1,1,415,0,4.803159," ","integrate(sin(f*x+e)**3*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{5 a^{2} c x \sin^{6}{\left(e + f x \right)}}{16} - \frac{15 a^{2} c x \sin^{4}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{16} + \frac{3 a^{2} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{15 a^{2} c x \sin^{2}{\left(e + f x \right)} \cos^{4}{\left(e + f x \right)}}{16} + \frac{3 a^{2} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} - \frac{5 a^{2} c x \cos^{6}{\left(e + f x \right)}}{16} + \frac{3 a^{2} c x \cos^{4}{\left(e + f x \right)}}{8} + \frac{11 a^{2} c \sin^{5}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{16 f} + \frac{a^{2} c \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 a^{2} c \sin^{3}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{6 f} - \frac{5 a^{2} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{4 a^{2} c \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 a^{2} c \sin{\left(e + f x \right)} \cos^{5}{\left(e + f x \right)}}{16 f} - \frac{3 a^{2} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} + \frac{8 a^{2} c \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) \sin^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*a**2*c*x*sin(e + f*x)**6/16 - 15*a**2*c*x*sin(e + f*x)**4*cos(e + f*x)**2/16 + 3*a**2*c*x*sin(e + f*x)**4/8 - 15*a**2*c*x*sin(e + f*x)**2*cos(e + f*x)**4/16 + 3*a**2*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 - 5*a**2*c*x*cos(e + f*x)**6/16 + 3*a**2*c*x*cos(e + f*x)**4/8 + 11*a**2*c*sin(e + f*x)**5*cos(e + f*x)/(16*f) + a**2*c*sin(e + f*x)**4*cos(e + f*x)/f + 5*a**2*c*sin(e + f*x)**3*cos(e + f*x)**3/(6*f) - 5*a**2*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 4*a**2*c*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + 5*a**2*c*sin(e + f*x)*cos(e + f*x)**5/(16*f) - 3*a**2*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) + 8*a**2*c*cos(e + f*x)**5/(15*f) - 2*a**2*c*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)*sin(e)**3, True))","A",0
2,1,301,0,2.795939," ","integrate(sin(f*x+e)**2*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{3 a^{2} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 a^{2} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{2} c x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + \frac{a^{2} c \sin^{4}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{5 a^{2} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{4 a^{2} c \sin^{2}{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{8 a^{2} c \cos^{5}{\left(e + f x \right)}}{15 f} - \frac{2 a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) \sin^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*c*x*sin(e + f*x)**4/8 - 3*a**2*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a**2*c*x*sin(e + f*x)**2/2 - 3*a**2*c*x*cos(e + f*x)**4/8 + a**2*c*x*cos(e + f*x)**2/2 + a**2*c*sin(e + f*x)**4*cos(e + f*x)/f + 5*a**2*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + 4*a**2*c*sin(e + f*x)**2*cos(e + f*x)**3/(3*f) - a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + 3*a**2*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 8*a**2*c*cos(e + f*x)**5/(15*f) - 2*a**2*c*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)*sin(e)**2, True))","A",0
3,1,245,0,1.358884," ","integrate(sin(f*x+e)*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{3 a^{2} c x \sin^{4}{\left(e + f x \right)}}{8} - \frac{3 a^{2} c x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{3 a^{2} c x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + \frac{5 a^{2} c \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} + \frac{a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{3 a^{2} c \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) \sin{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*a**2*c*x*sin(e + f*x)**4/8 - 3*a**2*c*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a**2*c*x*sin(e + f*x)**2/2 - 3*a**2*c*x*cos(e + f*x)**4/8 + a**2*c*x*cos(e + f*x)**2/2 + 5*a**2*c*sin(e + f*x)**3*cos(e + f*x)/(8*f) + a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + 3*a**2*c*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*a**2*c*cos(e + f*x)**3/(3*f) - a**2*c*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c)*sin(e), True))","A",0
4,1,133,0,0.700371," ","integrate((a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\begin{cases} - \frac{a^{2} c x \sin^{2}{\left(e + f x \right)}}{2} - \frac{a^{2} c x \cos^{2}{\left(e + f x \right)}}{2} + a^{2} c x + \frac{a^{2} c \sin^{2}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{f} + \frac{a^{2} c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} + \frac{2 a^{2} c \cos^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} c \cos{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a \sin{\left(e \right)} + a\right)^{2} \left(- c \sin{\left(e \right)} + c\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*c*x*sin(e + f*x)**2/2 - a**2*c*x*cos(e + f*x)**2/2 + a**2*c*x + a**2*c*sin(e + f*x)**2*cos(e + f*x)/f + a**2*c*sin(e + f*x)*cos(e + f*x)/(2*f) + 2*a**2*c*cos(e + f*x)**3/(3*f) - a**2*c*cos(e + f*x)/f, Ne(f, 0)), (x*(a*sin(e) + a)**2*(-c*sin(e) + c), True))","A",0
5,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","- a^{2} c \left(\int \left(- \sin{\left(e + f x \right)} \csc{\left(e + f x \right)}\right)\, dx + \int \sin^{2}{\left(e + f x \right)} \csc{\left(e + f x \right)}\, dx + \int \sin^{3}{\left(e + f x \right)} \csc{\left(e + f x \right)}\, dx + \int \left(- \csc{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*c*(Integral(-sin(e + f*x)*csc(e + f*x), x) + Integral(sin(e + f*x)**2*csc(e + f*x), x) + Integral(sin(e + f*x)**3*csc(e + f*x), x) + Integral(-csc(e + f*x), x))","F",0
6,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","- a^{2} c \left(\int \left(- \sin{\left(e + f x \right)} \csc^{2}{\left(e + f x \right)}\right)\, dx + \int \sin^{2}{\left(e + f x \right)} \csc^{2}{\left(e + f x \right)}\, dx + \int \sin^{3}{\left(e + f x \right)} \csc^{2}{\left(e + f x \right)}\, dx + \int \left(- \csc^{2}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*c*(Integral(-sin(e + f*x)*csc(e + f*x)**2, x) + Integral(sin(e + f*x)**2*csc(e + f*x)**2, x) + Integral(sin(e + f*x)**3*csc(e + f*x)**2, x) + Integral(-csc(e + f*x)**2, x))","F",0
7,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","- a^{2} c \left(\int \left(- \sin{\left(e + f x \right)} \csc^{3}{\left(e + f x \right)}\right)\, dx + \int \sin^{2}{\left(e + f x \right)} \csc^{3}{\left(e + f x \right)}\, dx + \int \sin^{3}{\left(e + f x \right)} \csc^{3}{\left(e + f x \right)}\, dx + \int \left(- \csc^{3}{\left(e + f x \right)}\right)\, dx\right)"," ",0,"-a**2*c*(Integral(-sin(e + f*x)*csc(e + f*x)**3, x) + Integral(sin(e + f*x)**2*csc(e + f*x)**3, x) + Integral(sin(e + f*x)**3*csc(e + f*x)**3, x) + Integral(-csc(e + f*x)**3, x))","F",0
8,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-1,0,0,0.000000," ","integrate(csc(f*x+e)**7*(a+a*sin(f*x+e))**2*(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,0,0,0,0.000000," ","integrate(sin(d*x+c)**2*(a+a*sin(d*x+c))**(3/2)*(c-c*sin(d*x+c)),x)","- c \left(\int \left(- a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{2}{\left(c + d x \right)}\right)\, dx + \int a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"-c*(Integral(-a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**2, x) + Integral(a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**4, x))","F",0
13,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/sin(f*x+e)/(c-c*sin(f*x+e)),x)","- \frac{\int \frac{\sqrt{a \sin{\left(e + f x \right)} + a}}{\sin^{2}{\left(e + f x \right)} - \sin{\left(e + f x \right)}}\, dx}{c}"," ",0,"-Integral(sqrt(a*sin(e + f*x) + a)/(sin(e + f*x)**2 - sin(e + f*x)), x)/c","F",0
14,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","- \frac{\int \frac{1}{\sqrt{a \sin{\left(e + f x \right)} + a} \sin^{2}{\left(e + f x \right)} - \sqrt{a \sin{\left(e + f x \right)} + a} \sin{\left(e + f x \right)}}\, dx}{c}"," ",0,"-Integral(1/(sqrt(a*sin(e + f*x) + a)*sin(e + f*x)**2 - sqrt(a*sin(e + f*x) + a)*sin(e + f*x)), x)/c","F",0
15,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e)),x)","- \frac{\int \frac{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a \sin{\left(e + f x \right)} + a}}{\sin{\left(e + f x \right)} - 1}\, dx}{c}"," ",0,"-Integral(sqrt(g*sin(e + f*x))*sqrt(a*sin(e + f*x) + a)/(sin(e + f*x) - 1), x)/c","F",0
16,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))/(g*sin(f*x+e))**(1/2),x)","- \frac{\int \frac{\sqrt{a \sin{\left(e + f x \right)} + a}}{\sqrt{g \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} - \sqrt{g \sin{\left(e + f x \right)}}}\, dx}{c}"," ",0,"-Integral(sqrt(a*sin(e + f*x) + a)/(sqrt(g*sin(e + f*x))*sin(e + f*x) - sqrt(g*sin(e + f*x))), x)/c","F",0
17,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","- \frac{\int \frac{\sqrt{g \sin{\left(e + f x \right)}}}{\sqrt{a \sin{\left(e + f x \right)} + a} \sin{\left(e + f x \right)} - \sqrt{a \sin{\left(e + f x \right)} + a}}\, dx}{c}"," ",0,"-Integral(sqrt(g*sin(e + f*x))/(sqrt(a*sin(e + f*x) + a)*sin(e + f*x) - sqrt(a*sin(e + f*x) + a)), x)/c","F",0
18,0,0,0,0.000000," ","integrate(1/(c-c*sin(f*x+e))/(g*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","- \frac{\int \frac{1}{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a \sin{\left(e + f x \right)} + a} \sin{\left(e + f x \right)} - \sqrt{g \sin{\left(e + f x \right)}} \sqrt{a \sin{\left(e + f x \right)} + a}}\, dx}{c}"," ",0,"-Integral(1/(sqrt(g*sin(e + f*x))*sqrt(a*sin(e + f*x) + a)*sin(e + f*x) - sqrt(g*sin(e + f*x))*sqrt(a*sin(e + f*x) + a)), x)/c","F",0
19,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(1/2)/sin(f*x+e),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}{\sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))/sin(e + f*x), x)","F",0
20,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/sin(f*x+e)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(sqrt(-c*(sin(e + f*x) - 1))*sin(e + f*x)), x)","F",0
21,0,0,0,0.000000," ","integrate((c-c*sin(f*x+e))**(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))/(sqrt(a*(sin(e + f*x) + 1))*sin(e + f*x)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))*sin(e + f*x)), x)","F",0
23,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/sin(f*x+e)/(c+d*sin(f*x+e)),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\left(c + d \sin{\left(e + f x \right)}\right) \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/((c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
24,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right) \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
25,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)*(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e)),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{g \sin{\left(e + f x \right)}}}{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(g*sin(e + f*x))/(c + d*sin(e + f*x)), x)","F",0
26,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\sqrt{g \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(sqrt(g*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0
27,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{g \sin{\left(e + f x \right)}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(g*sin(e + f*x))/(sqrt(a*(sin(e + f*x) + 1))*(c + d*sin(e + f*x))), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{g \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*sqrt(g*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/sin(f*x+e)/(c+c*sin(f*x+e)),x)","\frac{\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\sin^{2}{\left(e + f x \right)} + \sin{\left(e + f x \right)}}\, dx}{c}"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(sin(e + f*x)**2 + sin(e + f*x)), x)/c","F",0
30,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)} + \sqrt{a + b \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx}{c}"," ",0,"Integral(1/(sqrt(a + b*sin(e + f*x))*sin(e + f*x)**2 + sqrt(a + b*sin(e + f*x))*sin(e + f*x)), x)/c","F",0
31,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)*(a+b*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e)),x)","\frac{\int \frac{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)} + 1}\, dx}{c}"," ",0,"Integral(sqrt(g*sin(e + f*x))*sqrt(a + b*sin(e + f*x))/(sin(e + f*x) + 1), x)/c","F",0
32,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))/(g*sin(f*x+e))**(1/2),x)","\frac{\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\sqrt{g \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{g \sin{\left(e + f x \right)}}}\, dx}{c}"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(sqrt(g*sin(e + f*x))*sin(e + f*x) + sqrt(g*sin(e + f*x))), x)/c","F",0
33,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))**(1/2),x)","\frac{\int \frac{\sqrt{g \sin{\left(e + f x \right)}}}{\sqrt{a + b \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{a + b \sin{\left(e + f x \right)}}}\, dx}{c}"," ",0,"Integral(sqrt(g*sin(e + f*x))/(sqrt(a + b*sin(e + f*x))*sin(e + f*x) + sqrt(a + b*sin(e + f*x))), x)/c","F",0
34,0,0,0,0.000000," ","integrate(1/(c+c*sin(f*x+e))/(g*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(1/2),x)","\frac{\int \frac{1}{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)} + \sqrt{g \sin{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}}}\, dx}{c}"," ",0,"Integral(1/(sqrt(g*sin(e + f*x))*sqrt(a + b*sin(e + f*x))*sin(e + f*x) + sqrt(g*sin(e + f*x))*sqrt(a + b*sin(e + f*x))), x)/c","F",0
35,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(1/2)/sin(f*x+e),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{c + d \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(c + d*sin(e + f*x))/sin(e + f*x), x)","F",0
36,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}{\sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))/(sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
37,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/(sqrt(a*(sin(e + f*x) + 1))*sin(e + f*x)), x)","F",0
38,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(e + f*x) + 1))*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
39,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*sin(f*x+e))**2/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)/sin(f*x+e)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{c + d \sin{\left(e + f x \right)}}}{\left(a + b \sin{\left(e + f x \right)}\right) \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*sin(e + f*x))/((a + b*sin(e + f*x))*sin(e + f*x)), x)","F",0
41,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\left(a + b \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/((a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
42,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)*(a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e)),x)","\int \frac{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}}}{c + d \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(g*sin(e + f*x))*sqrt(a + b*sin(e + f*x))/(c + d*sin(e + f*x)), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\sqrt{g \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(sqrt(g*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0
44,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{g \sin{\left(e + f x \right)}}}{\sqrt{a + b \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(g*sin(e + f*x))/(sqrt(a + b*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0
45,0,0,0,0.000000," ","integrate(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}} \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(g*sin(e + f*x))*sqrt(a + b*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0
46,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))**(1/2)*(g*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \sin{\left(e + f x \right)}} \sqrt{c + d \sin{\left(e + f x \right)}}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(g*sin(e + f*x))*sqrt(c + d*sin(e + f*x))/(a + b*sin(e + f*x)), x)","F",0
47,0,0,0,0.000000," ","integrate((g*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{g \sin{\left(e + f x \right)}}}{\left(a + b \sin{\left(e + f x \right)}\right) \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(g*sin(e + f*x))/((a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)*(c+d*sin(f*x+e))**(1/2)/sin(f*x+e),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}} \sqrt{c + d \sin{\left(e + f x \right)}}}{\sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))/sin(e + f*x), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}}}{\sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))/(sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
50,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))**(1/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{a + b \sin{\left(e + f x \right)}} \sqrt{c + d \sin{\left(e + f x \right)}} \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/(sqrt(a + b*sin(e + f*x))*sqrt(c + d*sin(e + f*x))*sin(e + f*x)), x)","F",0
51,-1,0,0,0.000000," ","integrate((a+a*sin(f*x+e))**m*(A+B*sin(f*x+e))**p*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
