1,1,105,0,10.286525," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{a \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**7/(35*d) + 8*a*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a*sin(c + d*x)**3*cos(c + d*x)**4/d + a*sin(c + d*x)*cos(c + d*x)**6/d - a*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**7, True))","A",0
2,1,172,0,6.702090," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{5 a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*x*sin(c + d*x)**6/16 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a*x*cos(c + d*x)**6/16 + 5*a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**6, True))","A",0
3,1,83,0,3.648785," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**5/(15*d) + 4*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a*sin(c + d*x)*cos(c + d*x)**4/d - a*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**5, True))","A",0
4,1,124,0,2.175742," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c)),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{3 a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{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 + 3*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**4, True))","A",0
5,1,60,0,1.015837," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**3/(3*d) + a*sin(c + d*x)*cos(c + d*x)**2/d - a*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**3, True))","A",0
6,1,71,0,0.534482," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c)),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{a \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{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) - a*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**2, True))","A",0
7,1,34,0,0.219457," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{a \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)**2/(2*d) + a*sin(c + d*x)/d, Ne(d, 0)), (x*(a*sin(c) + a)*cos(c), True))","A",0
8,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
9,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
10,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
11,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int \sec^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**4, x) + Integral(sec(c + d*x)**4, x))","F",0
12,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{5}{\left(c + d x \right)}\, dx + \int \sec^{5}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**5, x) + Integral(sec(c + d*x)**5, x))","F",0
13,1,398,0,14.952039," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{5 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{5 a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{73 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{5 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{11 a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a^{2} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**8/128 + 5*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 5*a**2*x*sin(c + d*x)**6/16 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 5*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**2*x*cos(c + d*x)**8/128 + 5*a**2*x*cos(c + d*x)**6/16 + 5*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 5*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 73*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 5*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 5*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 11*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a**2*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c)**6, True))","A",0
14,1,158,0,8.340121," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{8 a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{8 a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{4 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{2} \cos^{6}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sin(c + d*x)**7/(105*d) + 4*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 8*a**2*sin(c + d*x)**5/(15*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + 4*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**4/d - a**2*cos(c + d*x)**6/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c)**5, True))","A",0
15,1,287,0,5.219043," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a^{2} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**6/16 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**2*x*sin(c + d*x)**4/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**2*x*cos(c + d*x)**6/16 + 3*a**2*x*cos(c + d*x)**4/8 + a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a**2*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c)**4, True))","A",0
16,1,107,0,3.051086," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{2 a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{2 a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a^{2} \cos^{4}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sin(c + d*x)**5/(15*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**2/d - a**2*cos(c + d*x)**4/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c)**3, True))","A",0
17,1,180,0,1.997516," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**4/8 + a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**2*x*sin(c + d*x)**2/2 + a**2*x*cos(c + d*x)**4/8 + a**2*x*cos(c + d*x)**2/2 + a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + a**2*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*a**2*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c)**2, True))","A",0
18,1,53,0,0.818305," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin^{2}{\left(c + d x \right)}}{d} + \frac{a^{2} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)**2/d + a**2*sin(c + d*x)/d, Ne(d, 0)), (x*(a*sin(c) + a)**2*cos(c), True))","A",0
19,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int 2 \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(2*sin(c + d*x)*sec(c + d*x), x) + Integral(sin(c + d*x)**2*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
20,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int 2 \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(2*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
21,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int 2 \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(2*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(sin(c + d*x)**2*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
22,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int 2 \sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int \sec^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(2*sin(c + d*x)*sec(c + d*x)**4, x) + Integral(sin(c + d*x)**2*sec(c + d*x)**4, x) + Integral(sec(c + d*x)**4, x))","F",0
23,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,439,0,21.326746," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{15 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{5 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{15 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{5 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{73 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{5 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{15 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{11 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a^{3} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{3 a^{3} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*a**3*x*sin(c + d*x)**8/128 + 15*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 5*a**3*x*sin(c + d*x)**6/16 + 45*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 15*a**3*x*cos(c + d*x)**8/128 + 5*a**3*x*cos(c + d*x)**6/16 + 15*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + 5*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 73*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + 5*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 15*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 11*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a**3*cos(c + d*x)**9/(63*d) - 3*a**3*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c)**6, True))","A",0
28,1,196,0,13.395505," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{8 a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{4 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{8 a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{4 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{3} \cos^{8}{\left(c + d x \right)}}{24 d} - \frac{a^{3} \cos^{6}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sin(c + d*x)**7/(35*d) + 4*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 8*a**3*sin(c + d*x)**5/(15*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + 4*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) + a**3*sin(c + d*x)*cos(c + d*x)**4/d - a**3*cos(c + d*x)**8/(24*d) - a**3*cos(c + d*x)**6/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c)**5, True))","A",0
29,1,335,0,9.999012," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{3 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**6/16 + 9*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**3*x*sin(c + d*x)**4/8 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**3*x*cos(c + d*x)**6/16 + 3*a**3*x*cos(c + d*x)**4/8 + 3*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 5*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a**3*cos(c + d*x)**7/(35*d) - 3*a**3*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c)**4, True))","A",0
30,1,146,0,5.777546," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{2 a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a^{3} \cos^{6}{\left(c + d x \right)}}{12 d} - \frac{3 a^{3} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*sin(c + d*x)**5/(5*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 2*a**3*sin(c + d*x)**3/(3*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**4/(4*d) + a**3*sin(c + d*x)*cos(c + d*x)**2/d - a**3*cos(c + d*x)**6/(12*d) - 3*a**3*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c)**3, True))","A",0
31,1,226,0,3.721555," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 a^{3} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{a^{3} \cos^{3}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**4/8 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**3*x*sin(c + d*x)**2/2 + 3*a**3*x*cos(c + d*x)**4/8 + a**3*x*cos(c + d*x)**2/2 + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + a**3*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*a**3*cos(c + d*x)**5/(15*d) - a**3*cos(c + d*x)**3/d, Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c)**2, True))","A",0
32,1,70,0,1.114065," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{3 a^{3} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{a^{3} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)**4/(4*d) + a**3*sin(c + d*x)**3/d + 3*a**3*sin(c + d*x)**2/(2*d) + a**3*sin(c + d*x)/d, Ne(d, 0)), (x*(a*sin(c) + a)**3*cos(c), True))","A",0
33,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int 3 \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(3*sin(c + d*x)*sec(c + d*x), x) + Integral(3*sin(c + d*x)**2*sec(c + d*x), x) + Integral(sin(c + d*x)**3*sec(c + d*x), x) + Integral(sec(c + d*x), x))","F",0
34,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int 3 \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(3*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(3*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(sec(c + d*x)**2, x))","F",0
35,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int 3 \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(3*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(3*sin(c + d*x)**2*sec(c + d*x)**3, x) + Integral(sin(c + d*x)**3*sec(c + d*x)**3, x) + Integral(sec(c + d*x)**3, x))","F",0
36,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,1,558,0,127.889134," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{8 a^{8} \sin^{13}{\left(c + d x \right)}}{1287 d} + \frac{4 a^{8} \sin^{11}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{99 d} + \frac{32 a^{8} \sin^{11}{\left(c + d x \right)}}{99 d} + \frac{a^{8} \sin^{9}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{9 d} + \frac{16 a^{8} \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{9 d} + \frac{16 a^{8} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{4 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{8 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{32 a^{8} \sin^{7}{\left(c + d x \right)}}{15 d} - \frac{4 a^{8} \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{14 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{112 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{8 a^{8} \sin^{5}{\left(c + d x \right)}}{15 d} - \frac{a^{8} \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{28 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{28 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{4 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{2 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{5 d} - \frac{14 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{3 d} - \frac{28 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{a^{8} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{8} \cos^{12}{\left(c + d x \right)}}{15 d} - \frac{14 a^{8} \cos^{10}{\left(c + d x \right)}}{15 d} - \frac{7 a^{8} \cos^{8}{\left(c + d x \right)}}{3 d} - \frac{4 a^{8} \cos^{6}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{8} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**8*sin(c + d*x)**13/(1287*d) + 4*a**8*sin(c + d*x)**11*cos(c + d*x)**2/(99*d) + 32*a**8*sin(c + d*x)**11/(99*d) + a**8*sin(c + d*x)**9*cos(c + d*x)**4/(9*d) + 16*a**8*sin(c + d*x)**9*cos(c + d*x)**2/(9*d) + 16*a**8*sin(c + d*x)**9/(9*d) + 4*a**8*sin(c + d*x)**7*cos(c + d*x)**4/d + 8*a**8*sin(c + d*x)**7*cos(c + d*x)**2/d + 32*a**8*sin(c + d*x)**7/(15*d) - 4*a**8*sin(c + d*x)**6*cos(c + d*x)**6/(3*d) + 14*a**8*sin(c + d*x)**5*cos(c + d*x)**4/d + 112*a**8*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 8*a**8*sin(c + d*x)**5/(15*d) - a**8*sin(c + d*x)**4*cos(c + d*x)**8/d - 28*a**8*sin(c + d*x)**4*cos(c + d*x)**6/(3*d) + 28*a**8*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + 4*a**8*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - 2*a**8*sin(c + d*x)**2*cos(c + d*x)**10/(5*d) - 14*a**8*sin(c + d*x)**2*cos(c + d*x)**8/(3*d) - 28*a**8*sin(c + d*x)**2*cos(c + d*x)**6/(3*d) + a**8*sin(c + d*x)*cos(c + d*x)**4/d - a**8*cos(c + d*x)**12/(15*d) - 14*a**8*cos(c + d*x)**10/(15*d) - 7*a**8*cos(c + d*x)**8/(3*d) - 4*a**8*cos(c + d*x)**6/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**8*cos(c)**5, True))","A",0
42,1,1280,0,94.801954," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{7 a^{8} x \sin^{12}{\left(c + d x \right)}}{1024} + \frac{21 a^{8} x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{512} + \frac{21 a^{8} x \sin^{10}{\left(c + d x \right)}}{64} + \frac{105 a^{8} x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{1024} + \frac{105 a^{8} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{64} + \frac{105 a^{8} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{35 a^{8} x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{256} + \frac{105 a^{8} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{105 a^{8} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{7 a^{8} x \sin^{6}{\left(c + d x \right)}}{4} + \frac{105 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{1024} + \frac{105 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{315 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{21 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{8} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{21 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{512} + \frac{105 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{64} + \frac{105 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{21 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{7 a^{8} x \cos^{12}{\left(c + d x \right)}}{1024} + \frac{21 a^{8} x \cos^{10}{\left(c + d x \right)}}{64} + \frac{105 a^{8} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{7 a^{8} x \cos^{6}{\left(c + d x \right)}}{4} + \frac{3 a^{8} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{7 a^{8} \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{1024 d} + \frac{119 a^{8} \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3072 d} + \frac{21 a^{8} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} - \frac{281 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{2560 d} + \frac{49 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{32 d} + \frac{105 a^{8} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} - \frac{8 a^{8} \sin^{6}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{231 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{2560 d} - \frac{14 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{385 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} + \frac{7 a^{8} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{48 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{56 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{119 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{3072 d} - \frac{49 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{32 d} - \frac{385 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{64 d} + \frac{14 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 a^{8} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{64 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{105 d} - \frac{32 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{5 d} - \frac{56 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{7 a^{8} \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{1024 d} - \frac{21 a^{8} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{64 d} - \frac{105 a^{8} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{7 a^{8} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{4 d} + \frac{5 a^{8} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{128 a^{8} \cos^{11}{\left(c + d x \right)}}{1155 d} - \frac{64 a^{8} \cos^{9}{\left(c + d x \right)}}{45 d} - \frac{16 a^{8} \cos^{7}{\left(c + d x \right)}}{5 d} - \frac{8 a^{8} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{8} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((7*a**8*x*sin(c + d*x)**12/1024 + 21*a**8*x*sin(c + d*x)**10*cos(c + d*x)**2/512 + 21*a**8*x*sin(c + d*x)**10/64 + 105*a**8*x*sin(c + d*x)**8*cos(c + d*x)**4/1024 + 105*a**8*x*sin(c + d*x)**8*cos(c + d*x)**2/64 + 105*a**8*x*sin(c + d*x)**8/64 + 35*a**8*x*sin(c + d*x)**6*cos(c + d*x)**6/256 + 105*a**8*x*sin(c + d*x)**6*cos(c + d*x)**4/32 + 105*a**8*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 7*a**8*x*sin(c + d*x)**6/4 + 105*a**8*x*sin(c + d*x)**4*cos(c + d*x)**8/1024 + 105*a**8*x*sin(c + d*x)**4*cos(c + d*x)**6/32 + 315*a**8*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 21*a**8*x*sin(c + d*x)**4*cos(c + d*x)**2/4 + 3*a**8*x*sin(c + d*x)**4/8 + 21*a**8*x*sin(c + d*x)**2*cos(c + d*x)**10/512 + 105*a**8*x*sin(c + d*x)**2*cos(c + d*x)**8/64 + 105*a**8*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 21*a**8*x*sin(c + d*x)**2*cos(c + d*x)**4/4 + 3*a**8*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 7*a**8*x*cos(c + d*x)**12/1024 + 21*a**8*x*cos(c + d*x)**10/64 + 105*a**8*x*cos(c + d*x)**8/64 + 7*a**8*x*cos(c + d*x)**6/4 + 3*a**8*x*cos(c + d*x)**4/8 + 7*a**8*sin(c + d*x)**11*cos(c + d*x)/(1024*d) + 119*a**8*sin(c + d*x)**9*cos(c + d*x)**3/(3072*d) + 21*a**8*sin(c + d*x)**9*cos(c + d*x)/(64*d) - 281*a**8*sin(c + d*x)**7*cos(c + d*x)**5/(2560*d) + 49*a**8*sin(c + d*x)**7*cos(c + d*x)**3/(32*d) + 105*a**8*sin(c + d*x)**7*cos(c + d*x)/(64*d) - 8*a**8*sin(c + d*x)**6*cos(c + d*x)**5/(5*d) - 231*a**8*sin(c + d*x)**5*cos(c + d*x)**7/(2560*d) - 14*a**8*sin(c + d*x)**5*cos(c + d*x)**5/(5*d) + 385*a**8*sin(c + d*x)**5*cos(c + d*x)**3/(64*d) + 7*a**8*sin(c + d*x)**5*cos(c + d*x)/(4*d) - 48*a**8*sin(c + d*x)**4*cos(c + d*x)**7/(35*d) - 56*a**8*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 119*a**8*sin(c + d*x)**3*cos(c + d*x)**9/(3072*d) - 49*a**8*sin(c + d*x)**3*cos(c + d*x)**7/(32*d) - 385*a**8*sin(c + d*x)**3*cos(c + d*x)**5/(64*d) + 14*a**8*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 3*a**8*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 64*a**8*sin(c + d*x)**2*cos(c + d*x)**9/(105*d) - 32*a**8*sin(c + d*x)**2*cos(c + d*x)**7/(5*d) - 56*a**8*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 7*a**8*sin(c + d*x)*cos(c + d*x)**11/(1024*d) - 21*a**8*sin(c + d*x)*cos(c + d*x)**9/(64*d) - 105*a**8*sin(c + d*x)*cos(c + d*x)**7/(64*d) - 7*a**8*sin(c + d*x)*cos(c + d*x)**5/(4*d) + 5*a**8*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 128*a**8*cos(c + d*x)**11/(1155*d) - 64*a**8*cos(c + d*x)**9/(45*d) - 16*a**8*cos(c + d*x)**7/(5*d) - 8*a**8*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**8*cos(c)**4, True))","A",0
43,1,422,0,50.556355," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{2 a^{8} \sin^{11}{\left(c + d x \right)}}{99 d} + \frac{a^{8} \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{9 d} + \frac{8 a^{8} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{4 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{4 a^{8} \sin^{7}{\left(c + d x \right)}}{d} - \frac{2 a^{8} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{14 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{56 a^{8} \sin^{5}{\left(c + d x \right)}}{15 d} - \frac{2 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{14 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{28 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{2 a^{8} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{8} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{28 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{14 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{8} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a^{8} \cos^{10}{\left(c + d x \right)}}{5 d} - \frac{7 a^{8} \cos^{8}{\left(c + d x \right)}}{3 d} - \frac{14 a^{8} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{2 a^{8} \cos^{4}{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{8} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**8*sin(c + d*x)**11/(99*d) + a**8*sin(c + d*x)**9*cos(c + d*x)**2/(9*d) + 8*a**8*sin(c + d*x)**9/(9*d) + 4*a**8*sin(c + d*x)**7*cos(c + d*x)**2/d + 4*a**8*sin(c + d*x)**7/d - 2*a**8*sin(c + d*x)**6*cos(c + d*x)**4/d + 14*a**8*sin(c + d*x)**5*cos(c + d*x)**2/d + 56*a**8*sin(c + d*x)**5/(15*d) - 2*a**8*sin(c + d*x)**4*cos(c + d*x)**6/d - 14*a**8*sin(c + d*x)**4*cos(c + d*x)**4/d + 28*a**8*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 2*a**8*sin(c + d*x)**3/(3*d) - a**8*sin(c + d*x)**2*cos(c + d*x)**8/d - 28*a**8*sin(c + d*x)**2*cos(c + d*x)**6/(3*d) - 14*a**8*sin(c + d*x)**2*cos(c + d*x)**4/d + a**8*sin(c + d*x)*cos(c + d*x)**2/d - a**8*cos(c + d*x)**10/(5*d) - 7*a**8*cos(c + d*x)**8/(3*d) - 14*a**8*cos(c + d*x)**6/(3*d) - 2*a**8*cos(c + d*x)**4/d, Ne(d, 0)), (x*(a*sin(c) + a)**8*cos(c)**3, True))","A",0
44,1,1018,0,37.274451," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{7 a^{8} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{35 a^{8} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{35 a^{8} x \sin^{8}{\left(c + d x \right)}}{32} + \frac{35 a^{8} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{35 a^{8} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{35 a^{8} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{35 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{105 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{105 a^{8} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{7 a^{8} x \sin^{4}{\left(c + d x \right)}}{2} + \frac{35 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{35 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{8} + \frac{105 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + 7 a^{8} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{a^{8} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{7 a^{8} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{35 a^{8} x \cos^{8}{\left(c + d x \right)}}{32} + \frac{35 a^{8} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{7 a^{8} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{a^{8} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{7 a^{8} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} - \frac{79 a^{8} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{35 a^{8} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{32 d} - \frac{8 a^{8} \sin^{6}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{7 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{30 d} - \frac{511 a^{8} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{96 d} + \frac{35 a^{8} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{16 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{56 a^{8} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{49 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{384 d} - \frac{385 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{96 d} - \frac{35 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{7 a^{8} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{64 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{224 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{56 a^{8} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{7 a^{8} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{35 a^{8} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{32 d} - \frac{35 a^{8} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{7 a^{8} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{a^{8} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{128 a^{8} \cos^{9}{\left(c + d x \right)}}{315 d} - \frac{64 a^{8} \cos^{7}{\left(c + d x \right)}}{15 d} - \frac{112 a^{8} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{8 a^{8} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{8} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((7*a**8*x*sin(c + d*x)**10/256 + 35*a**8*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 35*a**8*x*sin(c + d*x)**8/32 + 35*a**8*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 35*a**8*x*sin(c + d*x)**6*cos(c + d*x)**2/8 + 35*a**8*x*sin(c + d*x)**6/8 + 35*a**8*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 105*a**8*x*sin(c + d*x)**4*cos(c + d*x)**4/16 + 105*a**8*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 7*a**8*x*sin(c + d*x)**4/2 + 35*a**8*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 35*a**8*x*sin(c + d*x)**2*cos(c + d*x)**6/8 + 105*a**8*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 7*a**8*x*sin(c + d*x)**2*cos(c + d*x)**2 + a**8*x*sin(c + d*x)**2/2 + 7*a**8*x*cos(c + d*x)**10/256 + 35*a**8*x*cos(c + d*x)**8/32 + 35*a**8*x*cos(c + d*x)**6/8 + 7*a**8*x*cos(c + d*x)**4/2 + a**8*x*cos(c + d*x)**2/2 + 7*a**8*sin(c + d*x)**9*cos(c + d*x)/(256*d) - 79*a**8*sin(c + d*x)**7*cos(c + d*x)**3/(384*d) + 35*a**8*sin(c + d*x)**7*cos(c + d*x)/(32*d) - 8*a**8*sin(c + d*x)**6*cos(c + d*x)**3/(3*d) - 7*a**8*sin(c + d*x)**5*cos(c + d*x)**5/(30*d) - 511*a**8*sin(c + d*x)**5*cos(c + d*x)**3/(96*d) + 35*a**8*sin(c + d*x)**5*cos(c + d*x)/(8*d) - 16*a**8*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 56*a**8*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - 49*a**8*sin(c + d*x)**3*cos(c + d*x)**7/(384*d) - 385*a**8*sin(c + d*x)**3*cos(c + d*x)**5/(96*d) - 35*a**8*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) + 7*a**8*sin(c + d*x)**3*cos(c + d*x)/(2*d) - 64*a**8*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 224*a**8*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - 56*a**8*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 7*a**8*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 35*a**8*sin(c + d*x)*cos(c + d*x)**7/(32*d) - 35*a**8*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 7*a**8*sin(c + d*x)*cos(c + d*x)**3/(2*d) + a**8*sin(c + d*x)*cos(c + d*x)/(2*d) - 128*a**8*cos(c + d*x)**9/(315*d) - 64*a**8*cos(c + d*x)**7/(15*d) - 112*a**8*cos(c + d*x)**5/(15*d) - 8*a**8*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**8*cos(c)**2, True))","A",0
45,1,148,0,19.838540," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{a^{8} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{a^{8} \sin^{8}{\left(c + d x \right)}}{d} + \frac{4 a^{8} \sin^{7}{\left(c + d x \right)}}{d} + \frac{28 a^{8} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{14 a^{8} \sin^{5}{\left(c + d x \right)}}{d} + \frac{14 a^{8} \sin^{4}{\left(c + d x \right)}}{d} + \frac{28 a^{8} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{4 a^{8} \sin^{2}{\left(c + d x \right)}}{d} + \frac{a^{8} \sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{8} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**8*sin(c + d*x)**9/(9*d) + a**8*sin(c + d*x)**8/d + 4*a**8*sin(c + d*x)**7/d + 28*a**8*sin(c + d*x)**6/(3*d) + 14*a**8*sin(c + d*x)**5/d + 14*a**8*sin(c + d*x)**4/d + 28*a**8*sin(c + d*x)**3/(3*d) + 4*a**8*sin(c + d*x)**2/d + a**8*sin(c + d*x)/d, Ne(d, 0)), (x*(a*sin(c) + a)**8*cos(c), True))","A",0
46,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,1,1355,0,34.038293," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{75 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{150 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{150 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{75 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{15 d x}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} - \frac{50 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{80 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} - \frac{20 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{160 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{20 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{50 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} + \frac{16}{40 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 400 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 40 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{6}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c/2 + d*x/2)**10/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 75*d*x*tan(c/2 + d*x/2)**8/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 150*d*x*tan(c/2 + d*x/2)**6/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 150*d*x*tan(c/2 + d*x/2)**4/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 75*d*x*tan(c/2 + d*x/2)**2/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 15*d*x/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) - 50*tan(c/2 + d*x/2)**9/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 80*tan(c/2 + d*x/2)**8/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) - 20*tan(c/2 + d*x/2)**7/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 160*tan(c/2 + d*x/2)**4/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 20*tan(c/2 + d*x/2)**3/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 50*tan(c/2 + d*x/2)/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d) + 16/(40*a*d*tan(c/2 + d*x/2)**10 + 200*a*d*tan(c/2 + d*x/2)**8 + 400*a*d*tan(c/2 + d*x/2)**6 + 400*a*d*tan(c/2 + d*x/2)**4 + 200*a*d*tan(c/2 + d*x/2)**2 + 40*a*d), Ne(d, 0)), (x*cos(c)**6/(a*sin(c) + a), True))","A",0
52,1,530,0,18.772962," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{6 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{10 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{10 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 \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)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*tan(c/2 + d*x/2)**7/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*tan(c/2 + d*x/2)**6/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 10*tan(c/2 + d*x/2)**5/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 10*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*tan(c/2 + d*x/2)/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d), Ne(d, 0)), (x*cos(c)**5/(a*sin(c) + a), True))","A",0
53,1,558,0,11.379790," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{3 d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{12 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{4}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 3*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 12*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d), Ne(d, 0)), (x*cos(c)**4/(a*sin(c) + a), True))","A",0
54,1,158,0,5.795578," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} - \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) - 2*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**4 + 2*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)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a), True))","A",0
55,1,88,0,3.017826," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c)),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}{a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{a \sin{\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/(a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**2/(a*sin(c) + a), True))","A",0
56,1,24,0,0.503695," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(c + d*x) + 1)/(a*d), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a), True))","A",0
57,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
58,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
59,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
60,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
61,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**5/(sin(c + d*x) + 1), x)/a","F",0
62,1,2531,0,148.509030," ","integrate(cos(d*x+c)**8/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{105 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{630 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1575 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{2100 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1575 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{630 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{105 d x}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{270 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{960 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{890 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{960 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{660 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1920 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{660 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1920 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{890 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{192 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{270 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{192}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{8}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((105*d*x*tan(c/2 + d*x/2)**12/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 630*d*x*tan(c/2 + d*x/2)**10/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1575*d*x*tan(c/2 + d*x/2)**8/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 2100*d*x*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1575*d*x*tan(c/2 + d*x/2)**4/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 630*d*x*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 105*d*x/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 270*tan(c/2 + d*x/2)**11/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 960*tan(c/2 + d*x/2)**10/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 890*tan(c/2 + d*x/2)**9/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 960*tan(c/2 + d*x/2)**8/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 660*tan(c/2 + d*x/2)**7/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1920*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 660*tan(c/2 + d*x/2)**5/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1920*tan(c/2 + d*x/2)**4/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 890*tan(c/2 + d*x/2)**3/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 192*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 270*tan(c/2 + d*x/2)/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 192/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d), Ne(d, 0)), (x*cos(c)**8/(a*sin(c) + a)**2, True))","A",0
63,1,1037,0,92.862700," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{10 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} - \frac{20 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} + \frac{40 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} - \frac{20 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} + \frac{28 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} - \frac{20 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} + \frac{40 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} - \frac{20 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} + \frac{10 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{5 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 50 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 25 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{7}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((10*tan(c/2 + d*x/2)**9/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) - 20*tan(c/2 + d*x/2)**8/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) + 40*tan(c/2 + d*x/2)**7/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) - 20*tan(c/2 + d*x/2)**6/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) + 28*tan(c/2 + d*x/2)**5/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) - 20*tan(c/2 + d*x/2)**4/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) + 40*tan(c/2 + d*x/2)**3/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) - 20*tan(c/2 + d*x/2)**2/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d) + 10*tan(c/2 + d*x/2)/(5*a**2*d*tan(c/2 + d*x/2)**10 + 25*a**2*d*tan(c/2 + d*x/2)**8 + 50*a**2*d*tan(c/2 + d*x/2)**6 + 50*a**2*d*tan(c/2 + d*x/2)**4 + 25*a**2*d*tan(c/2 + d*x/2)**2 + 5*a**2*d), Ne(d, 0)), (x*cos(c)**7/(a*sin(c) + a)**2, True))","A",0
64,1,1243,0,58.826311," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{15 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{60 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{90 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{60 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{15 d x}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{18 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{96 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{66 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{96 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{66 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{32 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{18 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{32}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{6}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 60*d*x*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 90*d*x*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 60*d*x*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 15*d*x/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 18*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 96*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 66*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 96*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 66*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 32*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 18*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 32/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d), Ne(d, 0)), (x*cos(c)**6/(a*sin(c) + a)**2, True))","A",0
65,1,394,0,37.354781," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**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{12 \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{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{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{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 \cos^{5}{\left(c \right)}}{\left(a \sin{\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) - 12*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) + 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) - 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) + 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*cos(c)**5/(a*sin(c) + a)**2, True))","A",0
66,1,403,0,22.408589," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} + \frac{6 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} + \frac{3 d x}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} + \frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} + \frac{8 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} + \frac{8}{2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**4/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) + 6*d*x*tan(c/2 + d*x/2)**2/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) + 3*d*x/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) + 2*tan(c/2 + d*x/2)**3/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) + 8*tan(c/2 + d*x/2)**2/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) - 2*tan(c/2 + d*x/2)/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d) + 8/(2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d), Ne(d, 0)), (x*cos(c)**4/(a*sin(c) + a)**2, True))","A",0
67,1,150,0,1.788276," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2 \sin^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{\cos^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{2}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) + 2*log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) - 2*sin(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) - cos(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) + 2/(a**2*d*sin(c + d*x) + a**2*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a)**2, True))","A",0
68,1,95,0,6.925018," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{d x}{a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{4}{a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d*x*tan(c/2 + d*x/2)/(a**2*d*tan(c/2 + d*x/2) + a**2*d) - d*x/(a**2*d*tan(c/2 + d*x/2) + a**2*d) - 4/(a**2*d*tan(c/2 + d*x/2) + a**2*d), Ne(d, 0)), (x*cos(c)**2/(a*sin(c) + a)**2, True))","A",0
69,1,32,0,1.121269," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{1}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(a**2*d*sin(c + d*x) + a**2*d), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a)**2, True))","A",0
70,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
71,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
72,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**3/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
73,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**4/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
74,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**5/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
75,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,1,654,0,161.608633," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{2 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{14 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{16 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{14 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{7}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*tan(c/2 + d*x/2)**7/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)**6/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 14*tan(c/2 + d*x/2)**5/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 16*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 14*tan(c/2 + d*x/2)**3/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 2*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d), Ne(d, 0)), (x*cos(c)**7/(a*sin(c) + a)**3, True))","A",0
77,1,690,0,108.265928," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{15 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{45 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{45 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{15 d x}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{18 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{36 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{96 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{18 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} + \frac{44}{6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{6}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c/2 + d*x/2)**6/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 45*d*x*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 45*d*x*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 15*d*x/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 18*tan(c/2 + d*x/2)**5/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 36*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 96*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) - 18*tan(c/2 + d*x/2)/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d) + 44/(6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d), Ne(d, 0)), (x*cos(c)**6/(a*sin(c) + a)**3, True))","A",0
78,1,564,0,64.192187," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{16 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{8 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 16*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 8*log(tan(c/2 + d*x/2) + 1)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 8*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)**3/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 2*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d), Ne(d, 0)), (x*cos(c)**5/(a*sin(c) + a)**3, True))","A",0
79,1,478,0,40.793562," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{3 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{3 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{3 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{3 d x}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{8 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{10}{a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*d*x*tan(c/2 + d*x/2)**3/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 3*d*x*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 3*d*x*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 3*d*x/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 8*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 2*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d) - 10/(a**3*d*tan(c/2 + d*x/2)**3 + a**3*d*tan(c/2 + d*x/2)**2 + a**3*d*tan(c/2 + d*x/2) + a**3*d), Ne(d, 0)), (x*cos(c)**4/(a*sin(c) + a)**3, True))","A",0
80,1,299,0,1.946736," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{4 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{\cos^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 4*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - cos(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a)**3, True))","A",0
81,1,153,0,15.148515," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{6 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{2}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 2/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d), Ne(d, 0)), (x*cos(c)**2/(a*sin(c) + a)**3, True))","A",0
82,1,51,0,1.892542," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{1}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a)**3, True))","A",0
83,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
84,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
85,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**3/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
86,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**4/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
87,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**5/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
88,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,1,2006,0,42.649734," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{16 \sin^{6}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{77 \sin^{5}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{8 \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{155 \sin^{4}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{21 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{168 \sin^{3}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{6 \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{19 \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{104 \sin^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{7 \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{7 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{35 \sin{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{5 \cos^{6}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{\cos^{4}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} - \frac{\cos^{2}{\left(c + d x \right)}}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} + \frac{5}{35 a^{8} d \sin^{7}{\left(c + d x \right)} + 245 a^{8} d \sin^{6}{\left(c + d x \right)} + 735 a^{8} d \sin^{5}{\left(c + d x \right)} + 1225 a^{8} d \sin^{4}{\left(c + d x \right)} + 1225 a^{8} d \sin^{3}{\left(c + d x \right)} + 735 a^{8} d \sin^{2}{\left(c + d x \right)} + 245 a^{8} d \sin{\left(c + d x \right)} + 35 a^{8} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{7}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*sin(c + d*x)**6/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 77*sin(c + d*x)**5/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - 8*sin(c + d*x)**4*cos(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 155*sin(c + d*x)**4/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - 21*sin(c + d*x)**3*cos(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 168*sin(c + d*x)**3/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 6*sin(c + d*x)**2*cos(c + d*x)**4/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - 19*sin(c + d*x)**2*cos(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 104*sin(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 7*sin(c + d*x)*cos(c + d*x)**4/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - 7*sin(c + d*x)*cos(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 35*sin(c + d*x)/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - 5*cos(c + d*x)**6/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + cos(c + d*x)**4/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) - cos(c + d*x)**2/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d) + 5/(35*a**8*d*sin(c + d*x)**7 + 245*a**8*d*sin(c + d*x)**6 + 735*a**8*d*sin(c + d*x)**5 + 1225*a**8*d*sin(c + d*x)**4 + 1225*a**8*d*sin(c + d*x)**3 + 735*a**8*d*sin(c + d*x)**2 + 245*a**8*d*sin(c + d*x) + 35*a**8*d), Ne(d, 0)), (x*cos(c)**7/(a*sin(c) + a)**8, True))","A",0
90,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,1,1120,0,42.109504," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**8,x)","\begin{cases} - \frac{8 \sin^{4}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{21 \sin^{3}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} + \frac{12 \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{19 \sin^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} + \frac{14 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{7 \sin{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{15 \cos^{4}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} + \frac{2 \cos^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{1}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*sin(c + d*x)**4/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 21*sin(c + d*x)**3/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) + 12*sin(c + d*x)**2*cos(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 19*sin(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) + 14*sin(c + d*x)*cos(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 7*sin(c + d*x)/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 15*cos(c + d*x)**4/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) + 2*cos(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 1/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d), Ne(d, 0)), (x*cos(c)**5/(a*sin(c) + a)**8, True))","A",0
92,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,1,493,0,41.537462," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**8,x)","\begin{cases} \frac{6 \sin^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} + \frac{7 \sin{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} - \frac{15 \cos^{2}{\left(c + d x \right)}}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} + \frac{1}{105 a^{8} d \sin^{7}{\left(c + d x \right)} + 735 a^{8} d \sin^{6}{\left(c + d x \right)} + 2205 a^{8} d \sin^{5}{\left(c + d x \right)} + 3675 a^{8} d \sin^{4}{\left(c + d x \right)} + 3675 a^{8} d \sin^{3}{\left(c + d x \right)} + 2205 a^{8} d \sin^{2}{\left(c + d x \right)} + 735 a^{8} d \sin{\left(c + d x \right)} + 105 a^{8} d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*sin(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) + 7*sin(c + d*x)/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) - 15*cos(c + d*x)**2/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d) + 1/(105*a**8*d*sin(c + d*x)**7 + 735*a**8*d*sin(c + d*x)**6 + 2205*a**8*d*sin(c + d*x)**5 + 3675*a**8*d*sin(c + d*x)**4 + 3675*a**8*d*sin(c + d*x)**3 + 2205*a**8*d*sin(c + d*x)**2 + 735*a**8*d*sin(c + d*x) + 105*a**8*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a)**8, True))","A",0
94,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,1,128,0,42.269313," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**8,x)","\begin{cases} - \frac{1}{7 a^{8} d \sin^{7}{\left(c + d x \right)} + 49 a^{8} d \sin^{6}{\left(c + d x \right)} + 147 a^{8} d \sin^{5}{\left(c + d x \right)} + 245 a^{8} d \sin^{4}{\left(c + d x \right)} + 245 a^{8} d \sin^{3}{\left(c + d x \right)} + 147 a^{8} d \sin^{2}{\left(c + d x \right)} + 49 a^{8} d \sin{\left(c + d x \right)} + 7 a^{8} d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{8}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(7*a**8*d*sin(c + d*x)**7 + 49*a**8*d*sin(c + d*x)**6 + 147*a**8*d*sin(c + d*x)**5 + 245*a**8*d*sin(c + d*x)**4 + 245*a**8*d*sin(c + d*x)**3 + 147*a**8*d*sin(c + d*x)**2 + 49*a**8*d*sin(c + d*x) + 7*a**8*d), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a)**8, True))","A",0
96,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**4, x)","F",0
105,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**2, x)","F",0
107,1,58,0,0.678765," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\begin{cases} \frac{2 \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)}}{3 d} + \frac{2 \sqrt{a \sin{\left(c + d x \right)} + a}}{3 d} & \text{for}\: d \neq 0 \\x \sqrt{a \sin{\left(c \right)} + a} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)/(3*d) + 2*sqrt(a*sin(c + d*x) + a)/(3*d), Ne(d, 0)), (x*sqrt(a*sin(c) + a)*cos(c), True))","A",0
108,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sec(c + d*x), x)","F",0
109,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sec(c + d*x)**2, x)","F",0
110,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sec(c + d*x)**3, x)","F",0
111,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sec(c + d*x)**4, x)","F",0
112,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,1,252,0,127.616878," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\begin{cases} \frac{8 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{4}{\left(c + d x \right)}}{45 d} + \frac{152 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{3}{\left(c + d x \right)}}{315 d} + \frac{2 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{8 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{2}{\left(c + d x \right)}}{21 d} + \frac{4 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{8 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)}}{315 d} + \frac{2 a \sqrt{a \sin{\left(c + d x \right)} + a} \cos^{2}{\left(c + d x \right)}}{5 d} - \frac{16 a \sqrt{a \sin{\left(c + d x \right)} + a}}{315 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{\frac{3}{2}} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**4/(45*d) + 152*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**3/(315*d) + 2*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**2*cos(c + d*x)**2/(5*d) + 8*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**2/(21*d) + 4*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)*cos(c + d*x)**2/(5*d) + 8*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)/(315*d) + 2*a*sqrt(a*sin(c + d*x) + a)*cos(c + d*x)**2/(5*d) - 16*a*sqrt(a*sin(c + d*x) + a)/(315*d), Ne(d, 0)), (x*(a*sin(c) + a)**(3/2)*cos(c)**3, True))","A",0
119,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*cos(c + d*x)**2, x)","F",0
120,1,90,0,29.541749," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\begin{cases} \frac{2 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{2}{\left(c + d x \right)}}{5 d} + \frac{4 a \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)}}{5 d} + \frac{2 a \sqrt{a \sin{\left(c + d x \right)} + a}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{\frac{3}{2}} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**2/(5*d) + 4*a*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)/(5*d) + 2*a*sqrt(a*sin(c + d*x) + a)/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**(3/2)*cos(c), True))","A",0
121,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,0,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
160,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
162,1,32,0,1.212480," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\begin{cases} \frac{2 \sqrt{a \sin{\left(c + d x \right)} + a}}{a d} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\sqrt{a \sin{\left(c \right)} + a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sqrt(a*sin(c + d*x) + a)/(a*d), Ne(d, 0)), (x*cos(c)/sqrt(a*sin(c) + a), True))","A",0
163,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
164,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
165,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
166,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
167,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**5/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
168,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sec(c + d*x)**6/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
169,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,0,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**4/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
173,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
175,1,56,0,3.460730," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = \frac{3 \pi}{2} \vee c = - d x + \frac{3 \pi}{2}\right) \wedge \left(c = - d x + \frac{3 \pi}{2} \vee d = 0\right) \\\frac{x \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{\frac{3}{2}}} & \text{for}\: d = 0 \\- \frac{2}{a d \sqrt{a \sin{\left(c + d x \right)} + a}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(d, 0) | Eq(c, -d*x + 3*pi/2)) & (Eq(c, 3*pi/2) | Eq(c, -d*x + 3*pi/2))), (x*cos(c)/(a*sin(c) + a)**(3/2), Eq(d, 0)), (-2/(a*d*sqrt(a*sin(c + d*x) + a)), True))","A",0
176,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
177,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
178,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
179,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
180,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**6/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
182,-1,0,0,0.000000," ","integrate(cos(d*x+c)**10/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(cos(d*x+c)**9/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,1,267,0,26.903288," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = \frac{3 \pi}{2} \vee c = - d x + \frac{3 \pi}{2}\right) \wedge \left(c = - d x + \frac{3 \pi}{2} \vee d = 0\right) \\\frac{x \cos^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{\frac{5}{2}}} & \text{for}\: d = 0 \\- \frac{8 \sqrt{a \sin{\left(c + d x \right)} + a} \sin^{2}{\left(c + d x \right)}}{3 a^{3} d \sin^{2}{\left(c + d x \right)} + 6 a^{3} d \sin{\left(c + d x \right)} + 3 a^{3} d} - \frac{24 \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)}}{3 a^{3} d \sin^{2}{\left(c + d x \right)} + 6 a^{3} d \sin{\left(c + d x \right)} + 3 a^{3} d} - \frac{2 \sqrt{a \sin{\left(c + d x \right)} + a} \cos^{2}{\left(c + d x \right)}}{3 a^{3} d \sin^{2}{\left(c + d x \right)} + 6 a^{3} d \sin{\left(c + d x \right)} + 3 a^{3} d} - \frac{16 \sqrt{a \sin{\left(c + d x \right)} + a}}{3 a^{3} d \sin^{2}{\left(c + d x \right)} + 6 a^{3} d \sin{\left(c + d x \right)} + 3 a^{3} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(d, 0) | Eq(c, -d*x + 3*pi/2)) & (Eq(c, 3*pi/2) | Eq(c, -d*x + 3*pi/2))), (x*cos(c)**3/(a*sin(c) + a)**(5/2), Eq(d, 0)), (-8*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)**2/(3*a**3*d*sin(c + d*x)**2 + 6*a**3*d*sin(c + d*x) + 3*a**3*d) - 24*sqrt(a*sin(c + d*x) + a)*sin(c + d*x)/(3*a**3*d*sin(c + d*x)**2 + 6*a**3*d*sin(c + d*x) + 3*a**3*d) - 2*sqrt(a*sin(c + d*x) + a)*cos(c + d*x)**2/(3*a**3*d*sin(c + d*x)**2 + 6*a**3*d*sin(c + d*x) + 3*a**3*d) - 16*sqrt(a*sin(c + d*x) + a)/(3*a**3*d*sin(c + d*x)**2 + 6*a**3*d*sin(c + d*x) + 3*a**3*d), True))","A",0
190,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
191,1,65,0,25.470680," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\begin{cases} - \frac{2}{3 a^{2} d \sqrt{a \sin{\left(c + d x \right)} + a} \sin{\left(c + d x \right)} + 3 a^{2} d \sqrt{a \sin{\left(c + d x \right)} + a}} & \text{for}\: d \neq 0 \\\frac{x \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2/(3*a**2*d*sqrt(a*sin(c + d*x) + a)*sin(c + d*x) + 3*a**2*d*sqrt(a*sin(c + d*x) + a)), Ne(d, 0)), (x*cos(c)/(a*sin(c) + a)**(5/2), True))","A",0
192,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
193,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
194,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
196,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))*(e*cos(d*x+c))**(1/2),x)","a \left(\int \sqrt{e \cos{\left(c + d x \right)}}\, dx + \int \sqrt{e \cos{\left(c + d x \right)}} \sin{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sqrt(e*cos(c + d*x)), x) + Integral(sqrt(e*cos(c + d*x))*sin(c + d*x), x))","F",0
200,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))**(1/2),x)","a \left(\int \frac{1}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx + \int \frac{\sin{\left(c + d x \right)}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx\right)"," ",0,"a*(Integral(1/sqrt(e*cos(c + d*x)), x) + Integral(sin(c + d*x)/sqrt(e*cos(c + d*x)), x))","F",0
201,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))**(3/2),x)","a \left(\int \frac{1}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx + \int \frac{\sin{\left(c + d x \right)}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx\right)"," ",0,"a*(Integral((e*cos(c + d*x))**(-3/2), x) + Integral(sin(c + d*x)/(e*cos(c + d*x))**(3/2), x))","F",0
202,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
207,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sqrt{e \cos{\left(c + d x \right)}}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sqrt(e*cos(c + d*x))/(sin(c + d*x) + 1), x)/a","F",0
239,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))/(e*cos(d*x+c))**(1/2),x)","\frac{\int \frac{1}{\sqrt{e \cos{\left(c + d x \right)}} \sin{\left(c + d x \right)} + \sqrt{e \cos{\left(c + d x \right)}}}\, dx}{a}"," ",0,"Integral(1/(sqrt(e*cos(c + d*x))*sin(c + d*x) + sqrt(e*cos(c + d*x))), x)/a","F",0
240,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**2/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(15/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(13/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**3/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(15/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(13/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**4/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*(e*cos(c + d*x))**(3/2), x)","F",0
274,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sqrt{e \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sqrt(e*cos(c + d*x)), x)","F",0
275,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/(e*cos(d*x+c))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/sqrt(e*cos(c + d*x)), x)","F",0
276,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/(e*cos(d*x+c))**(3/2),x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/(e*cos(c + d*x))**(3/2), x)","F",0
277,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/(e*cos(d*x+c))**(5/2),x)","\int \frac{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))/(e*cos(c + d*x))**(5/2), x)","F",0
278,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(1/2)/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)*(e*cos(d*x+c))**(1/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{e \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*sqrt(e*cos(c + d*x)), x)","F",0
283,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)/sqrt(e*cos(c + d*x)), x)","F",0
284,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)/(e*cos(c + d*x))**(3/2), x)","F",0
285,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
298,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((e*cos(c + d*x))**(3/2)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
300,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sqrt{e \cos{\left(c + d x \right)}}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(e*cos(c + d*x))/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
301,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(c + d*x) + 1))*sqrt(e*cos(c + d*x))), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(c + d*x) + 1))*(e*cos(c + d*x))**(3/2)), x)","F",0
303,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
306,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**(3/2)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
308,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sqrt{e \cos{\left(c + d x \right)}}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(e*cos(c + d*x))/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(3/2)/(e*cos(d*x+c))**(1/2),x)","\int \frac{1}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/((a*(sin(c + d*x) + 1))**(3/2)*sqrt(e*cos(c + d*x))), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{1}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a*(sin(c + d*x) + 1))**(3/2)*(e*cos(c + d*x))**(3/2)), x)","F",0
311,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
316,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
317,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\sqrt{e \cos{\left(c + d x \right)}}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(e*cos(c + d*x))/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
318,-1,0,0,0.000000," ","integrate(1/(a+a*sin(d*x+c))**(5/2)/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/3)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/3)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(2/3)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{\frac{2}{3}}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((e*cos(c + d*x))**(2/3)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
324,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/3)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sqrt[3]{e \cos{\left(c + d x \right)}}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((e*cos(c + d*x))**(1/3)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(1/3)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sqrt[3]{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(c + d*x) + 1))*(e*cos(c + d*x))**(1/3)), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(4/3)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \left(e \cos{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral(1/(sqrt(a*(sin(c + d*x) + 1))*(e*cos(c + d*x))**(4/3)), x)","F",0
327,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \left(e \cos{\left(c + d x \right)}\right)^{p}\, dx + \int 2 \left(e \cos{\left(c + d x \right)}\right)^{p} \sin{\left(c + d x \right)}\, dx + \int \left(e \cos{\left(c + d x \right)}\right)^{p} \sin^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral((e*cos(c + d*x))**p, x) + Integral(2*(e*cos(c + d*x))**p*sin(c + d*x), x) + Integral((e*cos(c + d*x))**p*sin(c + d*x)**2, x))","F",0
330,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c)),x)","a \left(\int \left(e \cos{\left(c + d x \right)}\right)^{p}\, dx + \int \left(e \cos{\left(c + d x \right)}\right)^{p} \sin{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral((e*cos(c + d*x))**p, x) + Integral((e*cos(c + d*x))**p*sin(c + d*x), x))","F",0
331,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral((e*cos(c + d*x))**p/(sin(c + d*x) + 1), x)/a","F",0
332,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((e*cos(c + d*x))**p/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
333,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \left(e \cos{\left(c + d x \right)}\right)^{p}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*(e*cos(c + d*x))**p, x)","F",0
338,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \left(e \cos{\left(c + d x \right)}\right)^{p}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*(e*cos(c + d*x))**p, x)","F",0
339,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
340,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+a*sin(d*x+c))**(5/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/(a*(sin(c + d*x) + 1))**(5/2), x)","F",0
342,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \left(e \cos{\left(c + d x \right)}\right)^{p}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*(e*cos(c + d*x))**p, x)","F",0
343,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,1,5534,0,172.269166," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \cos^{5}{\left(c \right)} & \text{for}\: d = 0 \\\frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{4}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{48 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{72 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{48 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{20 \sin^{3}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{6 \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{56 \sin^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{8 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{52 \sin{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} - \frac{3 \cos^{4}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{2 \cos^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{16}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} & \text{for}\: m = -5 \\- \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{8 \sin^{4}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{4 \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{52 \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{6 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{72 \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{\cos^{4}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{2 \cos^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{28}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} & \text{for}\: m = -4 \\\frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{16 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{8 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} & \text{for}\: m = -3 \\\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{12 \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{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{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{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}\: m = -2 \\\frac{6 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{10 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{10 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 \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)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} & \text{for}\: m = -1 \\\frac{m^{4} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{m^{4} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{4 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{8 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{14 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{4 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{14 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{8 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{24 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{44 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{24 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{84 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{8 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{71 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{36 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{71 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{4 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{48 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{120 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{152 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{72 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{268 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{24 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{154 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{80 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{24 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{154 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{36 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{64 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{120 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{160 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{240 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{80 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{120 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{120 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{80 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{24 \left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*cos(c)**5, Eq(d, 0)), (12*log(sin(c + d*x) + 1)*sin(c + d*x)**4/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 48*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 72*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 48*log(sin(c + d*x) + 1)*sin(c + d*x)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 12*log(sin(c + d*x) + 1)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 20*sin(c + d*x)**3/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 6*sin(c + d*x)**2*cos(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 56*sin(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 8*sin(c + d*x)*cos(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 52*sin(c + d*x)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) - 3*cos(c + d*x)**4/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 2*cos(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 16/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d), Eq(m, -5)), (-12*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 12*log(sin(c + d*x) + 1)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 8*sin(c + d*x)**4/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 4*sin(c + d*x)**2*cos(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 52*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 6*sin(c + d*x)*cos(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 72*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - cos(c + d*x)**4/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 2*cos(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 28/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d), Eq(m, -4)), (8*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 16*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 8*log(tan(c/2 + d*x/2) + 1)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 8*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)**3/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 2*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 6*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**4 + 2*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d), Eq(m, -3)), (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) - 12*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) + 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) - 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) + 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), Eq(m, -2)), (6*tan(c/2 + d*x/2)**7/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*tan(c/2 + d*x/2)**6/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 10*tan(c/2 + d*x/2)**5/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 10*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*tan(c/2 + d*x/2)/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d), Eq(m, -1)), (m**4*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + m**4*(a*sin(c + d*x) + a)**m*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 4*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 8*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 14*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 4*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 14*m**3*(a*sin(c + d*x) + a)**m*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 8*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 24*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 44*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 24*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 84*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 8*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 71*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 36*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 71*m**2*(a*sin(c + d*x) + a)**m*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 4*m**2*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 48*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 120*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 152*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 72*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 268*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 24*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 154*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 80*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 24*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 154*m*(a*sin(c + d*x) + a)**m*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 36*m*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 64*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 120*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 160*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 240*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 80*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 120*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 120*(a*sin(c + d*x) + a)**m*cos(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 80*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 24*(a*sin(c + d*x) + a)**m/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d), True))","A",0
345,1,1114,0,21.470154," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \cos^{3}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{4 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{\cos^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{2}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: m = -3 \\\frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2 \sin^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{\cos^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{2}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: m = -2 \\\frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} - \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{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)} + a d} & \text{for}\: m = -1 \\\frac{m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{2 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{4 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{5 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{2 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{5 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{4 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{6 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{6 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{6 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \cos^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} - \frac{2 \left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*cos(c)**3, Eq(d, 0)), (-2*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 4*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - cos(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Eq(m, -3)), (2*log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) + 2*log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) - 2*sin(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) - cos(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) + 2/(a**2*d*sin(c + d*x) + a**2*d), Eq(m, -2)), (2*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) - 2*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**4 + 2*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)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d), Eq(m, -1)), (m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + m**2*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 2*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 4*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 5*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 2*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 5*m*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 4*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 6*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 6*(a*sin(c + d*x) + a)**m*sin(c + d*x)*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 6*(a*sin(c + d*x) + a)**m*cos(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) - 2*(a*sin(c + d*x) + a)**m/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d), True))","A",0
346,1,80,0,2.471771," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**m,x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{for}\: d = 0 \wedge m = -1 \\x \left(a \sin{\left(c \right)} + a\right)^{m} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} & \text{for}\: m = -1 \\\frac{\left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m + d} + \frac{\left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m + d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/(a*sin(c) + a), Eq(d, 0) & Eq(m, -1)), (x*(a*sin(c) + a)**m*cos(c), Eq(d, 0)), (log(sin(c + d*x) + 1)/(a*d), Eq(m, -1)), ((a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m + d) + (a*sin(c + d*x) + a)**m/(d*m + d), True))","A",0
347,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*sec(c + d*x), x)","F",0
348,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*cos(c + d*x)**4, x)","F",0
351,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*cos(c + d*x)**2, x)","F",0
352,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*sec(c + d*x)**2, x)","F",0
353,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
354,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \sqrt{e \cos{\left(c + d x \right)}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*sqrt(e*cos(c + d*x)), x)","F",0
357,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**m/(e*cos(d*x+c))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m/sqrt(e*cos(c + d*x)), x)","F",0
358,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**m/(e*cos(d*x+c))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m/(e*cos(c + d*x))**(3/2), x)","F",0
359,-1,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**m/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-4-m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-3-m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-2-m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-1-m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**m/((e*cos(d*x+c))**m),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \left(e \cos{\left(c + d x \right)}\right)^{- m}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*(e*cos(c + d*x))**(-m), x)","F",0
365,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1-m)*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \left(e \cos{\left(c + d x \right)}\right)^{1 - m}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*(e*cos(c + d*x))**(1 - m), x)","F",0
366,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(2-m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
369,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1-2*m)*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \left(e \cos{\left(c + d x \right)}\right)^{1 - 2 m}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*(e*cos(c + d*x))**(1 - 2*m), x)","F",0
370,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-1-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-3-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(4-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(2-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))**m/((e*cos(d*x+c))**(2*m)),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \left(e \cos{\left(c + d x \right)}\right)^{- 2 m}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*(e*cos(c + d*x))**(-2*m), x)","F",0
375,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-2-2*m)*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,1,83,0,4.423658," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{b \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**5/(15*d) + 4*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a*sin(c + d*x)*cos(c + d*x)**4/d - b*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a + b*sin(c))*cos(c)**5, True))","A",0
377,1,60,0,1.225454," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{b \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**3/(3*d) + a*sin(c + d*x)*cos(c + d*x)**2/d - b*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a + b*sin(c))*cos(c)**3, True))","A",0
378,1,34,0,0.245010," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{a \sin{\left(c + d x \right)}}{d} + \frac{b \sin^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)/d + b*sin(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*sin(c))*cos(c), True))","A",0
379,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sec(c + d*x), x)","F",0
380,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sec(c + d*x)**3, x)","F",0
381,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sec^{5}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sec(c + d*x)**5, x)","F",0
382,1,124,0,2.338698," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c)),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{3 a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{b \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \cos^{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 + 3*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - b*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a + b*sin(c))*cos(c)**4, True))","A",0
383,1,71,0,0.642960," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c)),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{b \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \cos^{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) - b*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a + b*sin(c))*cos(c)**2, True))","A",0
384,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sec(c + d*x)**2, x)","F",0
385,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sec(c + d*x)**4, x)","F",0
386,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,1,158,0,7.448475," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{8 a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a b \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{8 b^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sin(c + d*x)**5/(15*d) + 4*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**4/d - a*b*cos(c + d*x)**6/(3*d) + 8*b**2*sin(c + d*x)**7/(105*d) + 4*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c)**5, True))","A",0
388,1,107,0,3.162952," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{2 a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a b \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{2 b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**2/d - a*b*cos(c + d*x)**4/(2*d) + 2*b**2*sin(c + d*x)**5/(15*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c)**3, True))","A",0
389,1,53,0,0.769666," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \sin{\left(c + d x \right)}}{d} + \frac{a b \sin^{2}{\left(c + d x \right)}}{d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)/d + a*b*sin(c + d*x)**2/d + b**2*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c), True))","A",0
390,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sec(c + d*x), x)","F",0
391,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sec(c + d*x)**3, x)","F",0
392,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,1,398,0,13.092891," ","integrate(cos(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a b \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{5 b^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{5 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{5 b^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{73 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{5 b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**6/16 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**2*x*cos(c + d*x)**6/16 + 5*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a*b*cos(c + d*x)**7/(7*d) + 5*b**2*x*sin(c + d*x)**8/128 + 5*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 5*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 5*b**2*x*cos(c + d*x)**8/128 + 5*b**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 73*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 5*b**2*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c)**6, True))","A",0
394,1,287,0,4.685871," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a b \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b^{2} \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{\left(c \right)}\right)^{2} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**4/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**2*x*cos(c + d*x)**4/8 + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a*b*cos(c + d*x)**5/(5*d) + b**2*x*sin(c + d*x)**6/16 + 3*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b**2*x*cos(c + d*x)**6/16 + b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c)**4, True))","A",0
395,1,180,0,1.409989," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 a b \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{b^{2} \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{\left(c \right)}\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**2/2 + a**2*x*cos(c + d*x)**2/2 + a**2*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*a*b*cos(c + d*x)**3/(3*d) + b**2*x*sin(c + d*x)**4/8 + b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + b**2*x*cos(c + d*x)**4/8 + b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*sin(c))**2*cos(c)**2, True))","A",0
396,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sec(c + d*x)**2, x)","F",0
397,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sec(c + d*x)**4, x)","F",0
398,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,1,202,0,12.917435," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{8 a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{2} b \cos^{6}{\left(c + d x \right)}}{2 d} + \frac{8 a b^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{4 a b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{b^{3} \cos^{8}{\left(c + d x \right)}}{24 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sin(c + d*x)**5/(15*d) + 4*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**4/d - a**2*b*cos(c + d*x)**6/(2*d) + 8*a*b**2*sin(c + d*x)**7/(35*d) + 4*a*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**4/d - b**3*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) - b**3*cos(c + d*x)**8/(24*d), Ne(d, 0)), (x*(a + b*sin(c))**3*cos(c)**5, True))","A",0
401,1,151,0,4.867867," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{3 a^{2} b \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{2 a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} - \frac{b^{3} \cos^{6}{\left(c + d x \right)}}{12 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*sin(c + d*x)**3/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**2/d - 3*a**2*b*cos(c + d*x)**4/(4*d) + 2*a*b**2*sin(c + d*x)**5/(5*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d - b**3*sin(c + d*x)**2*cos(c + d*x)**4/(4*d) - b**3*cos(c + d*x)**6/(12*d), Ne(d, 0)), (x*(a + b*sin(c))**3*cos(c)**3, True))","A",0
402,1,73,0,1.273673," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin{\left(c + d x \right)}}{d} + \frac{3 a^{2} b \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)}}{d} + \frac{b^{3} \sin^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)/d + 3*a**2*b*sin(c + d*x)**2/(2*d) + a*b**2*sin(c + d*x)**3/d + b**3*sin(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a + b*sin(c))**3*cos(c), True))","A",0
403,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**3,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**3*sec(c + d*x), x)","F",0
404,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{3} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**3*sec(c + d*x)**3, x)","F",0
405,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,1,348,0,8.674152," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{3 a^{2} b \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{3 a b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 b^{3} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**4/8 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**3*x*cos(c + d*x)**4/8 + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 3*a**2*b*cos(c + d*x)**5/(5*d) + 3*a*b**2*x*sin(c + d*x)**6/16 + 9*a*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a*b**2*x*cos(c + d*x)**6/16 + 3*a*b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 3*a*b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - b**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*b**3*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a + b*sin(c))**3*cos(c)**4, True))","A",0
407,1,236,0,3.157185," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{a^{2} b \cos^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 b^{3} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(c + d*x)**2/2 + a**3*x*cos(c + d*x)**2/2 + a**3*sin(c + d*x)*cos(c + d*x)/(2*d) - a**2*b*cos(c + d*x)**3/d + 3*a*b**2*x*sin(c + d*x)**4/8 + 3*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a*b**2*x*cos(c + d*x)**4/8 + 3*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*b**3*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a + b*sin(c))**3*cos(c)**2, True))","A",0
408,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**3*sec(c + d*x)**2, x)","F",0
409,-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
410,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,1,614,0,119.110565," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{8 a^{8} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{8} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{8} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{4 a^{7} b \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{32 a^{6} b^{2} \sin^{7}{\left(c + d x \right)}}{15 d} + \frac{112 a^{6} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{28 a^{6} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{28 a^{5} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{7 a^{5} b^{3} \cos^{8}{\left(c + d x \right)}}{3 d} + \frac{16 a^{4} b^{4} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{8 a^{4} b^{4} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{14 a^{4} b^{4} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{28 a^{3} b^{5} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{14 a^{3} b^{5} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{3 d} - \frac{14 a^{3} b^{5} \cos^{10}{\left(c + d x \right)}}{15 d} + \frac{32 a^{2} b^{6} \sin^{11}{\left(c + d x \right)}}{99 d} + \frac{16 a^{2} b^{6} \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{9 d} + \frac{4 a^{2} b^{6} \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{4 a b^{7} \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{a b^{7} \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{2 a b^{7} \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{5 d} - \frac{a b^{7} \cos^{12}{\left(c + d x \right)}}{15 d} + \frac{8 b^{8} \sin^{13}{\left(c + d x \right)}}{1287 d} + \frac{4 b^{8} \sin^{11}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{99 d} + \frac{b^{8} \sin^{9}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{8} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**8*sin(c + d*x)**5/(15*d) + 4*a**8*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**8*sin(c + d*x)*cos(c + d*x)**4/d - 4*a**7*b*cos(c + d*x)**6/(3*d) + 32*a**6*b**2*sin(c + d*x)**7/(15*d) + 112*a**6*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 28*a**6*b**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - 28*a**5*b**3*sin(c + d*x)**2*cos(c + d*x)**6/(3*d) - 7*a**5*b**3*cos(c + d*x)**8/(3*d) + 16*a**4*b**4*sin(c + d*x)**9/(9*d) + 8*a**4*b**4*sin(c + d*x)**7*cos(c + d*x)**2/d + 14*a**4*b**4*sin(c + d*x)**5*cos(c + d*x)**4/d - 28*a**3*b**5*sin(c + d*x)**4*cos(c + d*x)**6/(3*d) - 14*a**3*b**5*sin(c + d*x)**2*cos(c + d*x)**8/(3*d) - 14*a**3*b**5*cos(c + d*x)**10/(15*d) + 32*a**2*b**6*sin(c + d*x)**11/(99*d) + 16*a**2*b**6*sin(c + d*x)**9*cos(c + d*x)**2/(9*d) + 4*a**2*b**6*sin(c + d*x)**7*cos(c + d*x)**4/d - 4*a*b**7*sin(c + d*x)**6*cos(c + d*x)**6/(3*d) - a*b**7*sin(c + d*x)**4*cos(c + d*x)**8/d - 2*a*b**7*sin(c + d*x)**2*cos(c + d*x)**10/(5*d) - a*b**7*cos(c + d*x)**12/(15*d) + 8*b**8*sin(c + d*x)**13/(1287*d) + 4*b**8*sin(c + d*x)**11*cos(c + d*x)**2/(99*d) + b**8*sin(c + d*x)**9*cos(c + d*x)**4/(9*d), Ne(d, 0)), (x*(a + b*sin(c))**8*cos(c)**5, True))","A",0
414,1,468,0,54.457656," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{2 a^{8} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{8} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{2 a^{7} b \cos^{4}{\left(c + d x \right)}}{d} + \frac{56 a^{6} b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{28 a^{6} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{14 a^{5} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{14 a^{5} b^{3} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{4 a^{4} b^{4} \sin^{7}{\left(c + d x \right)}}{d} + \frac{14 a^{4} b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{14 a^{3} b^{5} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{28 a^{3} b^{5} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{7 a^{3} b^{5} \cos^{8}{\left(c + d x \right)}}{3 d} + \frac{8 a^{2} b^{6} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{4 a^{2} b^{6} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{2 a b^{7} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{2 a b^{7} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{a b^{7} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{a b^{7} \cos^{10}{\left(c + d x \right)}}{5 d} + \frac{2 b^{8} \sin^{11}{\left(c + d x \right)}}{99 d} + \frac{b^{8} \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{8} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**8*sin(c + d*x)**3/(3*d) + a**8*sin(c + d*x)*cos(c + d*x)**2/d - 2*a**7*b*cos(c + d*x)**4/d + 56*a**6*b**2*sin(c + d*x)**5/(15*d) + 28*a**6*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - 14*a**5*b**3*sin(c + d*x)**2*cos(c + d*x)**4/d - 14*a**5*b**3*cos(c + d*x)**6/(3*d) + 4*a**4*b**4*sin(c + d*x)**7/d + 14*a**4*b**4*sin(c + d*x)**5*cos(c + d*x)**2/d - 14*a**3*b**5*sin(c + d*x)**4*cos(c + d*x)**4/d - 28*a**3*b**5*sin(c + d*x)**2*cos(c + d*x)**6/(3*d) - 7*a**3*b**5*cos(c + d*x)**8/(3*d) + 8*a**2*b**6*sin(c + d*x)**9/(9*d) + 4*a**2*b**6*sin(c + d*x)**7*cos(c + d*x)**2/d - 2*a*b**7*sin(c + d*x)**6*cos(c + d*x)**4/d - 2*a*b**7*sin(c + d*x)**4*cos(c + d*x)**6/d - a*b**7*sin(c + d*x)**2*cos(c + d*x)**8/d - a*b**7*cos(c + d*x)**10/(5*d) + 2*b**8*sin(c + d*x)**11/(99*d) + b**8*sin(c + d*x)**9*cos(c + d*x)**2/(9*d), Ne(d, 0)), (x*(a + b*sin(c))**8*cos(c)**3, True))","A",0
415,1,168,0,20.961141," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{a^{8} \sin{\left(c + d x \right)}}{d} + \frac{4 a^{7} b \sin^{2}{\left(c + d x \right)}}{d} + \frac{28 a^{6} b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{14 a^{5} b^{3} \sin^{4}{\left(c + d x \right)}}{d} + \frac{14 a^{4} b^{4} \sin^{5}{\left(c + d x \right)}}{d} + \frac{28 a^{3} b^{5} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{4 a^{2} b^{6} \sin^{7}{\left(c + d x \right)}}{d} + \frac{a b^{7} \sin^{8}{\left(c + d x \right)}}{d} + \frac{b^{8} \sin^{9}{\left(c + d x \right)}}{9 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{8} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**8*sin(c + d*x)/d + 4*a**7*b*sin(c + d*x)**2/d + 28*a**6*b**2*sin(c + d*x)**3/(3*d) + 14*a**5*b**3*sin(c + d*x)**4/d + 14*a**4*b**4*sin(c + d*x)**5/d + 28*a**3*b**5*sin(c + d*x)**6/(3*d) + 4*a**2*b**6*sin(c + d*x)**7/d + a*b**7*sin(c + d*x)**8/d + b**8*sin(c + d*x)**9/(9*d), Ne(d, 0)), (x*(a + b*sin(c))**8*cos(c), True))","A",0
416,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,1,1115,0,39.897124," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{a^{8} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{8} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{8} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{8 a^{7} b \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{7 a^{6} b^{2} x \sin^{4}{\left(c + d x \right)}}{2} + 7 a^{6} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \frac{7 a^{6} b^{2} x \cos^{4}{\left(c + d x \right)}}{2} + \frac{7 a^{6} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{7 a^{6} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{56 a^{5} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{112 a^{5} b^{3} \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{35 a^{4} b^{4} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{105 a^{4} b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{105 a^{4} b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{35 a^{4} b^{4} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{35 a^{4} b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{35 a^{4} b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{35 a^{4} b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{56 a^{3} b^{5} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{224 a^{3} b^{5} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{64 a^{3} b^{5} \cos^{7}{\left(c + d x \right)}}{15 d} + \frac{35 a^{2} b^{6} x \sin^{8}{\left(c + d x \right)}}{32} + \frac{35 a^{2} b^{6} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{105 a^{2} b^{6} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{35 a^{2} b^{6} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{8} + \frac{35 a^{2} b^{6} x \cos^{8}{\left(c + d x \right)}}{32} + \frac{35 a^{2} b^{6} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{32 d} - \frac{511 a^{2} b^{6} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{96 d} - \frac{385 a^{2} b^{6} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{96 d} - \frac{35 a^{2} b^{6} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{32 d} - \frac{8 a b^{7} \sin^{6}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{16 a b^{7} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{64 a b^{7} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{128 a b^{7} \cos^{9}{\left(c + d x \right)}}{315 d} + \frac{7 b^{8} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{35 b^{8} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{35 b^{8} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{35 b^{8} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{35 b^{8} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{7 b^{8} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{7 b^{8} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} - \frac{79 b^{8} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} - \frac{7 b^{8} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{30 d} - \frac{49 b^{8} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{384 d} - \frac{7 b^{8} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{8} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**8*x*sin(c + d*x)**2/2 + a**8*x*cos(c + d*x)**2/2 + a**8*sin(c + d*x)*cos(c + d*x)/(2*d) - 8*a**7*b*cos(c + d*x)**3/(3*d) + 7*a**6*b**2*x*sin(c + d*x)**4/2 + 7*a**6*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2 + 7*a**6*b**2*x*cos(c + d*x)**4/2 + 7*a**6*b**2*sin(c + d*x)**3*cos(c + d*x)/(2*d) - 7*a**6*b**2*sin(c + d*x)*cos(c + d*x)**3/(2*d) - 56*a**5*b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 112*a**5*b**3*cos(c + d*x)**5/(15*d) + 35*a**4*b**4*x*sin(c + d*x)**6/8 + 105*a**4*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 105*a**4*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 35*a**4*b**4*x*cos(c + d*x)**6/8 + 35*a**4*b**4*sin(c + d*x)**5*cos(c + d*x)/(8*d) - 35*a**4*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 35*a**4*b**4*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 56*a**3*b**5*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - 224*a**3*b**5*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - 64*a**3*b**5*cos(c + d*x)**7/(15*d) + 35*a**2*b**6*x*sin(c + d*x)**8/32 + 35*a**2*b**6*x*sin(c + d*x)**6*cos(c + d*x)**2/8 + 105*a**2*b**6*x*sin(c + d*x)**4*cos(c + d*x)**4/16 + 35*a**2*b**6*x*sin(c + d*x)**2*cos(c + d*x)**6/8 + 35*a**2*b**6*x*cos(c + d*x)**8/32 + 35*a**2*b**6*sin(c + d*x)**7*cos(c + d*x)/(32*d) - 511*a**2*b**6*sin(c + d*x)**5*cos(c + d*x)**3/(96*d) - 385*a**2*b**6*sin(c + d*x)**3*cos(c + d*x)**5/(96*d) - 35*a**2*b**6*sin(c + d*x)*cos(c + d*x)**7/(32*d) - 8*a*b**7*sin(c + d*x)**6*cos(c + d*x)**3/(3*d) - 16*a*b**7*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 64*a*b**7*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 128*a*b**7*cos(c + d*x)**9/(315*d) + 7*b**8*x*sin(c + d*x)**10/256 + 35*b**8*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 35*b**8*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 35*b**8*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 35*b**8*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 7*b**8*x*cos(c + d*x)**10/256 + 7*b**8*sin(c + d*x)**9*cos(c + d*x)/(256*d) - 79*b**8*sin(c + d*x)**7*cos(c + d*x)**3/(384*d) - 7*b**8*sin(c + d*x)**5*cos(c + d*x)**5/(30*d) - 49*b**8*sin(c + d*x)**3*cos(c + d*x)**7/(384*d) - 7*b**8*sin(c + d*x)*cos(c + d*x)**9/(256*d), Ne(d, 0)), (x*(a + b*sin(c))**8*cos(c)**2, True))","A",0
420,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
422,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,1,41,0,1.056437," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c)), Eq(d, 0)), (log(a/b + sin(c + d*x))/(b*d), True))","A",0
428,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
429,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
430,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*sin(c + d*x)), x)","F",0
431,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
435,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*sin(c + d*x)), x)","F",0
436,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a+b*sin(d*x+c)),x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**6/(a + b*sin(c + d*x)), x)","F",0
437,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,1,221,0,1.882034," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{x \cos^{3}{\left(c \right)}}{a^{2}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{2 \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 a^{2} \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{a b^{3} d + b^{4} d \sin{\left(c + d x \right)}} + \frac{2 a^{2}}{a b^{3} d + b^{4} d \sin{\left(c + d x \right)}} + \frac{2 a b \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)} \sin{\left(c + d x \right)}}{a b^{3} d + b^{4} d \sin{\left(c + d x \right)}} - \frac{2 b^{2} \sin^{2}{\left(c + d x \right)}}{a b^{3} d + b^{4} d \sin{\left(c + d x \right)}} - \frac{b^{2} \cos^{2}{\left(c + d x \right)}}{a b^{3} d + b^{4} d \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**3/a**2, Eq(b, 0) & Eq(d, 0)), ((2*sin(c + d*x)**3/(3*d) + sin(c + d*x)*cos(c + d*x)**2/d)/a**2, Eq(b, 0)), (x*cos(c)**3/(a + b*sin(c))**2, Eq(d, 0)), (2*a**2*log(a/b + sin(c + d*x))/(a*b**3*d + b**4*d*sin(c + d*x)) + 2*a**2/(a*b**3*d + b**4*d*sin(c + d*x)) + 2*a*b*log(a/b + sin(c + d*x))*sin(c + d*x)/(a*b**3*d + b**4*d*sin(c + d*x)) - 2*b**2*sin(c + d*x)**2/(a*b**3*d + b**4*d*sin(c + d*x)) - b**2*cos(c + d*x)**2/(a*b**3*d + b**4*d*sin(c + d*x)), True))","A",0
440,1,51,0,1.243616," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a^{2}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a^{2} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{1}{a b d + b^{2} d \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a**2, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a**2*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c))**2, Eq(d, 0)), (-1/(a*b*d + b**2*d*sin(c + d*x)), True))","A",0
441,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**2,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x))**2, x)","F",0
442,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x))**2, x)","F",0
443,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c))**2,x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*sin(c + d*x))**2, x)","F",0
444,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
448,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*sin(c + d*x))**2, x)","F",0
449,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-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
451,1,398,0,2.391848," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{x \cos^{3}{\left(c \right)}}{a^{3}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{2 \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d}}{a^{3}} & \text{for}\: b = 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\- \frac{2 a^{2} \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} - \frac{2 a^{2}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} - \frac{4 a b \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)} \sin{\left(c + d x \right)}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} - \frac{2 a b \sin{\left(c + d x \right)}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} - \frac{2 b^{2} \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} - \frac{b^{2} \cos^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 4 a b^{4} d \sin{\left(c + d x \right)} + 2 b^{5} d \sin^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**3/a**3, Eq(b, 0) & Eq(d, 0)), ((2*sin(c + d*x)**3/(3*d) + sin(c + d*x)*cos(c + d*x)**2/d)/a**3, Eq(b, 0)), (x*cos(c)**3/(a + b*sin(c))**3, Eq(d, 0)), (-2*a**2*log(a/b + sin(c + d*x))/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2) - 2*a**2/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2) - 4*a*b*log(a/b + sin(c + d*x))*sin(c + d*x)/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2) - 2*a*b*sin(c + d*x)/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2) - 2*b**2*log(a/b + sin(c + d*x))*sin(c + d*x)**2/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2) - b**2*cos(c + d*x)**2/(2*a**2*b**3*d + 4*a*b**4*d*sin(c + d*x) + 2*b**5*d*sin(c + d*x)**2), True))","A",0
452,1,73,0,1.970704," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a^{3}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a^{3} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\- \frac{1}{2 a^{2} b d + 4 a b^{2} d \sin{\left(c + d x \right)} + 2 b^{3} d \sin^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a**3, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a**3*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c))**3, Eq(d, 0)), (-1/(2*a**2*b*d + 4*a*b**2*d*sin(c + d*x) + 2*b**3*d*sin(c + d*x)**2), True))","A",0
453,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**3,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x))**3, x)","F",0
454,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x))**3, x)","F",0
455,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c))**3,x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*sin(c + d*x))**3, x)","F",0
456,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
460,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**3,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*sin(c + d*x))**3, x)","F",0
461,1,2530,0,47.443491," ","integrate(cos(d*x+c)**7/(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{x \cos^{7}{\left(c \right)}}{a^{8}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{16 \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{\sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d}}{a^{8}} & \text{for}\: b = 0 \\\frac{x \cos^{7}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{8}} & \text{for}\: d = 0 \\\frac{5 a^{6}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{35 a^{5} b \sin{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{104 a^{4} b^{2} \sin^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{a^{4} b^{2} \cos^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{168 a^{3} b^{3} \sin^{3}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{7 a^{3} b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{155 a^{2} b^{4} \sin^{4}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{19 a^{2} b^{4} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{a^{2} b^{4} \cos^{4}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{77 a b^{5} \sin^{5}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{21 a b^{5} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{7 a b^{5} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{16 b^{6} \sin^{6}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{8 b^{6} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} + \frac{6 b^{6} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} - \frac{5 b^{6} \cos^{6}{\left(c + d x \right)}}{35 a^{7} b^{7} d + 245 a^{6} b^{8} d \sin{\left(c + d x \right)} + 735 a^{5} b^{9} d \sin^{2}{\left(c + d x \right)} + 1225 a^{4} b^{10} d \sin^{3}{\left(c + d x \right)} + 1225 a^{3} b^{11} d \sin^{4}{\left(c + d x \right)} + 735 a^{2} b^{12} d \sin^{5}{\left(c + d x \right)} + 245 a b^{13} d \sin^{6}{\left(c + d x \right)} + 35 b^{14} d \sin^{7}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**7/a**8, Eq(b, 0) & Eq(d, 0)), ((16*sin(c + d*x)**7/(35*d) + 8*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*sin(c + d*x)**3*cos(c + d*x)**4/d + sin(c + d*x)*cos(c + d*x)**6/d)/a**8, Eq(b, 0)), (x*cos(c)**7/(a + b*sin(c))**8, Eq(d, 0)), (5*a**6/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 35*a**5*b*sin(c + d*x)/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 104*a**4*b**2*sin(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - a**4*b**2*cos(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 168*a**3*b**3*sin(c + d*x)**3/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - 7*a**3*b**3*sin(c + d*x)*cos(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 155*a**2*b**4*sin(c + d*x)**4/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - 19*a**2*b**4*sin(c + d*x)**2*cos(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + a**2*b**4*cos(c + d*x)**4/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 77*a*b**5*sin(c + d*x)**5/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - 21*a*b**5*sin(c + d*x)**3*cos(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 7*a*b**5*sin(c + d*x)*cos(c + d*x)**4/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 16*b**6*sin(c + d*x)**6/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - 8*b**6*sin(c + d*x)**4*cos(c + d*x)**2/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) + 6*b**6*sin(c + d*x)**2*cos(c + d*x)**4/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7) - 5*b**6*cos(c + d*x)**6/(35*a**7*b**7*d + 245*a**6*b**8*d*sin(c + d*x) + 735*a**5*b**9*d*sin(c + d*x)**2 + 1225*a**4*b**10*d*sin(c + d*x)**3 + 1225*a**3*b**11*d*sin(c + d*x)**4 + 735*a**2*b**12*d*sin(c + d*x)**5 + 245*a*b**13*d*sin(c + d*x)**6 + 35*b**14*d*sin(c + d*x)**7), True))","A",0
462,1,1425,0,43.300454," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{x \cos^{5}{\left(c \right)}}{a^{8}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{8 \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d}}{a^{8}} & \text{for}\: b = 0 \\\frac{x \cos^{5}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{8}} & \text{for}\: d = 0 \\- \frac{a^{4}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} - \frac{7 a^{3} b \sin{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} - \frac{19 a^{2} b^{2} \sin^{2}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} + \frac{2 a^{2} b^{2} \cos^{2}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} - \frac{21 a b^{3} \sin^{3}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} + \frac{14 a b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} - \frac{8 b^{4} \sin^{4}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} + \frac{12 b^{4} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} - \frac{15 b^{4} \cos^{4}{\left(c + d x \right)}}{105 a^{7} b^{5} d + 735 a^{6} b^{6} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{7} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{8} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{9} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{10} d \sin^{5}{\left(c + d x \right)} + 735 a b^{11} d \sin^{6}{\left(c + d x \right)} + 105 b^{12} d \sin^{7}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**5/a**8, Eq(b, 0) & Eq(d, 0)), ((8*sin(c + d*x)**5/(15*d) + 4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + sin(c + d*x)*cos(c + d*x)**4/d)/a**8, Eq(b, 0)), (x*cos(c)**5/(a + b*sin(c))**8, Eq(d, 0)), (-a**4/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) - 7*a**3*b*sin(c + d*x)/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) - 19*a**2*b**2*sin(c + d*x)**2/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) + 2*a**2*b**2*cos(c + d*x)**2/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) - 21*a*b**3*sin(c + d*x)**3/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) + 14*a*b**3*sin(c + d*x)*cos(c + d*x)**2/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) - 8*b**4*sin(c + d*x)**4/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) + 12*b**4*sin(c + d*x)**2*cos(c + d*x)**2/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7) - 15*b**4*cos(c + d*x)**4/(105*a**7*b**5*d + 735*a**6*b**6*d*sin(c + d*x) + 2205*a**5*b**7*d*sin(c + d*x)**2 + 3675*a**4*b**8*d*sin(c + d*x)**3 + 3675*a**3*b**9*d*sin(c + d*x)**4 + 2205*a**2*b**10*d*sin(c + d*x)**5 + 735*a*b**11*d*sin(c + d*x)**6 + 105*b**12*d*sin(c + d*x)**7), True))","A",0
463,1,636,0,41.333187," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{x \cos^{3}{\left(c \right)}}{a^{8}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{2 \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d}}{a^{8}} & \text{for}\: b = 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{8}} & \text{for}\: d = 0 \\\frac{a^{2}}{105 a^{7} b^{3} d + 735 a^{6} b^{4} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{5} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{6} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{7} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{8} d \sin^{5}{\left(c + d x \right)} + 735 a b^{9} d \sin^{6}{\left(c + d x \right)} + 105 b^{10} d \sin^{7}{\left(c + d x \right)}} + \frac{7 a b \sin{\left(c + d x \right)}}{105 a^{7} b^{3} d + 735 a^{6} b^{4} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{5} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{6} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{7} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{8} d \sin^{5}{\left(c + d x \right)} + 735 a b^{9} d \sin^{6}{\left(c + d x \right)} + 105 b^{10} d \sin^{7}{\left(c + d x \right)}} + \frac{6 b^{2} \sin^{2}{\left(c + d x \right)}}{105 a^{7} b^{3} d + 735 a^{6} b^{4} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{5} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{6} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{7} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{8} d \sin^{5}{\left(c + d x \right)} + 735 a b^{9} d \sin^{6}{\left(c + d x \right)} + 105 b^{10} d \sin^{7}{\left(c + d x \right)}} - \frac{15 b^{2} \cos^{2}{\left(c + d x \right)}}{105 a^{7} b^{3} d + 735 a^{6} b^{4} d \sin{\left(c + d x \right)} + 2205 a^{5} b^{5} d \sin^{2}{\left(c + d x \right)} + 3675 a^{4} b^{6} d \sin^{3}{\left(c + d x \right)} + 3675 a^{3} b^{7} d \sin^{4}{\left(c + d x \right)} + 2205 a^{2} b^{8} d \sin^{5}{\left(c + d x \right)} + 735 a b^{9} d \sin^{6}{\left(c + d x \right)} + 105 b^{10} d \sin^{7}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**3/a**8, Eq(b, 0) & Eq(d, 0)), ((2*sin(c + d*x)**3/(3*d) + sin(c + d*x)*cos(c + d*x)**2/d)/a**8, Eq(b, 0)), (x*cos(c)**3/(a + b*sin(c))**8, Eq(d, 0)), (a**2/(105*a**7*b**3*d + 735*a**6*b**4*d*sin(c + d*x) + 2205*a**5*b**5*d*sin(c + d*x)**2 + 3675*a**4*b**6*d*sin(c + d*x)**3 + 3675*a**3*b**7*d*sin(c + d*x)**4 + 2205*a**2*b**8*d*sin(c + d*x)**5 + 735*a*b**9*d*sin(c + d*x)**6 + 105*b**10*d*sin(c + d*x)**7) + 7*a*b*sin(c + d*x)/(105*a**7*b**3*d + 735*a**6*b**4*d*sin(c + d*x) + 2205*a**5*b**5*d*sin(c + d*x)**2 + 3675*a**4*b**6*d*sin(c + d*x)**3 + 3675*a**3*b**7*d*sin(c + d*x)**4 + 2205*a**2*b**8*d*sin(c + d*x)**5 + 735*a*b**9*d*sin(c + d*x)**6 + 105*b**10*d*sin(c + d*x)**7) + 6*b**2*sin(c + d*x)**2/(105*a**7*b**3*d + 735*a**6*b**4*d*sin(c + d*x) + 2205*a**5*b**5*d*sin(c + d*x)**2 + 3675*a**4*b**6*d*sin(c + d*x)**3 + 3675*a**3*b**7*d*sin(c + d*x)**4 + 2205*a**2*b**8*d*sin(c + d*x)**5 + 735*a*b**9*d*sin(c + d*x)**6 + 105*b**10*d*sin(c + d*x)**7) - 15*b**2*cos(c + d*x)**2/(105*a**7*b**3*d + 735*a**6*b**4*d*sin(c + d*x) + 2205*a**5*b**5*d*sin(c + d*x)**2 + 3675*a**4*b**6*d*sin(c + d*x)**3 + 3675*a**3*b**7*d*sin(c + d*x)**4 + 2205*a**2*b**8*d*sin(c + d*x)**5 + 735*a*b**9*d*sin(c + d*x)**6 + 105*b**10*d*sin(c + d*x)**7), True))","A",0
464,1,167,0,40.650065," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**8,x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a^{8}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a^{8} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{8}} & \text{for}\: d = 0 \\- \frac{1}{7 a^{7} b d + 49 a^{6} b^{2} d \sin{\left(c + d x \right)} + 147 a^{5} b^{3} d \sin^{2}{\left(c + d x \right)} + 245 a^{4} b^{4} d \sin^{3}{\left(c + d x \right)} + 245 a^{3} b^{5} d \sin^{4}{\left(c + d x \right)} + 147 a^{2} b^{6} d \sin^{5}{\left(c + d x \right)} + 49 a b^{7} d \sin^{6}{\left(c + d x \right)} + 7 b^{8} d \sin^{7}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a**8, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a**8*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c))**8, Eq(d, 0)), (-1/(7*a**7*b*d + 49*a**6*b**2*d*sin(c + d*x) + 147*a**5*b**3*d*sin(c + d*x)**2 + 245*a**4*b**4*d*sin(c + d*x)**3 + 245*a**3*b**5*d*sin(c + d*x)**4 + 147*a**2*b**6*d*sin(c + d*x)**5 + 49*a*b**7*d*sin(c + d*x)**6 + 7*b**8*d*sin(c + d*x)**7), True))","A",0
465,-1,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,1,83,0,0.552982," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**(1/2),x)","\begin{cases} \sqrt{a} x \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sqrt{a} \sin{\left(c + d x \right)}}{d} & \text{for}\: b = 0 \\x \sqrt{a + b \sin{\left(c \right)}} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{2 a \sqrt{a + b \sin{\left(c + d x \right)}}}{3 b d} + \frac{2 \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}}{3 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sqrt(a)*x*cos(c), Eq(b, 0) & Eq(d, 0)), (sqrt(a)*sin(c + d*x)/d, Eq(b, 0)), (x*sqrt(a + b*sin(c))*cos(c), Eq(d, 0)), (2*a*sqrt(a + b*sin(c + d*x))/(3*b*d) + 2*sqrt(a + b*sin(c + d*x))*sin(c + d*x)/(3*d), True))","A",0
476,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sec(c + d*x), x)","F",0
477,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sec(c + d*x)**3, x)","F",0
478,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cos(c + d*x)**4, x)","F",0
480,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cos(c + d*x)**2, x)","F",0
481,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sec(c + d*x)**2, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sec(c + d*x)**4, x)","F",0
483,-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
484,1,314,0,121.573268," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**(3/2),x)","\begin{cases} a^{\frac{3}{2}} x \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\a^{\frac{3}{2}} \left(\frac{2 \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d}\right) & \text{for}\: b = 0 \\x \left(a + b \sin{\left(c \right)}\right)^{\frac{3}{2}} \cos^{3}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{16 a^{4} \sqrt{a + b \sin{\left(c + d x \right)}}}{315 b^{3} d} + \frac{8 a^{3} \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}}{315 b^{2} d} + \frac{8 a^{2} \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{2}{\left(c + d x \right)}}{21 b d} + \frac{2 a^{2} \sqrt{a + b \sin{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)}}{5 b d} + \frac{152 a \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{3}{\left(c + d x \right)}}{315 d} + \frac{4 a \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{8 b \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{4}{\left(c + d x \right)}}{45 d} + \frac{2 b \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(3/2)*x*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (a**(3/2)*(2*sin(c + d*x)**3/(3*d) + sin(c + d*x)*cos(c + d*x)**2/d), Eq(b, 0)), (x*(a + b*sin(c))**(3/2)*cos(c)**3, Eq(d, 0)), (-16*a**4*sqrt(a + b*sin(c + d*x))/(315*b**3*d) + 8*a**3*sqrt(a + b*sin(c + d*x))*sin(c + d*x)/(315*b**2*d) + 8*a**2*sqrt(a + b*sin(c + d*x))*sin(c + d*x)**2/(21*b*d) + 2*a**2*sqrt(a + b*sin(c + d*x))*cos(c + d*x)**2/(5*b*d) + 152*a*sqrt(a + b*sin(c + d*x))*sin(c + d*x)**3/(315*d) + 4*a*sqrt(a + b*sin(c + d*x))*sin(c + d*x)*cos(c + d*x)**2/(5*d) + 8*b*sqrt(a + b*sin(c + d*x))*sin(c + d*x)**4/(45*d) + 2*b*sqrt(a + b*sin(c + d*x))*sin(c + d*x)**2*cos(c + d*x)**2/(5*d), True))","A",0
485,1,116,0,26.320728," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**(3/2),x)","\begin{cases} a^{\frac{3}{2}} x \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{a^{\frac{3}{2}} \sin{\left(c + d x \right)}}{d} & \text{for}\: b = 0 \\x \left(a + b \sin{\left(c \right)}\right)^{\frac{3}{2}} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{2 a^{2} \sqrt{a + b \sin{\left(c + d x \right)}}}{5 b d} + \frac{4 a \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}}{5 d} + \frac{2 b \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{2}{\left(c + d x \right)}}{5 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**(3/2)*x*cos(c), Eq(b, 0) & Eq(d, 0)), (a**(3/2)*sin(c + d*x)/d, Eq(b, 0)), (x*(a + b*sin(c))**(3/2)*cos(c), Eq(d, 0)), (2*a**2*sqrt(a + b*sin(c + d*x))/(5*b*d) + 4*a*sqrt(a + b*sin(c + d*x))*sin(c + d*x)/(5*d) + 2*b*sqrt(a + b*sin(c + d*x))*sin(c + d*x)**2/(5*d), True))","A",0
486,-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
487,-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
488,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-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
490,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**(3/2),x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**(3/2)*cos(c + d*x)**2, x)","F",0
491,-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
492,-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
493,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
495,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,-1,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
499,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
500,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,1,54,0,1.144344," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**(1/2),x)","\begin{cases} \frac{x \cos{\left(c \right)}}{\sqrt{a}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{\sqrt{a} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\sqrt{a + b \sin{\left(c \right)}}} & \text{for}\: d = 0 \\\frac{2 \sqrt{a + b \sin{\left(c + d x \right)}}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/sqrt(a), Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(sqrt(a)*d), Eq(b, 0)), (x*cos(c)/sqrt(a + b*sin(c)), Eq(d, 0)), (2*sqrt(a + b*sin(c + d*x))/(b*d), True))","A",0
509,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)/sqrt(a + b*sin(c + d*x)), x)","F",0
510,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/sqrt(a + b*sin(c + d*x)), x)","F",0
511,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**5/sqrt(a + b*sin(c + d*x)), x)","F",0
512,0,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**4/sqrt(a + b*sin(c + d*x)), x)","F",0
513,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/sqrt(a + b*sin(c + d*x)), x)","F",0
514,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/sqrt(a + b*sin(c + d*x)), x)","F",0
515,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sec(c + d*x)**4/sqrt(a + b*sin(c + d*x)), x)","F",0
516,-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
517,-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
518,1,56,0,3.008881," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**(3/2),x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a^{\frac{3}{2}}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a^{\frac{3}{2}} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{\frac{3}{2}}} & \text{for}\: d = 0 \\- \frac{2}{b d \sqrt{a + b \sin{\left(c + d x \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a**(3/2), Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a**(3/2)*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c))**(3/2), Eq(d, 0)), (-2/(b*d*sqrt(a + b*sin(c + d*x))), True))","A",0
519,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x))**(3/2), x)","F",0
520,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x))**(3/2), x)","F",0
521,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*sin(c + d*x))**(3/2), x)","F",0
522,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,0,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**4/(a + b*sin(c + d*x))**(3/2), x)","F",0
524,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a + b*sin(c + d*x))**(3/2), x)","F",0
525,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x))**(3/2), x)","F",0
526,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*sin(c + d*x))**(3/2), x)","F",0
527,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,1,304,0,23.929532," ","integrate(cos(d*x+c)**3/(a+b*sin(d*x+c))**(5/2),x)","\begin{cases} \frac{x \cos^{3}{\left(c \right)}}{a^{\frac{5}{2}}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{2 \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d}}{a^{\frac{5}{2}}} & \text{for}\: b = 0 \\\frac{x \cos^{3}{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{\frac{5}{2}}} & \text{for}\: d = 0 \\- \frac{16 a^{2}}{3 a b^{3} d \sqrt{a + b \sin{\left(c + d x \right)}} + 3 b^{4} d \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}} - \frac{24 a b \sin{\left(c + d x \right)}}{3 a b^{3} d \sqrt{a + b \sin{\left(c + d x \right)}} + 3 b^{4} d \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}} - \frac{8 b^{2} \sin^{2}{\left(c + d x \right)}}{3 a b^{3} d \sqrt{a + b \sin{\left(c + d x \right)}} + 3 b^{4} d \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}} - \frac{2 b^{2} \cos^{2}{\left(c + d x \right)}}{3 a b^{3} d \sqrt{a + b \sin{\left(c + d x \right)}} + 3 b^{4} d \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)**3/a**(5/2), Eq(b, 0) & Eq(d, 0)), ((2*sin(c + d*x)**3/(3*d) + sin(c + d*x)*cos(c + d*x)**2/d)/a**(5/2), Eq(b, 0)), (x*cos(c)**3/(a + b*sin(c))**(5/2), Eq(d, 0)), (-16*a**2/(3*a*b**3*d*sqrt(a + b*sin(c + d*x)) + 3*b**4*d*sqrt(a + b*sin(c + d*x))*sin(c + d*x)) - 24*a*b*sin(c + d*x)/(3*a*b**3*d*sqrt(a + b*sin(c + d*x)) + 3*b**4*d*sqrt(a + b*sin(c + d*x))*sin(c + d*x)) - 8*b**2*sin(c + d*x)**2/(3*a*b**3*d*sqrt(a + b*sin(c + d*x)) + 3*b**4*d*sqrt(a + b*sin(c + d*x))*sin(c + d*x)) - 2*b**2*cos(c + d*x)**2/(3*a*b**3*d*sqrt(a + b*sin(c + d*x)) + 3*b**4*d*sqrt(a + b*sin(c + d*x))*sin(c + d*x)), True))","A",0
529,1,87,0,22.735421," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c))**(5/2),x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a^{\frac{5}{2}}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin{\left(c + d x \right)}}{a^{\frac{5}{2}} d} & \text{for}\: b = 0 \\\frac{x \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{\frac{5}{2}}} & \text{for}\: d = 0 \\- \frac{2}{3 a b d \sqrt{a + b \sin{\left(c + d x \right)}} + 3 b^{2} d \sqrt{a + b \sin{\left(c + d x \right)}} \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a**(5/2), Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)/(a**(5/2)*d), Eq(b, 0)), (x*cos(c)/(a + b*sin(c))**(5/2), Eq(d, 0)), (-2/(3*a*b*d*sqrt(a + b*sin(c + d*x)) + 3*b**2*d*sqrt(a + b*sin(c + d*x))*sin(c + d*x)), True))","A",0
530,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*sin(c + d*x))**(5/2), x)","F",0
531,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*sin(c + d*x))**(5/2), x)","F",0
532,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*sin(c + d*x))**(5/2), x)","F",0
533,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a + b*sin(c + d*x))**(5/2), x)","F",0
537,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*sin(c + d*x))**(5/2), x)","F",0
538,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*sin(c + d*x))**(5/2), x)","F",0
539,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))*(e*cos(d*x+c))**(1/2),x)","\int \sqrt{e \cos{\left(c + d x \right)}} \left(a + b \sin{\left(c + d x \right)}\right)\, dx"," ",0,"Integral(sqrt(e*cos(c + d*x))*(a + b*sin(c + d*x)), x)","F",0
543,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))**(1/2),x)","\int \frac{a + b \sin{\left(c + d x \right)}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))/sqrt(e*cos(c + d*x)), x)","F",0
544,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))**(3/2),x)","\int \frac{a + b \sin{\left(c + d x \right)}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))/(e*cos(c + d*x))**(3/2), x)","F",0
545,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**2*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**2/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**2/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**2/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**2/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)*(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4*(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
573,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
574,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
575,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
576,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
589,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
590,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**2/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
591,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(13/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**3/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(15/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
606,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(13/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
607,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(11/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
608,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(9/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(7/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(1/(a+b*sin(d*x+c))**4/(e*cos(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(1/(e*cos(d*x+c))**(3/2)/(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,0,0,0,0.000000," ","integrate(1/(c*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{c \cos{\left(e + f x \right)}} \sqrt{a + b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(c*cos(e + f*x))*sqrt(a + b*sin(e + f*x))), x)","F",0
616,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**2,x)","\int \left(e \cos{\left(c + d x \right)}\right)^{p} \left(a + b \sin{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((e*cos(c + d*x))**p*(a + b*sin(c + d*x))**2, x)","F",0
618,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c)),x)","\int \left(e \cos{\left(c + d x \right)}\right)^{p} \left(a + b \sin{\left(c + d x \right)}\right)\, dx"," ",0,"Integral((e*cos(c + d*x))**p*(a + b*sin(c + d*x)), x)","F",0
619,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**(3/2),x)","\int \left(e \cos{\left(c + d x \right)}\right)^{p} \left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p*(a + b*sin(c + d*x))**(3/2), x)","F",0
625,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**(1/2),x)","\int \left(e \cos{\left(c + d x \right)}\right)^{p} \sqrt{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p*sqrt(a + b*sin(c + d*x)), x)","F",0
626,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/sqrt(a + b*sin(c + d*x)), x)","F",0
627,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/(a + b*sin(c + d*x))**(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\left(e \cos{\left(c + d x \right)}\right)^{p}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((e*cos(c + d*x))**p/(a + b*sin(c + d*x))**(5/2), x)","F",0
629,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**p*(a+b*sin(d*x+c))**m,x)","\int \left(e \cos{\left(c + d x \right)}\right)^{p} \left(a + b \sin{\left(c + d x \right)}\right)^{m}\, dx"," ",0,"Integral((e*cos(c + d*x))**p*(a + b*sin(c + d*x))**m, x)","F",0
630,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,1,99,0,2.205905," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**m,x)","\begin{cases} \frac{x \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \wedge m = -1 \\\frac{a^{m} \sin{\left(c + d x \right)}}{d} & \text{for}\: b = 0 \\x \left(a + b \sin{\left(c \right)}\right)^{m} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{\log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b d} & \text{for}\: m = -1 \\\frac{a \left(a + b \sin{\left(c + d x \right)}\right)^{m}}{b d m + b d} + \frac{b \left(a + b \sin{\left(c + d x \right)}\right)^{m} \sin{\left(c + d x \right)}}{b d m + b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(c)/a, Eq(b, 0) & Eq(d, 0) & Eq(m, -1)), (a**m*sin(c + d*x)/d, Eq(b, 0)), (x*(a + b*sin(c))**m*cos(c), Eq(d, 0)), (log(a/b + sin(c + d*x))/(b*d), Eq(m, -1)), (a*(a + b*sin(c + d*x))**m/(b*d*m + b*d) + b*(a + b*sin(c + d*x))**m*sin(c + d*x)/(b*d*m + b*d), True))","A",0
634,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**m,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{m} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**m*sec(c + d*x), x)","F",0
635,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*sin(d*x+c))**m,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{m} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**m*sec(c + d*x)**2, x)","F",0
640,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(5/2)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(3/2)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1/2)*(a+b*sin(d*x+c))**m,x)","\int \sqrt{e \cos{\left(c + d x \right)}} \left(a + b \sin{\left(c + d x \right)}\right)^{m}\, dx"," ",0,"Integral(sqrt(e*cos(c + d*x))*(a + b*sin(c + d*x))**m, x)","F",0
644,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**m/(e*cos(d*x+c))**(1/2),x)","\int \frac{\left(a + b \sin{\left(c + d x \right)}\right)^{m}}{\sqrt{e \cos{\left(c + d x \right)}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**m/sqrt(e*cos(c + d*x)), x)","F",0
645,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**m/(e*cos(d*x+c))**(3/2),x)","\int \frac{\left(a + b \sin{\left(c + d x \right)}\right)^{m}}{\left(e \cos{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**m/(e*cos(c + d*x))**(3/2), x)","F",0
646,-1,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**m/(e*cos(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-4-m)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-3-m)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-2-m)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(-1-m)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,0,0,0,0.000000," ","integrate((a+b*sin(d*x+c))**m/((e*cos(d*x+c))**m),x)","\int \left(e \cos{\left(c + d x \right)}\right)^{- m} \left(a + b \sin{\left(c + d x \right)}\right)^{m}\, dx"," ",0,"Integral((e*cos(c + d*x))**(-m)*(a + b*sin(c + d*x))**m, x)","F",0
652,0,0,0,0.000000," ","integrate((e*cos(d*x+c))**(1-m)*(a+b*sin(d*x+c))**m,x)","\int \left(e \cos{\left(c + d x \right)}\right)^{1 - m} \left(a + b \sin{\left(c + d x \right)}\right)^{m}\, dx"," ",0,"Integral((e*cos(c + d*x))**(1 - m)*(a + b*sin(c + d*x))**m, x)","F",0
653,-1,0,0,0.000000," ","integrate((e*cos(d*x+c))**(2-m)*(a+b*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
