*x)/(3+sin(7+3*x)**2)**(1/2),x)","\int \frac{\sin{\left(3 x + 7 \right)}}{\sqrt{\sin^{2}{\left(3 x + 7 \right)} + 3}}\, dx"," ",0,"Integral(sin(3*x + 7)/sqrt(sin(3*x + 7)**2 + 3), x)","F",0
116,-1,0,0,0.000000," ","integrate((a-a*sin(x)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((a-a*sin(x)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,0,0,0,0.000000," ","integrate((a-a*sin(x)**2)**(1/2),x)","\int \sqrt{- a \sin^{2}{\left(x \right)} + a}\, dx"," ",0,"Integral(sqrt(-a*sin(x)**2 + a), x)","F",0
119,0,0,0,0.000000," ","integrate(1/(a-a*sin(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{- a \sin^{2}{\left(x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(-a*sin(x)**2 + a), x)","F",0
120,0,0,0,0.000000," ","integrate(1/(a-a*sin(x)**2)**(3/2),x)","\int \frac{1}{\left(- a \sin^{2}{\left(x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-a*sin(x)**2 + a)**(-3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(1/(a-a*sin(x)**2)**(5/2),x)","\int \frac{1}{\left(- a \sin^{2}{\left(x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((-a*sin(x)**2 + a)**(-5/2), x)","F",0
122,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sin(e + f*x), x)","F",0
124,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*csc(e + f*x), x)","F",0
125,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*csc(e + f*x)**3, x)","F",0
126,0,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \csc^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*csc(e + f*x)**5, x)","F",0
127,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sin(e + f*x)**2, x)","F",0
129,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2), x)","F",0
130,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*csc(e + f*x)**2, x)","F",0
131,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*csc(e + f*x)**4, x)","F",0
132,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(csc(f*x+e)**7*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
146,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
147,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/sqrt(a + b*sin(e + f*x)**2), x)","F",0
148,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
150,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(e + f*x)**2), x)","F",0
151,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
152,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/sqrt(a + b*sin(e + f*x)**2), x)","F",0
153,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
157,-1,0,0,0.000000," ","integrate(sin(f*x+e)**6/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-3/2), x)","F",0
161,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
162,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
166,-1,0,0,0.000000," ","integrate(sin(f*x+e)**6/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-5/2), x)","F",0
170,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
171,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,0,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)**3),x)","\int \frac{\sin{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)/(a + b*sin(c + d*x)**3), x)","F",0
186,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)**3),x)","\int \frac{\csc{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(a + b*sin(c + d*x)**3), x)","F",0
187,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+b*sin(d*x+c)**3),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**3/(a + b*sin(c + d*x)**3), x)","F",0
188,-1,0,0,0.000000," ","integrate(csc(d*x+c)**5/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,0,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a+b*sin(d*x+c)**3),x)","\int \frac{\sin^{6}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**6/(a + b*sin(c + d*x)**3), x)","F",0
190,0,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a+b*sin(d*x+c)**3),x)","\int \frac{\sin^{4}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**4/(a + b*sin(c + d*x)**3), x)","F",0
191,0,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)**3),x)","\int \frac{\sin^{2}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2/(a + b*sin(c + d*x)**3), x)","F",0
192,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**3),x)","\int \frac{1}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*sin(c + d*x)**3), x)","F",0
193,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)**3),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a + b*sin(c + d*x)**3), x)","F",0
194,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate(sin(d*x+c)**9/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)**4),x)","\int \frac{\csc{\left(c + d x \right)}}{a - b \sin^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(a - b*sin(c + d*x)**4), x)","F",0
201,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a-b*sin(d*x+c)**4),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{a - b \sin^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**3/(a - b*sin(c + d*x)**4), x)","F",0
202,-1,0,0,0.000000," ","integrate(csc(d*x+c)**5/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(sin(d*x+c)**8/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a-b*sin(d*x+c)**4),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{a - b \sin^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2/(a - b*sin(c + d*x)**4), x)","F",0
209,0,0,0,0.000000," ","integrate(csc(d*x+c)**4/(a-b*sin(d*x+c)**4),x)","\int \frac{\csc^{4}{\left(c + d x \right)}}{a - b \sin^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**4/(a - b*sin(c + d*x)**4), x)","F",0
210,-1,0,0,0.000000," ","integrate(csc(d*x+c)**6/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate(csc(d*x+c)**8/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate(sin(d*x+c)**9/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate(sin(d*x+c)**8/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a-b*sin(d*x+c)**4)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate(sin(d*x+c)**9/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate(sin(d*x+c)**7/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate(sin(d*x+c)**8/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(sin(d*x+c)**6/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate(sin(d*x+c)**4/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate(1/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a-b*sin(d*x+c)**4)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,1,724,0,84.416079," ","integrate(1/(1-sin(x)**4),x)","\frac{54608393 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} + \frac{77227930 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{77227930 \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{54608393 \sqrt{2} \sqrt{3 - 2 \sqrt{2}} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{3 - 2 \sqrt{2}}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} + \frac{9369319 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} + \frac{13250218 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{13250218 \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{9369319 \sqrt{2} \sqrt{2 \sqrt{2} + 3} \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{\sqrt{2 \sqrt{2} + 3}} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{90478148 \tan{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}} - \frac{63977712 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{63977712 \sqrt{2} \tan^{2}{\left(\frac{x}{2} \right)} + 90478148 \tan^{2}{\left(\frac{x}{2} \right)} - 90478148 - 63977712 \sqrt{2}}"," ",0,"54608393*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))*tan(x/2)**2/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) + 77227930*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))*tan(x/2)**2/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 77227930*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 54608393*sqrt(2)*sqrt(3 - 2*sqrt(2))*(atan(tan(x/2)/sqrt(3 - 2*sqrt(2))) + pi*floor((x/2 - pi/2)/pi))/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) + 9369319*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))*tan(x/2)**2/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) + 13250218*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))*tan(x/2)**2/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 13250218*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 9369319*sqrt(2)*sqrt(2*sqrt(2) + 3)*(atan(tan(x/2)/sqrt(2*sqrt(2) + 3)) + pi*floor((x/2 - pi/2)/pi))/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 90478148*tan(x/2)/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2)) - 63977712*sqrt(2)*tan(x/2)/(63977712*sqrt(2)*tan(x/2)**2 + 90478148*tan(x/2)**2 - 90478148 - 63977712*sqrt(2))","B",0
237,-1,0,0,0.000000," ","integrate(1/(a+b*sin(x)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(1/(1+sin(x)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(sin(d*x+c)*(a+b*sin(d*x+c)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate(csc(d*x+c)*(a+b*sin(d*x+c)**4)**(1/2),x)","\int \sqrt{a + b \sin^{4}{\left(c + d x \right)}} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x)**4)*csc(c + d*x), x)","F",0
241,-1,0,0,0.000000," ","integrate(sin(d*x+c)**5/(a+b*sin(d*x+c)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(sin(d*x+c)**3/(a+b*sin(d*x+c)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,0,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\csc{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(csc(c + d*x)/sqrt(a + b*sin(c + d*x)**4), x)","F",0
245,0,0,0,0.000000," ","integrate(csc(d*x+c)**3/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\csc^{3}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(csc(c + d*x)**3/sqrt(a + b*sin(c + d*x)**4), x)","F",0
246,-1,0,0,0.000000," ","integrate(sin(d*x+c)**2/(a+b*sin(d*x+c)**4)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(c + d*x)**4), x)","F",0
248,0,0,0,0.000000," ","integrate(csc(d*x+c)**2/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\csc^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(csc(c + d*x)**2/sqrt(a + b*sin(c + d*x)**4), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)**5),x)","\int \frac{1}{a + b \sin^{5}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*sin(x)**5), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)**6),x)","\int \frac{1}{a + b \sin^{6}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*sin(x)**6), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(a+b*sin(x)**8),x)","\int \frac{1}{a + b \sin^{8}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a + b*sin(x)**8), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)**5),x)","\int \frac{1}{a - b \sin^{5}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a - b*sin(x)**5), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)**6),x)","\int \frac{1}{a - b \sin^{6}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a - b*sin(x)**6), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(a-b*sin(x)**8),x)","\int \frac{1}{a - b \sin^{8}{\left(x \right)}}\, dx"," ",0,"Integral(1/(a - b*sin(x)**8), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(1+sin(x)**5),x)","\int \frac{1}{\left(\sin{\left(x \right)} + 1\right) \left(\sin^{4}{\left(x \right)} - \sin^{3}{\left(x \right)} + \sin^{2}{\left(x \right)} - \sin{\left(x \right)} + 1\right)}\, dx"," ",0,"Integral(1/((sin(x) + 1)*(sin(x)**4 - sin(x)**3 + sin(x)**2 - sin(x) + 1)), x)","F",0
256,-1,0,0,0.000000," ","integrate(1/(1+sin(x)**6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,0,0,0,0.000000," ","integrate(1/(1+sin(x)**8),x)","\int \frac{1}{\sin^{8}{\left(x \right)} + 1}\, dx"," ",0,"Integral(1/(sin(x)**8 + 1), x)","F",0
258,0,0,0,0.000000," ","integrate(1/(1-sin(x)**5),x)","- \int \frac{1}{\sin^{5}{\left(x \right)} - 1}\, dx"," ",0,"-Integral(1/(sin(x)**5 - 1), x)","F",0
259,-1,0,0,0.000000," ","integrate(1/(1-sin(x)**6),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(1/(1-sin(x)**8),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,1,580,0,41.264488," ","integrate(cos(x)**9/(a-a*sin(x)**2),x)","\frac{70 \tan^{13}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{140 \tan^{11}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{602 \tan^{9}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{424 \tan^{7}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{602 \tan^{5}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{140 \tan^{3}{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a} + \frac{70 \tan{\left(\frac{x}{2} \right)}}{35 a \tan^{14}{\left(\frac{x}{2} \right)} + 245 a \tan^{12}{\left(\frac{x}{2} \right)} + 735 a \tan^{10}{\left(\frac{x}{2} \right)} + 1225 a \tan^{8}{\left(\frac{x}{2} \right)} + 1225 a \tan^{6}{\left(\frac{x}{2} \right)} + 735 a \tan^{4}{\left(\frac{x}{2} \right)} + 245 a \tan^{2}{\left(\frac{x}{2} \right)} + 35 a}"," ",0,"70*tan(x/2)**13/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 140*tan(x/2)**11/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 602*tan(x/2)**9/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 424*tan(x/2)**7/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 602*tan(x/2)**5/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 140*tan(x/2)**3/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a) + 70*tan(x/2)/(35*a*tan(x/2)**14 + 245*a*tan(x/2)**12 + 735*a*tan(x/2)**10 + 1225*a*tan(x/2)**8 + 1225*a*tan(x/2)**6 + 735*a*tan(x/2)**4 + 245*a*tan(x/2)**2 + 35*a)","B",0
262,1,311,0,18.895563," ","integrate(cos(x)**7/(a-a*sin(x)**2),x)","\frac{30 \tan^{9}{\left(\frac{x}{2} \right)}}{15 a \tan^{10}{\left(\frac{x}{2} \right)} + 75 a \tan^{8}{\left(\frac{x}{2} \right)} + 150 a \tan^{6}{\left(\frac{x}{2} \right)} + 150 a \tan^{4}{\left(\frac{x}{2} \right)} + 75 a \tan^{2}{\left(\frac{x}{2} \right)} + 15 a} + \frac{40 \tan^{7}{\left(\frac{x}{2} \right)}}{15 a \tan^{10}{\left(\frac{x}{2} \right)} + 75 a \tan^{8}{\left(\frac{x}{2} \right)} + 150 a \tan^{6}{\left(\frac{x}{2} \right)} + 150 a \tan^{4}{\left(\frac{x}{2} \right)} + 75 a \tan^{2}{\left(\frac{x}{2} \right)} + 15 a} + \frac{116 \tan^{5}{\left(\frac{x}{2} \right)}}{15 a \tan^{10}{\left(\frac{x}{2} \right)} + 75 a \tan^{8}{\left(\frac{x}{2} \right)} + 150 a \tan^{6}{\left(\frac{x}{2} \right)} + 150 a \tan^{4}{\left(\frac{x}{2} \right)} + 75 a \tan^{2}{\left(\frac{x}{2} \right)} + 15 a} + \frac{40 \tan^{3}{\left(\frac{x}{2} \right)}}{15 a \tan^{10}{\left(\frac{x}{2} \right)} + 75 a \tan^{8}{\left(\frac{x}{2} \right)} + 150 a \tan^{6}{\left(\frac{x}{2} \right)} + 150 a \tan^{4}{\left(\frac{x}{2} \right)} + 75 a \tan^{2}{\left(\frac{x}{2} \right)} + 15 a} + \frac{30 \tan{\left(\frac{x}{2} \right)}}{15 a \tan^{10}{\left(\frac{x}{2} \right)} + 75 a \tan^{8}{\left(\frac{x}{2} \right)} + 150 a \tan^{6}{\left(\frac{x}{2} \right)} + 150 a \tan^{4}{\left(\frac{x}{2} \right)} + 75 a \tan^{2}{\left(\frac{x}{2} \right)} + 15 a}"," ",0,"30*tan(x/2)**9/(15*a*tan(x/2)**10 + 75*a*tan(x/2)**8 + 150*a*tan(x/2)**6 + 150*a*tan(x/2)**4 + 75*a*tan(x/2)**2 + 15*a) + 40*tan(x/2)**7/(15*a*tan(x/2)**10 + 75*a*tan(x/2)**8 + 150*a*tan(x/2)**6 + 150*a*tan(x/2)**4 + 75*a*tan(x/2)**2 + 15*a) + 116*tan(x/2)**5/(15*a*tan(x/2)**10 + 75*a*tan(x/2)**8 + 150*a*tan(x/2)**6 + 150*a*tan(x/2)**4 + 75*a*tan(x/2)**2 + 15*a) + 40*tan(x/2)**3/(15*a*tan(x/2)**10 + 75*a*tan(x/2)**8 + 150*a*tan(x/2)**6 + 150*a*tan(x/2)**4 + 75*a*tan(x/2)**2 + 15*a) + 30*tan(x/2)/(15*a*tan(x/2)**10 + 75*a*tan(x/2)**8 + 150*a*tan(x/2)**6 + 150*a*tan(x/2)**4 + 75*a*tan(x/2)**2 + 15*a)","B",0
263,1,124,0,7.945544," ","integrate(cos(x)**5/(a-a*sin(x)**2),x)","\frac{6 \tan^{5}{\left(\frac{x}{2} \right)}}{3 a \tan^{6}{\left(\frac{x}{2} \right)} + 9 a \tan^{4}{\left(\frac{x}{2} \right)} + 9 a \tan^{2}{\left(\frac{x}{2} \right)} + 3 a} + \frac{4 \tan^{3}{\left(\frac{x}{2} \right)}}{3 a \tan^{6}{\left(\frac{x}{2} \right)} + 9 a \tan^{4}{\left(\frac{x}{2} \right)} + 9 a \tan^{2}{\left(\frac{x}{2} \right)} + 3 a} + \frac{6 \tan{\left(\frac{x}{2} \right)}}{3 a \tan^{6}{\left(\frac{x}{2} \right)} + 9 a \tan^{4}{\left(\frac{x}{2} \right)} + 9 a \tan^{2}{\left(\frac{x}{2} \right)} + 3 a}"," ",0,"6*tan(x/2)**5/(3*a*tan(x/2)**6 + 9*a*tan(x/2)**4 + 9*a*tan(x/2)**2 + 3*a) + 4*tan(x/2)**3/(3*a*tan(x/2)**6 + 9*a*tan(x/2)**4 + 9*a*tan(x/2)**2 + 3*a) + 6*tan(x/2)/(3*a*tan(x/2)**6 + 9*a*tan(x/2)**4 + 9*a*tan(x/2)**2 + 3*a)","B",0
264,1,15,0,2.859524," ","integrate(cos(x)**3/(a-a*sin(x)**2),x)","\frac{2 \tan{\left(\frac{x}{2} \right)}}{a \tan^{2}{\left(\frac{x}{2} \right)} + a}"," ",0,"2*tan(x/2)/(a*tan(x/2)**2 + a)","B",0
265,1,19,0,0.289936," ","integrate(cos(x)/(a-a*sin(x)**2),x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2 a} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2 a}"," ",0,"-log(sin(x) - 1)/(2*a) + log(sin(x) + 1)/(2*a)","B",0
266,0,0,0,0.000000," ","integrate(sec(x)**3/(a-a*sin(x)**2),x)","- \frac{\int \frac{\sec^{3}{\left(x \right)}}{\sin^{2}{\left(x \right)} - 1}\, dx}{a}"," ",0,"-Integral(sec(x)**3/(sin(x)**2 - 1), x)/a","F",0
267,1,473,0,12.926867," ","integrate(cos(x)**6/(a-a*sin(x)**2),x)","\frac{3 x \tan^{8}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{12 x \tan^{6}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{18 x \tan^{4}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{12 x \tan^{2}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{3 x}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} - \frac{10 \tan^{7}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{6 \tan^{5}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} - \frac{6 \tan^{3}{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a} + \frac{10 \tan{\left(\frac{x}{2} \right)}}{8 a \tan^{8}{\left(\frac{x}{2} \right)} + 32 a \tan^{6}{\left(\frac{x}{2} \right)} + 48 a \tan^{4}{\left(\frac{x}{2} \right)} + 32 a \tan^{2}{\left(\frac{x}{2} \right)} + 8 a}"," ",0,"3*x*tan(x/2)**8/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 12*x*tan(x/2)**6/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 18*x*tan(x/2)**4/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 12*x*tan(x/2)**2/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 3*x/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) - 10*tan(x/2)**7/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 6*tan(x/2)**5/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) - 6*tan(x/2)**3/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a) + 10*tan(x/2)/(8*a*tan(x/2)**8 + 32*a*tan(x/2)**6 + 48*a*tan(x/2)**4 + 32*a*tan(x/2)**2 + 8*a)","B",0
268,1,153,0,4.920779," ","integrate(cos(x)**4/(a-a*sin(x)**2),x)","\frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a} + \frac{2 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a} + \frac{x}{2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a} - \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{2 a \tan^{4}{\left(\frac{x}{2} \right)} + 4 a \tan^{2}{\left(\frac{x}{2} \right)} + 2 a}"," ",0,"x*tan(x/2)**4/(2*a*tan(x/2)**4 + 4*a*tan(x/2)**2 + 2*a) + 2*x*tan(x/2)**2/(2*a*tan(x/2)**4 + 4*a*tan(x/2)**2 + 2*a) + x/(2*a*tan(x/2)**4 + 4*a*tan(x/2)**2 + 2*a) - 2*tan(x/2)**3/(2*a*tan(x/2)**4 + 4*a*tan(x/2)**2 + 2*a) + 2*tan(x/2)/(2*a*tan(x/2)**4 + 4*a*tan(x/2)**2 + 2*a)","B",0
269,1,2,0,1.599348," ","integrate(cos(x)**2/(a-a*sin(x)**2),x)","\frac{x}{a}"," ",0,"x/a","A",0
270,0,0,0,0.000000," ","integrate(sec(x)/(a-a*sin(x)**2),x)","- \frac{\int \frac{\sec{\left(x \right)}}{\sin^{2}{\left(x \right)} - 1}\, dx}{a}"," ",0,"-Integral(sec(x)/(sin(x)**2 - 1), x)/a","F",0
271,0,0,0,0.000000," ","integrate(sec(x)**2/(a-a*sin(x)**2),x)","- \frac{\int \frac{\sec^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} - 1}\, dx}{a}"," ",0,"-Integral(sec(x)**2/(sin(x)**2 - 1), x)/a","F",0
272,0,0,0,0.000000," ","integrate(sec(x)**4/(a-a*sin(x)**2),x)","- \frac{\int \frac{\sec^{4}{\left(x \right)}}{\sin^{2}{\left(x \right)} - 1}\, dx}{a}"," ",0,"-Integral(sec(x)**4/(sin(x)**2 - 1), x)/a","F",0
273,1,362,0,83.589823," ","integrate(cos(x)**9/(a-a*sin(x)**2)**2,x)","\frac{30 \tan^{9}{\left(\frac{x}{2} \right)}}{15 a^{2} \tan^{10}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 15 a^{2}} + \frac{40 \tan^{7}{\left(\frac{x}{2} \right)}}{15 a^{2} \tan^{10}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 15 a^{2}} + \frac{116 \tan^{5}{\left(\frac{x}{2} \right)}}{15 a^{2} \tan^{10}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 15 a^{2}} + \frac{40 \tan^{3}{\left(\frac{x}{2} \right)}}{15 a^{2} \tan^{10}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 15 a^{2}} + \frac{30 \tan{\left(\frac{x}{2} \right)}}{15 a^{2} \tan^{10}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 150 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 75 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 15 a^{2}}"," ",0,"30*tan(x/2)**9/(15*a**2*tan(x/2)**10 + 75*a**2*tan(x/2)**8 + 150*a**2*tan(x/2)**6 + 150*a**2*tan(x/2)**4 + 75*a**2*tan(x/2)**2 + 15*a**2) + 40*tan(x/2)**7/(15*a**2*tan(x/2)**10 + 75*a**2*tan(x/2)**8 + 150*a**2*tan(x/2)**6 + 150*a**2*tan(x/2)**4 + 75*a**2*tan(x/2)**2 + 15*a**2) + 116*tan(x/2)**5/(15*a**2*tan(x/2)**10 + 75*a**2*tan(x/2)**8 + 150*a**2*tan(x/2)**6 + 150*a**2*tan(x/2)**4 + 75*a**2*tan(x/2)**2 + 15*a**2) + 40*tan(x/2)**3/(15*a**2*tan(x/2)**10 + 75*a**2*tan(x/2)**8 + 150*a**2*tan(x/2)**6 + 150*a**2*tan(x/2)**4 + 75*a**2*tan(x/2)**2 + 15*a**2) + 30*tan(x/2)/(15*a**2*tan(x/2)**10 + 75*a**2*tan(x/2)**8 + 150*a**2*tan(x/2)**6 + 150*a**2*tan(x/2)**4 + 75*a**2*tan(x/2)**2 + 15*a**2)","B",0
274,1,144,0,40.557510," ","integrate(cos(x)**7/(a-a*sin(x)**2)**2,x)","\frac{6 \tan^{5}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{4 \tan^{3}{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 3 a^{2}} + \frac{6 \tan{\left(\frac{x}{2} \right)}}{3 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 9 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 3 a^{2}}"," ",0,"6*tan(x/2)**5/(3*a**2*tan(x/2)**6 + 9*a**2*tan(x/2)**4 + 9*a**2*tan(x/2)**2 + 3*a**2) + 4*tan(x/2)**3/(3*a**2*tan(x/2)**6 + 9*a**2*tan(x/2)**4 + 9*a**2*tan(x/2)**2 + 3*a**2) + 6*tan(x/2)/(3*a**2*tan(x/2)**6 + 9*a**2*tan(x/2)**4 + 9*a**2*tan(x/2)**2 + 3*a**2)","B",0
275,1,19,0,19.209828," ","integrate(cos(x)**5/(a-a*sin(x)**2)**2,x)","\frac{2 \tan{\left(\frac{x}{2} \right)}}{a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + a^{2}}"," ",0,"2*tan(x/2)/(a**2*tan(x/2)**2 + a**2)","B",0
276,1,22,0,7.455972," ","integrate(cos(x)**3/(a-a*sin(x)**2)**2,x)","- \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)}}{a^{2}} + \frac{\log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)}}{a^{2}}"," ",0,"-log(tan(x/2) - 1)/a**2 + log(tan(x/2) + 1)/a**2","B",0
277,1,117,0,1.059625," ","integrate(cos(x)/(a-a*sin(x)**2)**2,x)","- \frac{\log{\left(\sin{\left(x \right)} - 1 \right)} \sin^{2}{\left(x \right)}}{4 a^{2} \sin^{2}{\left(x \right)} - 4 a^{2}} + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4 a^{2} \sin^{2}{\left(x \right)} - 4 a^{2}} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)} \sin^{2}{\left(x \right)}}{4 a^{2} \sin^{2}{\left(x \right)} - 4 a^{2}} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4 a^{2} \sin^{2}{\left(x \right)} - 4 a^{2}} - \frac{2 \sin{\left(x \right)}}{4 a^{2} \sin^{2}{\left(x \right)} - 4 a^{2}}"," ",0,"-log(sin(x) - 1)*sin(x)**2/(4*a**2*sin(x)**2 - 4*a**2) + log(sin(x) - 1)/(4*a**2*sin(x)**2 - 4*a**2) + log(sin(x) + 1)*sin(x)**2/(4*a**2*sin(x)**2 - 4*a**2) - log(sin(x) + 1)/(4*a**2*sin(x)**2 - 4*a**2) - 2*sin(x)/(4*a**2*sin(x)**2 - 4*a**2)","B",0
278,0,0,0,0.000000," ","integrate(sec(x)/(a-a*sin(x)**2)**2,x)","\frac{\int \frac{\sec{\left(x \right)}}{\sin^{4}{\left(x \right)} - 2 \sin^{2}{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(x)/(sin(x)**4 - 2*sin(x)**2 + 1), x)/a**2","F",0
279,1,549,0,69.896756," ","integrate(cos(x)**8/(a-a*sin(x)**2)**2,x)","\frac{3 x \tan^{8}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{12 x \tan^{6}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{18 x \tan^{4}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{12 x \tan^{2}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{3 x}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} - \frac{10 \tan^{7}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{6 \tan^{5}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} - \frac{6 \tan^{3}{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}} + \frac{10 \tan{\left(\frac{x}{2} \right)}}{8 a^{2} \tan^{8}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{6}{\left(\frac{x}{2} \right)} + 48 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 32 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 8 a^{2}}"," ",0,"3*x*tan(x/2)**8/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 12*x*tan(x/2)**6/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 18*x*tan(x/2)**4/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 12*x*tan(x/2)**2/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 3*x/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) - 10*tan(x/2)**7/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 6*tan(x/2)**5/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) - 6*tan(x/2)**3/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2) + 10*tan(x/2)/(8*a**2*tan(x/2)**8 + 32*a**2*tan(x/2)**6 + 48*a**2*tan(x/2)**4 + 32*a**2*tan(x/2)**2 + 8*a**2)","B",0
280,1,178,0,31.081124," ","integrate(cos(x)**6/(a-a*sin(x)**2)**2,x)","\frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{2 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 4 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 2 a^{2}} + \frac{2 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 4 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 2 a^{2}} + \frac{x}{2 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 4 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 2 a^{2}} - \frac{2 \tan^{3}{\left(\frac{x}{2} \right)}}{2 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 4 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 2 a^{2}} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{2 a^{2} \tan^{4}{\left(\frac{x}{2} \right)} + 4 a^{2} \tan^{2}{\left(\frac{x}{2} \right)} + 2 a^{2}}"," ",0,"x*tan(x/2)**4/(2*a**2*tan(x/2)**4 + 4*a**2*tan(x/2)**2 + 2*a**2) + 2*x*tan(x/2)**2/(2*a**2*tan(x/2)**4 + 4*a**2*tan(x/2)**2 + 2*a**2) + x/(2*a**2*tan(x/2)**4 + 4*a**2*tan(x/2)**2 + 2*a**2) - 2*tan(x/2)**3/(2*a**2*tan(x/2)**4 + 4*a**2*tan(x/2)**2 + 2*a**2) + 2*tan(x/2)/(2*a**2*tan(x/2)**4 + 4*a**2*tan(x/2)**2 + 2*a**2)","B",0
281,1,3,0,13.004693," ","integrate(cos(x)**4/(a-a*sin(x)**2)**2,x)","\frac{x}{a^{2}}"," ",0,"x/a**2","A",0
282,1,20,0,5.642568," ","integrate(cos(x)**2/(a-a*sin(x)**2)**2,x)","- \frac{2 \tan{\left(\frac{x}{2} \right)}}{a^{2} \tan^{2}{\left(\frac{x}{2} \right)} - a^{2}}"," ",0,"-2*tan(x/2)/(a**2*tan(x/2)**2 - a**2)","B",0
283,0,0,0,0.000000," ","integrate(sec(x)**2/(a-a*sin(x)**2)**2,x)","\frac{\int \frac{\sec^{2}{\left(x \right)}}{\sin^{4}{\left(x \right)} - 2 \sin^{2}{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(x)**2/(sin(x)**4 - 2*sin(x)**2 + 1), x)/a**2","F",0
284,0,0,0,0.000000," ","integrate(sec(x)**4/(a-a*sin(x)**2)**2,x)","\frac{\int \frac{\sec^{4}{\left(x \right)}}{\sin^{4}{\left(x \right)} - 2 \sin^{2}{\left(x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(x)**4/(sin(x)**4 - 2*sin(x)**2 + 1), x)/a**2","F",0
285,1,354,0,14.471782," ","integrate(cos(f*x+e)**6*(a+b*sin(f*x+e)**2),x)","\begin{cases} \frac{5 a x \sin^{6}{\left(e + f x \right)}}{16} + \frac{15 a x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{15 a x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{5 a x \cos^{6}{\left(e + f x \right)}}{16} + \frac{5 a \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{5 a \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} + \frac{11 a \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} + \frac{5 b x \sin^{8}{\left(e + f x \right)}}{128} + \frac{5 b x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{15 b x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{5 b x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{5 b x \cos^{8}{\left(e + f x \right)}}{128} + \frac{5 b \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} + \frac{55 b \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{384 f} + \frac{73 b \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{384 f} - \frac{5 b \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right) \cos^{6}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*x*sin(e + f*x)**6/16 + 15*a*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 15*a*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 5*a*x*cos(e + f*x)**6/16 + 5*a*sin(e + f*x)**5*cos(e + f*x)/(16*f) + 5*a*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) + 11*a*sin(e + f*x)*cos(e + f*x)**5/(16*f) + 5*b*x*sin(e + f*x)**8/128 + 5*b*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 15*b*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 5*b*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 5*b*x*cos(e + f*x)**8/128 + 5*b*sin(e + f*x)**7*cos(e + f*x)/(128*f) + 55*b*sin(e + f*x)**5*cos(e + f*x)**3/(384*f) + 73*b*sin(e + f*x)**3*cos(e + f*x)**5/(384*f) - 5*b*sin(e + f*x)*cos(e + f*x)**7/(128*f), Ne(f, 0)), (x*(a + b*sin(e)**2)*cos(e)**6, True))","A",0
286,1,250,0,5.275575," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**2),x)","\begin{cases} \frac{3 a x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 a \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{5 a \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{b x \sin^{6}{\left(e + f x \right)}}{16} + \frac{3 b x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 b x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{b x \cos^{6}{\left(e + f x \right)}}{16} + \frac{b \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{b \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{b \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right) \cos^{4}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(e + f*x)**4/8 + 3*a*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a*x*cos(e + f*x)**4/8 + 3*a*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 5*a*sin(e + f*x)*cos(e + f*x)**3/(8*f) + b*x*sin(e + f*x)**6/16 + 3*b*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*b*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + b*x*cos(e + f*x)**6/16 + b*sin(e + f*x)**5*cos(e + f*x)/(16*f) + b*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - b*sin(e + f*x)*cos(e + f*x)**5/(16*f), Ne(f, 0)), (x*(a + b*sin(e)**2)*cos(e)**4, True))","A",0
287,1,150,0,1.416345," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**2),x)","\begin{cases} \frac{a x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a x \cos^{2}{\left(e + f x \right)}}{2} + \frac{a \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{b x \sin^{4}{\left(e + f x \right)}}{8} + \frac{b x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{b x \cos^{4}{\left(e + f x \right)}}{8} + \frac{b \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{b \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right) \cos^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(e + f*x)**2/2 + a*x*cos(e + f*x)**2/2 + a*sin(e + f*x)*cos(e + f*x)/(2*f) + b*x*sin(e + f*x)**4/8 + b*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + b*x*cos(e + f*x)**4/8 + b*sin(e + f*x)**3*cos(e + f*x)/(8*f) - b*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e)**2)*cos(e)**2, True))","A",0
288,1,51,0,0.247658," ","integrate(a+b*sin(f*x+e)**2,x)","a x + b \left(\begin{cases} \frac{x \sin^{2}{\left(e + f x \right)}}{2} + \frac{x \cos^{2}{\left(e + f x \right)}}{2} - \frac{\sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \sin^{2}{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x*sin(e + f*x)**2/2 + x*cos(e + f*x)**2/2 - sin(e + f*x)*cos(e + f*x)/(2*f), Ne(f, 0)), (x*sin(e)**2, True))","A",0
289,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**2),x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right) \sec^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)*sec(e + f*x)**2, x)","F",0
290,0,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**2),x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right) \sec^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)*sec(e + f*x)**4, x)","F",0
291,-1,0,0,0.000000," ","integrate(sec(f*x+e)**6*(a+b*sin(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(sec(f*x+e)**8*(a+b*sin(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,1,481,0,14.620247," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**2)**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 a^{2} x \cos^{4}{\left(e + f x \right)}}{8} + \frac{3 a^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{5 a^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{a b x \sin^{6}{\left(e + f x \right)}}{8} + \frac{3 a b x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{8} + \frac{3 a b x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{8} + \frac{a b x \cos^{6}{\left(e + f x \right)}}{8} + \frac{a b \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{a b \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a b \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{8 f} + \frac{3 b^{2} x \sin^{8}{\left(e + f x \right)}}{128} + \frac{3 b^{2} x \sin^{6}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{32} + \frac{9 b^{2} x \sin^{4}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{64} + \frac{3 b^{2} x \sin^{2}{\left(e + f x \right)} \cos^{6}{\left(e + f x \right)}}{32} + \frac{3 b^{2} x \cos^{8}{\left(e + f x \right)}}{128} + \frac{3 b^{2} \sin^{7}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{128 f} + \frac{11 b^{2} \sin^{5}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{128 f} - \frac{11 b^{2} \sin^{3}{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{128 f} - \frac{3 b^{2} \sin{\left(e + f x \right)} \cos^{7}{\left(e + f x \right)}}{128 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right)^{2} \cos^{4}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(e + f*x)**4/8 + 3*a**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*a**2*x*cos(e + f*x)**4/8 + 3*a**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 5*a**2*sin(e + f*x)*cos(e + f*x)**3/(8*f) + a*b*x*sin(e + f*x)**6/8 + 3*a*b*x*sin(e + f*x)**4*cos(e + f*x)**2/8 + 3*a*b*x*sin(e + f*x)**2*cos(e + f*x)**4/8 + a*b*x*cos(e + f*x)**6/8 + a*b*sin(e + f*x)**5*cos(e + f*x)/(8*f) + a*b*sin(e + f*x)**3*cos(e + f*x)**3/(3*f) - a*b*sin(e + f*x)*cos(e + f*x)**5/(8*f) + 3*b**2*x*sin(e + f*x)**8/128 + 3*b**2*x*sin(e + f*x)**6*cos(e + f*x)**2/32 + 9*b**2*x*sin(e + f*x)**4*cos(e + f*x)**4/64 + 3*b**2*x*sin(e + f*x)**2*cos(e + f*x)**6/32 + 3*b**2*x*cos(e + f*x)**8/128 + 3*b**2*sin(e + f*x)**7*cos(e + f*x)/(128*f) + 11*b**2*sin(e + f*x)**5*cos(e + f*x)**3/(128*f) - 11*b**2*sin(e + f*x)**3*cos(e + f*x)**5/(128*f) - 3*b**2*sin(e + f*x)*cos(e + f*x)**7/(128*f), Ne(f, 0)), (x*(a + b*sin(e)**2)**2*cos(e)**4, True))","A",0
294,1,314,0,4.842421," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**2)**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{a b x \sin^{4}{\left(e + f x \right)}}{4} + \frac{a b x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2} + \frac{a b x \cos^{4}{\left(e + f x \right)}}{4} + \frac{a b \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{4 f} - \frac{a b \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{4 f} + \frac{b^{2} x \sin^{6}{\left(e + f x \right)}}{16} + \frac{3 b^{2} x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 b^{2} x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{b^{2} x \cos^{6}{\left(e + f x \right)}}{16} + \frac{b^{2} \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} - \frac{b^{2} \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{b^{2} \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right)^{2} \cos^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(e + f*x)**2/2 + a**2*x*cos(e + f*x)**2/2 + a**2*sin(e + f*x)*cos(e + f*x)/(2*f) + a*b*x*sin(e + f*x)**4/4 + a*b*x*sin(e + f*x)**2*cos(e + f*x)**2/2 + a*b*x*cos(e + f*x)**4/4 + a*b*sin(e + f*x)**3*cos(e + f*x)/(4*f) - a*b*sin(e + f*x)*cos(e + f*x)**3/(4*f) + b**2*x*sin(e + f*x)**6/16 + 3*b**2*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*b**2*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + b**2*x*cos(e + f*x)**6/16 + b**2*sin(e + f*x)**5*cos(e + f*x)/(16*f) - b**2*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - b**2*sin(e + f*x)*cos(e + f*x)**5/(16*f), Ne(f, 0)), (x*(a + b*sin(e)**2)**2*cos(e)**2, True))","A",0
295,1,168,0,1.339322," ","integrate((a+b*sin(f*x+e)**2)**2,x)","\begin{cases} a^{2} x + a b x \sin^{2}{\left(e + f x \right)} + a b x \cos^{2}{\left(e + f x \right)} - \frac{a b \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 b^{2} x \sin^{4}{\left(e + f x \right)}}{8} + \frac{3 b^{2} x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{3 b^{2} x \cos^{4}{\left(e + f x \right)}}{8} - \frac{5 b^{2} \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{3 b^{2} \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} & \text{for}\: f \neq 0 \\x \left(a + b \sin^{2}{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + a*b*x*sin(e + f*x)**2 + a*b*x*cos(e + f*x)**2 - a*b*sin(e + f*x)*cos(e + f*x)/f + 3*b**2*x*sin(e + f*x)**4/8 + 3*b**2*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + 3*b**2*x*cos(e + f*x)**4/8 - 5*b**2*sin(e + f*x)**3*cos(e + f*x)/(8*f) - 3*b**2*sin(e + f*x)*cos(e + f*x)**3/(8*f), Ne(f, 0)), (x*(a + b*sin(e)**2)**2, True))","A",0
296,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**2)**2,x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right)^{2} \sec^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**2*sec(e + f*x)**2, x)","F",0
297,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate(sec(f*x+e)**6*(a+b*sin(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(sec(f*x+e)**8*(a+b*sin(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,-1,0,0,0.000000," ","integrate(sec(f*x+e)**10*(a+b*sin(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(cos(x)**7/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(cos(x)**6/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(cos(x)**5/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(cos(x)**4/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate(cos(x)**3/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate(cos(x)**2/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,1,87,0,1.339885," ","integrate(cos(x)/(a+b*sin(x)**2),x)","\begin{cases} \frac{\tilde{\infty}}{\sin{\left(x \right)}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{b \sin{\left(x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(x \right)}}{a} & \text{for}\: b = 0 \\- \frac{i \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)}}{2 \sqrt{a} b \sqrt{\frac{1}{b}}} + \frac{i \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)}}{2 \sqrt{a} b \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sin(x), Eq(a, 0) & Eq(b, 0)), (-1/(b*sin(x)), Eq(a, 0)), (sin(x)/a, Eq(b, 0)), (-I*log(-I*sqrt(a)*sqrt(1/b) + sin(x))/(2*sqrt(a)*b*sqrt(1/b)) + I*log(I*sqrt(a)*sqrt(1/b) + sin(x))/(2*sqrt(a)*b*sqrt(1/b)), True))","A",0
308,0,0,0,0.000000," ","integrate(sec(x)/(a+b*sin(x)**2),x)","\int \frac{\sec{\left(x \right)}}{a + b \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)/(a + b*sin(x)**2), x)","F",0
309,0,0,0,0.000000," ","integrate(sec(x)**2/(a+b*sin(x)**2),x)","\int \frac{\sec^{2}{\left(x \right)}}{a + b \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**2/(a + b*sin(x)**2), x)","F",0
310,0,0,0,0.000000," ","integrate(sec(x)**3/(a+b*sin(x)**2),x)","\int \frac{\sec^{3}{\left(x \right)}}{a + b \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**3/(a + b*sin(x)**2), x)","F",0
311,0,0,0,0.000000," ","integrate(sec(x)**4/(a+b*sin(x)**2),x)","\int \frac{\sec^{4}{\left(x \right)}}{a + b \sin^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)**4/(a + b*sin(x)**2), x)","F",0
312,-1,0,0,0.000000," ","integrate(sec(x)**5/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate(sec(x)**6/(a+b*sin(x)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate(cos(x)**6/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate(cos(x)**5/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate(cos(x)**4/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,-1,0,0,0.000000," ","integrate(cos(x)**3/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
318,-1,0,0,0.000000," ","integrate(cos(x)**2/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,1,340,0,15.378728," ","integrate(cos(x)/(a+b*sin(x)**2)**2,x)","\begin{cases} \frac{\tilde{\infty}}{\sin^{3}{\left(x \right)}} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{1}{3 b^{2} \sin^{3}{\left(x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(x \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 i \sqrt{a} b \sqrt{\frac{1}{b}} \sin{\left(x \right)}}{4 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \sin^{2}{\left(x \right)}} + \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)}}{4 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \sin^{2}{\left(x \right)}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)}}{4 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \sin^{2}{\left(x \right)}} + \frac{b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)}}{4 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \sin^{2}{\left(x \right)}} - \frac{b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \sin{\left(x \right)} \right)} \sin^{2}{\left(x \right)}}{4 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \sin^{2}{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo/sin(x)**3, Eq(a, 0) & Eq(b, 0)), (-1/(3*b**2*sin(x)**3), Eq(a, 0)), (sin(x)/a**2, Eq(b, 0)), (2*I*sqrt(a)*b*sqrt(1/b)*sin(x)/(4*I*a**(5/2)*b*sqrt(1/b) + 4*I*a**(3/2)*b**2*sqrt(1/b)*sin(x)**2) + a*log(-I*sqrt(a)*sqrt(1/b) + sin(x))/(4*I*a**(5/2)*b*sqrt(1/b) + 4*I*a**(3/2)*b**2*sqrt(1/b)*sin(x)**2) - a*log(I*sqrt(a)*sqrt(1/b) + sin(x))/(4*I*a**(5/2)*b*sqrt(1/b) + 4*I*a**(3/2)*b**2*sqrt(1/b)*sin(x)**2) + b*log(-I*sqrt(a)*sqrt(1/b) + sin(x))*sin(x)**2/(4*I*a**(5/2)*b*sqrt(1/b) + 4*I*a**(3/2)*b**2*sqrt(1/b)*sin(x)**2) - b*log(I*sqrt(a)*sqrt(1/b) + sin(x))*sin(x)**2/(4*I*a**(5/2)*b*sqrt(1/b) + 4*I*a**(3/2)*b**2*sqrt(1/b)*sin(x)**2), True))","A",0
320,-1,0,0,0.000000," ","integrate(sec(x)/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate(sec(x)**2/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate(sec(x)**3/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(sec(x)**4/(a+b*sin(x)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
325,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cos{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cos(e + f*x), x)","F",0
326,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sec{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sec(e + f*x), x)","F",0
327,0,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sec^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sec(e + f*x)**3, x)","F",0
328,-1,0,0,0.000000," ","integrate(sec(f*x+e)**5*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2), x)","F",0
332,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sec^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sec(e + f*x)**2, x)","F",0
333,0,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \sec^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*sec(e + f*x)**4, x)","F",0
334,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(sec(f*x+e)**5*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(sec(f*x+e)**7*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
345,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,0,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cos{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cos(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
347,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sec{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
348,0,0,0,0.000000," ","integrate(sec(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sec^{3}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)**3/sqrt(a + b*sin(e + f*x)**2), x)","F",0
349,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cos(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
351,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(e + f*x)**2), x)","F",0
352,0,0,0,0.000000," ","integrate(sec(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sec^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
353,0,0,0,0.000000," ","integrate(sec(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\sec^{4}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)**4/sqrt(a + b*sin(e + f*x)**2), x)","F",0
354,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,0,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cos{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(e + f*x)/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
356,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\sec{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(e + f*x)/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
357,0,0,0,0.000000," ","integrate(sec(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\sec^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(e + f*x)**3/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
358,-1,0,0,0.000000," ","integrate(cos(f*x+e)**6/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-3/2), x)","F",0
362,0,0,0,0.000000," ","integrate(sec(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\sec^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(e + f*x)**2/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
363,-1,0,0,0.000000," ","integrate(cos(f*x+e)**5/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-1,0,0,0.000000," ","integrate(cos(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,0,0,0,0.000000," ","integrate(sec(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\sec{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(e + f*x)/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
367,-1,0,0,0.000000," ","integrate(cos(f*x+e)**6/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-5/2), x)","F",0
371,0,0,0,0.000000," ","integrate(sec(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\sec^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(e + f*x)**2/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
372,-1,0,0,0.000000," ","integrate((d*cos(f*x+e))**m*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(f*x+e)**5*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
381,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,1,250,0,8.848712," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)**3),x)","\begin{cases} \frac{\tilde{\infty} x \cos{\left(c \right)}}{\sin^{3}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{1}{2 b d \sin^{2}{\left(c + d x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{a + b \sin^{3}{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{\sqrt[3]{-1} \sqrt[3]{\frac{1}{b}} \log{\left(- \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} + \sin{\left(c + d x \right)} \right)}}{3 a^{\frac{2}{3}} d} + \frac{\sqrt[3]{-1} \sqrt[3]{\frac{1}{b}} \log{\left(4 \left(-1\right)^{\frac{2}{3}} a^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}} + 4 \sqrt[3]{-1} \sqrt[3]{a} \sqrt[3]{\frac{1}{b}} \sin{\left(c + d x \right)} + 4 \sin^{2}{\left(c + d x \right)} \right)}}{6 a^{\frac{2}{3}} d} + \frac{\sqrt[3]{-1} \sqrt{3} \sqrt[3]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sqrt{3}}{3} - \frac{2 \left(-1\right)^{\frac{2}{3}} \sqrt{3} \sin{\left(c + d x \right)}}{3 \sqrt[3]{a} \sqrt[3]{\frac{1}{b}}} \right)}}{3 a^{\frac{2}{3}} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cos(c)/sin(c)**3, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-1/(2*b*d*sin(c + d*x)**2), Eq(a, 0)), (sin(c + d*x)/(a*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c)**3), Eq(d, 0)), (-(-1)**(1/3)*(1/b)**(1/3)*log(-(-1)**(1/3)*a**(1/3)*(1/b)**(1/3) + sin(c + d*x))/(3*a**(2/3)*d) + (-1)**(1/3)*(1/b)**(1/3)*log(4*(-1)**(2/3)*a**(2/3)*(1/b)**(2/3) + 4*(-1)**(1/3)*a**(1/3)*(1/b)**(1/3)*sin(c + d*x) + 4*sin(c + d*x)**2)/(6*a**(2/3)*d) + (-1)**(1/3)*sqrt(3)*(1/b)**(1/3)*atan(sqrt(3)/3 - 2*(-1)**(2/3)*sqrt(3)*sin(c + d*x)/(3*a**(1/3)*(1/b)**(1/3)))/(3*a**(2/3)*d), True))","A",0
386,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)**3),x)","\int \frac{\sec{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x)**3), x)","F",0
387,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c)**3),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x)**3), x)","F",0
388,0,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c)**3),x)","\int \frac{\cos^{4}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4/(a + b*sin(c + d*x)**3), x)","F",0
389,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c)**3),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a + b*sin(c + d*x)**3), x)","F",0
390,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**3),x)","\int \frac{1}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*sin(c + d*x)**3), x)","F",0
391,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c)**3),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \sin^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x)**3), x)","F",0
392,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c)**3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,1,155,0,8.904791," ","integrate(cos(d*x+c)/(a-b*sin(d*x+c)**4),x)","\begin{cases} \frac{\tilde{\infty} x \cos{\left(c \right)}}{\sin^{4}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{1}{3 b d \sin^{3}{\left(c + d x \right)}} & \text{for}\: a = 0 \\\frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{a - b \sin^{4}{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{\sqrt[4]{\frac{1}{b}} \log{\left(- \sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sin{\left(c + d x \right)} \right)}}{4 a^{\frac{3}{4}} d} + \frac{\sqrt[4]{\frac{1}{b}} \log{\left(\sqrt[4]{a} \sqrt[4]{\frac{1}{b}} + \sin{\left(c + d x \right)} \right)}}{4 a^{\frac{3}{4}} d} + \frac{\sqrt[4]{\frac{1}{b}} \operatorname{atan}{\left(\frac{\sin{\left(c + d x \right)}}{\sqrt[4]{a} \sqrt[4]{\frac{1}{b}}} \right)}}{2 a^{\frac{3}{4}} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cos(c)/sin(c)**4, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (1/(3*b*d*sin(c + d*x)**3), Eq(a, 0)), (sin(c + d*x)/(a*d), Eq(b, 0)), (x*cos(c)/(a - b*sin(c)**4), Eq(d, 0)), (-(1/b)**(1/4)*log(-a**(1/4)*(1/b)**(1/4) + sin(c + d*x))/(4*a**(3/4)*d) + (1/b)**(1/4)*log(a**(1/4)*(1/b)**(1/4) + sin(c + d*x))/(4*a**(3/4)*d) + (1/b)**(1/4)*atan(sin(c + d*x)/(a**(1/4)*(1/b)**(1/4)))/(2*a**(3/4)*d), True))","A",0
408,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(cos(d*x+c)**10/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
414,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a-b*sin(d*x+c)**4),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate(cos(f*x+e)**m*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cos(f*x+e)**5*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate(cos(f*x+e)**m*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(cos(f*x+e)**5*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,-1,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
435,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
436,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate(tan(d*x+c)**7/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,0,0,0,0.000000," ","integrate(tan(d*x+c)**5/(a+b*sin(d*x+c)**2),x)","\int \frac{\tan^{5}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**5/(a + b*sin(c + d*x)**2), x)","F",0
443,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*sin(d*x+c)**2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**3/(a + b*sin(c + d*x)**2), x)","F",0
444,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)**2),x)","\int \frac{\tan{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)/(a + b*sin(c + d*x)**2), x)","F",0
445,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)/(a + b*sin(c + d*x)**2), x)","F",0
446,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot^{3}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**3/(a + b*sin(c + d*x)**2), x)","F",0
447,0,0,0,0.000000," ","integrate(cot(d*x+c)**5/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot^{5}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**5/(a + b*sin(c + d*x)**2), x)","F",0
448,-1,0,0,0.000000," ","integrate(cot(d*x+c)**7/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate(tan(d*x+c)**8/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate(tan(d*x+c)**6/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,0,0,0,0.000000," ","integrate(tan(d*x+c)**4/(a+b*sin(d*x+c)**2),x)","\int \frac{\tan^{4}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**4/(a + b*sin(c + d*x)**2), x)","F",0
452,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*sin(d*x+c)**2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**2/(a + b*sin(c + d*x)**2), x)","F",0
453,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**2/(a + b*sin(c + d*x)**2), x)","F",0
454,0,0,0,0.000000," ","integrate(cot(d*x+c)**4/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot^{4}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**4/(a + b*sin(c + d*x)**2), x)","F",0
455,0,0,0,0.000000," ","integrate(cot(d*x+c)**6/(a+b*sin(d*x+c)**2),x)","\int \frac{\cot^{6}{\left(c + d x \right)}}{a + b \sin^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)**6/(a + b*sin(c + d*x)**2), x)","F",0
456,-1,0,0,0.000000," ","integrate(cot(d*x+c)**8/(a+b*sin(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**5,x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x)**5, x)","F",0
458,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**3,x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x)**3, x)","F",0
459,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x), x)","F",0
460,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a-a*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*cot(e + f*x), x)","F",0
461,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a-a*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*cot(e + f*x)**3, x)","F",0
462,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**6,x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x)**6, x)","F",0
463,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**4,x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x)**4, x)","F",0
464,0,0,0,0.000000," ","integrate((a-a*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**2,x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*tan(e + f*x)**2, x)","F",0
465,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a-a*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*cot(e + f*x)**2, x)","F",0
466,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a-a*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*cot(e + f*x)**4, x)","F",0
467,0,0,0,0.000000," ","integrate(cot(f*x+e)**6*(a-a*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)} \cot^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))*cot(e + f*x)**6, x)","F",0
468,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(e + f*x)**5/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
469,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(e + f*x)**3/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
470,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(e + f*x)/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
471,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(e + f*x)/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
472,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(e + f*x)**3/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
473,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(e + f*x)**4/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
474,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(e + f*x)**2/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
475,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(e + f*x)**2/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
476,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(e + f*x)**4/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
477,0,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a-a*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{6}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(e + f*x)**6/sqrt(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1)), x)","F",0
478,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
479,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
480,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
481,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
482,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
483,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
484,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
485,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
486,0,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a-a*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{6}{\left(e + f x \right)}}{\left(- a \left(\sin{\left(e + f x \right)} - 1\right) \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**6/(-a*(sin(e + f*x) - 1)*(sin(e + f*x) + 1))**(3/2), x)","F",0
487,-1,0,0,0.000000," ","integrate(cot(f*x+e)**8/(a-a*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**5,x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*tan(e + f*x)**5, x)","F",0
489,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**3,x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*tan(e + f*x)**3, x)","F",0
490,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2)*tan(f*x+e),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*tan(e + f*x), x)","F",0
491,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cot(e + f*x), x)","F",0
492,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cot(e + f*x)**3, x)","F",0
493,0,0,0,0.000000," ","integrate(cot(f*x+e)**5*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cot^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cot(e + f*x)**5, x)","F",0
494,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**4,x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*tan(e + f*x)**4, x)","F",0
495,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2)*tan(f*x+e)**2,x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*tan(e + f*x)**2, x)","F",0
496,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2), x)","F",0
497,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cot(e + f*x)**2, x)","F",0
498,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a+b*sin(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \sin^{2}{\left(e + f x \right)}} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x)**2)*cot(e + f*x)**4, x)","F",0
499,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2)*tan(f*x+e)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2)*tan(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2)*tan(f*x+e),x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(3/2)*tan(e + f*x), x)","F",0
502,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*sin(f*x+e)**2)**(3/2),x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(3/2)*cot(e + f*x), x)","F",0
503,-1,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2)*tan(f*x+e)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2)*tan(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a+b*sin(f*x+e)**2)**(3/2),x)","\int \left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(3/2)*cot(e + f*x)**2, x)","F",0
509,-1,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a+b*sin(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/sqrt(a + b*sin(e + f*x)**2), x)","F",0
511,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/sqrt(a + b*sin(e + f*x)**2), x)","F",0
512,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
513,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)/sqrt(a + b*sin(e + f*x)**2), x)","F",0
514,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/sqrt(a + b*sin(e + f*x)**2), x)","F",0
515,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/sqrt(a + b*sin(e + f*x)**2), x)","F",0
516,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/sqrt(a + b*sin(e + f*x)**2), x)","F",0
517,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
518,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(e + f*x)**2), x)","F",0
519,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/sqrt(a + b*sin(e + f*x)**2), x)","F",0
520,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*sin(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\sqrt{a + b \sin^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/sqrt(a + b*sin(e + f*x)**2), x)","F",0
521,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
522,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
523,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
526,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
527,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
528,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
529,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-3/2), x)","F",0
530,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*sin(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/(a + b*sin(e + f*x)**2)**(3/2), x)","F",0
532,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
533,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
534,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
535,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
536,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
537,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
538,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
539,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
540,0,0,0,0.000000," ","integrate(1/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*sin(e + f*x)**2)**(-5/2), x)","F",0
541,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
542,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*sin(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\left(a + b \sin^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/(a + b*sin(e + f*x)**2)**(5/2), x)","F",0
543,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)**p*(d*tan(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**2)**p*tan(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**2)**p*tan(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)**2)**p,x)","\int \left(a + b \sin^{2}{\left(c + d x \right)}\right)^{p} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**2)**p*cot(c + d*x), x)","F",0
547,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*sin(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**2)**p*tan(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**2)**p*tan(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*sin(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,0,0,0,0.000000," ","integrate(cot(x)**3/(a+b*sin(x)**3),x)","\int \frac{\cot^{3}{\left(x \right)}}{a + b \sin^{3}{\left(x \right)}}\, dx"," ",0,"Integral(cot(x)**3/(a + b*sin(x)**3), x)","F",0
553,0,0,0,0.000000," ","integrate(cot(x)*(a+b*sin(x)**3)**(1/2),x)","\int \sqrt{a + b \sin^{3}{\left(x \right)}} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(x)**3)*cot(x), x)","F",0
554,0,0,0,0.000000," ","integrate(cot(x)/(a+b*sin(x)**3)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a + b \sin^{3}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/sqrt(a + b*sin(x)**3), x)","F",0
555,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)**4)**(1/2),x)","\int \sqrt{a + b \sin^{4}{\left(c + d x \right)}} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x)**4)*cot(c + d*x), x)","F",0
556,0,0,0,0.000000," ","integrate(tan(d*x+c)**3/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\tan^{3}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**3/sqrt(a + b*sin(c + d*x)**4), x)","F",0
557,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\tan{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)/sqrt(a + b*sin(c + d*x)**4), x)","F",0
558,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\cot{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)/sqrt(a + b*sin(c + d*x)**4), x)","F",0
559,0,0,0,0.000000," ","integrate(cot(d*x+c)**3/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\cot^{3}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**3/sqrt(a + b*sin(c + d*x)**4), x)","F",0
560,0,0,0,0.000000," ","integrate(cot(d*x+c)**5/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\cot^{5}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**5/sqrt(a + b*sin(c + d*x)**4), x)","F",0
561,0,0,0,0.000000," ","integrate(tan(d*x+c)**2/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\tan^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(tan(c + d*x)**2/sqrt(a + b*sin(c + d*x)**4), x)","F",0
562,0,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*sin(c + d*x)**4), x)","F",0
563,0,0,0,0.000000," ","integrate(cot(d*x+c)**2/(a+b*sin(d*x+c)**4)**(1/2),x)","\int \frac{\cot^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**2/sqrt(a + b*sin(c + d*x)**4), x)","F",0
564,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p*tan(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p*tan(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p*tan(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*sin(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p*tan(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p*tan(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*sin(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c)**4)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**3*tan(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**2*tan(d*x+c)**m,x)","\int \left(a + b \sin^{n}{\left(c + d x \right)}\right)^{2} \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**n)**2*tan(c + d*x)**m, x)","F",0
576,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)*tan(d*x+c)**m,x)","\int \left(a + b \sin^{n}{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**n)*tan(c + d*x)**m, x)","F",0
577,0,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+b*sin(d*x+c)**n),x)","\int \frac{\tan^{m}{\left(c + d x \right)}}{a + b \sin^{n}{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)**m/(a + b*sin(c + d*x)**n), x)","F",0
578,-1,0,0,0.000000," ","integrate(tan(d*x+c)**m/(a+b*sin(d*x+c)**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,0,0,0,0.000000," ","integrate(cot(x)*(a+b*sin(x)**n)**(1/2),x)","\int \sqrt{a + b \sin^{n}{\left(x \right)}} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(x)**n)*cot(x), x)","F",0
580,0,0,0,0.000000," ","integrate(cot(x)/(a+b*sin(x)**n)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a + b \sin^{n}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/sqrt(a + b*sin(x)**n), x)","F",0
581,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p*tan(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p*tan(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p*tan(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*sin(d*x+c)**n)**p,x)","\int \left(a + b \sin^{n}{\left(c + d x \right)}\right)^{p} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x)**n)**p*cot(c + d*x), x)","F",0
585,-1,0,0,0.000000," ","integrate(cot(d*x+c)**3*(a+b*sin(d*x+c)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p*tan(d*x+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p*tan(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate(cot(d*x+c)**2*(a+b*sin(d*x+c)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e)**2)/(g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate((c*cos(f*x+e))**m*(d*sin(f*x+e))**n*(a+b*sin(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,0,0,0,0.000000," ","integrate((a+(c*cos(f*x+e)+b*sin(f*x+e))**2)**(1/2),x)","\int \sqrt{a + \left(b \sin{\left(e + f x \right)} + c \cos{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + (b*sin(e + f*x) + c*cos(e + f*x))**2), x)","F",0
594,0,0,0,0.000000," ","integrate(1/(a+(c*cos(f*x+e)+b*sin(f*x+e))**2)**(1/2),x)","\int \frac{1}{\sqrt{a + \left(b \sin{\left(e + f x \right)} + c \cos{\left(e + f x \right)}\right)^{2}}}\, dx"," ",0,"Integral(1/sqrt(a + (b*sin(e + f*x) + c*cos(e + f*x))**2), x)","F",0
